Related papers: The formal roots of Platonism
In this introductory note, I describe my particular view of the notion of ontological commitments as honest and pragmatic working hypotheses that assume the existence (out there) of certain entities represented by the symbols in our theory.…
In this paper we analyse logic of false belief in intuitionistic setting. This logic, studied in its classical version by Steinsvold, Fan, Gilbert and Venturi, describes the following situation: a formula F is not satisfied in a given…
In this essay we describe a platonic metaphysics where time is a fundamental idea such that the passage of time is independent of observers and the laws of physics. Furthermore, time serves to distinguish between a real and an abstract…
In this paper we discuss contrastive explanations for formal argumentation - the question why a certain argument (the fact) can be accepted, whilst another argument (the foil) cannot be accepted under various extension-based semantics. The…
We consider a philosophical question that is implicit in Selmer Bringsjord's paper, "The narrational case against Church's Thesis": If, as Mendelson argues, the classically accepted definitions of foundational concepts such as "partial…
We analyze the informal notion of truth and conclude that it can be formalized in essentially two distinct ways: constructively, in terms of provability, or classically, as a hierarchy of concepts which satisfy Tarski's biconditional in…
A model of knowledge representation is described in which propositional facts and the relationships among them can be supported by other facts. The set of knowledge which can be supported is called the set of cognitive units, each having…
Ordinary and transfinite recursion and induction and ZF set theory are used to construct from a fully interpreted object language and from an extra formula a new language. It is fully interpreted under a suitably defined interpretation.…
We offer a view of mathematics as an experimental science where axioms play the role of foundational theories like general relativity and quantum mechanics in physics. Under this view, axioms are provisional and inferred from experience…
Our understanding about things is conceptual. By stating that we reason about objects, it is in fact not the objects but concepts referring to them that we manipulate. Now, so long just as we acknowledge infinitely extending notions such as…
It is a widespread belief that results like G\"odel's incompleteness theorems or the intrinsic randomness of quantum mechanics represent fundamental limitations to humanity's strive for scientific knowledge. As the argument goes, there are…
The paper defends the thesis that analysis of truth problem in the context of interpretations of quantum logic allows to reveal the prospect of elicitation of specifics of the relations between quantum mechanics and quantum logic in a…
We investigate the reasons of having confidence in mathematical theorems. The formalist point of view maintains that formal derivations underlying proofs, although usually not carried out in practice, contribute to this confidence. Opposing…
We argue for a compositional semantics grounded in a strongly typed ontology that reflects our commonsense view of the world and the way we talk about it in ordinary language. Assuming the existence of such a structure, we show that the…
At the heart of intuitionistic type theory lies an intuitive semantics called the "meaning explanations"; crucially, when meaning explanations are taken as definitive for type theory, the core notion is no longer "proof" but "verification".…
The concept of informal mathematical proof considered in intuitionism is apparently vulnerable to a version of the liar paradox. However, a careful reevaluation of this concept reveals a subtle error whose correction blocks the…
The traditional concept of knowledge is a justified true belief. The bulk of contemporary epistemology has focused primarily on that task of justification. Truth seems to be a quite obvious criterion-does the belief in question correspond…
This article supports the epistemological claim that sound human reasoning about ultimate knowledge is either foundational or circularly justified. In particular, questions which naturally arise in theology, philosophy, and related…
We argue about a conceptual approach to quantum formalism. Starting from philosophical conjectures (Platonism, Idealism and Realism) as basic ontic elements (namely: math world, data world, and state of matter), we will analyze the quantum…
Classical interpretations of Goedel's formal reasoning imply that the truth of some arithmetical propositions of any formal mathematical language, under any interpretation, is essentially unverifiable. However, a language of general,…