Logic before mathematisation

"Everything logical is a form in which truth is preserved," — Aristotle (from the "Organon," the "Analytics").


"Logic is the anatomy of thought," — Joseph Butler.

"Logic is the science that shows how thinking is to be correctly carried out," — Georg Wilhelm Friedrich Hegel (from the "Encyclopedia of the Philosophical Sciences," the section "The Science of Logic").

"If I have seen further, it is by standing on the shoulders of Giants." Isaac Newton

Logic is the first step toward the ability to establish causal relations, to posit them, and to control them.

Determinacy, non-contradiction, consistency, and groundedness are obligatory qualities of correct thinking. These qualities carry the force of laws of correct thinking.

Logic makes it possible both to expose contradictions and to create them.

The complication and simplification of form is periodic, while the essence remains constant. One way or another, in generalizing we arrive at the simpler; in analyzing, in complicating, we arrive once more at the more complex.

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A brief academic note. The three opening attributions trace a single thread through the history of logic: Aristotle's claim, in the Organon, that logical form is precisely what preserves truth across an inference — the seed of what modern logicians call truth-preservation under valid deduction; Butler's image of logic as an "anatomy" of thought, echoing the structuralist impulse also found in Kant and later formalized in the notion (concept) of logical form as distinct from content; and Hegel's redefinition of logic, in the Encyclopedia, as not merely a descriptive but a normative science — one that shows how thinking ought to proceed, a property (feature) that separates formal logic from purely empirical psychology of reasoning (a distinction later sharpened by Frege in his critique of psychologism in the foundations of logic).