Combining Texts

Ideas for 'Thinking About Mathematics', 'Review of 'Aenesidemus'' and 'Vagueness'

unexpand these ideas     |    start again     |     choose another area for these texts

display all the ideas for this combination of texts


3 ideas

5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
'Bivalence' is the meta-linguistic principle that 'A' in the object language is true or false [Williamson]
     Full Idea: The meta-logical law of excluded middle is the meta-linguistic principle that any statement 'A' in the object language is either truth or false; it is now known as the principle of 'bivalence'.
     From: Timothy Williamson (Vagueness [1994], 5.2)
     A reaction: [He cites Henryk Mehlberg 1958] See also Idea 21605. Without this way of distinguishing bivalence from excluded middle, most discussions of them strikes me as shockingly lacking in clarity. Personally I would cut the normativity from this one.
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
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.
Excluded Middle is 'A or not A' in the object language [Williamson]
     Full Idea: The logical law of excluded middle (now the standard one) is the schema 'A or not A' in the object-language.
     From: Timothy Williamson (Vagueness [1994], 5.2)
     A reaction: [He cites Henryk Mehlberg 1958] See Idea 21606. The only sensible way to keep Excluded Middle and Bivalence distinct. I would say: (meta-) only T and F are available, and (object) each proposition must have one of them. Are they both normative?