Combining Philosophers

Ideas for Douglas Lackey, Michal Walicki and Friedrich Jacobi

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7 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 / 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

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]

5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / b. Cantor's paradox

21554

Sets always exceed terms, so all the sets must exceed all the sets [Lackey]

5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / c. Burali-Forti's paradox

21553

It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey]