2.1 The Concept of Function

As explained in the introductory section, teleology, as I shall approach it, is the study of a cluster of interrelated concepts including those of function and goal. This section uses a discussion of the philosophy of functions as a springboard for the metaphysical investigation of goal-directedness that we begin in Section 3.

Talk of functions is pervasive. In everyday contexts we readily ascribe functions to the artefacts around us, such as a chair or toothbrush. Functions are also part of the explanatory practices of many branches of science, particularly in biology, medicine, and technology. Some argue that functions can even be ascribed in cases of physical, chemical, biochemical, and sociopolitical systems such the water and rock cycles, autocatalysis, Bénard cells, vitamin B12, mineral species, and welfare systems.Footnote ⁹ If we are to take all this talk of functions at face value, we require an analysis of functions which explains how they arise in the natural world.

We start this section by offering a critical survey of two popular philosophical approaches to functions which are sometimes interpreted as trying to provide a fully general analysis of functions. These analyses received much attention in the 1970s and are still discussed today. We begin with the selectionist or ‘etiological’ approaches (e.g., Reference GarsonGarson 2017, Reference Garson2019a, Reference Garson2019b; Reference MitchellMitchell 1993; Reference NeanderNeander 1991; Reference WimsattWimsatt 1972; Reference WrightWright 1973), before moving on to the causal role view (e.g., Reference CumminsCummins 1975). There is by now a vast literature on the philosophy of functions, with sophisticated versions of each approach. There are also hybrid theories which incorporate elements of both the selectionist and causal role views, such as the organizational theories of Reference McLaughlinMcLaughlin (2001) and Reference Mossio, Saborido and MorenoMossio et al. (2009). It is not our aim here to undertake a broad survey of all the various versions and their nuances;Footnote ¹⁰ we shall, however, try to go into enough detail to provide preliminary support for the idea that our theory of functions requires a sufficiently developed notion of goal-hood. In their basic forms, neither the selectionist nor the causal role analyses place much weight on the notion of goals. But this creates a problem on both sides for those who want their theory to provide a single, fully general account of functions across the board. On the one hand, selectionist analyses are arguably narrow because they apply mainly to the biological (and perhaps technological) domains, and it appears that in many domains function ascriptions are appropriate in cases lacking the appropriate causal history of selection (Section 2.2). This limitation motivates the causal role analysis, which accommodates functions that are not naturally selected. Unfortunately, however, the causal role theory arguably goes too far the other way and over-generates functions (Section 2.3).

In Section 2.4, we see how this dilemma can be avoided by employing the notion of goal-directedness. In order for some causal feature of an entity to count as a function, it must be one that contributes to the goal(s) of a system. We shall follow others in calling this the ‘goal-contribution’ theory of functions. Importantly, the concept of goal-directedness is not so narrow that it applies only to naturally selected functions and biological systems. On the contrary, as we shall see in Sections 3 and 4, influential analyses of goal-directedness (e.g., Reference BabcockBabcock 2023) allow us to posit functions in wholly inorganic systems. What the goal-contribution account provides is thus a general metaphysical analysis of functions which can be applied in many different domains of science.

To be clear from the outset, we certainly do not deny that the selectionist approach carves out an important type of function in biology (and, perhaps, technology) that delivers the kinds of ‘backward-looking’ explanations described in Section 1. In line with the explanatory desideratum (ED), any adequate metaphysical account of functions must be able to accommodate the backward-looking explanatory roles of selected functions. On the other hand, we would expect a fully general metaphysical analysis of function to be able to accommodate non-selected functions, if such there are. Again, we shall argue that the goal-contribution theory of function ticks all of these boxes. In Section 2.4, we discuss how the goal-contribution theory of function is able to accommodate selected functions in biology and their backward-looking explanatory roles. Section 2.6 also shows that a goal-contribution theory of function is compatible with a range of specific approaches to functions in the philosophy of biology. The key point is just that the goal-contribution account is a metaphysical theory that is broad enough to accommodate cases of functions that might fall outside the scope of the selectionist analysis. This means that the goal-contribution theory is not restricted to the biological domain and can accommodate talk of functions in many areas of science and everyday life. For that reason, it is hoped that the conclusions of this section will have broad appeal. Nonetheless, substantial difficulties arise in Section 3, where we attempt to provide a more detailed metaphysical analysis of goal-directedness.

2.2 The Selectionist Theory

Selectionist or ‘etiological’ theories of function rely on the idea that a function claim should explain the very presence of the function bearer, such as a trait of an organism. On this view, the main point of a function statement is to provide an answer to the question ‘why is X there?’ This type of question is prominent in biology, and in that context such explanations are made possible by the fact that instances of certain traits had effects in the past which explain their occurrences today. Such explanations thus take the form of a causal-historical story about natural selection (e.g., Reference BourratBourrat 2021; Reference GarsonGarson 2017, Reference Garson2019a, Reference Garson2019b; Reference MillikanMillikan 1984; Reference NeanderNeander 1991). This is the dominant and widely held theory of function within the philosophy of biology.

Without doubt, the selectionist approach carves out a very important class of functions. And a clear attraction of the selectionist theory is that it is thoroughly naturalistic. Rather than being grounded in, say, the intentions of a divine designer, teleology is grounded firmly in evolutionary biology. The theory is also able to ground the normative aspect of selected functions in a transparent way, in line with the normative desideratum (ND): the reason why, say, a heart should beat is that it is by virtue of their beating that hearts exist in the first place (see Reference GarsonGarson 2019a: Ch. 7 for further discussion of this example). Thus, the selectionist theory also promises to shed light on how normative truths can be grounded by the natural world in at least some cases.

Abstracting away from the details of evolutionary natural selection, Wright proposed one of the first etiological definitions of function, which had the following two conditions:

‘The function of X is Z means

1. a) X is there because it does Z,

2. b) Z is a consequence (or result) of X’s being there’ (Reference Wright1973: 161).

Interestingly, this definition is general enough that it might also apply in some non-biological cases. For instance, the function of an artefact like a chair might explain the chair’s existence in the following sense: it is on the basis of certain characteristics (e.g., being comfortable to sit on) that chairs like this have been selected by agents like us for production. Indeed, artefactual functions look like teleological properties par excellence given that artefacts are designed with purposes in mind by agents like us. So, it appears to be an advantage of the selectionist analysis that it can subsume both the biological and artefactual cases. Nonetheless, it is arguable that the selectionist analysis still does not tell the full story about functions, because it applies only to functions which have just the right kind of causal history. For example, if there are (or could be) functions which are acquired accidentally rather than through a process of selection, then the selectionist approach will not apply to them. We shall explore possible examples in this Section.

Another noteworthy feature of selectionist functions is that they are somewhat contingent and extrinsic. Assuming that the causal history of the world is contingent, it is thereby contingent that a characteristic performs a certain function. This also means that, in such cases, function performance is not fully a here-and-now feature of an item. The attribution of a function to an item can only be made retrospectively once items of that kind have been reproduced on the basis of their effects in the past. Some have found this extrinsicality and contingency to be counterintuitive (e.g., Reference Bigelow and PargetterBigelow and Pargetter 1987: 187–188; Reference Christensen and BickhardChristensen and Bickhard 2002; Reference Mossio, Saborido and MorenoMossio et al. 2009: 821). Some have also found it objectionable that the selectionist theory allows us to say that a current trait has certain functions (based on ancestral natural selection) even though it no longer performs those functions for its possessors (Reference Bigelow and PargetterBigelow and Pargetter 1987: 196).Footnote ¹¹ Possible examples of such ‘vestigial’ features include the pelvis of the whale and the eyes of certain fish who live in darkness.

I do not think that, by themselves, these objections are decisive. The selectionists are obviously happy to accept the extrinsic, historical, and contingent nature of functions and will be inclined to dismiss intuitions to the contrary. And as noted already, the selectionist approach to functions is deeply entrenched in the philosophy of biology. Nonetheless, as metaphysicians we are entitled to ask whether all functions, across all scientific domains, have to arise through processes of selection. If the answer is ‘no’, then we must accept that the selectionist approach applies only to a proper subset of all possible functions, albeit a large and important subset.

Not only does it appear coherent to imagine functions that lack an appropriate causal history of selection, but arguably there are actual examples of functions that lack a selective history, or at least cases in which there is no evidence of natural selection. Reference Godfrey-SmithGodfrey-Smith (1993: Sect. 3.3) goes as far as to suggest that there is now some consensus on this matter. Anatomy and morphology (Reference Amundson and LauderAmundson and Lauder 1994), biochemistry and neuroscience (Reference Godfrey-SmithGodfrey-Smith 1993), and even ecology (Reference Bouchard and HunemanBouchard 2013), have all been identified as areas in which the functions of primary concern are often not the result of natural selection.Footnote ¹² Consequently, many who are otherwise sympathetic towards the selectionist theory have softened their position and accept that the theory might not cover all possible cases of function attribution in all domains of science.Footnote ¹³

Reference BoorseBoorse (1976, Reference Boorse, Ariew, Cummins and Perlman2002) helpfully collates a range of actual and possible counterexamples to the Wright-type etiological analysis, some of which come from within biology itself. Among these are cases of so-called ‘exaptation’ proposed by Reference Gould and VrbaGould and Vrba (1982). Gould and Vrba introduced the notion of exaptation to modern biology after noticing that many features of organisms are co-opted by those organisms and their descendants for uses for which those features were not naturally selected. One of Boorse’s favourite examples of possible exaptation is of sea turtles who dig egg holes with their flippers: surely this is a current function of the flippers, regardless of whether the flipper was originally selected for that function (Reference Boorse, Ariew, Cummins and PerlmanBoorse 2002: 66). Reference Gould and VrbaGould and Vrba (1982: 7–11) present other possible (and surprising) examples of exaptation. For example, there is a conjecture that the enlarged feathers on the hands of birds were originally selected for insect-catching rather than flying. But even if this were so, surely we should not revise our judgement that the contribution to flying is a function of wing feathers. Another theory has it that in vertebrates, bones were originally selected for their ability to store minerals such as phosphate, rather than their ability to support and protect.Footnote ¹⁴ And note that even if the historical details in these cases turn out to be incorrect, the mere possibility of unselected functions is sufficient to cast doubt on the selectionist theory as a fully general analysis.

To be clear once again, the proposal is not that function statements never play the kind of important explanatory role that selectionist theories focus on. Backward-looking functional explanations are clearly crucial in some areas of science – particularly in evolutionary biology. The point is just that not all function statements have to play this role. What this ultimately suggests is that function statements can be used to answer more than one kind of ‘why’-question. According to Reference GarsonGarson (2018), there are at least two different kinds of ‘why’-question in biology and related disciplines such as neuroscience and psychology (see also Reference MitchellMitchell 1993: 258–259 and Reference TahkoTahko 2020: Sect. 2). Understanding this distinction provides the key to understanding the different explanatory roles of function statements and is therefore crucial for satisfying the explanatory desideratum (ED). The first type of question is the ‘why-is-it-there?’ question (Reference GarsonGarson 2018: 1102), and this is where selected functions are called for, for reasons discussed already in this section. However, another why-question is what Garson calls the ‘what-does-it-do?’ question, which we ask when we want to know how a trait or mechanism contributes to a certain system-level capacity. In order to answer questions of this latter kind, what we require are function claims that focus more on the causal role(s) of the function bearer. Even within a particular branch of science, it seems that both kinds of questions may come into play (Reference Forber and McDonoughForber 2020: 277). With this in mind, we shall now explore another notion of function that focuses more on the causal role(s) of its bearer.

2.3 The Causal Role Theory

According to the causal role approach, what makes talk of functions appropriate in both selected and unselected cases is that the functions play certain causal roles. Indeed, the second condition of Wright’s analysis (Section 2.2) acknowledges this, since it concerns the contribution made by a function bearer. The causal role approach puts this idea at centre stage. According to this theory, being able to play an appropriate causal role is the necessary and sufficient feature of a function, while being naturally selected is a feature that some but not all functions have.

According to Reference CumminsCummins (1975), by focusing too much on the need to explain the presence of a function bearer, selectionist theories overlook a core feature of functions across the sciences and even within biology itself. To use one of Cummins’s illustrations, ‘The function of the contractile vacuole in protozoans is elimination of excess water from the organism’ (Reference Cummins1975: 749). In the example, the presence of the contractile vacuole allows there to be a semi-permeable membrane around the organism, which is necessary for the movement of waste out of it. According to Cummins, the explanatory value of this function ascription is that it informs us about what is responsible (in part) for the elimination of the relevant organism’s excess water, and in turn explains how the presence of the contractile vacuole contributes to the survival of that organism. Importantly, however, this is not to say that survival value is constituted by natural selection. For Cummins, the traits of organisms are determined by their genetic plans, as are their survival-enhancing roles. What natural selection does is merely react to these genetic plans, ‘weeding out’ the bad ones (Reference CumminsCummins 1975: 751). Whether or not a genetic trait is subsequently weeded out depends on whether it has survival-enhancing capacities in the first place. Thus, Cummins’s theory shifts the focus of function statements towards the dispositions of a trait.Footnote ¹⁵

Cummins’s work has undoubtedly provided helpful insights, particularly in emphasizing the causal contributions that functions make. However, one might still have doubts about whether Cummins’s causal role theory can itself deliver the whole story about functions. The problem, as Cummins acknowledges, is that just about any effect or activity contributes to the persistence of some condition of a containing system. For example, ‘Heart activity … keeps the circulatory system from being entirely quiet’ (Reference Cummins1975: 752): yet this is surely not a function of heart activity.Footnote ¹⁶ So, prima facie, Cummins’s theory faces a problem of overbreadth: if not all dispositions are functions, then a purely dispositional account inevitably leaves us with too many functions. And this prima facie impression is reinforced when we look at different areas of science, since it does indeed seem fair to say that not all dispositions are treated as functions. As Bigelow and Pargetter note, a meteorologist would not say that a function of mist is to produce rainbows (Reference Bigelow and Pargetter1987: 184), nor would a geologist think that a function of rocks in a river is to widen a river delta (Reference KitcherKitcher 1993: 390), even though mists and rocks do have the corresponding dispositions. To use another common example, it also does not seem right to say that oncogenes have the function to cause damage to organisms, even though they do have such dispositions.

An obvious response for the causal role theorists is to reply that a genuine function is one that contributes to some other function that its containing system has as a whole. We might then emphasize that oncogenes thwart rather than aid these overall functions. However, this merely pushes the problem back a step, for we have appealed to a further function concept, and if that further function is then clarified with reference to yet another function or a further containing system, we face the threat of a vicious regress, as Cummins acknowledges. For example, we might try to explain the function of a heart with reference to the overall function of the circulatory system; but if the function of the circulatory system in turn depends on further functions of an organism, then ‘[e]ither we are launched on a regress, or the analysis breaks down at some level for lack of functions, or perhaps for lack of a plausible candidate for containing systems’ (Reference Cummins1975: 752).

