Philosophy of logic

The philosophy of logic is a part of the philosophy of science which is interested in the set of theoretical problems which traditionally come under logic, essentially comprising first of all the question of its essence, its history from its Aristotelian origin and within of the philosophical question, of the extension of its field and of its limits, alongside the philosophy of language, the philosophy of science, psychologism and mathematics.

Etymology

Regarding the meaning of “logic”, coming from the Greek logiké epistémé where it signified one of the sectors of “being”, that of logos, next to ethos and phusis, in accordance with the division of philosophy in three branches, this meaning remains from the philosophical point of view a problem.

Origin and traditional basis of logic

For Hervé Barreau, Aristotle dominated by his philosophical positions the age of Greek science. An age that lasted until the Middle Ages and the Renaissance. Aristotle would not consider logic as a science but as a tool of reasoning, propaedeutic to science but without a particular object.

Kant’ developed a transcendental logic, and Hegel a dialectical logic.

Formal logic in the hands of mathematicians: the mathematization of logic in two stages.

1. Boole’s algebra
2. The logic of Morgan’s relationships.

Then the link with mathematics is too strong to isolate philosophy from pure logic.

Pierce emphasizes the general character of the oscillation relationship and with it reinterprets the Aristotelian syllogistics. He developed modern quantifiers.

Frege relieves the logic of functions with the logic of propositions thanks to the analysis of the proposition (function, argument) and the regulated use of quantifiers. First axiomatic of these two logics.

Russell and Whitehead finalize classical logic, still taught at the start of the 21st century in two parts: proposition logic and predicate logic.

Philosophical questions

The philosophical questioning of a particular science is an extension of the philosophy of science in general.

This questioning relates in particular to the discipline, its history (its mathematization, for example) and the links that this discipline maintains or not with other disciplines.

The main question remains the status of logic: What about its foundation and in particular the principle of non-contradiction? What about the principle of the excluded third party? The usual distinction between the theory of judgment and the theory of syllogism will also have to be justified.

Articulation of logic with modal logic (possible, impossible, necessary)?

Is the current formal logic, a tool for all scientific disciplines and in particular mathematics, fruitful in other fields of knowledge?

The nature of the new logics proposed by certain disciplines: Chronosophy as a logic of time by analogy to geometry which would be a logic of space?

Impacts on the logic of Gödel’s work on consistency and completeness in mathematics.

Concerning the philosophical approach of logic relating to the question of the definition of its essence, it is necessary, among other things, to approach the contribution of the philosopher Martin Heidegger.