Combining Philosophers

Ideas for Hermarchus, Rescher,N/Oppenheim,P and Timothy Williamson

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

display all the ideas for this combination of philosophers

---

9 ideas

5. Theory of Logic / A. Overview of Logic / 3. Value of Logic

6858	Formal logic struck me as exactly the language I wanted to think in [Williamson]
	Full Idea: As soon as I started learning formal logic, that struck me as exactly the language that I wanted to think in.
	From: Timothy Williamson (Interview with Baggini and Stangroom [2001])
	A reaction: It takes all sorts… It is interesting that formal logic might be seen as having the capacity to live up to such an aspiration. I don't think the dream of an ideal formal language is dead, though it will never encompass all of reality. Poetic truth.

5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=

21611	Formal semantics defines validity as truth preserved in every model [Williamson]
	Full Idea: An aim of formal semantics is to define in mathematical terms a set of models such that an argument is valid if and only if it preserves truth in every model in the set, for that will provide us with a precise standard of validity.
	From: Timothy Williamson (Vagueness [1994], 5.3)

5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence

21606	'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

21605	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?

5. Theory of Logic / G. Quantification / 1. Quantification

18492	Not all quantification is either objectual or substitutional [Williamson]
	Full Idea: We should not assume that all quantification is either objectual or substitutional.
	From: Timothy Williamson (Truthmakers and Converse Barcan Formula [1999], p.262)
	A reaction: [see Prior 1971:31-4] He talks of quantifying into sentence position.

5. Theory of Logic / G. Quantification / 4. Substitutional Quantification

15136	Substitutional quantification is metaphysical neutral, and equivalent to a disjunction of instances [Williamson]
	Full Idea: If quantification into sentence position is substitutional, then it is metaphysically neutral. A substitutionally interpreted 'existential' quantification is semantically equivalent to the disjunction (possibly infinite) of its substitution instances.
	From: Timothy Williamson (Truthmakers and Converse Barcan Formula [1999], §2)
	A reaction: Is it not committed to the disjunction, just as the objectual reading commits to objects? Something must make the disjunction true. Or is it too verbal to be about reality?

5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification

15138	Not all quantification is objectual or substitutional [Williamson]
	Full Idea: We should not assume that all quantification is objectual or substitutional.
	From: Timothy Williamson (Truthmakers and Converse Barcan Formula [1999], §2)

5. Theory of Logic / H. Proof Systems / 4. Natural Deduction

21612	Or-elimination is 'Argument by Cases'; it shows how to derive C from 'A or B' [Williamson]
	Full Idea: Argument by Cases (or or-elimination) is the standard way of using disjunctive premises. If one can argue from A and some premises to C, and from B and some premises to C, one can argue from 'A or B' and the combined premises to C.
	From: Timothy Williamson (Vagueness [1994], 5.3)

5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')

21599	A sorites stops when it collides with an opposite sorites [Williamson]
	Full Idea: A sorites paradox is stopped when it collides with a sorites paradox going in the opposite direction. That account will not strike a logician as solving the sorites paradox.
	From: Timothy Williamson (Vagueness [1994], 3.3)