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'On the Philosophy of Logic', 'Introduction to Mathematical Logic' and 'Sentences'
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7 ideas
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
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To determine the patterns in logic, one must identify its 'building blocks' [Walicki]
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5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
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Classical logic is: excluded middle, non-contradiction, contradictions imply all, disjunctive syllogism [Fisher]
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5. Theory of Logic / C. Ontology of Logic / 2. Platonism in Logic
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Logic formalizes how we should reason, but it shouldn't determine whether we are realists [Fisher]
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
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A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki]
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5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
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The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki]
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5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
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A compact axiomatisation makes it possible to understand a field as a whole [Walicki]
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Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki]
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