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There are, of course, many styles of philosophizing; but it is sometimes illuminating to think of philosophers as divided into two broad types: the Socratic and the Platonic. The former are the critics, the ones who never cease questioning the grounds of accepted opinions and turning over the details of arguments; the latter are the systematizers, the ones who have a sweeping vision that they take more seriously than the details. On this division Arthur Pap is a Socratic philosopher. As he himself says in describing (Pap 1958c, cited in this Introduction as SNT), “It will hardly escape the reader’s notice that very few definitive conclusions are reached in this book, that perhaps more problems have been formulated than have been solved” (, Preface, xiv). Although Pap was very much an analytic philosopher, a good part of his most philosophically rewarding work are critiques of two prominent strands of analytic philosophy in the 1940s and 1950s. One of these is logical positivism or logical empiricism, the movement stemming from the Vienna Circle of Moritz Schlick and Rudolf Carnap and the Berlin school of Hans Reichenbach, which dominated analytic philosophy, especially in the USA, from the end of World War II through most of the 1960s. The other is ordinary language philosophy, deriving from the work of Gilbert Ryle and the followers of Ludwig Wittgenstein, which played a significant and in certain ways oppositional role, in post-war British analytic philosophy until the end of the 1960s. There were many differences and disputes between positivism and ordinary language philosophy, yet in certain respects their central, as it were popular, ideas converged. In order to understand Pap’s work and appreciate its relevance to contemporary philosophy, it will be useful to begin with a brief sketch of some major preoccupations of the analytic philosophy of this period that included this convergence. The doctrines I will outline characterize logical empiricism and ordinary language philosophy as philosophical movements, and so should not be confused with the much more nuanced views of, e.g., Carnap and Wittgenstein.

In this paper I am mainly concerned with an analysis of the Aristotelian concept of “hypothetical necessity.” It will be defined as a functional synthesis that avoids both the Platonistic reduction of necessity to abstract or mathematical necessity (what the scholastics called “simple” necessity, as contrasted with necessity “”) and the empiricistic reduction of necessity (cf. John Stuart Mill) to genetically explicable, yet logically ungrounded, generalization of contingent conjunction. What is characteristic of the Platonistic interpretation of necessity as a formal relation between intensions or essences, is that it involves the banishment of necessity from existence: “Whatever is, might not be,” as Hume said. The empiricist, then, emphasizes that, insofar as a necessary judgment is existential in reference, it represents a generalization of a contingent “,” which generalization will have a cause, ., the “generalizing propensity,” in Mill’s phrase, or the “gentle forces” of association, in Hume’s phrase, but no , and will never represent a necessary . The concept of hypothetical necessity helps, as I shall endeavor to show, to avoid the exclusive disjunction, advocated by Hume and his positivistic followers: either existential or necessary, but not both.

I am going to distinguish three kinds of : the or , the , and a priori. With these three kinds of there are associated three types of or necessity, as characterizing logical truths, whether the latter be called “,” as by logical positivists, or “truths of reason,” as by Leibniz; necessity (Aristotle’s “hypothetical necessity”), predicable of conceptual means in relation to objectives or ends of inquiry; and the kind of necessity that one might call , if it were not the case that the chief proponents of this kind, the kind of necessity that is traditionally defined by or the inconceivability of the opposite, are explicitly opposed to “psychologism” in logic (I am referring to the school of phenomenology, or “Gegenstandstheorie,” as founded by Husserl and Meinong).

The distinguished American logician, C. H. Langford, recently published a paper (Langford 1949), as brief and alarming as what the title, “A Proof that Synthetic Propositions Exist,” claims for it. Although this publication has, to my knowledge, had no noticeable repercussions in the literature of analytic philosophy, it deserves credit for reopening (for open minds, that is) an issue which according to the logical positivists has been decided once and for all. One of the merits of logical positivism which I would be the last one to deny is to have revealed a typical character of disagreements, viz., the fact that many (or most, or all?) philosophical controversies are rooted in differences of verbal usage. I am fairly sure that paper constitutes, indeed, further confirmation of this positivistic thesis, for a positivist is not likely to deny the cogency of Langford’s proof of the existence of synthetic propositions in Langford’s sense of “synthetic .” He would rather criticize Langford for having suggested by his terminology an accomplishment which he cannot really claim. I hope, therefore, to shed some light on this issue by scrutinizing the Kantian concepts involved in terms of modern logic. Indeed, it seems to me just as futile to discuss the nature of logic without a clear understanding of the distinctions which Kant strove (though rather unsuccessfully) to clarify as to discuss those distinctions without regard (be it ignorance or oblivion) to modern logic.

