Analyticity

Abstract

Bolzano’s theory of analyticity is a favoured topic in the literature — cf. Bar-Hillel 1950; Etchemendy 1988; Künne 2006; Lapointe 2000, 2008; Morscher 2003b; Neeman 1970; Proust 1981, 1989; Textor 2001. This should be no surprise, and there are many reasons why Bolzano’s theory should be seen to be significant and to deserve a thorough treatment. For one thing, it rests on a substitutional procedure that had until the end of the nineteenth century no equivalent. Besides, it anticipated in great detail the definition of logical truth we find in the works of Quine. Bolzano’s theory of analyticity in fact offered the first alternative to the Kantian idea that analyticity is defined by the inclusion of the predicate in the subject. The connection to Kant is not unimportant. At least until 1812, Bolzano seemed to have thought that he was retaining the letter of the Kantian definition:

It remains one of Kant’s great merits to have for the first time drawn our attention to the important difference between the analytic part of our knowledge and the synthetic part, though we cannot accept nor take into account everything our philosopher otherwise says about the intrinsic nature of our synthetic judgements. Assuredly the truth of analytic judgements rests on an entirely different ground (Grund) than that of synthetic judgements. If they do deserve the name of genuine judgements (what I grant them not without reserve), then they all rest in this unique universal proposition which is expressed by the following formula: ’(A cum B) is a kind of A’ […] and we can say that the principle of contradiction is the universal source of all analytic judgements.

(Bolzano 1810, Appendix, §1)

The division of judgements into analytic and synthetic is however very important. a. An analytic judgement is such that its predicate is a component of the concept of the subject. For instance, the judgement: “A pocket mirror is a mirror” — or “A pocket mirror is something one can carry in their pocket“. b. A synthetic judgement is any other judgement whose predicate is not a component in the subject, such as for instance: “The Sun warms”.

(Bolzano 1812, § 30)