Types of relativism. Critics of relativism.

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Epistemological relativism Epistemological relativism, before being asserted, was an accusation, formulated in particular against Thomas Samuel Kuhn (challenge taken up by Paul Feyerabend). George Lakoff defines relativism in his book Metaphors We Live By, as a rejection of subjectivism and … Read More

Classical, minimal, and intuitionist logic

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The axioms and rules of propositional calculus for the classical logic induce the proposition p ∨ ¬p, called the principle of excluded middle, the proposition ¬¬p → p, called elimination of double negation and the proposition ((p → q) → … Read More

Main properties of propositional logic

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Propositional calculus has several different ways to “validate” propositions: deduction systems that demonstrate theorems and semantic methods that define tautologies. The question that arises is whether these methods coincide. Decidability, coherence, completeness, compactness The fact that any proposition is demonstrable … Read More

Semantics of propositional logic

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Semantics determines the rules for interpreting propositions. Assigning truth values to each of the elementary propositions intervening in a proposition amounts to choosing a model of this proposition. More precisely, if we place ourselves in classical logic, the interpretation of … Read More

The syntax of the propositional logic

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The constituents of language At the base of the syntax of the calculus of propositions are the propositional variables or atomic propositions, denoted by p, q, etc., which generally constitute a countable infinite set. The second basic constituents of the … Read More

Major types of logic

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Syllogistic logic Organon is Aristotle’s principal work of logic, including the Prior Analytics; it constitutes the first explicit work of formal logic, with in particular the introduction of syllogistics. The works of Aristotle are considered in Europe and the Middle … Read More

Argument from Analogy

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The “argument from analogy” is an argument which compares two ratios, that is to say four terms, in a crossed reasoning, of the type ”if a is to b what c is to d”. It is therefore a matter of … Read More

Modal logic

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In mathematical logic, modal logic is a type of formal logic that extends propositional logic, first-order logic, or higher-order logic with modalities. A specific modality of the qualities of truth. For example, a proposition like “it’s raining” can be preceded … Read More

Metaphysical and logical arguments for the existence of God

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During the history of philosophy and theology, many arguments for and against the existence of God have been made. The God in question here is what is sometimes called the God of the philosophers, namely the God of the great … Read More

Henri Poincaré, Mathematics and logic

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A few years ago, I had the opportunity to expose some ideas about the logic of the infinite; on the use of the infinite in Mathematics, on the use made of it since Cantor; I explained why I did not … Read More

Henri Poincaré, The logic of infinity: An overview

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The antinomies to which certain logicians have been led come from the fact that they could not avoid certain vicious circles. It happened to them when they considered finite collections, but it happened to them much more often when they … Read More

Henri Poincaré, The logic of infinity: The memory of Mr. Zermelo

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It is in a totally different direction that Mr. Zermelo is seeking the solution of the difficulties we have pointed out. He tries to establish a system of axioms a priori, which must allow him to establish all the mathematical … Read More

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