mathematical-logic

This document formally compares the core theological and ecclesiological differences between the Catholic and Orthodox Christian traditions using the language of symbolic logic. We define predicates for key doctrines, establish axioms for each tradition, demonstrate logical contradictions, highlight areas of equivalence, and conclude with a modal analysis of necessity versus possibility. ( direct…

Carpe diem sed post (legaliter, ethice et logice )“ Seize the day — but consequence as, legal, ethical and logical” 1. Preamble In an age of instantaneous action and diminishing reflection, humanity risks mistaking motion formeaning. The call of our era is not to act less, but to act more wisely. The Sinani Principle arisesfrom this necessity — an invitation to harmonize vitality with virtue, and…

This is a follow-up to my previous question, here: Is there a single equation which is equivalent to $1$ being a two-sided identity?. As in that question, let our signature be $\{*,1\}$, that is, a ...

In this series of posts, we’ll be featuring mathematical video and streaming channels from all over the internet, by speaking to the creators of the channel and asking them about what they do. We spoke to Deniz & Thorsten, who host the aboutlogic channel. Channel title: aboutlogicLink: youtube.com/@aboutlogicTopics covered: Philosophy, logic, and mathematicsAverage video length:…

_Journal of Philosophy_. forthcomingA well-known problem, due to Carnap, concerns how the meanings of logical connectives can possibly arise from the rules governing their use. Much less discussed is an analogous problem for quantifiers. This paper argues that the problem for quantifiers is serious, resists the usual solutions, and (on plausible semantic and metasemantic assumptions) forces us in…

I know this has been probably posted many times before but, I am a first year university student and want to learn more about philosophy especially metaphysics and Logic which interest me a-lot. I am ...

_Journal of Philosophical Logic_. 2026This paper draws attention to key logical relations between two distinct and independently intelligible notions, compatibility and implication. We identify a set of inference rules governing compatibility and show how crucial principles concerning conditionals can be derived from these rules, on the assumption that implication is definable in terms of compati…

_Logique Et Analyse_ 32 (128):241-245. 1989In 1979 Meyer, Routley and Dunn found a new form of Russell's paradox, different from that found by Curry. By means of elementary syntactic transformations it is possible to clarify the relation which these paradoxes have with each other. Also, we will find new relationships with important metatheoric results relative to Peano's arithmetic (PA). We will …

Terence Tao notes AI can now rigorously check mathematical proofs up to 100,000 lines, raising questions about the future of mathematics and its goals.

This book presents a systematic development of Refined Quadruple Neutrosophic (T, I, N, F) Logic, extending classical neutrosophic logic by distinguishing Neutrality (N) from Pure Indeterminacy (I) and by refining each of the four components—Truth, Indeterminacy, Neutrality, and Falsehood—into semantically labeled subcomponents. The resulting n-valued structure provides a multidimensional represe…

Contents (This is a stub) Idea Subtractive logic is an extension of (propositional or first order) intuitionistic logic with a new connective, subtraction, dual to implication, such that each sentence have a “dual” verifying if and only if . Propositional subtractive logic is a conservative extension over propositional intuitionistic logic, but it is not the case for the first order case. Synt…

Are there semantically adequate languages that are authorities of their own truth but have no meta-language, so they are the sole authority of their own truth? A language on top of Tarski's infinite tower would be such a language. This can be proved by demonstration. We will now demonstrate it by building a rigorous paraconsistent model inside a non-well-founded set domain.

constructive mathematics, realizability, computability propositions as types, proofs as programs, computational trinitarianism topos, homotopy topos type theory, homotopy type theory canonical form, univalence Bishop set, h-set decidable equality, decidable subset, inhabited set, subsingleton A proof assistant or proof management system is a kind of software designed to help with proofs in formal…

constructive mathematics, realizability, computability propositions as types, proofs as programs, computational trinitarianism topos, homotopy topos type theory, homotopy type theory canonical form, univalence Bishop set, h-set decidable equality, decidable subset, inhabited set, subsingleton The arithmetical hierarchy or arithmetic hierarchy or Kleene–Mostowski hierarchy is a hierarchy used in c…

HIGHLIGHTS ▸ A theorem that identifies a pathology owes a test for identifying it. The Inversion Theorem states what inversion is: a disposition deprived of its substrate does not diminish but persists in form, occupied by the power that emptied it. It does not state how to determine, in a given case, whether inversion has occurred or whether something has merely worn out. Until it does, the theo…