相关论文: Why we must heed Wittgenstein's "notorious paragra…

In this paper, we provide a complete classification for the first-order Goedel logics concerning the property that the formulas admit logically equivalent prenex normal forms. We show that the only first-order Goedel logics that admit such…

We present some arguments for the thesis that a set-theoretic inspired faith, in the ability of intuitive truth to faithfully reflect relationships between elements of a Platonic universe, may be as misplaced as an assumption that such…

In a 1985 commentary to his collected works, Kolmogorov informed the reader that his 1932 paper 'On the interpretation of intuitionistic logic' "was written in hope that with time, the logic of solution of problems [i.e., intuitionistic…

In 1931, G\"odel presented in K\"onigsberg his famous Incompleteness Theorem, stating that some true mathematical statements are unprovable. Yet, this result gives us no idea about those independent (that is, true and unprovable)…

There is a longstanding debate in the logico-philosophical community as to why the G\"odelian sentences of a consistent and sufficiently strong theory are true. The prevalent argument seems to be something like this: since every one of the…

This is a 20-year old review on singularities and singularity theorems. The main reason to submit it now is -apart from increasing its availability- to correct a very strange error that appears in the journal's online version: it contains…

A sketch of three senses of emergence and a suggestive view on the emergence of time and the direction of time is presented. After trying to identify which issues philosophers interested in emergent phenomena in physics view as important I…

In this paper we sketch how some fundamental concepts of modern topology (as well as logic and category theory) can be understood philosophically in the light of Hegel's Science Logic as well how modern topological concepts can provide…

We make some remarks on the mathematics and metaphysics of the hole argument, in response to a recent article in this journal by Weatherall ([2018]). Broadly speaking, we defend the mainstream philosophical literature from the claim that…

The paper adresses the problem of reasoning with ambiguities. Semantic representations are presented that leave scope relations between quantifiers and/or other operators unspecified. Truth conditions are provided for these representations…

The paper aims at emphasizing that, even relaxed, the hypothesis of compositionality has to face many problems when used for interpreting natural language texts. Rather than fixing these problems within the compositional framework, we…

We formally define a "mathematical object" and "set". We then argue that expressions such as "(Ax)F(x)", and "(Ex)F(x)", in an interpretation M of a formal theory P, may be taken to mean "F(x) is true for all x in M", and "F(x) is true for…

We argue that Godel's completeness theorem is equivalent to completability of consistent theories, and Godel's incompleteness theorem is equivalent to the fact that this completion is not constructive, in the sense that there are some…

Bohr's interpretation of quantum mechanics has been criticized as incoherent and opportunistic, and based on doubtful philosophical premises. If so Bohr's influence, in the pre-war period of 1927-1939, is the harder to explain, and the…

Deficiencies in Kauffman's proposal regarding a new way for building scientific theories are pointed out. A suggestion to overcome them, and in fact, independently construct mathematical theories which are beyond the reach of Goedel's…

In 1927 Heisenberg discovered that the ``more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa''. Four years later G\"odel showed that a finitely specified, consistent formal…

What is the proper explanation of intuitionistic hypothetical judgment, and thence propositional implication? The answer is unclear from the writings of Brouwer and Heyting, who in their lifetimes propounded multiple (sometimes conflicting)…

The purpose of this paper is to address some criticisms recently raised by John Horty in two articles against the validity of two commonly accepted defeasible reasoning patterns, viz. reinstatement and floating conclusions. I shall argue…

Hilbert's Entscheidungsproblem has given rise to a broad and productive line of research in mathematical logic, where the classification process of decidable classes of first-order sentences represent only one of the remarkable results.…

The interpretations of solutions of Einstein field's equations led to the prediction and the observation of physical phenomena which confirm the important role of general relativity, as well as other relativistic theories in physics. In…