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Structuralism and informal provability
Mathematical structuralism can be understood as a theory of mathematical ontology, of the objects that mathematics is about. It can also be...
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Non-deterministic Logic of Informal Provability has no Finite Characterization
Recently, in an ongoing debate about informal provability, non-deterministic logics of informal provability BAT and CABAT were developed to model the...
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Solutions to the Knower Paradox in the Light of Haack’s Criteria
The knower paradox states that the statement ‘We know that this statement is false’ leads to inconsistency. This article presents a fresh look at...
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Rigor and formalization
This paper critically examines and evaluates Yacin Hamami’s reconstruction of the standard view of mathematical rigor. We will argue that the...
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A defense of Isaacson’s thesis, or how to make sense of the boundaries of finite mathematics
Daniel Isaacson has advanced an epistemic notion of arithmetical truth according to which the latter is the set of truths that we grasp on the basis...
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A Generic Solution to the Sorites Paradox
This paper offers a generic revenge-proof solution to the Sorites paradox that is compatible with several philosophical approaches to vagueness,...
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Is there an inconsistent primitive recursive relation?
The present paper focuses on Graham Priest’s claim that even primitive recursive relations may be inconsistent. Although he carefully presented his...
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Logics of (Formal and Informal) Provability
Provability logics are, roughly speaking, modal logics meant to capture the formal principles of various provability operators (which apply to...
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Frege’s Class Theory and the Logic of Sets
We compare Fregean theorizing about sets with the theorizing of an ontologically non-committal, natural-deduction based, inferentialist. The latter...
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Varieties of Self-Reference in Metamathematics
This paper investigates the conditions under which diagonal sentences can be taken to constitute paradigmatic cases of self-reference. We put forward...
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The Calculus of Natural Calculation
The calculus of Natural Calculation is introduced as an extension of Natural Deduction by proper term rules. Such term rules provide the capacity of...
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Logic Discovered and Logic Imposed (A Purim Story)
In his Philosophical Investigations, Wittgenstein said that “turning our whole investigation around” is the only way to shake the illusion of a...
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Gödel’s Absolute Proofs and Girard’s Ludics: Mutual Insights
Is it possible to characterize the notion of proof in terms of acts, without focusing on a specific domain of application and a specific linguistic...
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On the difficulty of discovering mathematical proofs
An account of mathematical understanding should account for the differences between theorems whose proofs are “easy” to discover, and those whose...
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Gödel’s Introduction to Deduction
This is a companion to a paper entitled “Gödel on deduction”, which examined the links between some philosophical views ascribed to Gödel and general...
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De-Modalizing the Language
With the aim of providing an empiricist-friendly rational reconstruction of scientists’ modal talk, I represent and defend the following unoriginal...
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Deduction at the Crossroads
I provide a general introduction to the notion at issue in this volume, i.e. deduction, and to some akin notions like inference and reasoning. I also...
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Paradox and context shift
The Liar sentence L , which reads ‘ L is not true’, can be used to produce an apparently valid argument proving that L is not true and that L is true....
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Propositional Modal Axiom Systems
Historically, most of the best-known modal logics had axiomatic characterizations long before either tableau systems or semantical approaches were...
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Another Look at Reflection
Reflection principles are of central interest in the development of axiomatic theories. Whereas they are independent statements they appear to have a...