Cummins’s response to this problem is somewhat surprising. In order to draw the distinction between functions and mere accidental effects without appealing to further functions, Cummins appeals to the ‘analytical context’ in which the functional ascription is being made: ‘It is appropriate to say that the heart functions as a pump against the background of an analysis of the circulatory system’s capacity to transport food, oxygen, wastes, and so on, which appeals to the fact that the heart is capable of pumping’ (Reference Cummins1975: 762). However, relative to some other capacity of a containing system, the functions of that system’s components may well be different. On this view, what counts as a function (as opposed to a mere disposition) ultimately depends on the theoretical interests of those ascribing the function. The aforementioned regress is terminated because, relative to a certain analytical context, it is simply taken as a given that a system has a certain capacity. And what is taken as given depends on the interests of the observer. If the context shifts, then some other capacity can come into focus and what counts as a contributing function may then change. This openly epistemic, contextualist view has been influential in recent causal approaches to function, such as the neo-mechanist account of Reference Craver and HunemanCraver (2013).Footnote ¹⁷

Unfortunately, this epistemic and contextualist approach to functions leads to the obvious worry that without the perspectives or interests of observers, things do not really have functions, even though they have relevant dispositions. Some might welcome this conclusion, especially those who are generally sceptical of metaphysical teleology. However, others have found this alleged interest-relativity of functions implausible. For example, Bigelow and Pargetter urge that ‘biological structures would have had the functions they do have even if we had not been here to take an interest in them at all’ (Reference Bigelow and Pargetter1987: 183), and also that ‘some of the effects of structures that we take an interest in have nothing to do with their function’ (Reference Bigelow and Pargetter1987: 184).

Notice also that this epistemic approach is likely to weaken the normative credentials of functional explanations. As highlighted by our normative desideratum (ND) in Section 1, a theory of function should accommodate the normativity of functions, including the distinction between normal function and accidental function. However, insofar as Cummins’s theory retains the normative dimension of function statements, this too will be contextual. Relative to our interest in capacity c of a system, a certain component might have a certain normal function, with other behaviour being regarded as merely accidental. But relative to our interest in capacity c′ of that same system, it may be that the normal function of that same component is different. On this account, it is difficult to see how the natural world in itself fully grounds these normative claims.

For those seeking a more robust basis for function ascriptions in science, the selectionist approach has a significant advantage over the Cummins-type causal role theory, because the former can at least provide an objective, observer-independent basis for normative claims about many functions in terms of what an entity has been naturally selected for (see e.g., Reference BellazziBellazzi forthcoming: Sect. 5.1, Reference GarsonGarson 2017, Reference Garson2019a; Reference MillikanMillikan 1989; Reference NeanderNeander 2017). The selectionist approach therefore fares well with the normative desideratum (ND). Nonetheless, the causal role theory does contain some important insights. In the following subsection we shall explore a theory that preserves some of the insights of Cummins’s theory while offering a more robust theoretical foundation for function claims and their normative implications. The theory in question is the so-called ‘goal-contribution’ approach to functions. In the course of our discussion, we shall also explain how a goal-contribution approach can accommodate the sorts of ‘backward-looking’ functional explanations that philosophers of biology are particularly interested in.

2.4 The Goal-Contribution Approach

In the 1970s, Reference BoorseBoorse (1976), Reference NagelNagel (1979: Ch. 12), and Reference AdamsAdams (1979) rejuvenated a view known as the goal-contribution theory of functions, which has its roots in earlier works in philosophy of science by, among others, Reference BecknerBeckner (1959), Reference BraithwaiteBraithwaite (1953), Reference SommerhoffSommerhoff (1950), and Reference NagelNagel (1961). More recently, the goal-contribution account of function and teleology, or variants thereof, have been endorsed to varying degrees by, among others, Reference BabcockBabcock (2023), Reference Boorse, Ariew, Cummins and PerlmanBoorse (2002), Reference Lee and McSheaLee and McShea (2020), Reference McSheaMcShea (2012), Reference SchaffnerSchaffner (1993), and Reference TrestmanTrestman (2012).

The goal-contribution account is sometimes regarded as an extension of the causal role approach, insofar as it focuses in part on the causal contributions that a functional item makes to a system. Indeed, Nagel’s goal-contribution analysis contains an explicit causal component according to which a functional entity makes a necessary contribution to a certain effect. However, unlike Cummins’s account, the goal-contribution theory insists that an entity can only be said to perform a function if it contributes specifically to a goal of a system, understood as a characteristic state that the system strives to bring about. Thus, the goal-contribution account invokes the core concepts of systems and their goals, about which we shall say more in a moment and in Section 3. The important point for current purposes is that the goal requirement promises to impose an objective restriction on the kinds of causal contribution that can count as functional. The idea is that this restriction will allow us to avoid Cummins’s overbreadth problem discussed earlier, and thereby help to satisfy the desideratum of extensional adequacy (EAD) introduced in Section 1. As Adams puts it:

Referring back to the truthmaking desideratum (TD) of Section 1, the proposal is that certain systems have objective goals, and the causal contributions made to those goals by the relevant function bearers are what make the functional truths true. Given that Boorse has offered one of the most detailed and general goal-contribution analyses of function, I shall focus mainly on his theory and see how the theory applies in different cases of function. In Section 3, we shall then move on to Nagel’s specific ‘cybernetic’ understanding of goals.

For Boorse there is more than one kind of function ascription, and the one that is most widely applicable has the form ‘X is performing function Z’. This kind of function statement is widely applicable, in part, because it is sometimes applied even if the function in question is performed only once in a somewhat accidental way. For example, one might say of a particular pocketbook that it performed the function of stopping a bullet hitting a soldier, even if this only happens once (Reference BoorseBoorse 1976: 80). Alternatively, one might say that a rock performed the function of a coffee table for a person on a particular occasion. A function claim like this cannot be generalized but rather applies at a particular point in time. Hence, Boorse’s analysis of function performance involves time variables (t). And due to the important requirement of systemic goal contribution, the analysis also includes variables relating to systems (S) and the systemic goal (G) to which a functional item (X) contributes. In the cases above, the goals are those of the people involved. This leads to the following analysis:

Since this definition employs the important concept of a system, we should say a little more about what that means. The term ‘system’ is broad and can be applied to any group of things that are connected in some way. Talk of systems is pervasive in many branches of natural science, which are typically concerned with causal or nomic connections between concrete, spatiotemporally located things. At school we learn, for example, about planetary systems, weather systems, and immune systems. However, the term is not restricted to the concrete realm. We also find talk of systems in the rational sciences: for instance, there are different systems of logic, where propositions are connected via various rules of inference. Given that the concept of a system is so broad, it is not easy to provide a general definition.

In the current context, however, we can at least say that the systems of interest are concrete ones with causally interacting parts. One of the important lessons of Cummins’s work, I take it, is that the concept of function is, first and foremost, a causal one. That is not to say that all concrete systems will count as being goal-directed, however. For example, it is far from clear what the goal of, say, the solar system could be. On the other hand, we need not restrict the notion of goal-directedness only to organic systems. Although the notion of a goal is often associated with the concept of intention or desire, goal-contribution theorists typically do not want to restrict talk of functions and goals only to systems capable of having intentions. We discuss this point further in Section 3. Boorse also urges that it would be a mistake to align the concept of a goal too closely with either reproductive fitness, usefulness, or the good, as certain philosophers have sometimes tried to do (Reference Boorse1976: 77). The flexibility that Boorse endorses is, I think, to be welcomed, and I shall say more about it in Section 2.6. The relevant point for current purposes is that philosophers could agree about the goal-contribution analysis of functions but have further in-house disagreements about which cases satisfy the schema.

After defining the notion of function performance, Boorse introduces a more general kind of function statement. Intuitively, not all functions performed by X are its characteristic functions. Although someone’s pocketbook might perform a useful bullet-stopping function on one occasion, this is not the general function of that book. Rather, the general characteristic function of a book is, I assume, to be read. Other general function locutions include ‘X has the function Z’ and ‘A function of X is Z’ (Reference Boorse, Ariew, Cummins and PerlmanBoorse 2002: 71). How, then, should we understand the difference between the more general function locutions and the specific statements which are merely to do with a function performed – perhaps somewhat accidentally – by X on a particular occasion? The thrust of Boorse’s answer is that the appropriateness of a general function statement is largely to do with how often the relevant function is performed by X (Reference Boorse1976: 80–81): ‘If Schaffner’s mutant bursa of Fabricius (Reference Schaffner1993: 388) blocked viral infections throughout its owner’s life, it would be quite natural to call antiviral defense the bursa’s function in this man’ (Reference Boorse, Ariew, Cummins and Perlman2002: 71). Returning to the earlier example, blocking bullets not the general function of a particular book because it is not something the book will do for people on a consistent basis.

Notice also that the goal-contribution approach allows that something can simultaneously contribute to the goals of more than one system. So, when we speak of the general function of a particular item, what we really mean is the function of the thing within such-and-such system. For instance, a bird’s capacity for eating insects is clearly a function, but when we ask which goal the insect-eating is serving there are several possible answers depending on which biological system we are considering: eating insects not only contributes to the survival of the individual bird in question, but also arguably to the survival of its species, of its genes, or the equilibrium of the insect population (Reference BoorseBoorse 1976: 83). However, this does not mean that the goal-contribution theory leads to a merely perspectival or human-dependent account of functions. To secure the objectivity of function, what is important is that judgements about the goals of a system are grounded by the nature of the relevant system itself. There is more to be said about this issue and we shall return to it in Sections 3 and 4, where we examine the nature of goals and goal-directedness in more detail.

Let us now consider some of the advantages of a goal-contribution analysis of function, of which there are several. First, the goal-contribution analysis of function can accommodate the selected functions discussed in Section 2.2. In goal-theoretic terms, naturally selected biological functions are ones which previously contributed to the goal of the survival of the genes that generated them. Importantly, the theory can also accommodate the etiological explanations associated with such functions, thereby satisfying the explanatory desideratum (ED). The disposition of a trait to contribute to the goal of an organism (i.e., fitness) will, in conjunction with evolutionary theory and environmental facts regarding habitat, explain the prevalence of present tokens of that trait (Reference Boorse, Ariew, Cummins and PerlmanBoorse 2002: 79). In other words, given that past tokens of the trait contributed to the goal of fitness, such tokens will tend to propagate. The main difference between this account and the selectionist theory is just that the goal-contribution approach does not write such explanations into the very analysis of function ascriptions. And given that not all functions are selected, this looks like a benefit.

Importantly, although the goal-contribution theory has considerable flexibility, it is still less flexible than Cummins’s version of the causal role theory. We saw in the previous section that Cummins’s theory faces the problem of overbreadth. However, it looks as though the goal-contribution theory has the resources to weed out the common counterexamples facing the causal role theory. In general terms, the counterexamples will be avoided if the items in question are not a part of the relevant system or if the effects in question do not really make a causal contribution to a genuine goal of a system. A glance at some of the counterexamples mentioned earlier suggests that the goal-contribution restriction does indeed help. Since oncogenes cause damage to organic systems, they cannot be said to contribute to the system’s goals – on the assumption, at least, that the biological goal of life is health and fitness (Reference Boorse, Ariew, Cummins and PerlmanBoorse 2002: 73, 76). And although science regards rocks as being parts of some systems, such as the rock cycle, river water systems are arguably not among them, implying that it is not really a function of rocks in a river to widen a river delta. Of course, questions remain about what it takes to be a goal-directed system and we shall address these in Sections 3 and 4. I also leave it as an open question as to whether the goal-contribution account of function is itself counterexample-free.Footnote ¹⁸ The important point for current purposes is just that the goal-contribution account of functions is more discerning than the Cummins-type causal role theory, which looks like progress.

2.5 Goal-Contribution Functions and Normativity

In this section, we shall briefly look at some of the details that Reference Boorse, Ariew, Cummins and PerlmanBoorse (2002) adds to his theory in order to account for the normativity of functions. As we saw in Section 1, it is a desideratum of a theory of functions that it accommodates the normative force of various function statements (ND). The literature on selected functions fares well in this respect: the normal or proper function of an item is that for which it was naturally selected. However, if not all functions are selected, we need some other general way of accommodating the normativity of functions. In order to do so, recall, the analysis must at least be able to draw a distinction between non-function and malfunction, and a distinction between normal (or proper) function and mere accidents (Reference WrightWright 1973: 165; see more recently Reference GarsonGarson 2019a: Chs. 7 and 8).

Perceptive readers may have noticed in the previous subsection that Boorse’s more general kind of function statement already generates a function–accident distinction. X’s contribution to some system’s goal can happen only once and be fortuitous. In that case, X has performed a certain function just on that particular occasion. Although such cases of function performance exist, it does not follow from this that X generally has that function. A function performed is not the same thing as a function possessed (Reference Boorse, Ariew, Cummins and PerlmanBoorse 2002: 71). However, if X makes the same kind of goal contribution often enough, we would be inclined to regard the contribution as being a normal function of X. This general notion of function applies to a particular token item. But in science, we also make important generalizations about what is typical of a type or species of thing. Often, when we say that someone’s kidney is functioning normally, we mean not only that this particular kidney has the function in question, but also that this function is typical of this type of organ. In order to accommodate attributions of normal or proper function in such cases, we must appeal to type-level concepts.

In other work, Boorse analysed normal functions in medicine using the type–token distinction and facts about statistically typical behaviour (e.g., Reference Boorse1977: 554–563). On the assumption that the ultimate biological goal of an organism is fitness, we may say that a normal function of a given type ‘is analysable as an output within a statistically typical range of contributions to survival and reproduction by tokens of that type in an age group of a sex of a species’ (Reference Boorse, Ariew, Cummins and PerlmanBoorse 2002: 72). Thus, at the level of types, we may say that some causal contribution to a systemic goal is a normal function if this function is typical among the members of the relevant type. Such normative judgements require us to look beyond the behaviour of an individual item X and examine the relevant statistical distributions of behaviour concerning other tokens of X’s kind.

To be clear, the fact that a token item X is performing a function is determined locally. However, if the function performed is not species-typical, then we may conclude that the function is not normal or proper for that type of entity. Boorse concedes that he cannot specify precisely how many times a function needs to be performed within a species or kind in order to make a function normal. However, Boorse notes that this sort of imprecision is a feature of other theories of functions too. For example, if we accept a general selectionist analysis of function, we are left with the similar question of how often a contribution of a trait must make its bearers better able to reproduce, in order to be regarded as a normal or proper function.Footnote ¹⁹

There is, however, a fairly obvious problem case for this statistical account of type-level normal function. This is what we may call, following Reference NeanderNeander (1983: 80–81), the problem of species-typical fortuitous consequences. Well-known examples of widespread fortuitous effects include the common ways in which noses support eyeglasses and the common ways in which hearts produce sounds that help doctors to diagnose various illnesses. Both of these effects can contribute to the well-being of an individual, and well-being is surely one of the goals of an organism. However, if we arrive at a point at which most people wear glasses, it seems Boorse will have to say that supporting eyeglasses has become a normal function of the nose. Neander takes this to be the wrong verdict.

Boorse’s response (Reference Boorse, Ariew, Cummins and Perlman2002: 88) is to bite the bullet and accept that, in these cases, it would indeed be acceptable to say that the human nose has taken on a new function. Boorse cites other examples that are analogous, including the sea turtle example mentioned earlier. At present, sea turtles often use their flippers for egg-hole digging, thereby aiding reproduction. It is not plausible to think that these flippers were naturally selected for this purpose, yet it seems far from absurd to say that egg-hole digging has become a normal function of the sea turtles’ flippers. If the goal-contribution theory is attractive in other independent respects, then perhaps Boorse is entitled to stand his ground on this issue.Footnote ²⁰

Regarding the non-function/malfunction distinction, the challenge is to make sense of how an item can be deemed defective. For example, neither a severely diseased heart nor a wooden spoon has the ability to beat and pump blood effectively. Nonetheless, we are inclined to say there is an important difference between these two cases. The diseased heart is defective in the sense that it should beat but doesn’t: it is malfunctioning. How, then, can a goal-contribution theorist account for such malfunction? Boorse’s answer (Reference Boorse, Ariew, Cummins and Perlman2002: 88–89) is to draw once again on the type–token distinction and the notion of normal functioning. Neither the severely diseased heart nor the wooden spoon can perform the function of beating. Nonetheless, this particular heart is a member of an anatomical type – being a heart – whose normal function is to beat. This is to say that, statistically speaking, tokens of this type typically beat for the benefit of some goal. In contrast, a wooden spoon is not a member of a type that typically beats. Hence, we may rightly draw the verdict that in terms of beating, the diseased heart is defective while the wooden spoon is not.

This is not quite the end of the matter, however. We have just seen that Boorse’s analysis of normal function faces the problem of species-typical fortuitous consequences. The account of malfunction faces an analogous problem. It is, for example, conceivable that there could be a devastating pandemic which results in, say, very few hearts beating. In such a scenario, it would not be species-typical for those hearts to beat, and yet surely it would remain the case that the non-beating hearts are defective or dysfunctional. We would still believe that the function of a heart is to beat even though most hearts would no longer happen to perform that function. How, then, can goal-contribution theorists like Boorse accommodate this fact? Reference MelanderMelander (1997), Reference MillikanMillikan (1993), Reference NeanderNeander (1991, Reference Neander, Weingarten and Schlosser2002), and Reference PlantingaPlantinga (1993) have all raised this kind of worry using various examples, some actual and some merely possible.

Boorse’s response to such counterexamples is lengthy (Reference Boorse, Ariew, Cummins and Perlman2002: 92–103), and so I shall focus on what I take to be the main thrust of his solution. Boorse replies that we should be flexible about what counts as the relevant reference class when assessing statistical normality. In particular, it is in many cases sensible to examine an extended time-slice of the kind or species. Boorse thinks this is an inevitable feature of the approach, because ‘If the whole earth went dark for two days and most human beings could not see anything, it would be absurd to say that vision ceased to be a normal function of the human eye’ (Reference Boorse, Ariew, Cummins and Perlman2002: 99). Hence, even if the devastating pandemic occurred, and most current hearts failed to beat, we could still insist that the function of the human heart is to beat given that this is what hearts have typically done in the extended past. Hence, if Boorse’s account utilizes the relevant historical data, it can accommodate the idea that most hearts are malfunctioning in the pandemic example (for further discussion see Reference Garson and PiccininiGarson and Piccinini 2014 and Reference GarsonGarson 2019b).

This does, however, leave us with the question of just how far we are meant to go back in history in order to fix judgements about malfunctioning. In epidemiological contexts, it is far from clear how far back our reference classes should go (Reference SmartSmart 2016: Ch. 2). In Boorse’s work, the answer appears to be anywhere between two lifetimes and a millennium (Reference GirouxGiroux 2015: 185). Again, this brings to light the fact that normalcy and typicality are not precise concepts. I shall leave readers to judge how problematic (if at all) this imprecision is. But in doing so, we should not lose sight of the many benefits of the goal-contribution theory. There is, I think, no guarantee in philosophy and science that all our theoretical concepts can be defined in a perfectly precise way.

In the final subsection of this section, we shall outline a further attraction of the goal-contribution theory, which is that it is compatible with many of the more fine-grained theories of function in the recent literature on philosophy of biology.

2.6 Compatibility of the Goal-Contribution Approach with Recent Theories of Function

A benefit of the goal-contribution account of function, touched upon already, is its generality and hence flexibility. It allows that different kinds of system, including non-biological ones, may have very different goals, and it remains neutral about the specific details in each case. Indeed, in Section 3 we shall discuss cases of goal-directedness involving cybernetic systems. We have also seen how the goal-contribution theory can accommodate the sorts of backward-looking functional explanations that are prominent in evolutionary biology. In the current subsection, we shall see that the goal-contribution theory is also compatible with various other popular theories in recent philosophy of biology regarding the nature of functions. In what follows I give three examples, namely, the survival and reproduction account, the organizational theory, and the neo-Aristotelian approach. To this we could also add the theological approach to teleology that we mentioned briefly in Section 1, since the goal-contribution theory is compatible with the further idea that the goals of, say, organic systems like us are ultimately determined by some divine power.

According to the survival and reproduction account, biological functions are those which contribute, or are disposed to contribute, to biological fitness in various ways (e.g., Reference Bigelow and PargetterBigelow and Pargetter 1987; Reference CanfieldCanfield 1964; Reference RuseRuse 1971). It is easy to see that this approach could be interpreted in goal-theoretic terms, because this is precisely Boorse’s view in the case of biology and medicine (Reference Boorse, Ariew, Cummins and Perlman2002: 64, 108). In Boorse’s view, the survival and/or reproduction of an organism are precisely its ‘apical’ goals (Reference Boorse, Ariew, Cummins and Perlman2002: 76), and each of its functioning subsystems contributes to these ultimate goals in one way or another. Elsewhere, the goal-directedness of developmental biology has also been emphasized by some philosophers of science. For example, Austin highlights the goal-directed nature of models in dynamic systems theory, which privilege certain end-state morphologies (Reference Austin, Simpson, Koons and TehAustin 2017: 200).

Organizational or ‘organismic’ accounts of biological function have also become prominent in recent literature. Such accounts come in various forms which overlap in various ways with the causal role and survival and reproduction accounts. However, the idea is roughly that an item has a biological function if it plays an appropriate role in the maintenance of the system on which it reciprocally depends (e.g., Reference Barandiaran and MorenoBarandiaran and Moreno 2008; Reference Kertész and KodajKertész and Kodaj 2023; Reference McLaughlinMcLaughlin 2001; Reference Mossio, Saborido and MorenoMossio et al. 2009; Reference Mossio and BichMossio and Bich 2017). This reciprocity requires a certain kind of organizational complexity, which all self-maintaining biological systems share. Reference Mossio, Saborido and MorenoMossio et al. (2009) spell out this complexity in terms of the notions of ‘organizational closure’ and ‘organizational differentiation’ (Reference Mossio, Saborido and Moreno2009: 824, 826). A system is organizationally closed when there is a ‘circular causal relation between some macroscopic (or higher-level) pattern or structure and the microscopic (or lower-level) dynamics and reactions’ (Reference Mossio, Saborido and Moreno2009: 824). This idea is closely related to the biological notion of autopoiesis developed by Reference Maturana and VarelaMaturana and Varela (1980), whereby biological functions are said to be continually realized and regenerated via the organization of organisms (see also Reference MeinckeMeincke 2019). The important point for current purposes is that organizational closure can be spelt out naturally in goal-theoretic terms. Reference Mossio, Saborido and MorenoMossio et al. (2009: 824) indicate as much when they say that ‘in an organizationally closed system the goal states are the stability points (or set of points) through which the system can exist’.

Austin and Marmodoro’s neo-Aristotelian account of organisms (Reference Austin, Marmodoro, Simpson, Koons and Teh2017) also aims to do justice to these organizational features (see also Reference OderbergOderberg 2007: Ch. 8). The novelty of their account is that such organization is underpinned by neo-Aristotelian realism about powers, which we discuss further in Section 4 when considering the metaphysical foundations of goal-directedness. When applying the powers metaphysics to the specific case of biological functional, Austin and Marmodoro propose that organisms have self-directed ‘structural powers’ which engage in ‘cyclopoietic’ activity: ‘in traversing a kind of causal loop among the constituents of an organism, each is tied together in a continual diachronic cycle of co-production and maintenance’ (Reference Austin, Marmodoro, Simpson, Koons and Teh2017: 171). Austin and Marmodoro go on to spell out the nature of these structural powers in goal-theoretic terms: ‘The self-directedness of structural powers therefore consists in the recursive nature of this unifying activity—they are “self-orientated” precisely because the goal of that activity is to establish the cyclical perpetuation of its own operation’ (Reference Austin, Marmodoro, Simpson, Koons and TehAustin and Marmodoro 2017: 171–2). More recently, Reference Paolini Paoletti, Jansen and SandstadPaolini Paoletti (2021a) has developed a more general powers-based account of function, and he explicitly acknowledges that the theory is compatible with a goal-contribution interpretation of functions (Reference Paolini Paoletti, Jansen and Sandstad2021a: 128). Again, we shall return to the important topic of powers in Section 4.

Finally, there is another sense in which the goal-contribution account is flexible – a sense which brings us to key questions to be addressed in Sections 3 and 4. So far, we have said little about whether goal attributions commit us to the existence of irreducible teleological properties in the world. As we shall see in Section 3, Nagel’s goal-contribution theory of functions (1979: Ch. 12) involves an analysis of goal-directed systems that has its roots in the reductive cybernetic tradition. Although Nagel thinks that our concept of goal-directedness captures an important class of complex systems, his view is that such systems can ultimately be characterized in non-teleological, mechanistic terms. So, we may regard Nagel as a deflationist or reductionist about teleology: as we put it in Section 1, Nagel thinks the world is teleological with a small ‘t’ rather than a big ‘T’.

However, we shall see that matters are not straightforward for the Nagelian reductionists. Objections raised by Reference SchefflerScheffler (1959, Reference Scheffler1963); Reference EhringEhring (1984a); Reference NissenNissen (1981, Reference Nissen1997) and others show that it is difficult for cybernetic theorists to explain goal-directed behaviour in cases where the relevant goals are not achieved. In Section 4, we argue that a realist theory of powers offers resources for overcoming this problem. According to that proposal, goal-directedness can be understood as a type of end-directedness that is grounded in certain powers of a complex, ‘directively organized’ system. Importantly, it is arguable that powers are themselves irreducibly teleological. If that is correct, then the prospects for eliminating teleology from our metaphysics are dim. Despite the array of philosophical literature suggesting the contrary, the world may well be teleological with a big ‘T’.

3.1 A Reductive Approach

As noted earlier, Boorse’s goal-contribution analysis of functions has its roots in earlier work by Reference NagelNagel (1961, Reference Nagel1979: Ch. 12) and others in the so-called ‘cybernetic’ tradition. According to Boorse and Nagel, function ascriptions are made relative to goals. As Nagel puts it: ‘A functional statement of the form: a function of item i in system S and environment E is F, presupposes … that S is goal-directed to some goal G, to the realization or maintenance of which F contributes’ (Reference Nagel1979: 312). If we accept this view, then we cannot fully understand the concept of function unless we understand the nature of goals and goal-directedness. Thus, in this section, we focus more directly on the concept of goal-directedness itself. In metaphysical terms, we may ask: What are the truthmakers for ascriptions of goals and goal-directed behaviour to a system? As far as I know, Boorse himself does not say a great deal about this important issue, perhaps because he thinks the earlier cybernetic literature has already shed light on the matter, notably via Nagel’s ‘system-property’ theory of goal-directedness. The cybernetic approaches offer an empirical, reductive, and largely behaviouristic account of goal-directedness: the truthmakers for truths about goals and goal-directedness are just patterns of behaviour of a certain sort, which are generated by mechanisms of a certain sort.

Nagel’s work has an openly reductive flavour, in the sense that talk of teleological goals is reduced to mechanistic language which does not itself employ teleological terms. This, in turn, has a knock-on effect regarding the goal-contribution account of functions, because functions can then be understood in terms of their contributions to systemic effects (the ‘goals’) which can, in principle, be characterized in entirely non-teleological terms. We shall explore the details in what follows. The upshot is that one cannot help thinking that if Nagel’s theory is right, then although talk of goals or functions might be convenient, and of heuristic value in biology and other special sciences, we should not think that the world is inherently teleological. Teleological explanations thus become neither indispensable nor fundamental. For Nagel, the difference between teleological explanations and their non-teleological equivalents is ultimately one of emphasis (Reference Nagel1961: 422). However, as we shall see, the cybernetic analysis of goal-directedness faces several counterexamples and problem cases, the most serious of which is the problem of goal failure. In seeking to overcome this problem, it is far from clear that we can avoid positing irreducibly teleological properties after all.

Let us start with an important clarification that was implicit in our discussion of the goal-contribution theory of function. Although functions arguably depend on goals, goals and functions are not the same thing. Reference NagelNagel (1961: 277) remarks that biologists sometimes use these terms interchangeably, but that it would be a mistake to do so across the board. In the sense that we have defined functions, something performs a function when it contributes to a goal of a system. But that is not to say that the item with the function is itself a system with a goal. For example, very simple artefacts like coat pegs or fridge magnets perform functions when utilized by us in our goal-directed behaviour, but they are not by themselves complex enough to exhibit goal-directed behaviour. Moreover, at the level of a system as a whole, the system’s goal may not be a function for anything because it may not contribute to a goal of some further system. Nonetheless, in the case of complex organic subsystems, their goal states do typically make contributions to the goals of a larger system, in which case the subsystem’s goal states are themselves performing a function relative to some larger system. In complex organisms like us, there is a hierarchy of systems and subsystems at different levels of complexity, from genes through to cells, tissues, organs, and multiple-organ systems. Arguably, many of these subsystems have functions and goals which contribute to the functions and goals of a further system next up in the hierarchy. At the apex of this hierarchy is the organic system as a whole, and there appears to be some consensus in biology that the overall goal of an organism is fitness, that is, survival and perhaps reproduction (Reference Boorse, Ariew, Cummins and PerlmanBoorse 2002: 70). Each subsystem can then be seen as contributing in some way to this overall goal.

So far, we have focused on biological examples, and in such cases it is quite natural to ascribe goals and speak of goal-directed behaviour – especially in relation to organisms capable of intentional thought. However, early goal-directed accounts of teleology were in fact inspired by technological developments of cybernetic machines, whose behaviour seems apt to be described as goal-directed (Reference Rosenblueth, Wiener and BigelowRosenblueth et al. 1943). The much-discussed examples include homing missiles, thermostats, a steam engine’s Watt governor, and, more recently, self-driving cars. The apparent goals in these examples are quite different: the homing missile’s goal is to destroy some external target, while the goal of a thermostat is to maintain a certain temperature in response to external conditions. In each case, the behaviour of the system is directively organized towards a certain end. That is to say, both homing missiles and thermostats adapt their behaviour in varying conditions so that the goal-states can still be achieved. If a homing missile’s target moves, the missile moves accordingly. If the temperature of a room rises above a certain level, the thermostat’s feedback mechanism ensures that the heating system stops producing more heat.

One of the aims of the cybernetic programme was to unpack precisely what it is that cybernetic machines and organic systems have in common, and thereby explain and justify talk of goal-directedness in both cases. According to the cybernetic analysis, goal-directedness is largely an intrinsic feature of systems, grounded in their behavioural profiles. If successful, then, the programme would allow us to ascribe goal-directedness to systems independently of human aims and purposes.Footnote ²¹ And if truths about goal-directedness can, in this way, be grounded in mechanistic patterns of behaviour, we are left with a thoroughly naturalistic and reductive theory of teleology. If this approach is the correct one, then we do not need to account for goal-directedness in terms of mentalistic teleological concepts such as intentionality. Indeed, in order to signify their move away from irreducible teleology, cybernetic theorists often refer to goal-directed systems as being ‘teleonomic’ rather than ‘teleological’ (e.g., Reference Pittendrigh, Roe and SimpsonPittendrigh 1958; Reference Mayr and MayrMayr 1988).

Given these naturalistic and reductive aims, the early cybernetic views are often regarded as taking a behaviouristic approach (e.g., Reference NissenNissen 1997: Ch. 1), meaning that the teleological truths are grounded primarily in overt patterns of behaviour. It is in these terms that Reference Rosenblueth, Wiener and BigelowRosenblueth et al. (1943) characterize their project, describing it as ‘the behaviouristic study of natural events’ (Reference Rosenblueth, Wiener and Bigelow1943: 18). Core behaviourist concepts appealed to in this respect are the cybernetic notions of plasticity and persistence, which we discuss in Section 3.2. However, as we shall see, in order to overcome certain counterexamples, the cybernetic theory also requires some mechanistic constraints; and even this may not be enough. Later on, we shall argue that in order to deliver an adequate theory of goal-directed behaviour, we may need to posit irreducibly teleological properties after all. Hence, it is far from clear that Nagel’s reductive ambitions can be achieved – at least where teleology is concerned.

3.2 Nagel’s ‘System-Property’ Cybernetic Analysis

For the time being, let us see what prominent cybernetic theorists have had to say about our key questions: What are the defining characteristics of behaviour that is goal-directed? And, in truthmaking terms, what does the world have to be like in order for it to be true that certain behaviour is goal-directed? What is striking about cybernetic systems is that they can adapt their behaviour in response to various interferences, in such a way that they can still achieve their goal – or at least remain on track to achieve their goal. We find this same adaptability in other kinds of teleological system. For example, the human body reacts in various ways to both low and high external temperatures in order to maintain an internal bodily temperature of around 37 degrees Celsius. The similarities of this human subsystem with the thermostat example are striking, albeit the thermostat’s mechanisms are much simpler. How, then, can this adaptability be spelt out in behavioural, empirical terms?

The cybernetic answer employs the concepts of plasticity and persistence, which were developed in the 1940s and 1950s by philosophers of biology such as Reference RussellE. S. Russell (1945), Reference SommerhoffSommerhoff (1950), Reference BraithwaiteBraithwaite (1953), and later Reference NagelNagel (1961, Reference Nagel1979: Ch. 12). Roughly, a system is plastic if its goal(s) can be reached via different causal paths or from different initial positions (Reference NagelNagel 1979: 286). As Garson notes (Reference Garson2016: 23), for theorists like Braithwaite, ‘initial positions’ does not merely mean different positions in a given environment but rather different environmental conditions altogether. As for persistence, this is more to do with the adaptability of the behaviour as it occurs, such that if one path to the goal is blocked, an alternative causal route to the goal is taken. As a system operates, any number of changes could occur – both in the external environment or within the system itself – which would prevent it from achieving its goal were its behaviour not modified. A system is persistent, then, if it is able to compensate for a range of such changes by modifying its behaviour in a way that still leads it towards the relevant goal (Reference NagelNagel 1961: 411). One way of thinking about this idea is that the achievement of the goal by the system is to some extent independent of specific internal and external variations, at least within a certain range.

Notice that, on the surface, the concepts of plasticity and persistence are empirical and therefore testable. That is, we can test for plasticity and persistence by placing a system in different situations and seeing if its outward behaviour is modified accordingly in order to reach some hypothesized goal(s). If it is, then we have prima facie evidence regarding the goal of the system, which can then be confirmed through further testing (see e.g., Reference Rosenblueth and WienerRosenblueth and Wiener 1950: 325; Reference BecknerBeckner 1959: 143–144). This also means we will often be able to make judgements about plasticity and persistence while knowing little about the precise internal mechanisms of a system. Hence, we can, in principle, identify the goals of a system prior to knowing about the specific functions of its parts. This is an important feature to highlight because it avoids a potential worry about epistemic circularity. If the goal-contribution theory of functions is correct, then knowledge about the functions of things depends on knowledge about how those things contribute to the goals of a given system. However, we would be caught in an epistemic circle if it were also the case that we have to identify the functions of things before we can determine the goals of relevant systems.

How, then, can we construct a more rigorous metaphysical analysis of a goal-directed system? Nagel’s own analysis is based on several formal elements (Reference Nagel1961: 411–18): S is the system in question, E is the external environment, and importantly G is some goal state that S either possesses or is at least capable of possessing under certain conditions. Note that the goal state is not merely accidental but rather ‘distinctive’ of the integrated system in question (Reference NagelNagel 1961: 422; see also Reference McLaughlinMcLaughlin 2001: 76). This implies that directively organized systems are individuated at least in part by their goal-types.

Next, we specify the components of the system which are causally relevant for the occurrence of the goal state, call them A, B, C … . There may be any number of such components. The states of such components are then represented by state variables ‘A_x’, ‘B_y’, ‘C_z’ and so on. These may or may not be numerical variables, depending on whether the states in question are quantitative or qualitative. The variables are such that they can change, and the overall state of S at any given time is expressed by the matrix (A_xB_yC_{z …}). Nagel also stipulates that the various state variables must be suitably independent of each other, or ‘orthogonal’, but we may set that idea aside for now.

Suppose that S is in its G state at t₀ but is such that a change in any one of the state variables A_x, B_y, C_z … would take S out of G (assuming that the values of the other variables remain the same). Following Nagel, call such a change a ‘primary variation’. Then, we can say that S is directively organized or goal-directed if S’s parts A, B, C … are such that if primary variation occurs, the states of the relevant components change in such a way that at some later time t₁ the system is still in state G (or perhaps tending towards G). In short, the idea is that when primary variation occurs, a directively organized system’s parts adapt and compensate in such a way that G tends to be maintained. This is just a more formal way of capturing the ideas of plasticity and persistence. One of the features of this formal definition is that it remains silent about the precise mechanisms which give rise to the compensatory behaviours (Reference NagelNagel 1961: 418). With this basic definition of directive organization in play, we can then add (as appropriate) the stipulation that S’s state variables also compensate for relevant environmental changes in such a way that G is maintained (or is on course to be maintained). To do so, we merely require a state variable for E (‘F_w’) as a further possible source of variation.

At this point, one might wonder just how many potential changes a system needs to be able to compensate for in order to be regarded as plastic and persistent. This is a delicate question because to put any specific number on it would seem somewhat arbitrary. The answer given by Reference Rosenblueth and WienerRosenblueth and Wiener (1950), Reference BraithwaiteBraithwaite (1953), and Reference NagelNagel (1961) is that plasticity and persistence come in degrees. This idea has been developed more recently by Reference BabcockBabcock (2023), Reference Lee and McSheaLee and McShea (2020), and Reference McSheaMcShea (2012). In Nagel’s analysis, a directively organized system compensates for so-called primary variations in order to maintain some goal state G. However, the range of primary variations that a system can compensate for – call it K_A′ – may vary between cases. Hence, systems can be more or less directively organized depending on how inclusive the range K_A′ is (Reference NagelNagel 1961: 417). We shall return to this issue in Section 4.7.

With all these details in place, we can reconstruct the Nagelian theory roughly as follows, starting with the notion of directive organization (‘DO’):

Recall that the goal-contribution analysis of function performance (‘GCF’), which Nagel also appears to endorse, is as follows:

Importantly, with these definitions in play, it seems we can generate non-teleological equivalents of function statements and functional explanations. When we explain something’s behaviour functionally, we are merely explaining what contributions the behaviour makes to the plastic and persistent behaviour of some complex system. And for the Nagelian reductionist, plasticity and persistence are defined in non-teleological behaviouristic terms. Hence, although Nagel is a goal-contribution theorist about functions, it turns out that, for him, talk of goal-contribution (and thus functions) is a convenient heuristic that can ultimately be explained away. This suggests that the cybernetic theory of goal-directedness is compatible with purely mechanistic worldviews, such as those inspired by Descartes and Hume, where the only kind of causation at work is so-called efficient causation. According to the Humean metaphysics, the world is just a mosaic of loose and separate qualities which happen to form certain patterns (see Reference WilliamsWilliams 2019: Chs. 1 and 2). On this view, these patterns are brute facts which are not explained by any deeper metaphysical principles. This kind of picture stands in stark contrast to the anti-Humean theory of goal-directedness proposed in Section 4, which appeals to irreducible, end-directed powers.

Assuming for now that the Nagelian reductive analysis is feasible, why do the explanatory practices of biologists and other special scientists often favour teleological formulations? This is a compulsory question, because even Nagel accepts that teleological explanations are pervasive in some areas of science and are often taken to be indispensable. Nagel’s answer is that whether one deploys a teleological or a purely mechanistic explanation is context dependent and largely to do with emphasis or selective attention. Explanations involving goals are forward-looking, placing an emphasis on the end point of a systemic process to which various parts contribute. In contrast, mechanistic explanations are more backward-looking, focusing on the conditions that give rise to the relevant process (Reference NagelNagel 1961: 405, 421–422; see also Reference SchaffnerSchaffner 1993: 391).

With the core elements of this reductive strategy in place, let us discuss some problems facing the theory.Footnote ²²

3.3 The Problem of Extensional Adequacy

As with most philosophical analyses purporting to provide necessary and sufficient conditions for some phenomenon, critics have promptly replied with alleged counterexamples. In response to the alleged counterexamples, cybernetic theorists have either bitten the bullet and accepted the (perhaps counterintuitive) consequences of the analysis, or modified the analysis accordingly. In this section we shall outline some of the moves that cybernetic theorists have made in response to various alleged counterexamples. However, since such counterexamples tend to rely on intuitions about what does and does not fall under a concept, it is difficult to say whether firm conclusions can be drawn from this area of the debate. For this reason, I shall not dwell on this issue for too long.

The counterexamples that cybernetic theorists have taken most seriously are those which threaten the sufficiencyFootnote ²³ of the plasticity and persistence conditions for goal-directed behaviour, suggesting that the analysis is guilty of overbreadth. Reference NagelNagel (1961, Reference Nagel1979) discusses several examples of relatively simple processes which appear to display plastic and persistent behaviour.Footnote ²⁴ One example concerns a ball at the bottom of a bowl that is disturbed in various ways but always behaves in such a way that it returns to its initial position (Reference Nagel1979: 288). Another example involves a pendulum (Reference TaylorTaylor 1950a: 316, Reference NagelNagel 1961: 419–420) which is disturbed by a gust of wind but returns to its lowest point via gradually decreasing oscillations. What these examples have in common is that some equilibrium state is restored in the face of disruption. Such processes are familiar in physics and Reference BedauBedau (1992b) discusses a range of similar examples, arguing that we would not regard them as cases displaying teleology.

Faced with such examples, cybernetic theorists have typically been reluctant to bite the bullet and accept that such systems are goal directed. Instead, they have added more necessary conditions for goal-directedness in order to preclude those cases from counting as goal directed. It is not obvious that this is the correct strategy, however. As noted earlier, Braithwaite and Nagel accept that directive organization comes in degrees: one system can be more or less plastic and persistent than another. With this in mind, one wonders why we shouldn’t just accept that the ball in a bowl is goal-directed but to a lesser degree than, say, a homing missile (see e.g. Reference McSheaMcShea 2012; Reference BabcockBabcock 2023: Sect. 3).Footnote ²⁵ If one takes the ball out of the bowl, then of course it will not modify its behaviour in such a way that it travels back into the bottom of the bowl. Nonetheless, there is a relatively narrow range of circumstances, within the bowl, in which the ball persistently makes its way back to its starting position. This strategy would still accommodate the intuition that homing missiles and renal systems are the more paradigmatic examples of goal-directedness, on the basis that they are goal directed to a much higher degree. I leave readers to judge the merits of that strategy. For completeness, I shall also briefly outline the sorts of modifications that Nagel and others have made in response to these perceived counterexamples.

As Garson puts it (Reference Garson2016: 23), in order to preclude pendulums and balls-in-bowls from counting as goal-directed systems, the cybernetic theories have taken an overtly ‘mechanistic’ turn. What Garson means is that cybernetic theorists have taken a closer look at the internal mechanisms of goal-directed systems, with a view to showing that pendulums and balls do not have the right sorts of inner organizational complexity to count as being goal-directed. A typical ball, for example, is ‘internally homogenous’ (Reference Garson2016: 23), whereas paradigmatic goal-directed systems have clearly delineated parts which make distinctive contributions in a coordinated effort towards a goal.

In the philosophical literature, there are at least two different ways of spelling out this further condition of organizational complexity, though the two are arguably compatible and complementary. The Nagelian condition, which has its roots in the work of Reference SommerhoffSommerhoff (1950), is a formal condition requiring that the states of the parts of a directively organized system are independent, in the sense that the values of the state variables they instantiate must not determine the values instantiated by other parts of the system at that same time. In Nagel’s terminology, the different variables must be ‘orthogonal’ (Reference Nagel1979: 288). Consider the following example from Reference NagelNagel (1979: 289): the function of a Watt governor in a steam engine is to maintain speed (within a certain range) by controlling the amount of steam entering the engine cylinders. As with other negative feedback mechanisms, the system involving the engine-plus-governor is plastic and persistent. And, importantly for current purposes, if the ‘Watts governor of a steam engine is not hitched up to the engine, any speed of the engine is compatible with any speed of the arms of the governor; for there are no known laws of nature according to which, in the assumed circumstances, the spread of the arms depends on the engine speed’ (Reference NagelNagel 1979: 289).

Since the Watt governor system is a goal-directed system par excellence, this raises the prospect that independence of the relevant variables is a necessary condition for goal-directedness. Importantly, this condition appears to preclude pendulums and balls-in-bowls from being goal directed. In the ball case, the relevant variables that determine the ball’s motion, that is, those concerning restoring and displacement forces, are not independent of each other because they are both fixed by the laws of motion.

The other way of imposing an appropriate mechanistic constraint is to insist that goal-directed systems involve negative feedback mechanisms. The Watt governor is, like a thermostat, an example of a negative feedback mechanism – arguably one of the first. Reference Rosenblueth, Wiener and BigelowRosenblueth et al. (1943) were arguably the first to offer a negative feedback analysis of goal-directed behaviour, which was taken up subsequently by Reference AdamsAdams (1979) and Reference FaberFaber (1986). How, then, are negative feedback mechanisms best characterized? As one would expect from a plastic and persistent system, a feedback mechanism exhibits complex behaviour (the output) in response to an input. Hence, such systems have something resembling a detector or sensor, which allows them to detect the values of relevant variables so that the output can be adjusted accordingly. However, in a feedback system there is also a causal loop. As Reference Rosenblueth, Wiener and BigelowRosenblueth et al. (1943: 19) put it, in feedback systems ‘some of the output energy of an apparatus or machine is returned as input’, resulting in a continuous cycle of output and input. In cases of negative feedback, the input can be used to restrict rather than amplify the output, ensuring that a certain goal-threshold is not exceeded. If such systems can react accordingly to a range of inputs, then such systems will naturally satisfy the behaviouristic criteria of plasticity and persistence discussed earlier. Homeostatic mechanisms such as thermostats provide good examples: as Taylor nicely puts it, ‘a thermostat controls, and is in turn controlled by, temperature’ (Reference Taylor1950a: 315). In more complex examples such as that of a self-driving car, the system continually monitors the environmental conditions and adjusts its behaviour accordingly, typically through regression algorithm computation.

Clearly, pendulums and balls-in-bowls are not negative feedback mechanisms, so the negative feedback requirement also avoids the salient counterexamples. Moreover, I take this strategy and Nagel’s independence condition to be complementary, for it is difficult to think of an example of a negative feedback system whose controlling variables are not nomically independent. So, one way of thinking about the negative feedback condition is that it specifies a mechanism which realizes Nagel’s formal independence condition. But whether other mechanisms could also perform this role is an interesting question that we shall not address here.

