Buddhist Philosophy of Logic

Logic in Buddhist Philosophy concerns the systematic study of anumāna (often translated as inference) as developed by Dignāga (480-540 c.e.) and Dharmakīti (600-660 c.e.). Buddhist logicians think of inference as an instrument of knowledge (pramāṇa) and, thus, logic is considered to constitute part of epistemology in the Buddhist tradition. According to the prevalent 20th and early 21st century ‘Western’ conception of logic, however, logical study is the formal study of arguments. If we understand the nature of logic to be formal, it is difficult to see what bearing logic has on knowledge. In this paper, by weaving together the main threads of thought that are salient in Dignāga’s and Dharmakīti’s texts, I shall re-conceive the nature of logic in the context of epistemology and demarcate the logical part of epistemology which can be recognised as logic. I shall demonstrate that we can recognise the logical significance of inference as understood by Buddhist logicians despite the fact that its logical significance lies within the context of knowledge

The philosophy of logic

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Philosophy of Logic – Reexamining the Formalized Notion of Truth

Tarski "proved" that there cannot possibly be any correct formalization of the notion of truth entirely on the basis of an insufficiently expressive formal system that was incapable of recognizing and rejecting semantically incorrect expressions of language. The only thing required to eliminate incompleteness, undecidability and inconsistency from formal systems is transforming the formal proofs of symbolic logic to use the sound deductive inference model

'What the Tortoise said to Achilles': Lewis Carroll's Paradox of Inference

Lewis Carroll’s 1895 paper, 'What the Tortoise Said to Achilles' is widely regarded as a classic text in the philosophy of logic. This special issue of 'The Carrollian' publishes five newly commissioned articles by experts in the field. The original paper is reproduced, together with contemporary correspondence relating to the paper and an extensive bibliography

What Isn’t Obvious about ‘obvious’: A Data-driven Approach to Philosophy of Logic

It is often said that ‘every logical truth is obvious’ (Quine 1970: 82), that the ‘axioms and rules of logic are true in an obvious way’ (Murawski 2014: 87), or that ‘logic is a theory of the obvious’ (Sher 1999: 207). In this chapter, I set out to test empirically how the idea that logic is obvious is reflected in the scholarly work of logicians and philosophers of logic. My approach is data-driven. That is to say, I propose that systematically searching for patterns of usage in databases of scholarly works, such as JSTOR, can provide new insights into the ways in which the idea that logic is obvious is reflected in logical and philosophical practice, i.e., in the arguments that logicians and philosophers of logic actually make in their published work

Prospects for practice-based philosophy of logic

We explore prospects for practice-based approaches to logical theory, in particular the link between classical and intuitionistic logic and the inferential structure of traditional practices of representation & argument in science and mathematics. After discussing some key notions about practice, we outline the connection between representation practices and classical logic, and then consider a spectrum of actual practices followed or proposed by (real) scientists. Intuitionistic logic helps to clarify the potential of practice-based approaches for understanding pluralism, and to hammer some key points about the general thesis.Ministerio de Economía y Competitividad FFI2009-1002

An Overview of Edmund Husserl’s Views on Philosophy of Logic and Mathematics

An Overview of Edmund Husserl’s Views on Philosophy of Logic and Mathematic

Psychologism and neopsychologism in philosophy of logic

Thesis focuses on psychologism – a philosophical theory according to which the ontological and epistemological foundations of logic and mathematics are our mental states. Neopsychologism is a new set of psychologistic ideas that appeared already in the XXth century and are influenced by new psychology including cognitive science and artificial intelligence. Its central idea is that the main problem of the early psychologism in logic criticized by Husserl and Frege (Willard 1980) is resolved in the contemporary neopsychologistic research.https://www.ester.ee/record=b517884

The Prolog Inference Model refutes Tarski Undefinability

The generalized conclusion of the Tarski and Gödel proofs: All formal systems of greater expressive power than arithmetic necessarily have undecidable sentences. Is not the immutable truth that Tarski made it out to be it is only based on his starting assumptions. When we reexamine these starting assumptions from the perspective of the philosophy of logic we find that there are alternative ways that formal systems can be defined that make undecidability inexpressible in all of these formal systems