Combining Texts

Ideas for 'Defending the Axioms', 'Introduction to Mathematical Logic' and 'Phaedo'

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8 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic

17741

To determine the patterns in logic, one must identify its 'building blocks' [Walicki]

5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism

17620

Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy]

5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models

17747

A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki]

5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems

17748

The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki]

5. Theory of Logic / K. Features of Logics / 1. Axiomatisation

17605

Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy]

17625

If two mathematical themes coincide, that suggest a single deep truth [Maddy]

17761

A compact axiomatisation makes it possible to understand a field as a whole [Walicki]

17763

Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki]