In A History of the Mathematical Theory of Probability (1865), I. Todhunter tells that among the “learned conversations” of the Florentine gentlemen the following question was once proposed: “A horse is really worth a hundred crowns, one person estimated it at ten crowns and another at a thousand; which of the two made the more extravagant estimate?” When consulted on this matter, Galileo pronounced the two estimates to be equally extravagant, “because the ratio of a thousand to a hundred is the same as the ratio of a hundred to ten”. A priest named Nozzolini thought that the higher estimate is more mistaken, since “the excess of a thousand above a hundred is greater than that of a hundred above ten.” (p. 5).

Todhunter's comment on this issue is interesting: it does not appear to him that “the discussion is of any scientific interest or value”.

The Modern Synthesis, according to Gould (1980, p. 119), “has broken down on both its fundamental claims: extrapolationism (gradual allelic substitution for all evolutionary change) and nearly exclusive reliance on selection leading to adaptation.” In another place (1982b, p. 380), he writes that “the essence of Darwinism lies in the claim that natural selection is a creative force, and in the reductionist assertion that selection upon individual organisms is the locus of evolutionary change.” There is a trivial question of terminology here, and perhaps a less trivial question of historiography. Does Darwinism have an essence, and was the Modern Synthesis as monolithic as all that? Sewall Wright used to be routinely cited as one of the main synthesizers. Does it now turn out that his models of interdemic selection retroactively cast him into the outer darkness (on which see Orzack 1981 and Gould 1981)?

As a biologist who has been looking to philosophers of biology for fifteen years for help with epistemological problems, it was a surprise to me to be asked by Marjorie Grene and Richard Burian to prescribe some philosophical problems which have arisen in molecular biology developments such as those described by Alan Maxam. I thoroughly enjoyed the NEH Summer Institute on the “Philosophy of Biology” which they organized at Cornell and feel that they have raised many challenges to my own thinking in my field of molecular evolution and the origins of life. I believe that an analysis of Professor Ayala's, Kauffman's, and Maxam's papers is relevant to developments in molecular evolutionary theory. First, just as the punctuated equilibria versus phylogenetic gradualism debate in macroevolutionary theory has been seen by some as a challenge to Neo-Darwinism, notably not Professor Ayala, debates about neutralism versus selectionism has been viewed by others as a similar challenge.

Risk assessment, or risk-cost-benefit analysis (RCBA), an offshoot of decision analysis, has been widely touted as a “developing science” (see, for example, Levine 1979, p. 634). Used to help administrators make decisions on how to spend money, this set of procedures is directed at calculating whether the expected benefits from a proposed activity outweigh its expected risks or costs. For example, experts might wish to determine, given the risk of nuclear core melt and the possible resultant release of radioactive materials, whether additional containment (for reactor vessels) would be cost-effective.

In the sixties, RCBA was integrated into the planning and budgeting efforts of many federal agencies in the defense, aerospace, and energy fields. In the seventies, a number of regulatory agencies controlling environmental and occupational hazards likewise began to use the technique.

There are many ways to characterize what we are talking about when we speak of modernity and post-modernity. But one description—as it pertains to philosophy—might go something like this. The “core problem” for philosophy in the modern world has been to resolve what Michael Dummett has called the “scandal” of philosophy:—“the scandal caused by philosophy's lack of a systematic methodology.”

In a recent paper, Shrader-Frechette (1977) has argued that there is a serious (and perhaps fatal) unclarity in the notions of particle and fundamental particle currently used in high energy physics. Shrader-Frechette focuses on the notion of a virtual particle as one of the contributors to this unclarity. Among the reasons offered for this focus are: (1) virtual particles are (in some sense) not observable, and (2) they are introduced merely to balance the “books” so conservation laws hold.

More recently, Hendrick and Murphy (1981) have argued that Shrader-Frechette's overall critique of the notions of particle and fundamental particle rests on a number of confusions and in this I am in complete agreement. Here, I am just interested in their response to Shrader-Frechette's remarks about virtual particles.

