Related papers: Intuitionism and the liar paradox
Riddles are concise linguistic puzzles that describe an object or idea through indirect, figurative, or playful clues. They are a longstanding form of creative expression, requiring the solver to interpret hints, recognize patterns, and…
Fuzziness and randomicity widespread exist in natural science, engineering, technology and social science. The purpose of this paper is to present a new logic - uncertain propositional logic which can deal with both fuzziness by taking…
The semantic paradoxes are associated with self-reference or referential circularity. However, there are infinitary versions of the paradoxes, such as Yablo's paradox, that do not involve this form of circularity. It remains an open…
Researchers have argued against deficit-based explanations of students' troubles with mathematical sense-making, pointing instead to factors such as epistemology: students' beliefs about the nature of knowledge and learning can hinder them…
It is standard to regard the intuitionistic restriction of a classical logic as increasing the expressivity of the logic because the classical logic can be adequately represented in the intuitionistic logic by double-negation, while the…
In recent years, the logic of questions and dependencies has been investigated in the closely related frameworks of inquisitive logic and dependence logic. These investigations have assumed classical logic as the background logic of…
Prior research in computational argumentation has mainly focused on scoring the quality of arguments, with less attention on explicating logical errors. In this work, we introduce four sets of explainable templates for common informal…
Doubts are raised concerning the usual interpretation of the alleged failure, by quantum mechanics, of the distributive law of classical logic. The difficulty raised by incompatible sets of observables is overcome within an epistemic…
Language is not only used to transmit neutral information; we often seek to persuade by arguing in favor of a particular view. Persuasion raises a number of challenges for classical accounts of belief updating, as information cannot be…
We introduce incongruent normal form (INF), a structural representation for self-referential semantic sentences. An INF replaces a self-referential sentence with a finite family of non-self-referential sentences that are individually…
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…
Wittgenstein's paradoxical theses that unproved propositions are meaningless, proofs form new concepts and rules, and contradictions are of limited concern, led to a variety of interpretations, most of them centered on the rule-following…
Knowing the truth is rarely enough -- we also seek out reasons why the fact is true. While much is known about how we explain contingent truths, we understand less about how we explain facts, such as those in mathematics, that are true as a…
For a newcomer, paraconsistent logics can be difficult to grasp. Even experts in logic can find the concept of paraconsistency to be suspicious or misguided, if not actually wrong. The problem is that although they usually have much in…
A prominent weakness of modern language models (LMs) is their tendency to generate factually incorrect text, which hinders their usability. A natural question is whether such factual errors can be detected automatically. Inspired by…
We demonstrate that, in itself and in the absence of extra premises, the following argument scheme is fallacious: The sentence A says about itself that it has a certain property F, and A does in fact have the property F; therefore A is…
In this article we demonstrate how algorithmic probability theory is applied to situations that involve uncertainty. When people are unsure of their model of reality, then the outcome they observe will cause them to update their beliefs. We…
A key assumption fuelling optimism about the progress of large language models (LLMs) in accurately and comprehensively modelling the world is that the truth is systematic: true statements about the world form a whole that is not just…
Hidden-variable models aim to reproduce the results of quantum theory and to satisfy our classical intuition. Their refutation is usually based on deriving predictions that are different from those of quantum mechanics. Here instead we…
The classical platonist / formalist dilemma in philosophy of mathematics can be expressed in lay terms as a deceptively naive question: \emph{Is new mathematics discovered or invented? Using examples from my own mathematical work during the…