Munich Center for Mathematical Philosophy (MCMP)

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New Logics for the Verificationistic Enterprise

Funded by the DFG (2013-2016)
Andreas Kapsner

The project aims to take a fresh look at the verificationistic theory of meaning and its consequences on logical principles. That adopting such a verificationistic theory should lead to logical revision has been extensively argued by Michael Dummett. He claimed that a serious endorsement of verificationism had to result in the equally serious endorsement of a constructive logic. Usually it is assumed that this constructive logic has to be intuitionistic logic. However, I claim that a verificationistic theory that goes beyond the realm of mathematics cannot plausibly lead to the adoption of intuitionistic logic. Rather, I propose to investigate non-monotonic versions of so-called Nelson logics.

The reason for followers of Dummett to move towards non-monotonicity has recently been well put by John Burgess:

"Outside mathematics one would have to contend with the fact that one generally has, by way of verification, not conclusive proof, but only defeasible presumption, which is nonmonotonic in the sense that what one is warranted in presuming and asserting given certain information may become unwarranted given more. (Even what is ‘proved beyond a reasonable doubt’ in a criminal case may turn out to be wrong when surprising new evidence is uncovered, whereas what is mathematically proved stays proved.)" (Burgess (2009), p.123)

The reason I investigate non-monotonic systems of Nelson logic rather than intuitionistic logic is that the way negation is explained in intuitionistic mathematics does not seem to work well in empirical discourse. As Dummett came to realize himself, verifications alone cannot give the full account of logical vocabulary (Here, the essay “What is a Theory of Meaning (II)”, reprinted in Dummett (1993), is the most important source). It is necessary to invoke falsifications, and the result of this move has some surprising consequences, the most important one being that the argument no longer univocally supports intuitionistic logic; rather, Nelson logic seems to fit the bill much better. The bulk of this part of the argument has been published in early 2015 in my book Logics and Falsifications (Trends in Logic series, Vol. 40, Springer).

  • Burgess, J. (2009). Philosophical logic. Princeton University Press.
  • Dummett, M. (1993). The seas of language. Clarendon Press.