¹ Mind and the World Order, p. 142n. It is interesting to note that Lewis doesn't come right out and say that the implication involved in the contrary to fact conditionals with which it is concerned is strict implication. His turn of phrase is a curious one, indicating, I should like to think, some degree of uneasiness.

² For simplicity of expression, I shall adopt the following convention with respect to the values of an expression. Instead of saying that the values of, say, ‘x’ are ‘x₁’, ’x₂’, …, I shall say that the values of ‘x’ are x₁, x₂). … Similarly, I shall mean by ‘particulars’ not the individual constants of a language, but rather the designata of these constants.

³ I shall use the expression “possible particulars” instead of Lewis' phrase “thinkable things” for two reasons: (1) The word “thing” is dangerous as suggesting dispositional properties—for these are at the core of the everyday meaning of the word—and hence as making for a superficial, because merely verbal, solution of the problem of possibility and counterfactual conditionals. (2) The term “possible” has the advantage, which “thinkable” does not, of making it clear that our problem has nothing to do with empirical psychology. Furthermore, little would seem to be gained by substituting “what possible acts of thought are about” for “the possible.”

It is important to understand that I am not offering the phrase “possible particular” as a philosophically more luminous phrase than “thinkable thing.” Philosophical clarity comes only with system and structure, and not with the substitution of one isolated phrase for another. The value of the terminology we have selected will become apparent only at the end of our argument, where it will be clear that to have followed Lewis' terminological signposts would have meant taking the wrong road.

We are going to be as deliberately naive throughout most of our argument with respect to the contrast between “thinkable things” and “existing things” (though in our own terminology) as Lewis is for a passing moment. Thus, we shall assume that in some sense of “exist” there exist possible particulars as well as actual particulars. The fruitfulness of this assumption can only emerge in the course of our argument, and I ask the suspicious reader to bear with me.

⁴ Lewis writes, “every thinkable thing which should have the property φ must also have the property Ψ,” however the “should” and the “must” are ill-considered. (1) There is no obvious reason why the “thinkable things” interpretation should require a “should,” when a “should” would clearly be out of place in the “existing things” interpretation. It is dangerous to take for granted that when dealing with thinkable things the indicative mood should be dropped in favor of the subjunctive, for to do this is to take for granted that no implication relating to thinkable things can be a material or formal implication. Is Lewis, perhaps, confusing together “every thinkable which has the property φ …” and “every existing thing which should have the property φ …”? (2) The same caution applies to the use of the term “must”. While its use may be warranted by the extension of the scope of ‘x’ to include things which are thinkable but do not exist, its introduction is unwise until the statement with the extended scope has been explicated in such a way as to make this clear.

These remarks are not captious. It will turn out that I am not criticizing Lewis for a mere failure to justify what is in point of fact a correct introduction of “should” and “must” at this point. We shall find, indeed, that his introduction of these terms embodies a most serious mistake.

⁵ The minimum content of this statement is that laws of nature are not analytic in the “Kantian” sense according to which ‘(x) φx ⊃ Ψx’ is analytic if Ψ is either identical with or a constituent of φ. However, even if the scope of the term ‘analytic’ is broadened to include logical necessity which is not of this simple form, so that statements can be analytic without being analytic in the Kantian sense, it is prima facie highly improbable that laws of nature are analytic even in this broader sense.

⁶ If the reader is impatient of the notion that material or truth-functional implication is appropriately used in connection with statements about possible particulars (“Surely there is truth and falsity only with respect to the actual!”), I urge him to hold his fire for a page or two, as the usage will be justified shortly.

⁷ If it is pointed out that this sounds like Bosanquet and the Neo-Hegelians, I can only say that much is to be learned from this movement. I have indicated elsewhere (“Realism and the New Way of Words,” Philosophy and Phenomenological Research, June, 1948) the extent to which the coherence theory of meaning and truth must be absorbed—after proper translation—into an adequate empiricism.

⁸ For a brief account, see “Epistemology and the New Way of Words,” The Journal of Philosophy, Vol. XLIV, No. 24, November 20, 1947. A longer and more complete account is to be found in “Realism and the New Way of Words,” Philosophy and Phenomenological Research, Vol. VIII, No. 4, 1948.

⁹ See note 3 above.

¹⁰ Thus, Carnap's distinction (Meaning and Necessity, pp. 8 ff.) between ‘possible states of the universe’ (expressed by false state descriptions) and the actual state of the universe' (expressed by the true state description) does not correspond to the distinction we are attempting to draw between possible histories and the actual history. In so far as our conception is sound—and we have just begun to expound it—Carnap's distinction must be made with respect to each possible history as well as the actual history. Thus each possible history is the fundamentum of a set of slate descriptions, and is ‘the actual state of the universe’ which makes one of these state descriptions true.

¹¹ Except to a superficial and inadequate extent which will be brought out in the discussion which follows.

¹² Our discussion of the diversity of different universals will proceed, as has our entire discussion to date, on the assumption that there must be absolutely simple universals. This assumption, though it cannot, indeed, be clarified within the naive frame of reference to which we are restricted, strikes us, within this frame, as a necessary truth. It is the purpose of our argument to discover such “necessities,” and explore their inter-relation, not to attempt an isolated explication of each “necessity” as we find it.

¹³ Indeed, it might seem that since we have accepted the Leibnitzian account of the identity of particulars, any attempt to explicate the diversity of universals in terms of the diversity of particulars must lead to an obvious circle. Three comments are relevant: (1) We have been limiting our discussion recently to the diversity of simple non-relational universals. May it not be the case that the diversity of particulars is to be understood in terms of their position in a relational structure? (2) While circularity is indeed to be avoided, we may find a reciprocal dependence of the diversities of universals and particulars. (3) Note that our above discussion takes only actual particulars into account.