I leave readers to judge the merits of these modifications.Footnote ²⁶ But regardless of their merits, the reductive cybernetic analyses still face problems that are more fundamental, namely the problems related to goal failure and underdetermination. These objections stem from the behaviouristic roots of the cybernetic theory, and it is to those problems that we now turn.

3.4 The Big Bad Bug: The Problems of Goal Failure and Underdetermination

In its basic form, the cybernetic view is based upon patterns of plastic and persistent behaviour, and therefore assumes that the goal states of a system are typically achieved. For something to demonstrate goal-directed behaviour, it must show that it can follow more than one causal pathway to the goal, and also modify its behaviour so that it still reaches its goal. As Nissen puts it, the cybernetic theory of Braithwaite and others is based on trial and success (Reference Nissen1997: 7). This leads to what Nissen calls the problem of goal failure.

The problem is that it is overwhelmingly plausible to think there can be goal-directed behaviour even if the relevant goal is never achieved. To use one of our stock examples, a homing missile might miss its target if the target emits sophisticated decoy countermeasures. But even in that case, it still seems correct to say that the missile’s goal was to destroy the target. There can also be goal-directed behaviour in cases where the object of the goal never exists, as when scientists search to discover a certain element without hope of success. In such cases, it is difficult to see how the condition of plasticity can be satisfied, for if the goal never exists, there cannot be alternative causal routes to it. This problem looks especially serious for those theories that include the negative feedback condition. As Reference NissenNissen (1997: 30) and Reference GarsonGarson (2016: 27) remark, it is arguable that by definition, negative feedback systems are ones which modify their behaviour by receiving input from their target. In that case, it is surely impossible for a negative feedback system to exhibit plasticity and persistence if the target does not exist.

Cases of goal failure or missing goals were identified as a problem for behaviourist analyses of goal-directedness as long ago as 1950 (Reference TaylorTaylor 1950b: 329), and have since been elaborated by, amongst others, Reference SchefflerScheffler (1959, Reference Scheffler1963), Reference BecknerBeckner (1959), Reference HullHull (1973), Reference EhringEhring (1984a), and Reference NissenNissen (1997). To deal with such cases, goal theorists must surely avoid any implication that a goal-directed system has to achieve its goals. However, this is not a straightforward task for the cybernetic theorists. As soon as they accept goal-directedness in cases where the goal is never achieved, they are left with a problem of underdetermination. In its basic form, the cybernetic theory grounds goal-directedness in patterns of behaviour, but in cases of goal failure the behaviour that occurs does not lead to the achievement of a goal. But if a goal does not come about, then who is to say what it is that the behaviour is directed towards? For example, I imagine, sadly, that there have been times at night when our baby son has cried, but we haven’t attended to him due to being in deep sleep. Who is to say what the goal of the crying was in those cases? Was the goal to acquire milk, to play, to be cuddled, or … ? Note that this underdetermination problem is not merely epistemic; for the cybernetic theorists it is also metaphysical. Intuitively, there should be a determinate fact of the matter as to what the goal is in such cases, but within a behaviouristic metaphysics it is not easy to see how there can be such a fact.

One is tempted, of course, to say that the goal in my example is determined by my son’s intention to, say, be fed. But this solution is not an option for cybernetic theorists because they typically reject intentional theories of goals and functions. For one thing, it is far from clear that the concept of intentionality is non-teleological and hence admissible in an analysis of teleology that purports to be reductive. And even setting that issue aside, remember that the theory is meant to be applicable to inorganic cybernetic systems, which do not seem to be the sorts of things that can exhibit intentionality, except in a mere metaphorical sense.

Another option would be to ground the goals of cybernetic systems extrinsically in the purposes for which they are designed or used by human agents. But, again, this solution does not sit well with the cybernetic approach. As Taylor acknowledges (Reference Taylor1950a: 312), Rosenblueth et al. are clear that cybernetic systems are intrinsically purposeful (Reference Rosenblueth, Wiener and Bigelow1943: 19). Moreover, if the goals of cybernetic systems were determined extrinsically by the intentions of their human designers, this would push the cybernetic theory towards the kind of selectionist analysis of teleology discussed in Section 2. Reference Rosenblueth and WienerRosenblueth and Wiener (1950) are sceptical of that approach in the case of goals, partly because they think that the goal-directedness of a machine could clearly differ from what its designer intended. For example, a complex weapon that we design could end up being disposed to kill unintended targets in a plastic and persistent way (Reference Rosenblueth and Wiener1950: 318). Bigelow and Pargetter raise the same sort of problem for design-based theories of function, for it seems perfectly plausible that some things can regularly perform functions for which they were not originally designed and created (Reference Bigelow and Pargetter1987: 185).

In order to overcome the problem of underdetermination, two main options have been offered by the cybernetic theorists. The first option is a counterfactual strategy and the second involves positing properties of inner representation in the relevant systems, as a way to determine the relevant goals. We shall begin in the next subsection with the counterfactual strategy, before briefly discussing the representation strategy in Section 3.6. Although these solutions are consistent with the intrinsicality of goal-directedness, we shall see that both theories face serious problems.

3.5 The Counterfactual Formulation

The earlier definition of directive organization (Section 3.2) captures what (allegedly) happens in actual cases of goal-directed behaviour. One of the lessons of Section 3.4 is that we should not insist that a system is goal-directed only if it actually demonstrates plastic and persistent behaviour. However, even if a goal-directed system does not actually demonstrate such behaviour, one might expect that certain hypothetical truths or ‘counterfactuals’ will hold, namely, that if a range of internal or external primary variations were to occur, then the system would adapt its behaviour in a way that still leads towards the goal. That is to say, in other words, that the modal profiles of directively organized systems have a plastic and persistent structure. Nagel himself occasionally acknowledges this point.Footnote ²⁷ When discussing the example of the human subsystem that moderates water content in the blood, Nagel expresses the goal-directedness in counterfactual terms: ‘were the blood inundated with water to a greater or lesser extent than was actually the case, the activity of the kidneys or of the muscles and skin would have been appropriately modified’ (Reference Nagel1979: 287). Perhaps, then, such counterfactuals could be put to work to determine the goals of a system in cases where the goal is not achieved. Even if something prevented a particular human body from moderating its water content, the goal of water moderation would nonetheless be grounded by relevant counterfactuals concerning the kidney, muscles, and skin.

Consider Scheffler’s favoured example of a dog that is trapped in a cave and is pawing at the door (Reference Scheffler1963: 119). This looks like a case of goal-directed behaviour par excellence. It is easy enough to imagine that by pawing at the door, the dog is striving towards the goal of leaving the cave. But if the door is never opened and the goal is never achieved, in what sense can we say that the dog’s behaviour is goal-directed? If we want to avoid appealing to the dog’s intentions, a counterfactual solution looks like the obvious way to go (Reference WoodfieldWoodfield 1976: 49). Even if the dog’s goal is not in fact achieved, we might insist that the following counterfactual is still true of the dog: if the door had opened in various ways, then the dog would have exited. The idea, then, is that the consequents of such counterfactuals determine the goals towards which the systems are directed.

On the face of it, this looks like a neat and straightforward solution. However, this strategy faces at least two significant challenges. The first problem is raised by Reference NissenNissen (1997: 8). As I interpret Nissen, the worry is that the counterfactuals might not always line up perfectly with what the goal really is. Even if the goal of the dog’s pawing really is to be let out of the cave, there is no guarantee that, counterfactually, the dog would leave if the door were opened. For one thing, goals can change in unexpected ways due to internal or environmental factors. For example, suppose that outside the cave there is a deep freeze. After the door were opened, the dog might feel the bitter cold on its nose and decide that, after all, it is better to stay in the cave. So, the counterfactual would deliver the wrong verdict, suggesting that the goal was to stay in the cave rather than exit.

There are technical modifications that the cybernetic theorists could attempt so that the counterfactuals deliver the correct verdicts. But it is not going to be easy. The wrinkle in the counterexample was that the dog’s goal was changed at the last minute. So, the counterfactual theorist might insert the following sort of proviso: if the door were opened in some way or other, and the dog’s goal were not altered, then the dog would exit the cave. However, clearly this will not do. Again, the aim of Nagel and other reductive theorists is to analyse talk of goals and goal-directedness in non-teleological terms, so that the analysans does not itself involve terms like ‘goal’ or related ones such as ‘purpose’ or ‘intention’. The problem with the proviso is that it deploys the very concept of goals that we are trying to understand.

Another option is to include a proviso in the counterfactuals’ antecedents that appeals to ‘ideal’ or ‘ordinary’ conditions. In the example, perhaps the very cold weather outside the cave is just an unusual situation that the dog finds non-ideal. However, it might be urged that this is no counterexample because being goal-directed towards exiting the cave just means that, if the circumstances were ideal, the dog would leave the cave when the door were opened in one way or another. This solution is still not straightforward, however. In the debate about reductive counterfactual analyses of dispositions, the difficulty of spelling out ‘ideal’ provisos in an informative way is often highlighted (e.g., Reference MartinMartin 1994).Footnote ²⁸ It would be unrealistic to offer a disjunctive list of all the possible ideal circumstances, for such a list would be incredibly long and impossible to formulate. And more worryingly, it seems we would already have to have some grip on what the dog’s goal is in order to decide what does and does not count as an ideal circumstance. This is because the whole point of the ‘ideal conditions’ clause is that it captures just those circumstances in which the dog’s goal is not altered or otherwise thwarted. So, one cannot help thinking that there is still circularity, albeit more covertly.

Even if a technical fix can be found which avoids circularity and is not too ad hoc, there is still a more fundamental and difficult metaphysical question to face. What exactly is it that determines the truth of the relevant counterfactuals? One should not let the truth of counterfactuals ‘hang on air’, as Armstrong would say (Reference Armstrong2004: 3), for that would render them mysterious. In the dog example, what is it about the dog or the world at large which determines how the dog would behave in the relevant counterfactual scenarios? The danger for reductionists like Nagel is that the answer will inevitably invoke teleological properties: it is precisely the goals or intentions of the dog that make it true that it would go through the door if it were opened in various ways. To put the worry in a slightly different way, the cybernetic theorists face a Euthyphro dilemma: do goals determine the relevant counterfactuals, or do the relevant counterfactuals determine the goals? For the cybernetic theory to succeed in its reductive aims, it needs to uphold the second disjunct in a way that does not presuppose teleological facts. I cannot rule out that there is some way to achieve this, but how to do so is, at the very least, far from obvious.

3.6 Inner Representational Properties

Other cybernetic theorists have employed a rather different strategy in order to address the sorts of problems raised in Section 3.4. This involves adding a new requirement, which is that a goal-directed system must contain some internal representation of the goal state (e.g., Reference AdamsAdams 1979; Reference FaberFaber 1986; Reference ManierManier 1971). In Adams’s view, a negative feedback system operates not by receiving feedback signals from the target itself, but rather from a representation of the target. The idea, then, is that whenever the overt behaviour of a system underdetermines the goal, the goal is nonetheless fixed by an inner representation of the goal. For example, in the case of a thermostat, the target might be represented by the position of the temperature dial (Reference AdamsAdams 1979: 507). Even if the target is not achieved, for whatever reason, the representational state of the feedback system determines the goal towards which it is directed.

To be clear, the claim that feedback systems like thermostats have inner representations is not to be interpreted merely as a metaphorical claim. Nor is it being claimed that goal-directed systems represent merely in the sense that minded creatures like us can interpret them in a certain way – as when we read a thermostat dial to learn which temperature it is helping to maintain. Again, the cybernetic theory typically regards the goal-directedness of, say, a homing missile as an intrinsic property of the missile. So, it had better be the case that the required inner representations are intrinsic to a goal-directed system.

With these clarifications in place, one might protest that such a view is clearly absurd, and insist that only organisms – and perhaps computers of a certain complexity – can literally have inner representations. Surely a thermostat is not complex enough to represent anything to itself, given that it doesn’t have anything resembling a mind. Perhaps we could accept that talk of representation is appropriate in such cases in some sense, but only in the sense that we are employing a mentalistic metaphor or analogy (e.g., Reference WoodfieldWoodfield 1976: 183, 194).

One way of developing this worry in a more precise way is to argue that representation requires intentionality and that many goal-directed machines clearly do not exhibit intentional states.Footnote ²⁹ One reason for thinking that intentionality is required for representation is precisely that representational states can often represent things that do not exist. As we have seen, the cybernetic theory must be able to accommodate cases of goal-directedness towards missing goals, and in those cases it looks as though the object of the relevant representation will have to be an intentional object. However, this point again threatens the reductive ambitions of the cybernetic theory, because it is far from clear that the concept of intentionality is non-teleological. Moreover, intentionality is often regarded as the mark of the mental (Reference BrentanoBrentano 2015/1874). Again, surely it cannot be claimed with much plausibility that simple feedback mechanisms like thermostats literally have something resembling a mind.

One way of responding to this worry is to accept that goal-directed systems exhibit intentionality but deny Brentano’s thesis that intentionality is the mark of the mental. That is, one could try to water down the notion of intentionality in some way and accept that cybernetic machines such as thermostats are in physical (i.e., non-mental) states of intentionality. How could one motivate such a claim? Here we might turn to a theory developed by Reference Molnar and MumfordMolnar (2003) that says that many physical properties are causal powers and that power instantiations have the marks of intentionality. This is an interesting and underexplored proposal, but unfortunately, as we shall see in Section 4.2, Molnar’s intentionality account of physical powers faces serious problems. Again, there remains a feeling that insofar as we can ascribe states of intentionality to physical, non-minded things, we are doing little more than employing a mentalistic analogy or metaphor. But if that is all we are doing, then cybernetic machines cannot really be said to have inner properties of intentionality. And hence, as far as our theory of teleology is concerned, it remains far from clear which features of a cybernetic system ground its goal-directedness, especially in cases of goal failure.

3.7 Taking Stock

In this section, we have examined the reductive cybernetic theory of goals, which promises to explain goal-directedness and function attributions in entirely non-teleological, mechanistic terms. Because of its behaviourist roots, the theory faces the serious difficulty of accommodating and explaining goal-directedness in cases where the relevant goals are not (or even cannot) be achieved. We have explored two possible strategies for overcoming this problem, a counterfactual approach and one based on properties of inner representation. Both of these strategies face serious difficulties. As things stand, therefore, we are still in need of a theory of goal-directedness that is able to provide an adequate metaphysical foundation for the goal-contribution account of functions. In the fourth and final section, we explore a novel non-reductive account according to which many cases of goal-directedness are grounded in certain end-directed powers of a system. According to this alternative view, while certain behavioural patterns and counterfactual truths might well be evidence of goal-directedness, they are not constitutive of it.

4.1 The Metaphysics of Properties: Powerful or Categorical?

So far, we have examined two related teleological phenomena that are familiar in many branches of science, namely, functions and goal-directedness. In this section, we shall investigate another related concept which is arguably teleological: the concept of power. The metaphysical concept of power has Aristotelian roots and has attracted much interest in contemporary philosophy. However, there is still much work to be done when it comes to understanding the connections between powers and other teleological phenomena such as that of goal-directedness. Later on, we shall explore the possibility that, in at least some cases, goal-directedness is grounded in certain powers that are exhibited by directively organized systems. I shall not attempt to argue conclusively in favour of the powers metaphysics, but what I do hope to show is that the powers theory provides resources for overcoming problems discussed in the previous section regarding goal-directedness. Let us begin by introducing realism about powers, exploring its teleological implications, and explaining why powers are important in contemporary metaphysics of science.

