Combining Texts

All the ideas for 'Conditionals', 'Paradox without Self-Reference' and 'Letters to Varignon'

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6 ideas

5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox

9138	An infinite series of sentences asserting falsehood produces the paradox without self-reference [Yablo, by Sorensen]
	Full Idea: Banning self-reference is too narrow to avoid the liar paradox. With 1) all the subsequent sentences are false, 2) all the subsequent sentences are false, 3) all the subsequent... the paradox still arises. Self-reference is a special case of this.
	From: report of Stephen Yablo (Paradox without Self-Reference [1993]) by Roy Sorensen - Vagueness and Contradiction 11.1
	A reaction: [Idea 9137 pointed out that the ban was too narrow. Sorensen p.168 explains why this one is paradoxical] This is a nice example of progress in philosophy, since the Greeks would have been thrilled with this idea (unless they knew it, but it was lost).

10. Modality / B. Possibility / 8. Conditionals / a. Conditionals

13768	Validity can preserve certainty in mathematics, but conditionals about contingents are another matter [Edgington]
	Full Idea: If your interest in logic is confined to applications to mathematics or other a priori matters, it is fine for validity to preserve certainty, ..but if you use conditionals when arguing about contingent matters, then great caution will be required.
	From: Dorothy Edgington (Conditionals [2001], 17.2.1)

10. Modality / B. Possibility / 8. Conditionals / b. Types of conditional

13770	There are many different conditional mental states, and different conditional speech acts [Edgington]
	Full Idea: As well as conditional beliefs, there are conditional desires, hopes, fears etc. As well as conditional statements, there are conditional commands, questions, offers, promises, bets etc.
	From: Dorothy Edgington (Conditionals [2001], 17.3.4)

10. Modality / B. Possibility / 8. Conditionals / c. Truth-function conditionals

13764	Are conditionals truth-functional - do the truth values of A and B determine the truth value of 'If A, B'? [Edgington]
	Full Idea: Are conditionals truth-functional - do the truth values of A and B determine the truth value of 'If A, B'? Are they non-truth-functional, like 'because' or 'before'? Do the values of A and B, in some cases, leave open the value of 'If A,B'?
	From: Dorothy Edgington (Conditionals [2001], 17.1)
	A reaction: I would say they are not truth-functional, because the 'if' asserts some further dependency relation that goes beyond the truth or falsity of A and B. Logical ifs, causal ifs, psychological ifs... The material conditional ⊃ is truth-functional.

13765	'If A,B' must entail ¬(A & ¬B); otherwise we could have A true, B false, and If A,B true, invalidating modus ponens [Edgington]
	Full Idea: If it were possible to have A true, B false, and If A,B true, it would be unsafe to infer B from A and If A,B: modus ponens would thus be invalid. Hence 'If A,B' must entail ¬(A & ¬B).
	From: Dorothy Edgington (Conditionals [2001], 17.1)
	A reaction: This is a firm defence of part of the truth-functional view of conditionals, and seems unassailable. The other parts of the truth table are open to question, though, if A is false, or they are both true.

27. Natural Reality / G. Biology / 3. Evolution

19414	Men are related to animals, which are related to plants, then to fossils, and then to the apparently inert [Leibniz]
	Full Idea: Men are related to animals, these to plants, and the latter directly to fossils which will be linked in their turn to bodies which the senses and the imagination represent to us as perfectly dead and formless.
	From: Gottfried Leibniz (Letters to Varignon [1702], 1702)
	A reaction: Leibniz would be a bit surprised to find the way in which this has turned out to be largely true, since he is basing it on his picture of a hierarchy of monads. Nevertheless, the idea that we are all related wasn't invented in 1859.