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Ideas for 'Thinking About Mathematics', 'Parts' and 'A Short History of Decay'

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4 ideas

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
8729 Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
     Full Idea: Intuitionists in mathematics deny excluded middle, because it is symptomatic of faith in the transcendent existence of mathematical objects and/or the truth of mathematical statements.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2)
     A reaction: There are other problems with excluded middle, such as vagueness, but on the whole I, as a card-carrying 'realist', am committed to the law of excluded middle.
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
12876 Philosophy is stuck on the Fregean view that an individual is anything with a proper name [Simons]
     Full Idea: Modern philosophy is still under the spell of Frege's view that an individual is anything that has a proper name. (Note: But not only are empty names now recognised, but some are aware of the existence of plural reference).
     From: Peter Simons (Parts [1987], 8.1)
     A reaction: Presumably every electron in the universe is an individual, and every (finite) number which has never been named has a pretty clear identity. Presumably Pegasus, John Doe, and 'the person in the kitchen' have to be accommodated.
5. Theory of Logic / G. Quantification / 6. Plural Quantification
12845 Some natural languages don't distinguish between singular and plural [Simons]
     Full Idea: The syntactic distinction between singular and plural is not a universal feature of natural languages. Chinese manages nicely without it, and Sanskrit makes a tripartite distinction between singular, dual, and plural (more than two).
     From: Peter Simons (Parts [1987], 4.3)
     A reaction: Simons is mounting an attack on the way in which modern philosophy and logic has been mesmerised by singular terms and individuated objects. Most people seem now to agree with Simons. There is stuff, as well as plurals.
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
19632 An axiom has no more authority than a frenzy [Cioran]
     Full Idea: This earth is a place where can confirm anything with an equal likelihood: here axioms and frenzies are interchangeable.
     From: E.M. Cioran (A Short History of Decay [1949], 3)
     A reaction: A perceptive and poetic expression of the modern anti-Euclidean and anti-Fregean view of axioms, as purely formal features of a model or system.