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'', 'Intro to Gdel's Theorems' and 'Philosophical Analysis'
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9 ideas
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
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Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt]
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The sense of a connective comes from primitively obvious rules of inference [Rumfitt]
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5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
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The 'range' of a function is the set of elements in the output set created by the function [Smith,P]
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Two functions are the same if they have the same extension [Smith,P]
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A 'partial function' maps only some elements to another set [Smith,P]
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A 'total function' maps every element to one element in another set [Smith,P]
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An argument is a 'fixed point' for a function if it is mapped back to itself [Smith,P]
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5. Theory of Logic / E. Structures of Logic / 7. Predicates in Logic
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The Comprehension Schema says there is a property only had by things satisfying a condition [Smith,P]
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5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
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A 'theorem' of a theory is a sentence derived from the axioms using the proof system [Smith,P]
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