The title question of this paper admits of two different interpretations. It might be a question like “Are all swans white?” or it might be a question like “Are all statements of probability statistical statements?” “Are all causal statements, statements of regular sequence?” etc. If these two types of questions were contrasted with each other by calling the former “empirical” and the latter “philosophical,” little light would be shed on the distinction, since what is to be understood by a “philosophical” question is extremely controversial. Perhaps the following is a clearer way of describing the essential difference: the concept “swan” is on about the same level of clarity or exactness as the concept “white,” and one can easily decide whether the subject-concept is applicable in a given case of knowing whether the predicated concept applies. On the other hand, the second class of questions might be called questions of logical analysis, i.e., the predicated concept is supposed to the subjectconcept. They can thus be interpreted as questions concerning the adequacy of a proposed analysis (frequency theory of probability, regularity theory of causation); and the very form of the question indicates that the suggested analysis will not be accepted as adequate unless it fits all uses of the analyzed concept. Now, when I ask, as several philosophers before me have asked, whether all necessary propositions are analytic, I mean to ask just this sort of a question. I assume that those who, with no hesitation at all, give an affirmative answer to the question, consider their statement as a clarification of a somewhat inexact concept of traditional philosophy, ., the concept of a necessary truth, by means of a clearer concept. I feel, however, that little will be gained by the substitution of the term “analytic” for the term “necessary,” unless the former is used more clearly and more consistently than it seems to me to be used in many contemporary discussions. And I shall attempt to show in this paper that once the concept “analytic” is used clearly and consistently, it will have to be admitted that there are propositions which no philosopher would hesitate to call “necessary” and which nevertheless we have no good grounds for classi-fying as analytic. Moreover, I shall show that even if the concepts “necessary” and “analytic” had the same extension, they would remain different concepts. To prove this it will be sufficient to show that a proposition necessary and synthetic.

Logical empiricism, a powerful and in many ways sanitary philosophical movement which was started by the “Vienna Circle,” propagated in England mainly through Wittgenstein, and in the United States mainly through Carnap, has always been committed to some kind of “linguistic” or “conventionalist” theory of necessary propositions, though it would be dificult to pin down a party line as regards the precise form of such a theory. Such jargons as “the laws of logic are rules of the transformation of symbols,” “all knowledge consists in decisions concerning the use of symbols,” are well known to students of logical empiricism. “Logic formulates rules of language—that is why logic is analytic and empty,” writes a famous logical empiricist. In a sense this theory denies that there is such a thing as knowledge, knowledge of necessary propositions. If, as Schlick wrote, “7 + 5 = 12” is just a rule of symbolic transformation, telling us that we may interchange “12” and “7 + 5” in any context, and a proposition is something that is true or false and that may be believed or disbelieved, then this equation does not express a proposition.

In Carnap 1942, Carnap tells us, following Tarski, that a criterion of adequacy to be satisfied by an acceptable definition of truth is that

Those philosophers who conduct analyses of concepts in a formal way generally lay down formal and material conditions of adequacy for the definition which is to be constructed. The formal conditions of adequacy concern the formal features of the language in which the definition is to be constructed; an example would be the rule that any variable which occurs free (unbound by quantifiers) in the must likewise occur free in the . The material conditions of adequacy, however, are philosophically more interesting: they are sentences which must be provable on the basis of an adequate definition, and which are intended to guarantee that the defined term A designates on the basis of the constructed definition the same concept it designates in its ordinary usage in the “natural” language (whether conversational or scientific)—or at least a closely similar concept. The material conditions of adequacy, then, are sentences containing A which must themselves satisfy the following requirements:

The repudiation of propositions as “obscure entities,” which is prevalent among logicians and philosophers of “nominalistic” persuasion, is frequently justified by pointing out that no agreement seems ever to have been reached about the of propositions. And if we cannot specify, so they argue, under what conditions two sentences express the same proposition, then we use the word “proposition” without any clear meaning. Quine, for example, feels far less uneasy about quantification over class-variables than about quantification over attribute-variables and propositional variables, because there is a clear criterion for deciding whether we are dealing with two classes or with only one class referred to by different predicates: two classes are identical if they have the same membership. And such a criterion of identity is alleged to be lacking for intensions.

It is by no means beyond dispute what precisely the terms “realism” and “nominalism,” in the age-long controversy about the status of universals, have stood for. Without any regard to historical complexities and shifts of meaning, I shall, in this paper, define “realism” and “nominalism” as follows: According to realism, universals exist, to employ the scholastic phrase, , i.e., one and the same property (in the wide sense in which both qualities and relations are properties) is often simultaneously exemplified by several particulars. “Property” and “universal” are here used as synonyms. A property, in this usage, is the intension (or logical connotation) of any predicate, of whichever degree (relations are thus the intensions of predicates of degree 2 or any higher degree). According to the nominalists, on the other hand, there are no “ontological” universals. In the impressive language of metaphysicians, “only particulars have ontological status,” according to nominalism. There are, indeed, ; but it is a mistake to suppose that, like proper names and definite descriptions, general words stand for, or refer to, an entity. Predicates (which are general words) are, indeed, applicable to several particulars that each other in certain respects. But if the word has a unique referent, the latter is not a universal whose identical presence constitutes the resemblance, but at best a of similar particulars.