Professor Bernstein has shown how, coming from three distinct orientations in twentieth century philosophy, Gadamer, Habermas and Rorty have arrived at strikingly similar conclusions. The upshot of their thought, as Professor Bernstein points out, is a powerful critique of traditional foundationalism. There is no uninterpreted “given”, no theory-neutral set of “facts”, no timeless structure of reason, no disinterested vantage point for research, outside of the interpretations and interests of the community of interpreters that are embodied in our current social practices. The collapse of the bad old dream of firm foundations and of ultimate convergence on the truth is taken as a fait accompli by Bernstein. The question that confronts us now is what to make of this situation. On the face of it there appear to be two types of stance open to us.

The experimental procedures of physics assign values to physical quantities; we measure the temperature of a gas, the luminosity of a light source, the momentum of a particle. Any pair, q = (A, Δ), with A an observable quantity, Δ a Borel subset of the reals, we will call an experimental question, though some prefer the term proposition. For example, in lowering my big toe into the bath, I address the experimental question (T,Δ) to the system consisting of my bathwater, where T is the temperature measured in °F, and Δ is (approximately) the interval (110,120). Theory tells us what answers we may expect, given certain initial conditions. A determinist theory like classical mechanics tells us that, under specified conditions, the measurement of a quantity will yield a particular result with certainty, whereas a statistical theory like quantum mechanics tells us what probability attaches to various possible outcomes of a measurement.

A great deal of literature on the status and meaning of the Laws of Inertia in spacetime theories has nurtured and given wide currency to the claim that the laws are conventional in character, that they are definitions, or circular and without empirical content.

Philosophers who argue for the conventional character of the laws, do so, either emphasizing epistemological or ontological considerations concerning the structure of spacetime.

Those who argue for their conventional character mainly on epistemic grounds, point out, that the laws do not supply independent criteria of what is to count as force-free or natural motion. The only way of knowing when no forces act on a body is that it moves as a free particle traveling along the geodesies of spacetime. But how, without already knowing the geodetic structure of spacetime is one to determine which particles are free and which are not?

With his usual deftness and sensitivity to the spirit of our times, Richard Bernstein has brought us to the center of current philosophical debates concerning modernity and postmodernity. He has sought to identify the common ground shared by three of the principals in these debates, in contradistinction to the usual stress placed on the differences separating them. He finds this common ground in the vision of a “non-foundational” or “anti-foundational pragmatic humanism” which is said to inspire all three, and next to which the usually perceived differences — which he does not’ deny — fade to differences of emphasis.

One job of a commentator is to set a discussion in motion, and the easiest way to do that here is obviously to recall the familiar differences, to argue that they are basic, and to suggest that next to them the alleged common ground shades to philosophical insignificance.

Albert Einstein distinguished sharply between the context of discovery and the context of invention. For example, in a letter of 6 January 1948 to Michele Besso, Einstein wrote:

By “invention” Einstein meant the mind's ability to leap across what he took to be the essential abyss between perceptions and data on the one side in order to create concepts and axioms on the other. Although sometimes Einstein interchanged the terms discovery and invention, he deemed invention to be the route of creative scientific thinking.

The basic equations of the Special Theory of Relativity (STR) imply that no massive particle travelling at a velocity less than the velocity of light in vacuo (call that ‘c’) can be accelerated to a velocity either equal to or greater than c. For instance, the total energy E of a particle is given by the formula

(1)

where m is the rest mass of the particle and v its velocity in some given co-ordinate system (CS). One can choose units so that c = 1; hence for ordinary particles (|v| < 1) as v approaches 1, E grows without bound. That is, as a particle accelerates, its total energy increases and ever-increasing amounts of energy are required to accelerate it. So no ordinary particle (tardyon, bradyon) can be accelerated continuously from velocity v < 1 to velocity v = 1, much less to velocity v > 1.

Einstein himself had a few words to say about the writing of the history of science. From the first of his famous conversations with Einstein, Robert Shankland relates: “Then he gave me his ideas on historical writing of science. ‘Nearly all historians of science are philologists and do not comprehend what physicists were aiming at, how they thought and wrestled with their problems… .’ The struggle with their:problems, their trying everything to find a solution which came at last often by very indirect means, is the correct picture.” (Shankland 1963, p. 50).

