Online research in philosophy

Quine’s criticism of the notion of analyticity applies, at best, to Carnap’s notion, not to those of Frege or Husserl. The failure of logicism is also the failure of Frege’s definition of analyticity, but it does not even touch Husserl’s views, which are based on logical form. However, some relatively concrete number-theoretic statements do not admit such a formalization salva veritate. A new definition of analyticity based not on syntactical but on semantical logical form is proposed and argued for.

Quine’s criticism of the notion of analyticity applies, at best, to Carnap’s notion, not to those of Frege or Husserl. The failure of logicism is also the failure of Frege’s definition of analyticity, but it does not even touch Husserl’s views, which are based on logical form. However, some relatively concrete number-theoretic statements do not admit such a formalization salva veritate. A new definition of analyticity based not on syntactical but on semantical logical form is proposed and argued for.

Paul Boghossian advocates a version of the analytic theory of a priori knowledge. His defense of an "epistemic" notion of analyticity is based on an implicit definition account ofthe meaning of the logical constants. Boghossian underestimates the power of the classical Quinean criticisms, however; the challenge to substantiate the distinction between empirical and non-empirical sentences, as forcefully presented in Two Dogmas, still stands, and the regress from Truth by Convention still needs to be avoided. Here, Quine also showed that there are no implicit definers for the logical constants. Moreover, even if they existed, their epistemic analyticity would, on Boghossian's own account, be doubtful.

According to Kant's most important definition an analytic judgement obtains when the predicate of a judgement is already contained intensionally in the subject. It has been objected (most recently by Robert Hanna) that whereas this containment is a sufficient criterion, nevertheless there are analytic judgements that do not have a corresponding conceptual content . In these cases one needs to add an extensional criterion. The chief goal of this essay is to examine this argument critically and to reject it on the grounds that although an analytic judgement can be defined extensionally, this does not achieve anything more than a conventional intensional definition. To this end Kant's argumentation on intension and extension will be reconstructed and this distinction will then be set in relation to the distinction between analytic and synthetic propositions. This discussion requires especially a clarification of the role of modality.

In the Critique of Pure Reason Kant appears to characterize analytic judgments in four distinct ways: once in terms of “containment,” a second time in terms of “identity,” a third time in terms of the explicative–ampliative contrast, and a fourth time in terms of the notion of “cognizability in accordance with the principle of contradiction.” The paper asks: Which of these characterizations—or apparent characterizations—best captures Kant’s conception of analyticity in the first Critique? It suggests: “the second.” It argues, further, that Kant’s distinction is intended to apply only to judgments of subject–predicate form, and that the fourth alleged characterization is not properly speaking a characterization at all. These theses are defended in the course of a more general investigation of the distinction’s meaning, its epistemology, and its tenability.

Quine criticised the semantic notion of analyticity that is often attributed to Frege and Kant for presupposing an essentialist theory of meaning. In what follows I trace back the notion from Quine via Carnap to Frege and Kant, and eventually examine Kant's distinction between analytic and synthetic judgements in more detail. It turns out that the so called Frege-Kant-notion of analyticity can not be attributed to Kant. In contrast, Kant had a distinctly pragmatic notion of analytic judgements. According to him analytic propositions elucidate certain presuppositions of our conceptual scheme, thereby serving the anti-metaphysical project of transcendental philosophy.

The traditional understanding of analyticity in terms of concept containment is revisited, but with a concept explicitly understood as a certain kind of mental representation and containment being read correspondingly literally. The resulting conception of analyticity avoids much of the vagueness associated with attempts to explicate analyticity in terms of synonymy by moving the locus of discussion from the philosophy of language to the philosophy of mind. The account provided here illustrates some interesting features of representations and explains, at least in part, the special epistemic status of analytic judgments.

1. In Critique of Pure Reason Kant introduced the term ‘analytic’ for judgments whose truth is guaranteed by a certain relation of ‘containment’ between the constituent concepts, and ‘synthetic’ for judgments which are not like this. Closely related terms were found in earlier writings of Locke, Hume and Leibniz. In Kant’s definition, an analytic judgment is one in which ‘the predicate B belongs to the subject A, as something which is (covertly) contained in this concept A’ ([1781/1787] 1965: 48). Kant called such judgments ‘explicative’, contrasting them with synthetic judgments which are ‘ampliative’. A paradigmatic analyticity would be: bachelors are unmarried. Kant assumed that knowledge of analytic necessities has a uniquely transparent sort of explanation. In the succeeding two centuries the terms ‘analytic’ and ‘synthetic’ have been used in a variety of closely related but not strictly equivalent ways. In the early 1950s Morton White (1950) and W.V. Quine (1951) argued that the terms were fundamentally unclear and should be eschewed. Although a number of prominent philosophers have rejected their arguments, there prevails a scepticism about ‘analytic’ and the idea that there is an associated category of necessary truths having privileged epistemic status.

Officially, for Kant, judgments are analytic iff the predicate is "contained in" the subject. I defend the containment definition against the common charge of obscurity, and argue that arithmetic cannot be analytic, in the resulting sense. My account deploys two traditional logical notions: logical division and concept hierarchies. Division separates a genus concept into exclusive, exhaustive species. Repeated divisions generate a hierarchy, in which lower species are derived from their genus, by adding differentia(e). Hierarchies afford a straightforward sense of containment: genera are contained in the species formed from them. Kant's thesis then amounts to the claim that no concept hierarchy conforming to division rules can express truths like '7+5=12.' Kant is correct. Operation concepts ( ) bear two relations to number concepts: and are inputs, is output. To capture both relations, hierarchies must posit overlaps between concepts that violate the exclusion rule. Thus, such truths are synthetic.