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On the Provable Contradictions of the Connexive Logics C and C3
Despite the tendency to be otherwise, some non-classical logics are known to validate formulas that are invalid in classical logic. A subclass of...
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Double Negation as Minimal Negation
N. Kamide introduced a pair of classical and constructive logics, each with a peculiar type of negation: its double negation behaves as classical and...
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Categoricity Problem for LP and K3
Even though the strong relationship between proof-theoretic and model-theoretic notions in one’s logical theory can be shown by soundness and...
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Consistent Theories in Inconsistent Logics
The relationship between logics with sets of theorems including contradictions (“inconsistent logics”) and theories closed under such logics is...
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One Heresy and One Orthodoxy: On Dialetheism, Dimathematism, and the Non-normativity of Logic
In this paper, Graham Priest’s understanding of dialetheism, the view that there exist true contradictions, is discussed, and various kinds of...
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Proof-Theoretic Aspects of Paraconsistency with Strong Consistency Operator
In order to develop efficient tools for automated reasoning with inconsistency (theorem provers), eventually making Logics of Formal inconsistency ( LFI...
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Co** with Inconsistencies in Legal Reasoning
Law cases are triggered by conflicting opinions on juridical matter. Legal discourse reflects these contradictions. One may “index them away” in...
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Paraconsistent Metatheory: New Proofs with Old Tools
This paper is a step toward showing what is achievable using non-classical metatheory—particularly, a substructural paraconsistent framework. What...
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Paradoxes, Intuitionism, and Proof-Theoretic Semantics
In this note, we review paradoxes like Russell’s, the Liar, and Curry’s in the context of intuitionistic logic. One may observe that one cannot blame...
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A Non-alethic Multi-agent Doxastic Logic as a Solution to Epistemic Conflicts
The non-alethic systems N 1 of da Costa and A of Grana are both paraconsistent and paracomplete. Based on them, a multi-agent doxastic logic N A DK can...
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Simple Systems and Complex Systems
In relational system theory, the difference between a simple system and a complex system is that a simple system is predicative while a complex...
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A Neo-Organicist Approach to Formal Science: The Case of Mathematical Logic
What I’ve been calling the explanatory inversion thesis says that all mechanical systems whatsoever, whether formal or natural, are explanatorily and...
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Connexive Logic, Connexivity, and Connexivism: Remarks on Terminology
Over the past ten years, the community researching connexive logics is rapidly growing and a number of papers have been published. However, when it...
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What is Intuitionistic Arithmetic?
L.E.J. Brouwer famously took the subject’s intuition of time to be foundational and from there ventured to build up mathematics. Despite being...
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Paul Cohen’s philosophy of mathematics and its reflection in his mathematical practice
This paper studies Paul Cohen’s philosophy of mathematics and mathematical practice as expressed in his writing on set-theoretic consistency proofs...
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Confirmation, Coincidence, and Contradiction
While it is natural to assume that contradiction between alleged witness testimonies to some event disconfirms the event, this generalization is...
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Topic Transparency and Variable Sharing in Weak Relevant Logics
In this paper, we examine a number of relevant logics’ variable sharing properties from the perspective of theories of topic or subject-matter. We...
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Should Theories of Logical Validity Self-Apply?
Some philosophers argue that a theory of logical validity should not interpret its own language, because a Russellian argument shows that...
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Non-Reflexive Nonsense: Proof Theory of Paracomplete Weak Kleene Logic
Our aim is to provide a sequent calculus whose external consequence relation coincides with the three-valued paracomplete logic ‘of nonsense’...