PHILOS 146 Lecture Notes - Lecture 19: George Boolos, Equinumerosity, Lambda Calculus
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The property r that something has iff x is not in the extension of r b. i. 1. Rx iff x-eext(r: frege"s logicism, analyticity of arithmetic a. i. Provable from general logical laws and definitions: platonism: the truths of arithmetic are objective and concern a realm of independently existing objects (the natural numbers, neo-fregean logicism agrees with principles of frege"s logicism, abstraction principles a. i. Over whatever entities @ and b stand for (e. g. objects, concepts, etc. ) a. ii. First order - (@ and b are variables over objects) a. ii. 1. a. a. ii. 1. a. i. a. ii. 1. a. ii. a. ii. 1. a. iii. dir(a)=dir(b) iff a || b dir() = s. Defining direction by abstraction over an equivalence relation on the lines. Defining identity conditions for a new set of objects. For frege thinks we need to a. ii. 1. a. iii. 1. fix the sense of numerical identities a. ii. 2. Second order - (@ and b are variables over concepts) a. ii. 2. a. a. ii. 2. b. a. ii. 2. c.
