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Truthmakers and Model Theory

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2020, Master of Science, Ohio State University, Mathematics.
Sentences in a formal language are true or false in a given structure, or model. A theory of truthmakers aims to provide an account of \why sentences are true or false. This thesis studies a theory of model-relative truthmakers developed by Neil Tennant in a series of recent works. One of the key facts about this theory is that for any model M there exists an M-relative truthmaker for a sentence phi if and only if phi is true in M in the usual Tarskian sense. After arithmetizing Tennant's theory of truthmakers, I show that the weak theory RCA_0 suffices to prove this equivalence between Tarskian truth and the existence of a truthmaker. I turn next to notions of logical consequence. The standard Tarskian definition of logical consequence requires that truth be preserved from the premises to the conclusion. In the truthmaker-theoretic setting, we can generalize this to require that ways of being true be preserved from the premises to the conclusion. This in turn can be understood to say that phi is a consequence of Delta if there is a way to transform any truthmakers for the members of Delta into a truthmaker for phi. Tennant had proposed a series of reduction procedures analogous to proof-theoretic normalization that were meant to accomplish this truthmaker-transformation. I show that Tennant's procedure is flawed, failing to transform a truthmaker for B into a truthmaker for "if A then (A and B)". I offer a solution to this problem by defining a slightly more complicated procedure for transforming truthmakers of the premises of an argument into a truthmaker for the conclusion. I prove this solution to be adequate in the sense that the resulting conception of logical consequence is coextensive with the standard Tarskian definition, provided the premise set is consistent.
Chris Miller (Advisor)
Neil Tennant (Committee Member)
65 p.

Recommended Citations

Citations

  • Brauer, E. (2020). Truthmakers and Model Theory [Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1586176557329917

    APA Style (7th edition)

  • Brauer, Ethan. Truthmakers and Model Theory. 2020. Ohio State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1586176557329917.

    MLA Style (8th edition)

  • Brauer, Ethan. "Truthmakers and Model Theory." Master's thesis, Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1586176557329917

    Chicago Manual of Style (17th edition)