The best way to introduce realism about powers is by contrast with its main rival: categoricalism. Categoricalism and the powers theory are opposing metaphysical theories about the properties of individuals, such as the property of mass that is exemplified by all physical bodies. Other examples of properties include electric charge, molecular structure, biological traits, and the colours of a flag. All individuals have properties and typically many of them. According to categoricalism, properties have a primitive non-dispositional essence. Although categorical properties determine how things are, they do not in themselves dictate what things can do. For the categoricalists, worldly individuals are thus inherently inert and require the laws of nature to animate them. And such laws are typically regarded by categoricalists as being wholly contingent and external to individuals.Footnote ³⁰

In contrast, powers theorists claim that the relationship between an individual’s properties and its behavioural dispositions is much more intimate. In their view, the connection is one of metaphysical necessity: if an individual has certain properties, then it cannot fail to have certain behavioural dispositions. It is thus properties, and properties alone, that explain the dispositions of things and the counterfactual truths associated with those dispositions. For powers theorists, individuals are inherently powerful by virtue of the properties that they instantiate;Footnote ³¹ we do not need external laws of nature to animate a world that is otherwise static and inert.Footnote ³² This is taken to be a significant benefit of the powers theory, because categoricalist theories of laws arguably face serious problems.Footnote ³³ Moreover, the very notion of a categorical property strikes many metaphysicians of science as being obscure. We gain knowledge about the natural world through causal engagement with it, but if the categorical properties of individuals are wholly distinct from their causal dispositions, it is far from clear how we could ever gain knowledge about categorical properties.

What, though, does it mean to say that a property is inherently powerful rather than categorical? And why do many powers theorists regard powers as teleological entities? These are questions that we shall probe in the following two subsections, before exploring possible connections between powers and goal-directedness. An important point to acknowledge for now is that power properties are characterized, at least in part, by the end-states or ‘manifestations’ that they are powers for. Thus, when explaining powers, considerable emphasis is placed on the directedness that a power has towards its manifestation(s). Indeed, it is this directedness which distinguishes a power-type from others. For example, if someone wished to know about the powers associated with a certain mass property, we would naturally highlight the gravitational and inertial behaviours towards which the relevant masses are disposed. So, it seems that the identity of a power is determined, at least in part, by a certain end (or ends) towards which the power is directed. Such characterizations are forward-looking and therefore appear to be teleological in some sense.

Reference Molnar and MumfordGeorge Molnar (2003) was one of the first powers theorists to put the directedness of all powers at centre stage, but as we shall see in Section 4.2, Molnar arguably takes the idea too far when he characterizes power directedness as a species of intentionality. In Section 4.3, we shall explore a more promising proposal, which is that powers are primitive telic states. If the powers theory is correct, the world is arguably teleological with a big ‘T’.

4.2 The Intentionality Theory of Powers

Dispositions and their directedness were traditionally analysed in terms of counterfactual conditionals: for example, some would say that fragility is directed towards breakage in virtue of the fact that if a fragile object were struck with suitable force, then it would break. However, Reference Molnar and MumfordMolnar (2003) and others raised many serious problems and counterexamples for counterfactual analyses of dispositions (see Reference Friend and Kimpton-NyeFriend and Kimpton-Nye 2023 and Reference SchrenkSchrenk 2016: Ch. 2 for historical summaries). Although disposition ascriptions might well entail certain counterfactuals, the prospects for analysing dispositions in wholly counterfactual terms appear dim. This has led to a resurgence of the idea that dispositions and their directedness cannot be analysed away in the way that neo-Humean reductionists hope. Dispositions and their directedness might well be irreducible features of the world.

This philosophical background provides the context for Molnar’s work on powers, which sees the need for a new approach to dispositions. It is one that aligns dispositions with intentionality rather than counterfactuals. Notice that when creatures like us have thoughts, we invariably focus in on objects. That is to say, our thoughts are about and directed at objects. The essential aboutness of thought is what philosophers call ‘intentionality’. Given that intentional states are directed at certain objects, Molnar was led to consider whether powers just are states of so-called physical intentionality.

The parallels between dispositions and mental intentionality had been highlighted earlier by Reference Martin and PfeiferMartin and Pfeifer (1986) and Reference PlacePlace (1996). The intentional theory of powers is prima facie appealing because, like intentional states, dispositions are directed entities and can (it seems) be directed towards non-existent outcomes. For example, solubility is directed towards dissolving, even if soluble substances are never placed in circumstances where dissolving occurs. Similarly, in the case of mental intentionality, one can have a belief that is directed at unicorns even if there are no unicorns. Nonetheless, despite these surface similarities, it seems fair to say that Molnar’s intentionality proposal is radical. Since fundamental physical entities such as electrons have powers like charge and spin, Molnar has to say that even electrons have intentional states. On the assumption that electrons do not exhibit mental properties, Molnar’s theory implies that Reference BrentanoBrentano (2015/1874) was mistaken when he declared that intentionality is the mark of the mental: rather, for Molnar, intentionality is the mark of power.Footnote ³⁴

For all its attractions, it seems fair to say that the intentionality theory of powers has gained few adherents.Footnote ³⁵ Most powers theorists would agree that there are some loose similarities between powers and intentionality, and in what follows we shall acknowledge some of those similarities. However, there remains a feeling that Place and Molnar take a step too far in claiming that powers literally are intentional states. Reference MumfordMumford (1999), Reference BirdBird (2007), Reference OderbergOderberg (2017), and Reference Marmodoro, Austin, Marmodoro and RoselliMarmodoro (2022), among others, have put forward several objections, many of which look strong.

A preliminary worry is that the explanations commonly given for the existence of intentionality are inappropriate in the case of physical powers. For example, many think that intentionality and representation are intimately connected: a thought can be about a non-existent object precisely because of the representational capacities of the thinker (e.g. Reference KrollKroll 2017: 32; Reference Marmodoro, Austin, Marmodoro and RoselliMarmodoro 2022: 7).Footnote ³⁶ However, we saw in Section 3.6 that it is not easy to make sense of the idea that inanimate systems like thermostats have inner representations, not to mention simple entities like electrons.

There are, however, other general features that intentionality is commonly taken to have. Reference BirdBird (2007: 119–120) lists a number of such features, which include the following:

1. i) Directedness towards an object: for example, a thought about George Molnar.

2. ii) The intentional object may not exist: for example, a thought about a unicorn.

3. iii) Intensionality: for example, it might be true that Sapna believes George Orwell wrote 1984, but false that Sapna believes Eric Blair wrote 1984, even though ‘George Orwell’ and ‘Eric Blair’ are co-referential.

4. iv) Indeterminacy of intentional objects: for example, a thought about the pint pot being somewhere on the bar but not anywhere in particular.

Now, Bird and others are happy to concede that powers have the characteristics i) and ii), suitably understood. However, it is far from clear that any firm conclusions can be drawn from this regarding the connection between powers and intentionality. In many cases the directedness involved in powers looks rather different to that which is typically involved in mental intentionality. In Brentano’s work, the directedness of intentionality is first and foremost an aboutness. But as Marmodoro rightly notes (Reference Marmodoro, Austin, Marmodoro and Roselli2022: 7–8), the directedness of powers is more dynamic: powers strive causally to bring about their manifestations when activated. In contrast, there is nothing inherently dynamic about intentional aboutness, for we can have a belief about an object without striving for that object. So it is far from clear that the directedness of intentionality is relevant for understanding the nature of powers. These observations feed into a more general point, which is that directedness can occur in all manner of ways. For example, an arrow can be directed towards a target but not in the sense of intentional aboutness (Reference MumfordMumford 1999: 221).

What about the other marks of intentionality? Bird argues that they fail to hold in the case of powers. I shall not go through all of Bird’s arguments here, but the indeterminacy condition (iv) is worth a closer look because here one might think that Molnar is on stronger ground.

Thoughts can be indeterminate in the sense that we can abstract away from certain details concerning intentional objects: we can think about a pint pot being somewhere on the bar without thinking of it being anywhere in particular on the bar (see e.g., Reference Anscombe and ButlerAnscombe 1968: 161). Is there a similar phenomenon in the case of powers? Here, Molnar appeals to powers that are probabilistic, namely, propensities. Science suggests that the world may well be indeterministic, at least at certain scales. When an electron is released in the double slit experiment, there is no way of predicting exactly where it will end up. This suggests that the electron’s power for motion is a propensity rather than a sure-fire disposition. In such cases, one might think there is vagueness regarding what the eventual manifestation will be, in the same way that there can be vagueness about where on the bar the pint pot is located in one’s thought about it. So there is arguably some kind of parallel here. However, there are reasons to think that the analogy is not close enough to show that powers and intentionality are the same kind of phenomenon – especially given all the other worries that have been raised about Molnar’s proposal.

The reason why the analogy is only rough is that the main source of indeterminacy in the case of thought is that of abstraction (see e.g., Reference OderbergOderberg 2017: Sect. 6). Details of where exactly the pint pot is located on the bar could in principle be filled in, but when thinking of the pint pot we choose to ignore unnecessary details and abstract away from them. However, in the case of propensities, surely nothing like abstraction is taking place. Rather, the indeterminacy of propensities consists in the fact that any one of a number of determinate states might come about: propensities have a less-than-one chance of doing this or that, even in ideal circumstances. This means that the future behaviour of the propensity’s possessor is not fully determined. Hence, the kind of indeterminacy here looks rather different to that in our pint pot example. In the latter example, it is not as though we are unsure as to which determinate location we are thinking about; rather, all such determinacy has been completely abstracted away. So, although there is perhaps a loose analogy here, inasmuch as both cases involve vagueness of some sort, the vagueness involved in each case is rather different and has a different source. As Bird puts it, one can’t help thinking that Molnar is conflating indeterminacy and indeterminism (Reference BirdBird 2007: 125).

I think we have already said enough to cast doubt on Molnar’s intentionality account of dispositional directedness. Even though the account does justice to the directedness of powers, as well as the idea that powers can be directed towards manifestations that do not occur, on close inspection the directedness of powers appears to differ from intentionality in important respects. We shall now, in Section 4.3, examine Kroll’s more recent alternative (Reference Kroll2017), which is overtly teleological. In the subsections to follow, we shall then return to the topic of goal-directedness and see how the powers theory can help us to tackle the problem of goal failure.

4.3 Powers as Telic States

In the previous section, we have considered one attempt to explain the directedness of powers in terms of some other concept: that of intentionality. In the absence of such an explanation, some recent powers theorists have proposed that it is simply a primitive fact about powers that they are end-directed, teleological states (e.g., Reference Koons, Pruss and JacobsKoons and Pruss 2017; Reference KrollKroll 2017; Reference OderbergOderberg 2017; Reference Tugby and MeinckeTugby 2020; Reference Witt and GroffWitt 2008). This idea is sometimes thought to rejuvenate the Aristotelian concept of final causation: powers act in the way that they do precisely because they are directed at certain end states rather than others (e.g., Reference Giannini, Mumford, Jansen and SandstadGiannini and Mumford 2021: 88; Reference OderbergOderberg 2017). The view we shall consider does not try to explain the directedness of powers in more basic terms; it thus regards the world as being irreducibly teleological with a big ‘T’. Nonetheless, as we shall now see, we can gain understanding of this directedness through the theoretical roles that powers play.

In what follows, I focus on Kroll’s recent teleological analysis, partly because it is one of the most detailed of its kind, and also because the analysis emphasizes the end-directedness of all dispositional states. To begin, a quick terminological point is in order: Kroll frames his discussion using the terminology of dispositions rather than powers; however, as we shall see, it seems clear that Kroll holds a powers-based view about dispositions. But unlike Molnar, Kroll spells out the nature of powers in terms of a primitive notion of end-directedness rather than intentional directedness, leading to an overtly teleological account of dispositions (‘TAD’). Kroll helpfully summarises TAD with three theses labelled (T2), (T3), and (T4):

(T2) tells us what it takes for some property to count as dispositional, while (T3) is a metaphysical thesis telling us that each dispositional property is identical with a certain state of directedness. (T3) supports my judgement above that, on this theory, dispositions are powers, because the right-hand side of (T3) describes what looks very much like a power. As we have already seen, a power is commonly defined precisely as a state of directedness towards its manifestation, as in Reference Molnar and MumfordMolnar (2003, Ch. 3; see also Reference BirdBird 2007; Reference Lowe and MarmodoroLowe 2010; Reference TugbyTugby 2013). Indeed, Kroll is explicit that ‘Following Reference Molnar and MumfordMolnar (2003), I claim that directedness is what sets dispositions apart from non-disposition properties’ (Reference Kroll2017: 20). In what follows, then, I shall continue to use the terms ‘disposition’ and ‘power’ interchangeably.Footnote ³⁷

The teleological part of the analysis is, of course, ‘the state directed at the end that one Ms when C’. We can understand this primitive teleological notion of end-directedness through some of its theoretical roles and implications. (T4) is one such implication: a state of directedness is something which, when activated, either ensures that the target manifestation occurs immediately, or else ensures a process occurs which is directed at the end that x Ms.

This second disjunct of (T4) introduces a second primitive notion of teleological directedness that applies to processes rather than properties. Such processes are initiated when a power is activated, as when a soluble substance begins the process of dissolution.Footnote ³⁸ Again, although the directedness of a process like dissolution is a teleological primitive, we can gain understanding of it through its theoretical roles. For example, Kroll proposes the following principle regarding teleological processes (2017: 19):

Here, Kroll is drawing upon Makin’s Aristotelian insight that ‘a teleological process has a privileged stage to which it runs in normal conditions, unless interfered with or hindered: the [end] to which it is directed’ (Reference MakinMakin 2006: 194, quoted in Reference KrollKroll 2017: 19). Putting these ideas together, Kroll arrives at the following conditional truth about dispositions:

(*) if the process were to continue without interruption, x would M’ (Reference KrollKroll 2017: 19).

Now, although this theory of dispositions is clearly teleological, Kroll does not himself employ talk of goals or goal-directedness in his paper. In line with standard dispositional terminology, Kroll describes the relevant ends as manifestations and describes teleological behaviour in terms of the end-directedness of powers or processes.Footnote ³⁹ Nonetheless, since powers come in different shapes and sizes, it would not be surprising if this powers framework could also yield a concept of goal-directedness in certain cases. Our discussion of goal-directedness in Section 3 already provides clues about what a powers-based notion of goal-directedness might look like. We could think of goal-directedness as a special case of end-directedness that we find only at certain levels of complexity, where the relevant powers have a plastic and persistent modal profile. In such cases, we might speak of a directively organized system’s ends as its goals and describe its directed behaviour as goal-directed behaviour. To return to a point made in Section 3, in mechanistic terms, goal-directed powers will be the kinds of powers had by negative feedback systems, where the output of the behaviour is returned as input as part of a regulatory, reciprocal process.Footnote ⁴⁰ Notice also that by restricting talk of goal-directedness to the powers of directively organized systems, we would avoid the problem facing Cummins’s causal role theory of over-generating functions.Footnote ⁴¹ A powers theorist could insist that it is only goal-directed systems that involve functions, even though all powers (systemic and non-systemic) are teleological. In other words, the powers theorist could draw a distinction between powers that are merely end-directed, such as the powers associated with the charge of an electron, and those plastic and persistent powers of complex systems which are goal-directed.

In the remaining subsections, we shall explore this powers-based account of goal-directedness in more detail and consider whether all cases of goal-directedness can be grounded in powers. We shall start, in Section 4.4, by saying more about the powers of directively organized systems and how such powers might provide a solution to the problem of goal failure.

4.4 Another Look at Goal-Directedness: A Powerful Approach

In Section 3, we introduced the notion of a directively organized, plastic and persistent system. Such systems have one or more ‘goal’ states, which are a proper subset of the possible overall states of the system. It is plausible that various types of directively organized system are individuated, at least in part, by the kinds of goal-directed behaviours that are distinctive of them (Reference NagelNagel 1961: 422). This is especially evident in the case of feedback systems because such systems are defined, at least in part, by their inputs and outputs.Footnote ⁴² However, this does not mean that a system must always be actively engaged in its goal-directed behaviour in order to be regarded as a goal-directed system. Systems can be in a latent state, as when a thermostat is switched off. Indeed, it seems perfectly possible for a thermostat to forever remain switched off and yet still be regarded as a goal-directed system, providing it has the potential for goal-directed behaviour. Nagel’s counterfactual formulation of the cybernetic theory, discussed in Section 3.5, accommodates this point, but we saw that it remained unclear what grounds the truth of such counterfactuals.

It is here that the metaphysics of powers can be put to work because the powers theory insists that counterfactuals are grounded in dispositional properties, rather than vice versa. This theory maintains an intimate connection between dispositions and counterfactuals while resisting the tradition of reducing the former to the latter (as in Reference LewisLewis 1997). Within this dispositional realist framework, we may regard goal-directed systems as having powers to bring about the relevant goals. We might then think of artefacts like thermostats as having an irreducible dispositional character or essence. This idea reflects Mumford’s point that ‘[t]hermometer, light switch, computer, bookcase, towel rail, engine, and door handle can all reasonably be called dispositional terms’ (Reference Mumford1998: 197).

If we maintain that the characteristic powers of a directively organized system determine its goals and guide its goal-directed behaviour, it seems we have a firm theoretical foundation for talk of goal-directedness in at least some cases. Here we can take broad inspiration from recent authors such as Reference Anjum and MumfordAnjum and Mumford (2018: Chs. 2 and 9), Reference Austin, Marmodoro, Simpson, Koons and TehAustin and Marmodoro (2017), Reference CartwrightCartwright (2019, Ch. 2), Reference FeserFeser (2009, Reference Feser2014), Reference Koons, Pruss and JacobsKoons and Pruss (2017), Reference KrollKroll (2017), Reference OderbergOderberg (2017, Reference Oderberg2020), Reference PagePage (2015, Reference Page2021), Reference Paolini PaolettiPaolini Paoletti (2021b), Reference Tugby and MeinckeTugby (2020), and Reference WittWitt (2003, Reference Witt and Groff2008), who all see that realist dispositions or powers are intertwined with various teleological notions. However, as far as I know, few authors have put the powers metaphysics to work in the specific case of goal-directed systems. Importantly, if it can be shown that the metaphysics of powers can deliver an account of goal-directedness, a new and neglected advantage of the powers theory will be revealed.

Some clarifications might be helpful before proceeding. First, the proposal is not that goal-directed systems have only a dispositional character. Some systems might have a morphological nature too. The human blood circulation system is often called the ‘cardiovascular system’, conveying the idea that such a system must at least have a heart and blood vessels as anatomical parts. Nonetheless, it is clear that if some type of biological system did not generally have the disposition to pump blood, then it would not be regarded as a circulatory system. On the other hand, in some cases physical structure seems to play little, if any, role when it comes to individuating a system. This partly reflects the fact that many systems are multiply realizable: the same type of system, such as a thermostat, can be realized by different mechanisms, and we can often categorize systems while knowing little about their inner workings.Footnote ⁴³ If a putative thermostat has the disposition to help regulate temperature in a certain way, then we can be pretty sure it really is a thermostat, regardless of what its inner structure turns out to be.

Note also that although we are employing the notion of a disposition, our theory diverges in important ways from Cummins’s theory of functions that we discussed in Section 2. Cummins’s causal role theory is often regarded as providing a dispositional analysis of function. Nagel’s reductive version of the goal-contribution theory of functions is also sometimes characterized in dispositional terms (as in Reference FaberFaber 1986: 61). However, it would be a mistake to think that the theory of goal-directedness explored in this section is aligned with the theories of Cummins or Nagel. Although, like Nagel, we favour a goal-contribution analysis of function (Section 2), the difference is that we are proposing an underlying metaphysical framework that involves a heavyweight notion of dispositionality, whereby dispositions are real, irreducible powers out there in the world. If we adopt a powers-based version of the goal-contribution account of functions, functions will be ascribable to a system’s parts when they are able to contribute to the system’s powers to produce the relevant goal state(s). Cummins’s causal role theory and Nagel’s version of the goal-contribution theory of function make no such metaphysical commitments to powers, and their mechanistic theories are compatible with reductionist or deflationist conceptions of dispositions, for example those on which disposition ascriptions are reducible to counterfactuals. Another way of putting this point is to highlight that such mechanistic theories are perfectly compatible with a neo-Humean metaphysics, on which causation supervenes entirely on the spatiotemporal arrangement of instantiated categorical properties. In contrast, the theory we are exploring is very much anti-Humean: dispositional properties – whether they be those of a system’s parts or of a system as a whole – are taken to be powers that are irreducibly modal and teleological.

Another important clarification, to avoid misunderstanding, is that a powers-based theory of goal-directedness, and the goal-contribution account of function that goes naturally with it, are perfectly consistent with the fact that some branches of science employ those ‘backward-looking’ functional explanations that we discussed earlier in Section 2. As we saw, such explanations are pervasive in evolutionary biology. Within our powers-based understanding of goal-directedness, the idea would be that the properties described in such explanations are naturally selected powers, which are essentially directed towards certain goals. In the case of biology, naturally selected biological functions will typically be powers of traits which previously contributed to the goal of the survival of the genes that generate them. These goal-directed powers will then, along with evolutionary theory and environmental facts regarding habitat, explain the prevalence of present tokens of the relevant traits. In short, the powers-based account of teleology fully accommodates naturally selected functions, but as a general metaphysical analysis it also makes room for non-selected functions and goals in other domains.

One way of resisting the powers-based conception of goal-directed systems is to argue that it is in many cases inappropriate to posit power properties at non-fundamental, macro levels (see, e.g., Reference BirdBird 2016). For example, according to some ‘sparse’ conceptions of properties, it is only fundamental entities like particles and waves which instantiate genuine properties (see e.g., Reference ArmstrongArmstrong 1978; Reference HeilHeil 2021; Reference LewisLewis 1983). If we accept this view, then we would have to say that complex entities, such as systems, do not really have power properties, even though it is perhaps useful to speak as if they do.

Elsewhere, I have questioned this overly sparse conception of properties (2022a, 2022b). This is not because I accept that all predicates correspond to properties. In my view, we should accept the existence of higher-level, multiply realizable properties only if they can perform certain theoretical and explanatory work. Properties in the special sciences provide salient examples. Many special scientists such as chemists, biologists, and psychologists would accept (or suspect) that the properties they posit depend existentially in some way on the lower-level properties of physics. Nonetheless, the special sciences, and the properties they posit, have an explanatory power that would be lost if we could speak only of the properties of physics. For example, if we want to know what the function of the human thymus is, an explanation involving movements of electrons and protons is unlikely to be illuminating. This is mainly why the special sciences exist in addition to physics and have had so much predictive and explanatory success. Accordingly, recent powers theorists have been more sympathetic to the idea that there are higher-level, macro powers. For example, Reference VetterVetter (2018) and Reference MumfordMumford (2021) have defended certain kinds of macro powers against criticisms from Reference BirdBird (2016),Footnote ⁴⁴ while Reference Kimpton-NyeKimpton-Nye (2022) has argued that if we accept a certain grounding-based conception of powers, a commitment to higher-level powers plausibly follows.

Notice that a more liberal conception of power properties need not commit us to thinking that higher-level properties are strongly emergent or wholly autonomous. Importantly, powers and other properties can do important explanatory work even if they are metaphysically grounded in properties that are more fundamental (see Reference Guo, Tugby, Austin, Marmodoro and RoselliGuo and Tugby 2023).Footnote ⁴⁵ Although there is more one could say about these issues, I shall assume in what follows that we should countenance powers at different levels of complexity.Footnote ⁴⁶ Even if higher-level powers are metaphysically grounded in lower-level ones, it would be a disservice to the higher-level powers (and to the special sciences generally) to regard them as somehow second-rate. Moreover, if we are in the business of explaining the goal-directedness of directively organized systems, it seems inevitable that we must appeal to higher-level properties of one sort or another. As we saw in Section 3, cybernetic theorists appeal to properties such as plasticity, persistence, or representation, which are unlikely to be involved in fundamental physical theory. So, in the current context, allowing higher-level properties to do explanatory work ought to be relatively uncontroversial.

Let us round of this subsection by highlighting a key benefit of a powers-based account of goal-directedness, which is that it can accommodate some intuitive but subtly different notions of goal-directedness. Here I mention two relevant distinctions; whether there are others is a question I leave open. First, there is arguably an important distinction to be drawn between what we might call ‘latent’ and ‘active’ goal-directedness.Footnote ⁴⁷ For example, when a heat-seeking missile is dormant in its holding bay, it is not actively seeking a target even though it is inherently directed towards the destruction of some target. This is goal-directedness in the latent sense. On the other hand, once a missile has been launched, its goal-directedness is no longer latent, for it is now actively seeking out a target. The powers theory can straightforwardly accommodate this intuitive distinction because it is widely acknowledged that powers can exist in a latent state, independently of their activation. Even if a homing missile is not doing anything, its goal-directedness is nonetheless grounded by the relevant latent power.

Second, another distinction concerns what we might call ‘immediate’ versus ‘iterated’ goals. For example, we might think that, in some sense, a doctor has both a complex power to heal people and also a complex power to murder people. This might puzzlingly suggest that the doctor has contrary goals, which could create difficulties for practical deliberation. However, we can avoid any puzzles here by distinguishing immediate and iterated powers (see e.g., Reference VetterVetter 2015: Ch. 4). Assuming that the doctor is benevolent, the immediate overriding power at work will be the power to heal. The doctor may well have the physiology required to commit a complex murderous act, but she will not have the power to murder in any immediate sense given her benevolent nature. Nonetheless, this is consistent with the doctor having an iterated power to acquire the immediate power to murder. For instance, if the doctor were to undergo radical psychological changes, perhaps she would then gain an operative power to murder. Thus, if goal-directedness is grounded in powers, it is not difficult to accommodate this intuitive distinction between immediate and iterated goal-directedness, where the latter concerns possibilities that are much more remote.Footnote ⁴⁸

4.5 Another Look at the Problem of Goal-Failure: A Powerful Solution

With a powers-based account of goal-directedness now on the table, the important question is whether this account can provide a solution to the problems of goal failure and underdetermination that we discussed at length in Section 3.4. The problem with the reductive cybernetic analysis of goal-directedness, recall, was that it did not provide the resources to make sense of goal-directedness in cases where the goal was not achieved. However, if we accept that goal-directed systems have teleological dispositions in Kroll’s sense, then a metaphysically robust notion of end-directedness is built in from the start. And as the consequent of Kroll’s (CDC) in Section 4.3 implies, like all other dispositions, there will be no guarantee that the dispositions of directively organized systems always manifest their goals when activated, because certain interferences might prevent those manifestations. If we accept a powers-based account of goal-directedness, goal failure is entirely to be expected in many cases. But even if the relevant goals are not achieved, the dispositions of directively organized systems may nonetheless be responsible for the behaviours that are trying to bring about those goals.

More precisely, if we apply the Kroll-type teleological analysis of dispositions to the powers of directively organized systems, we may say that a directively organized system’s powers are such that, when activated, they either reach their goals immediately or initiate a goal-directed process which leads to the goal – unless the process is interrupted. In the case of systems that are highly plastic and persistent, there might not be many possible obstacles that could frustrate the goal-directed process. However, failure is always a possibility for any power. Indeed, in some cases a goal-directed system might consistently miss its target, as in Ehring’s example (Reference Ehring1984a: 502) of a bird that regularly fails to kill its prey due to interfering factors. Such failures are consistent with the bird having the power to kill prey, providing that it has, say, the right anatomical and psychological features. This may be so even if the interfering factor is another internal feature of the bird (see e.g., Reference TugbyTugby 2016 for a discussion of dispositions that are subject to so-called intrinsic finks and antidotes).

It is clear, then, that a powers-based theory of goal-directedness can accommodate failure cases, but recall that the problem of goal failure also led to the problem of underdetermination. If the goal of a system is not achieved, then what is it that determines what the goal of the system was meant to be? A powers-based account of goal-directedness delivers a metaphysical answer. The goal is whatever manifestation it is that the system’s characteristic (plastic and persistent) powers are directed towards.Footnote ⁴⁹ These powers, in turn, ground the sorts of counterfactuals discussed in Section 3.5. Even if, for whatever reason, a goal fails to be achieved, it can still be the case that the goal would have been achieved in certain hypothetical scenarios. Our complaint in Section 3.5 was that it remained unclear what it is in the world that determines the truth of such counterfactuals. But with realist powers in play, we have at least one way of meeting this challenge. For if (CDC) or something like it is correct, then powers have counterfactual implications even if they cannot themselves be analysed in counterfactual terms (see also Reference MumfordMumford 1998: Ch. 4).

To conclude, if a metaphysics of directed powers is accepted, the prospects look good for a solution to the problem of how there can be goal-directedness in cases where the relevant goals fail to occur. And because powers can be intrinsic to their possessors, this view can accommodate the intrinsicality of goal-directedness, which means that it is not committed to the design-based theories of teleology discussed earlier (e.g., Section 3.4), on which the goals of systems are determined by the intentions of a designer such as a human agent or God. Nonetheless, this is not quite the end of the matter. There is still more to be said about the details of a powers-based solution to the problem of goal failure. Despite what has been said so far, some critics of the powers theory have been puzzled about how any intrinsic dispositional state can be directed towards a manifestation that does not (or may never) occur. As we shall see now see, in the powers literature some specific strategies have been explored to deal with this puzzle, one of which entails a commitment to a Platonic conception of properties.

4.6 A Platonic Twist?

I suspect that critics of a powers-based account of goal-directedness will insist that it remains mysterious how exactly an intrinsic power, or a process that it initiates, can be directed towards an end or goal that may never occur. Even if the end-directedness is primitive, surely we ought nonetheless try to make it intelligible how there can be directedness of any kind towards entities (in this case power manifestations) that do not occur. Even if a reductive analysis of end-directedness is out of the question, further explication is surely needed if we are to understand how dispositions can ‘point towards’ their non-occurring manifestations; or so the objection goes. Notice, though, that it seems unlikely that work in philosophy of science can shed much light on the nature of end-directedness, which is fundamentally a metaphysical issue. There are philosophers of science who have seen the value of appealing to dispositional concepts in accounts of teleological explanation (e.g., Reference Bigelow and PargetterBigelow and Pargetter 1987; Reference Walsh and RuseWalsh 2008: 119). As far as I can tell, most of these philosophers think that as soon as we appeal to dispositional concepts, puzzles about the forward-looking nature of many teleological explanations automatically go away. However, some critics might remain unconvinced.

