logic

Can logic be fully detached from philosophy and absorbed into mathematics? In Logic: From Philosophy to Mathematics? Towards George Boole’s Algebra of Logic, Christian Toumba Patalé examines George Boole’s transformative project of recasting logic as a mathematical science. Traditionally rooted in Aristotelian and Stoic philosophies, logic underwent a major shift in the nineteenth century when Bo…

This paper argues that standard mathematical frameworks treat infinity as a completed magnitude, and continuity as constructed from discrete elements, thereby distorting the structure of infinity and of the continuum. The existing foundations of mathematics attempt to represent infinite and continuous domains on the basis of finite and discrete constructions, whereas the present framework treats …

Abstract An apparent issue for the Revision Theory of definitions has long been that its most plausible versions engender $\omega $-inconsistencies. In this paper I develop a new $\omega $-consistent revision theory and use it to argue that revision theorists can and should embrace $\omega $-consistency. I show how my theory, called $\mathbf{S}^{\#N}$, withstands the theoretical pressures towards…

Kolmogorov and Alexandrov on a trip. From CultureMath , 2022. Problems, Problems Everywhere There’s a particular kind of mathematical paper that begins with a modest goal and ends up quietly connecting half a century of ideas across logic, category theory, and the philosophy of mathematics. Today I want to talk about one of those papers. In Kolmogorov–Veloso Problems and Dialectica Categories , S…

This paper introduces a finite row-based semantics for a non-nested fragment of first-order predicate logic. Rows are assignments of signs to monadic predicates, including projections of polyadic relations, and configurations of rows represent admissible individuals. Quantified formulas constrain configurations, while ground atomic formulas impose relational constraints without assigning constant…

_Mind_. forthcomingMy aim in this paper is to offer a novel justification for β-Equivalence. β-Equivalence is a standard principle of higher-order logic, but it is metaphysically controversial. My argument for β-Equivalence is based on a distinctively Fregean conception of predication. I argue that the Fregean conception motivates a non-standard notation for predicates, which can then be used to …

Question 0: How do injective envelopes work in constructive mathematics? For example, Question 1: How strong is it to assert internally that there are enough injectives (in the category of sets, say)? ...

Let $G$ be a Polish group, $X$ a Polish space and $a : G \times X \to X$ be a Borel action. Is it the case that every orbit of this action is Borel? It is clear that every orbit is analytic. I also ...

By "mathematical modality" or "mathematical necessity" I mean the sort of necessity that makes mathematical propositions true. The modal understanding of logic is that a deduction ...

Hopefully this is not a too silly question, but I'm trying to understand the design choices made by the developers of proof assistants and how these choices help (or impede) human mathematicians to ...

Skolem is not constructive (but sometimes it can be) On what goes wrong when you try to eliminate quantifiers intuitionistically proof theory constructive logic Skolemization works. That's the starting point — not a caveat, not a qualification. In classical first-order logic, it is a perfectly sound and complete procedure for eliminating existential quantifiers. It feels right. Given a formula wi…

Throughout the history of philosophy and theoretical science, structural limits have repeatedly appeared in different domains. Kant identified contradictions that arise when reason attempts to determine the structure of the world as a totality. Gödel demonstrated intrinsic limits within formal systems. Wittgenstein examined the boundaries of meaningful language, and Turing established fundamental…

This paper challenges the ontological bias in modern physics that equates mathematics with truth itself, proposing instead the Theory of Mathematical Derivativity. We argue that the primordial condition of existence is Difference, and that space—along with its emergent physical phenomena—is a direct generative product of "this-that" relations. Mathematics, much like natural language, serves merel…

Fine’s logic of ground treats asymmetry — the claim that ground runs in one direction — as a constitutive formal feature of an unanalyzable primitive. This paper argues that asymmetry is not brute: it is a structural ordering relation whose source Fine’s framework cannot identify. The argument proceeds through the Midchain Theorem (Shchevyev,2026a), which establishes that no domain theory can non…

Description / Abstract We present a constructive proof that a single premise — "There exists at least one undefined syntactic position" — logically entails the emergence of a self-sustaining dynamical universe. Within the JiaBaolong Universal Axiom System, we formalize the derivation chain: Undefined → Self-Reference → Paradox (PR) → Resolution (LE) → Structure (ER) → New Undefined → Loop Through…

_Revista Perspectiva Filosófica_ 52 (2):207-229. 2025Logics of Formal Inconsistency (LFIs) are usually considered a philosophically neutral logicwith respect to paraconsistency, in the sense that they provide a good basis to think in termsof dialetheias, i.e. true contradictions, or in terms of conflicting information, a notion weakerthan truth. In this article, I will show how this claim of neut…

Some seemingly simple sequences of multiplication and addition grow so quickly that they question the very foundations of mathematics. In doing so, they demand a whole new level of logic

David Lehnherr has successfully defended his Ph.D. thesis on 8 December 2025; the thesis is titled “Simplicial Structures for Epistemic Reasoning in Multi-agent Systems”. As the title reveals, this work is truly interdisciplinary and relates to logic and to distributed computing, spanning the fields between the research groups on Logic and Theory and Distributed Computing and Cryptography.

Uncertainty, indeterminacy, and inconsistency are intrinsic features of real-world systems, requiring mathematical and conceptual frameworks that extend beyond classical binary logic. Building upon earlier developments in fuzzy sets and intuitionistic fuzzy sets, neutrosophy introduces a triadic structure in which each element is characterized by independent degrees of truth, indeterminacy, and f…

This paper argues that the extension of vague predicates is neither uniquely determined by structural facts nor governed by any single privileged semantic rule. Through a set of interconnected counterexamples, I show that a single physical configuration can support multiple incompatible yet equally reasonable classification rules. This shifts the problem of vagueness from first-order boundary ind…