The Logic of Conceivability

Thomas Ferguson


LoC online seminar session on Wednesday, February 3: Thomas Ferguson on Rethinking Griss’ Negationless Intuitionistic Mathematics

Time: 17:00- 19.00 (Amsterdam time)

Location: virtually (zoom)

If you are interested in attending the talk, please, contact Anthia Solaki (a.solaki2 at uva dot nl) to get the zoom link. 

Title: Rethinking Griss’ Negationless Intuitionistic Mathematics
Abstract: 

The philosopher and mathematician George F. C. Griss is known for proposing a number of refinements to Brouwer's constructivism, outlined over a series of papers on *inconsistent intuitionistic mathematics*. Although the corresponding philosophy of mathematics differs in several respects from intuitionism, the central thesis distinguishing Griss' program is the insistence that a mathematical construction cannot be vacuously applied. Consequently, if a statement A is inconceivable (e.g., is inconsistent), one cannot produce a construction transforming proofs of A into proofs of any other statement B, barring what Andreas Kapsner has called an "empty promise conversion."

 

The task of formalizing Griss' theses into a corresponding logic has been difficult; attempts at formalization have required somewhat baroque features in order to capture Griss' words. The goal of this talk is to outline several dimensions that need to be considered to define a constructive logic and mathematics in the spirit of Griss. These features include:

 

* the interpretation of the negation implicit in Griss' negationless mathematics and its relationship to David Nelson's constructive falsity

 

* the problem of representing syncategoramatic content as outlined by Fine and its relationship to the Ackermann and converse Ackermann properties

 

* the matter of a conceivability requirement on the antecedent of constructive conditionals and its relationship to Priest-style connexive logic

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