Earlier, we saw how the powers-based solution to the problem of goal failure relies on the fact that powers in general can be directed towards non-existent manifestations. However, it is not entirely clear that, for example, Kroll’s analysis sheds much light on this aspect of powers. If one is puzzled about how intrinsic dispositions can be directed towards certain manifestations that do not occur, it probably does not help much to be told that a disposition is a primitive, end-directed state. Indeed, some commentators have complained that Kroll’s primitive notion of teleological directedness is no better understood than the concept of a disposition itself (Reference Manley and WassermanManley and Wasserman 2017: 48; see also Reference Marmodoro, Austin, Marmodoro and RoselliMarmodoro 2022: Sect. 1.2).

One of the problems here is that many theories of dispositions or powers leave important questions unanswered. For instance, a simple but important question is whether teleological directedness is relational or not. As I have noted in a different context (Reference TugbyTugby 2013), dispositional directedness certainly looks like a relation: it is a case of an entity being orientated towards something else. If it is a relation, then we could partly shed light on end-directedness by clarifying what are the relata. However, if the directedness of a power or process can occur in the absence of a physical instantiation of the manifestation or goal, it is far from obvious what the relata can be (Reference ArmstrongArmstrong 1997). As Armstrong puts it, it seems that a disposed object ‘points to a thing that does not exist’ (Reference Armstrong1997: 79). Prima facie, then, realists about powers are committed to the idea that unmanifested dispositions are directed towards non-existent ‘Meinongian’ entities. So-called Meinongian entities are certainly taken by many to be obscure, since they do not exist and yet they can somehow be quantified over.Footnote ⁵⁰ If, on the other hand, directedness is not a genuine relation, how is it that a non-relational state can be orientated towards, and individuated by, a merely potential manifestation?

On close inspection, Armstrong’s challenge stems from the difficulty of reconciling two facts about dispositions regarding their directedness. Let us call the first fact the ‘directedness’ principle and the second fact the ‘independence’ principle:Footnote ⁵¹

Despite their independent plausibility, the conjunction of these two principles generates the puzzle that we have already alluded to. If a disposition can be instantiated in the absence of its manifestation (per the independence principle), how can that disposition at the same time be directed towards the manifestation, as the directedness principle requires? Is there a way to reconcile these two principles while avoiding the Meinongian metaphysics to which Armstrong refers?

According to the Platonic solution that I favour, there is a type–token ambiguity in the principles as stated. When we say that a forever-dry cube of salt has the unmanifested disposition of water-solubility, what we surely mean is that this particular cube of salt has not been engaged in any concrete, token dissolving episodes. The independence principle, then, is best understood in terms of independence of token manifestations. In contrast, I take it that the directedness principle concerns manifestations considered as types. That is, the directedness principle is a more general principle about the connection of individuation between dispositions and manifestations qua types of properties. To use a familiar example, the disposition of fragility is individuated, at least in part, as that disposition which is directed towards the manifestation of breakage. But here we are clearly talking about breakage as a type of manifestation, rather than a specific token of breakage. In itself, something’s being fragile is compatible with different concrete breakages at different points in space and time; and so, the directedness principle abstracts away from specific token manifestations. Oderberg puts the point well when he describes the directedness of powers as specific indifference (Reference Oderberg2017: Sect. 3). Dispositions are for specific types of manifestation but are indifferent regarding the when or where of their token manifestations.

How, then, do these clarifications help with our puzzle about non-existent manifestations? The answer lies in adopting a robust Platonic realism about types and viewing dispositional directedness as a second-order affair, holding between types rather than tokens. Let us imagine a scenario in which no soluble object ever manifests its solubility in any token dissolving events. Does this mean that we require Meinongian manifestations in order to secure the directedness (and hence identity) of the solubility property? The answer is ‘no’. According to a Meinongian approach, such manifestations do not exist even though we can (somehow) quantify over them. However, an alternative option is to accept that the solubility property is directed towards a manifestation type (in this case, the property type of dissolving) that exists in the full-blooded, ontologically committing sense of the term. This solution commits us to a realist Platonic metaphysics, which has a long history in philosophy. According to that metaphysics, such property types – which include the uninstantiated ones – are actual abstract entities which do not ontologically depend on their concrete instantiations.Footnote ⁵²

It must be acknowledged that Aristotelians are also realists about property types (e.g., Reference LoweLowe 2006). However, Aristotelians insist that property types must be instantiated at least once in order to exist. This means, unfortunately, that Aristotelian realism does not provide enough metaphysical resources to deal with the solubility example described, given that the manifestation property is not instantiated at all. It seems the only option for Aristotelians in such cases is to deny that the relevant disposition exists. This is a significant bullet to bite and a neglected drawback of many Aristotelian accounts of dispositions (see Reference TugbyTugby 2013 for further discussion).

I would urge, therefore, that Platonism is to be preferred when it comes to shedding light on the end-directedness of dispositions. If we apply the Platonic version of dispositional realism to goal-directed systems, then goal-directedness is what we get when systems have characteristic plastic and persistent powers that are essentially directed towards their (Platonic) manifestation-types. Importantly, these types exist regardless of whether they are ever instantiated.Footnote ⁵³ This, in turn, allows us to make metaphysical sense of goal-directedness in cases where the relevant goals fail to be achieved.

Despite the power of this argument (no pun intended), many powers theorists appear to be happy with the rival Aristotelian theory of properties. Reference OderbergOderberg (2017: 2403), for example, has argued that Aristotelianism offers an adequate framework for unmanifested powers and that Platonism does not provide significant theoretical gains.Footnote ⁵⁴ Others, meanwhile, have accounted for unmanifested manifestations in terms of either unrealized possibilia or mere logical existents (see, e.g., Reference BirdBird 2006; Reference GianniniGiannini 2021; Reference McKitrickMcKitrick 2018: Ch. 3).Footnote ⁵⁵ I shall leave the issue at this point and allow readers to judge for themselves. What we have at least shown is that Platonism provides one possible way of shedding light on the directedness of powers. In Section 4.8, we shall also see how Platonism proves to be helpful when it comes to accommodating certain cases of goal-directedness involving physically impossible goals.

In the meantime, let us broach an important question regarding the extent of goal-directed teleology.

4.7 Further Work: The Extent of Teleology

A noteworthy implication of the powers theory is that goal-directedness is not the only teleological phenomenon. If Kroll’s theory is along the right lines, then all dispositional states are essentially end-directed, and this applies as much to the powers of simples, like electrons, as to those of complex systems. On this view, the character of any concrete causal interaction is ultimately explained by the end-directedness of the powers involved.Footnote ⁵⁶ And if many powers are essential to their possessors, we will have a robust metaphysical foundation for normativity in the case of systemic goal-directed processes. For if the relevant powers are what characterize the systems in question, there is an important sense in which those systems should exhibit the relevant goal-directed behaviour if they are functioning normally. For further discussion of the connection between dispositions, essence, and natural normativity, see for example, Reference LoweLowe (1980, Reference Lowe1982, Reference Lowe1987), Reference KorsgaardKorsgaard (2009: Ch. 2), and Reference Oderberg and ZaborowskiOderberg (2010, Reference Oderberg2020).

Now, although all dispositions are end-directed, it does not follow that all dispositions are goal-directed. Rather, our previous discussions suggest that goal-directedness is what we get when dispositional end-directed states are instantiated at a certain level of systemic complexity. However, this leaves us with interesting and difficult questions about where to draw the line. What exactly distinguishes goal-directed dispositions from the more basic end-directed dispositions that we would not regard as being goal-directed? This is a complex question, and I am not able to fully settle it here. Nonetheless, aspects of the cybernetic theory of goal-directedness might prove helpful. According to that theory, what many (if not all) goal-directed systems have in common is that they can display plastic and persistent behaviour. In dispositional terms, the idea is that systemic, goal-directed dispositions have a modal flexibility and adaptability that more primitive end-directed dispositional states lack. Unlike a homing missile, if a marble is rolling towards you and someone pushes it off course, it will not adjust its direction of travel in such a way as to maintain its original course. Although a marble’s state of sphericality is dispositionally directed towards rolling, one could not plausibly regard this as a goal-directed state.

There is a complication, though, which is that plasticity and persistence arguably come in degrees (Section 3.2). In Nagel’s view, a system’s degree of directive organization depends on how many different internal and external variations it is able to compensate for when pursuing its goal (Reference NagelNagel 1961: 417). As Garson notes (Reference Garson2016: 24), a similar idea can be found in the work of Braithwaite, whose analysis concerns the range or ‘variancy’ of environmental field-conditions in which a system is able to achieve a given type of goal (Reference Braithwaite1953: 330). According to Braithwaite, a system is plastic merely if it is able to achieve a certain goal in more than one alternative set of field-conditions (Reference Braithwaite1953: 331).

If plasticity and persistence come in degrees, one might well wonder where the cut-off points lie. To what degree must a system’s overall powers be plastic and persistent in order for it to count as genuinely goal-directed? The goal-contribution account of functions allows for a variety of stances. Braithwaite for one sets the bar quite low, allowing that a goal-directed system might be plastic to a rather minimal degree. Nagel appears to be more ambivalent, suggesting that there might not be a clear cut-off point (Reference Nagel1961: 419). If Nagel is right, this might explain why there are so many disagreements about which systems can and cannot be ascribed functions (see Reference Oderberg and GonzálezOderberg 2008; Reference McSheaMcShea 2012; Reference Tugby and MeinckeTugby 2020; Reference BabcockBabcock 2023 for discussion). For my part, I am inclined to take a liberal stance, and accept that there can be goal-directedness even if the degree of plasticity and persistence is relatively low. However, I will have to leave this as a matter for further in-house discussion between goal-contribution theorists.

4.8 Further Work: Can There Be Goal-Directedness without Goal-Directed Powers?

So far, we have argued that a powers-based account of goal-directedness can provide a plausible account of goal-directedness in many cases. In doing so, we utilized some insights from the philosophy of science literature regarding cybernetic machines and the notions of plasticity and persistence. However, whether the powers-based account can provide a fully general analysis of all kinds of goal-directedness is a further question.

The most obvious sticking points for a fully general powers-based account of goal-directedness are cases allegedly involving goal-directedness in which the relevant goals are in some sense impossible. Ehring has already presented cases of impossible goals as counterexamples to the Nagelian analysis of goal-directedness, such as the example of Smith who apparently has the goal of accelerating a spaceship beyond the speed of light (Reference Ehring1984a: 500).Footnote ⁵⁷ Importantly, it looks as though these same cases might create an equally serious problem for a generalized powers-based account of goal-directedness. The worry is simply that in such cases there is genuine goal-directedness but no powers to bring about the relevant goals. This worry is driven by the thought that it is implausible to posit powers for impossible goals. One will find this especially implausible if, like Reference VetterVetter (2015), one thinks that there is a tight connection between powers and possibility.

The issue of powers with impossible goals is complex and we shall not be able to do it full justice here. However, we can at least set out some options for powers theorists and lay foundations for further discussion of the issue. In the process, I shall explain how a Platonic theory of powers might accommodate powers with impossible goals in many cases.

The question of whether there are powers for impossible manifestations has recently attracted attention, and there are philosophers who fall on both sides of the fence. For example, Reference Jenkins and NolanJenkins and Nolan (2012) offer theoretical reasons for positing a wide range of dispositions with impossible manifestations. Reference VetterVetter (2015), in contrast, draws a close metaphysical connection between powers and possibility, and therefore denies that there are powers for impossible manifestations.

Clearly, if we were to agree that there are no powers for impossible manifestations, while accepting cases of goal-directedness towards impossible goals, we would have to deny that all cases of goal-directedness are grounded in powers. In order to accommodate this idea, one could take inspiration from Reference SchefflerScheffler (1959) and try to draw a distinction between cases of goal-directedness involving an agent’s intentional action, and those that do not. Perhaps what the powers-based theory offers is a metaphysical account of goal-directedness in cases not involving intentional action. Cases of intentional action, it might be urged, involve a distinct, sui generis form of goal-directedness. Importantly, we could accommodate impossible goals in such cases as long as an agent can have intentions with impossible intentional objects. According to that strategy, then, goal-directed behaviour towards impossible goals does occur, but only when the behaviour is driven by a (misguided) intention. The disadvantage of that approach, however, is that it leaves us with a somewhat disunified analysis of goal-directedness.

What other options are there? Elsewhere, I have provided independent arguments for the existence of Platonic types whose instantiations are physically/nomically impossible in worlds like ours (see e.g., Reference TugbyTugby 2015, Reference Tugby2022a: Ch. 10, and Reference Giannini and TugbyGiannini and Tugby 2020). In line with terminology employed by Reference VetterVetter (2015: 69), I call such properties ‘super-alien’ properties, and possible examples include the property of being frictionless (Reference Giannini and TugbyGiannini and Tugby 2020: 133–134). Given that scientists often engage in modal reasoning about super-alien properties, and given that scientists appear to have non-trivial true beliefs about them, Platonism offers a plausible way to ground such truths in reality. Quite simply, such truths are grounded in the natures of the uninstantiated super-alien properties. If this argument succeeds, then we should count super-alien properties among the abstract types that exist. This, in turn, makes room for the idea that a property instantiated in our world might be dispositionally directed towards a super-alien manifestation type. For instance, following Reference Jenkins and NolanJenkins and Nolan (2012: 746), we might accept that a car has the power to move in a certain way on a frictionless plane, even though our physical world could never give rise to the manifestation of such a power. Similarly, in Ehring’s example, Platonism opens up the possibility that Smith’s behaviour is directed towards the super-alien, physically impossible property of travelling faster than the speed of light.

On the other hand, there will still be some limitations regarding how many super-alien Platonic properties there are. For example, it is difficult to see how properties could exist whose instantiations are metaphysically or logically impossible (Reference TugbyTugby 2015: 35). If there are no such properties, then a Platonic approach to powers would still not accommodate cases of goal-directed behaviour towards outcomes which are impossible in this stronger logical sense. An example of such a case would be behaviour that is allegedly directed towards proving a mathematical conjecture that is necessarily false. Whether there can be genuine cases of goal-directedness like this is an interesting question that I leave open for future research in this relatively new area of the debate.Footnote ⁵⁸ If there could be cases of goal-directed behaviour towards logically impossible goals, we might well have to accept that those cases involve a sui generis form of goal-directedness that does not involve a corresponding power.

4.9 Summing Up

The central aims of this section were to show that the powers metaphysics brings a new source of teleology to the world and that it provides better resources for explaining goal-directedness than the reductive cybernetic accounts examined in Section 3. Unlike those accounts, the powers-based theory takes teleological directedness to be a fundamental, irreducible feature of the world. This view thus rejects the reductive aims of goal theorists like Nagel, who tried to explain teleological truths in wholly non-teleological terms. In Section 3, we saw that the reductive project faces serious problems, in particular the problem of goal failure and underdetermination. One of the key lessons to draw from these problems, I believe, is that the prospects for a reductive analysis of teleology are dim. As soon as we accept that a system could be goal directed without ever achieving that goal, we are pushed towards accepting that the system is in a genuine teleological, goal-directed state. In line with the goal-contribution theory of functions, functions can then be ascribed to those parts of a system which have dispositions to make causal contributions to the system’s goal-directed behaviour. Suitably modified, contemporary realism about powers provides one way of fleshing out this metaphysical proposal. Importantly, this powers-based, goal-theoretic account is consistent with the sorts of ‘backward-looking’ selectionist functional explanations that we find in evolutionary biology. The theory can also accommodate functions in those domains of science where many functions are not selected for. However, whether all possible cases of functions and goal-directedness can be appropriately grounded in powers is an important question that I leave for future research.