Card 4.1.2 · Root IV — Logic

Predicate Logic

Why could two thousand years of logic not handle "every boy loves some girl"?

Predicate logic analyses the internal structure of statements — the objects, the properties and the quantities — rather than treating each statement as an unanalysed whole.

From The Coordinates of Thought by Syed Raheel Shahzad, card 4.1.2, page 184

On this card

Where it sits
The apparatus
Key figures
Connections
On Coordinates of Thought

Where it sits

Under 4.1 Formal logic. Depends on 4.1.1 Propositional logic. Feeds 4.3 Modal logic, 6.9 Philosophy of mathematics, 6.10.1 Reference.

The apparatus

Device	What it does
Predicates	Express properties and relations
Quantifiers	Express generality: ∀ for all, ∃ for some
Variables and binding	Let one quantifier govern a whole expression
Scope	Fix which quantifier governs which variable — the decisive innovation
Identity	Express sameness as part of the logic

Key figures

Figure	Dates	Tradition	Contribution
Aristotle	384–322 BCE	Greek	Syllogistic; the system this superseded
Gottlob Frege	1848–1925	Analytic	Begriffsschrift (1879); quantification and scope
Giuseppe Peano	1858–1932	Italian	Much of the surviving notation
Bertrand Russell	1872–1970	Analytic	Theory of descriptions; logic applied to natural language
Alfred Tarski	1901–1983	Polish	Formal semantics for the language
Gerhard Gentzen	1909–1945	German	Natural deduction and sequent calculus

Connections

→ 4.1, 4.1.1 · ↔ 4.3, 6.9, 6.10.1, 4.5 · ◇ logicism, formalism · ○ Modern; Table 3

→ narrower questions · ↔ questions it borders · ◇ the positions, mapped in Part III of the book · ○ the eras and comparison tables (Parts IV and V)

The full card is in the book

In The Coordinates of Thought this card goes on to a worked example that sets the answers against one case, and to where the question touches daily life — page 184.

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