Why should we take these words seriously? After all, Einstein was not an historian, and, unless we are to pose him as an authority on every topic, these comments represent but a personal opinion. This, however, is precisely why they should be taken seriously, if we are interested in the history of Einstein's own accomplishments.

Several philosophers in recent years, e.g., Baker (1974-5, 1979), Grünbaum (1971), Rescher (1973) and Salmon (1974) have argued that something they call “temporal becoming” is mind-dependent. They see the issue as analogous to the traditional one about the mind-dependence of secondary qualities. Do directly seen colors, felt coldness, and salty taste exist in the mind-independent world? Or only within experience? We know how the dialectic dances around that question….

“Roses are red, violets are blue, in the same way that some of our afterimages and sense-data are.”

“No, roses and violets don't really have colors. Roses only have the property of selectively reflecting light in the 7200 Å region. That makes them look red to us. But they aren't really red. Science shows that.“

One of the main advantages that has been claimed for the Sneedian “structuralist” approach is that with it one can actually represent real scientific theories. (I consider a “structuralist” approach to be one in which the objects of study are structures in the modeltheoretic sense, with at least some such structures thought of as representing physical situations or processes.) Using just Suppes’ structuralist approach, one can already give a reasonable representation of many features of scientific theories. Examples of such are the representations of classical particle mechanics (CPM) in McKinsey, Sugar & Suppes (1953), relativistic particle mechanics in Rubin & Suppes (1954), and rigid body mechanics in Adams (1959). Then with Sneed's (1971) modifications of Suppes’ approach, in particular with Sneed's introduction of the notion of a constraint between structures, the representational strength of a structuralist approach seems to increase dramatically.

It is a mistake to suppose that the units of selection controversy in biology centers around a single question. In this paper I will take Wimsatt's recent work (1980 and 1981) as defining the question ‘What are the units of selection?’. I will show that there is another important question, what I will call the levels of selection question, separable from the first but easily confused with it. Finally, I will try to show why the levels of selection question is important.

First I must make a terminological point. In this paper I will adopt the distinction between fitness and adaptedness. I will not defend the distinction here since that has been done elsewhere (Brandon 1978 and 1981), but I will briefly indicate what the distinction is. ‘Fitness’ in this usage refers to actual reproductive success. ‘Adaptedness’ refers to an expected fitness value, in the mathematical sense of expected value.

In the design and analysis of an experiment there are several places where an element of randomization can be used: the design can be selected at random, the result can have a random element adjoined to it, or the random element already present can be used in the analysis. The first technique is much used by statisticians; for example, in making a survey of a population, Basu (1980) calls it prerandomization.

R. C. Lewontin (1970) proposed three criteria as jointly sufficient for a unit of evolutionary change and immediately went on to argue that selection could operate simultaneously at a variety of levels of organization. For natural selection to operate on a unit, there must be variation in the objects in question: natural selection “chooses” between alternatives, so there must be different alternatives. This variation must affect fitness: the variation available must create different probabilities of reproductive success. Third, this variation in fitness must be heritable: there must be a correlation between parents and offspring for the traits yielding variation in fitness. In brief, for there to be evolution by natural selection, there must be heritable variation in fitness.

Among the concerns that might be raised over Lewontin's formula, one is particularly important. It was clearly brought out by Williams (1966) and is emphasized by Elliott Sober (1981).

R.A. Fisher began defending the use of randomized assignments of treatments to plots in agricultural field experiments in 1926 (Fisher 1926). His claims on behalf of randomization were challenged by many other statisticians including his friend and colleague W.S. Gosset, the celebrated “Student” (Gosset 1937). After Gosset's death, Fisher's insistence upon the critical importance of randomization to good experimental design became a cornerstone of methodological orthodoxy, a status it has continued to enjoy until recent years. Even so, an undercurrent of resistance to some of the more excessive claims on behalf of randomization has continued to influence thoughtful statisticians and methodologists.

Fisher's rationale for. randomization was grounded on the need to control or eliminate systematic error or bias. For example, the average yield of wheat on plots treated with one kind of fertilizer may be compared with the average yield of wheat of the same variety on plots treated with another kind of fertilizer.