Combining Texts

All the ideas for 'The Logic of Boundaryless Concepts', 'Anselm's Argument' and 'Truth and Probability'

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5 ideas

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

9390	Logic guides thinking, but it isn't a substitute for it [Rumfitt]
	Full Idea: Logic is part of a normative theory of thinking, not a substitute for thinking.
	From: Ian Rumfitt (The Logic of Boundaryless Concepts [2007], p.13)
	A reaction: There is some sort of logicians' dream, going back to Leibniz, of a reasoning engine, which accepts propositions and outputs inferences. I agree with this idea. People who excel at logic are often, it seems to me, modest at philosophy.

9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects

9389	Vague membership of sets is possible if the set is defined by its concept, not its members [Rumfitt]
	Full Idea: Vagueness in respect of membership is consistency with determinacy of the set's identity, so long as a set's identity is taken to consist, not in its having such-and-such members, but in its being the extension of a concept.
	From: Ian Rumfitt (The Logic of Boundaryless Concepts [2007], p.5)
	A reaction: I find this view of sets much more appealing than the one that identifies a set with its members. The empty set is less of a problem, as well as non-existents. Logicians prefer the extensional view because it is tidy.

10. Modality / B. Possibility / 8. Conditionals / d. Non-truthfunction conditionals

13766	'If' is the same as 'given that', so the degrees of belief should conform to probability theory [Ramsey, by Ramsey]
	Full Idea: Ramsey suggested that 'if', 'given that' and 'on the supposition that' come to the same thing, and that the degrees of belief in the antecedent should then conform to probability theory.
	From: report of Frank P. Ramsey (Truth and Probability [1926]) by Frank P. Ramsey - Law and Causality B
	A reaction: [compressed]

14. Science / C. Induction / 6. Bayes's Theorem

19143	Ramsey gave axioms for an uncertain agent to decide their preferences [Ramsey, by Davidson]
	Full Idea: Ramsey gave an axiomatic treatment of preference in the face of uncertainty, when applied to a particular agent.
	From: report of Frank P. Ramsey (Truth and Probability [1926]) by Donald Davidson - Truth and Predication 2
	A reaction: This is evidently the beginnings of Bayesian decision theory.

28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof

1422	God's existence is either necessary or impossible, and no one has shown that the concept of God is contradictory [Malcolm]
	Full Idea: God's existence is either impossible or necessary. It can be the former only if the concept of such a being is self-contradictory or in some way logically absurd. Assuming that this is not so, it follows that He necessarily exists.
	From: Norman Malcolm (Anselm's Argument [1959], §2)
	A reaction: The concept of God suggests paradoxes of omniscience, omnipotence and free will, so self-contradiction seems possible. How should we respond if the argument suggests God is necessary, but evidence suggests God is highly unlikely?