¹⁴ This sentence can be expanded as follows: It cannot be the case that for each type of relational array of n particulars, where the variety of such types depends solely on the character of the basic relations of the family and in no way on its “qualitative” universals, there are as many possible histories exemplifying the set of m universals associated with the family as mathematically calculable combinations of n elements taken n at a time with the members of another set of m elements, where each element of the first set is paired with one and only one element of the second set, whereas each element of the second set can be paired with any number (from 0 to n) of elements in the first set.

It will be noticed that I am assuming that the basic particulars of a history can each exemplify only one simple most determinate “qualitative” universal to constitute an atomic state of affairs. I established this in a recently completed paper. It follows from this contention, of course that the values of ‘x’ in ‘φ·Ψx’ must be derived individual constants. Let Us use ‘t’ instead of ‘x’ for the variable corresponding to derived individual constants. Now such derivation involves a “thing-making” relation. Call such a relation, however complex, ‘f’. We then have the schema ‘t = f (x_i,x_j,….)’ defining the thing t in terms of the atomic particulars x_i, x_j,. … We next define the relation Ingredience-in-a-thing, symbolized by ‘I’, as follows: ‘I (x, t)’ if and only if ‘t = f (…, x, …)’.

Given the atomic predicates ’φ_i,’, ‘φ_i’,. … we define ‘φ_it’, as short for ‘(Ex) I (x, t)·φ_ix’. It follows that ’φ_i·φ_it’ abbreviates ‘(Ex, y) I (x, t)·I(y, t)·φ_ix·φ_j,y’. We consequently see that if ‘Ψ’ is defined as ‘φ_i·φ_j’, this definition by no means involves merely the primitive predicates ’φ_i’ and ’φ_j’ together with the logical relation of conjunction.

¹⁵ The term ‘possible’ here means logically possible, for on the alternative we are considering, the expression ‘physically possible history’ is tautologous, a physically possible array being by definition a logically possible history. In other words, on this alternative there are no logically possible histories which violate material invariancies; there are no histories which are logically possible but physically impossible. This, however, does not mean that there is a general coincidence of the logically and the physically possible with respect to histories, for we must distinguish (as we have before) between the usage of ‘possible’ in which histories are possible, and that usage which is relative to a history and in terms of which Green x²₇ was said to beapossible state of affairs in history H². In the latter usage of ‘possible’ the logically and the physically possible do not coincide.

¹⁶ We must be careful to distinguish between “wild histories” as physical impossibilities relative to a conforming array (see concluding sentences of note 15 above) and “wild histories” as non-conforming arrays.

¹⁷ In the framework of logical empiricism, epistemology is the pure theory of empirically meaningful languages, that is to say, languages which are about worlds in which they are used. For a development of this conception, see “Realism and the New Way of Words,” Philosophy and Phenomenological Research, 1948.

A reader may ask, “Doesn't your whole discussion assume the soundness of metaphysical realism? Haven't the phenomenalists from Berkley to Bergmann shown that the only meaningful individual constants are ego-centric particulars”? But ego-centric particulars like ‘this’ and ‘that’ do not belong to the object-language! They belong in the pragmatic metalanguage. If a philosopher proposes to concern himself only with such pragmatic systems as involve a one-one correspondance between the ego-centric particulars of the “object-language segment” of the system, he should be quite clear that there is no sanction for such a restriction in the pure theory of pragmatic systems (Pure Pragmatics).

17a It is, of course, this analysis of physical necessity in terms of logical necessity which by note 20, page 656, of “Epistemology and the New Way of Words,” The Journal of Philosophy, Vol. 44, 1947.

¹⁸ From this perspective, the main trouble with the Idealistic doctrine of the Concrete Universal was that, like the Platonists, the Hegelians didn't go far enough. Their mistake was to speak of The Concrete Universal.

¹⁹ For a detailed discussion of this point, see my article, “Realism and the New Way of Words,” Philosophy and Phenomenological Research, Vol. VIII, June, 1948. See also Gustav Bergmann's important articles, “Pure Semantics, Sentences and Propositions,” Mind, Vol. LIII, 1944, and “A Positivistic Metaphysics of Consciousness,” Mind, Vol. LIV, 1945.

²⁰ Language, Truth and Logic, (2nd Ed.), p. 17.

²¹ From the standpoint of formal linguistics, one of the most interesting implications of our analysis is the conception of a truth-functional or extensional account of the prima facie non-extensional relationships of the primitive descriptive predicates of an empirical language in virtue of which they mean what they do. “Surely the meaning of the expressions of a language doesn't depend on what is the case!” Surprising though it may seem, from the standpoint of epistemological semantics the meanings of the expressions of a language do depend on what is the case, though not in “the actual world” (however this concept be analysed) but in the family of worlds which are the worlds of the language.

The formal characterization of the primitive one-place predicates of an empirical language by means of semantic techniques involves (a) the specification of one or more basic relations, (b) the specification of a set of “worlds” consisting of all relational arrays of atomic states of affairs exemplifying the qualitative universals designated by these primitive one-place predicates, where (c) certain formal implications (synthetic in the Kantian sense) involving these predicates and the basic relations are true of all these “worlds,” and where (d) each predicate can be distinguished from all the others in terms of the role it plays in this set of formal implications.