Bolzano and Quine on Nomic Truths

(Logic and 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:

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

Location: SR 1.006

Oguz Akcelik

(Middle East Technical University, Turkei)

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Last update: 2014-04-01.