SOPhiA 2018

Salzburgiense Concilium Omnibus Philosophis Analyticis

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Programme - Talk

Disagreement in Logic and the Meaning of Logical Constants
(Logic, English)

There are two ways in which disagreement between two logicians can turn out to be merely apparent. For the first such way consider a classical logician and one who uses ∧ (conjunction) in just the same way that the classical logician uses ∨ (disjunction), and vice versa. We are inclined to say that there is no real disagreement at stake here; that the two are making the very same claims in different vocabulary. For the second case, consider a classical and paraconsistent logician who disagree about whether ex falso quod libet, (A∧¬A)→B, is a theorem; in other words, whether conjunction, negation, and the conditional obey this principle. Quine (1970) argued that in such a case the disputants are not discussing the same subject matter anymore and must be seen as merely talking past each other.

I give a definition of what genuine disagreement in logic comes down to by discussing the two possible sources of mere apparentness. To rule out the first, I define a notion of notational variance between two logical systems based on the notion of a consequenceand structure-preserving translation between two logics (which can also be found in Humberstone, 2000). The first necessary condition for genuine disagreement thereby being that the logics in question must not be notational variants of one another.

To rule out the second possible source of mere apparentness I block Quine's argument by giving what I call a bi-aspectual view on what logical constants (including the sentential connectives) and their meanings are, positing two meaning constituents for each of them. For two logicians to be in genuine disagreement with regard to a certain connective, they must agree on its first and disagree over its second meaning constituent.

The first meaning aspect -- which needs to be agreed on -- I argue is a relational modal truth-condition in the style of Kripke semantics. The second one -- the actual source of disagreement -- is a set of properties on the accessibility relation figuring in these truth-conditions.

I conclude by giving an outlook on how my solutions to either variety of merely apparent disagreement can be exploited for debates outside of logic.

References:

Humberstone, L. (2000). Contra-classical logics. Australasian Journal of Philosophy, 78(4), 438--474.

Quine, W. (1970). Philosophy of logic. Harvard University Press.

Chair: Stefan Forster
Time: 10:00-10:30, 14 September 2018 (Friday)
Location: SR 1.006

Tobias Koch 
(Ruhr-Universität Bochum, Germany)

M.A. Student of philosophy at Ruhr-Universität Bochum, working on the philosophy logic. Especially interested in the nature of disagreement between rival systems of logic.

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