Combining Texts

All the ideas for 'God and Human Attributes', 'English as a Formal Language' and 'On the Foundations of Logic and Arithmetic'

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4 ideas

5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions

18779	'The' is a quantifier, like 'every' and 'a', and does not result in denotation [Montague]
	Full Idea: The expression 'The' turns out to play the role of a quantifier, in complete analogy with 'every' and 'a', and does not generate (in common with common noun phrases) denoting expressions
	From: Richard Montague (English as a Formal Language [1970], p.216), quoted by Bernard Linsky - Quantification and Descriptions 4
	A reaction: Linsky says that it is now standard to interpret definite descriptions as quantifiers

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism

17697	The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert]
	Full Idea: The standpoint of pure experience seems to me to be refuted by the objection that the existence, possible or actual, of an arbitrarily large number can never be derived through experience, that is, through experiment.
	From: David Hilbert (On the Foundations of Logic and Arithmetic [1904], p.130)
	A reaction: Alternatively, empiricism refutes infinite numbers! No modern mathematician will accept that, but you wonder in what sense the proposed entities qualify as 'numbers'.

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique

17698	Logic already contains some arithmetic, so the two must be developed together [Hilbert]
	Full Idea: In the traditional exposition of the laws of logic certain fundamental arithmetic notions are already used, for example in the notion of set, and to some extent also of number. Thus we turn in a circle, and a partly simultaneous development is required.
	From: David Hilbert (On the Foundations of Logic and Arithmetic [1904], p.131)
	A reaction: If the Axiom of Infinity is meant, it may be possible to purge the arithmetic from the logic. Then the challenge to derive arithmetic from it becomes rather tougher.

28. God / B. Proving God / 2. Proofs of Reason / c. Moral Argument

20713	God must be fit for worship, but worship abandons morally autonomy, but there is no God [Rachels, by Davies,B]
	Full Idea: Rachels argues 1) If any being is God, he must be a fitting object of worship, 2) No being could be a fitting object of worship, since worship requires the abandonment of one's role as an autonomous moral agent, so 3) There cannot be a being who is God.
	From: report of James Rachels (God and Human Attributes [1971], 7 p.334) by Brian Davies - Introduction to the Philosophy of Religion 9 'd morality'
	A reaction: Presumably Lionel Messi can be a fitting object of worship without being God. Since the problem is with being worshipful, rather than with being God, should I infer that Messi doesn't exist?