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

News

  • Graham Priest


    LoC online seminar session on Wednesday, May 12 : Graham Priest on Mission Impossible.

  • LoC (virtual) Conference 2021


    LoC (virtual) Conference: 7-9 June 2021

     

  • Thomas Ferguson


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

  • Federico Faroldi


    LoC online seminar session on Wednesday, November 18: Federico Faroldi (Ghent University) on The Structure of Reasons: Subtraction and Partiality

  • Hans Rott


    LoC online seminar session on Wednesday, October 21: Hans Rott (University of Regensburg)

     on Difference-making conditionals and the Relevant Ramsey Test

  • Daniel Hoek


    LoC online seminar session on Wednesday, October 7: Daniel Hoek (Virginia Tech) on Questions in Action

  • Jonathan Phillips


     LoC online seminar session on Wednesday, September 9: Jonathan Phillips (Dartmouth) on How we know what not to think

  • Jonathan Phillips


     

    [CANCELLED] Jonathan Phillips (Dartmouth) on Now we know what not to think

     

    LoC-DIP seminar session: Wednesday, March 11, 16:00- 17.30, at F1.15 @ ILLC

  • Heinrich Wansing and Christopher Badura


    Heinrich Wansing (Bochum) on Substructural negations as normal modal operators and 

    and Christopher Badura (Bochum) on Conditional Belief and Imaginative Episodes

     

    LoC seminar: Wednesday, February 12, 10:00-15:00, at OTM 141, Faculteitskamer. 

  • Talk by Fabrizio Cariani


    Fabrizio Cariani (Northwestern) on Indirect Evidence and the Easy Foreknowledge Puzzle. LoC seminar: Tuesday, December 17, 2019, 16:00-18:00, at the ILLC.

  • Talk by Barbara Vetter (Berlin)


    Barbara Vetter on agency-based approach to modal knowledge. Joint LoC/LIRa session: Thu, November 14, 2019, 16.30-18.00 at the ILLC. 

  • Talk by Dominic Gregory (Sheffield)


    Dominic Gregory on counterfactuals and beliefs about possibility. LoC seminar: Wed, October 16, 2019, 10:00-12:00 in Oude Turfmarkt 141. 

  • Talk by Igor Douven (CNRS, Paris)


    Igor Douven on abductive conditionals and Inferentialism: LoC seminar: Wed, April 24, 2019, 16.30-18.00 at the ILLC.

  • Talk by Margot Strohminger (Oxford)


    Margot Strohminger on belief in conditionals: LoC seminar: Wed, March 20, 2019, 10 am-12am in  Oude Turfmarkt 141-143.

  • Talk by Bjørn Jespersen (Utrecht)


    Bjørn Jespersen on Fregean semantics: LoC seminar: Wed, Oct 31, 2018, 2 pm-4pm at the ILLC

  • Talk by Catarina Dutilh Novaes


    Catarina Dutilh Novaes on deduction and cognition: LoC seminar: Wed, Oct 3, 2018, 2pm-4pm at the ILLC

  • Franz to St Andrews!


    LoC's PI Franz moves to St Andrews, but the LoC work continues as before.

Events