Bolzano and Quine on Nomic Truths

(Logic/Philosophy of Mathematics, English)

n this study, I will analyze and compare Bolzano's and Quine's conceptions of nomic truths. In the first part, I will focus on Bolzano's definition of universal validity as a form of nomic truth in his Theory of Science (1837/2014 II.sec.147). This definition is paraphrased by Bar-Hillel (1950, p.95) in a modernized and rigorized form as follows: "The proposition p is called universally valid with respect to the class of concepts A if and only if the propositions which may be developed from p by varying at will every occurrence of the elements in A " are all true. In the second part, I will focus on Quine's notion of essential vs. vacuous occurrence of a word for the purpose of defining logical truth Quine (1940). Subsequently Quine (1935/1976) notes that his definition of logical truth as pointed out by Bar-Hillel has been anticipated, in essence, by Bolzano. Quine distinguishes between logical, geological, economic, etc. vocabularies, characterizing the science into question. Accordingly, he defines the characteristic vocabularies in terms of nomic truths, provided they are lawlike. In the third part, I will compare Quine's discussion of logical truth with Bolzano's theory of logical analyticity, and I will conclude the following two points:

(1) The class of concepts A mentioned in Bolzano's definition of the universal validity of proposition p corresponds, in Quine's framework, to the set of constants occurring vacuously in the sentence expressing proposition p.

(2) The complement of the class of concepts A relatively to the total class of concepts constituting the proposition p corresponds to the set of constants occurring essentially in the sentence expressing proposition p.

Bar-Hillel, Y. 1950 "Bolzano's Definition of Analytic Propositions" Theoria 16 (2):91-117.

Bolzano, Bernard. 1837/2014. Theory of Science, Translated by Paul Rusnock and Rolf George, 4 vols., Oxford University Press.

Quine, W.V., 1935/1976 "Truth by Convention" in Ways of Paradox and Other Essays, enlarged ed. Harvard University Press.

Quine, W.V., 1940 Mathematical Logic, Harvard University Press.

Chair: Katia Parshina

Time: 14:00-14:30, 09. September 2022 (Friday)

Location: SR 1.006

Remark: CHANGE. The talk is cancelled!

Oguz Akcelik

(Middle East Technical University, Turkei)

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