Combining Texts

All the ideas for 'Frege's Theory of Numbers', 'The Bacchae' and 'Logic and Conversation'

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6 ideas

1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
Our ancient beliefs can never be overthrown by subtle arguments [Euripides]
     Full Idea: Teiresias: We have no use for theological subtleties./ The beliefs we have inherited, as old as time,/ Cannot be overthrown by any argument,/ Nor by the most inventive ingenuity.
     From: Euripides (The Bacchae [c.407 BCE], 201)
     A reaction: [trans. Philip Vellacott (Penguin)] Compare Idea 8243. While very conservative societies have amazing resilience in maintaining traditional beliefs, modern culture eats into them, not directly by argument, but by arguments at fifth remove.
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
     Full Idea: In Parsons's demonstrative model of counting, '1' means the first, and counting says 'the first, the second, the third', where one is supposed to 'tag' each object exactly once, and report how many by converting the last ordinal into a cardinal.
     From: report of Charles Parsons (Frege's Theory of Numbers [1965]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3
     A reaction: This sounds good. Counting seems to rely on that fact that numbers can be both ordinals and cardinals. You don't 'convert' at the end, though, because all the way you mean 'this cardinality in this order'.
10. Modality / B. Possibility / 8. Conditionals / c. Truth-function conditionals
Conditionals are truth-functional, but we must take care with misleading ones [Grice, by Edgington]
     Full Idea: Grice argued that the truth-functional account of conditionals can withstand objections, provided that we are careful to distinguish the false from the misleadingly true.
     From: report of H. Paul Grice (Logic and Conversation [1975]) by Dorothy Edgington - Do Conditionals Have Truth Conditions? 2
The odd truth table for material conditionals is explained by conversational conventions [Grice, by Fisher]
     Full Idea: According to Grice, it is the rules that govern conversation beyond the merely logical that account for the counter-intuitiveness of the truth table for the material conditional.
     From: report of H. Paul Grice (Logic and Conversation [1975]) by Jennifer Fisher - On the Philosophy of Logic 8.I
     A reaction: There is a conversational rule which says that replies should normally relevant to context. It would be nice if logical implications were also relevant to context.
Conditionals might remain truth-functional, despite inappropriate conversational remarks [Edgington on Grice]
     Full Idea: Grice defended the truth-functional account of conditionals, noting the gap between what we are justified in believing and what is appropriate to say. .But the problem arises at the level of belief, not at the level of inappropriate conversational remarks
     From: comment on H. Paul Grice (Logic and Conversation [1975]) by Dorothy Edgington - Conditionals 17.1.3
10. Modality / B. Possibility / 8. Conditionals / f. Pragmatics of conditionals
A person can be justified in believing a proposition, though it is unreasonable to actually say it [Grice, by Edgington]
     Full Idea: Grice drew attention to situations in which a person is justified in believing a proposition, which would nevertheless by an unreasonable thing for the person to say, in normal circumstances. I think he is right about disjunction and negated conjunctions.
     From: report of H. Paul Grice (Logic and Conversation [1975]) by Dorothy Edgington - Conditionals (Stanf) 2.4
     A reaction: Edgington considers Grice's ideas of implicature as of permanent value, especially as a clarification of 1950s ordinary language philosophy.