8 ideas
17831 | Cantor gives informal versions of ZF axioms as ways of getting from one set to another [Cantor, by Lake] |
Full Idea: Cantor gives informal versions of the axioms of ZF as ways of getting from one set to another. | |
From: report of George Cantor (Later Letters to Dedekind [1899]) by John Lake - Approaches to Set Theory 1.6 | |
A reaction: Lake suggests that it should therefore be called CZF. |
11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
Full Idea: If a designated conclusion follows from the premisses, but the argument involves two howlers which cancel each other out, then the moral is that the path an argument takes from premisses to conclusion does matter to its logical evaluation. | |
From: Ian Rumfitt ("Yes" and "No" [2000], II) | |
A reaction: The drift of this is that our view of logic should be a little closer to the reasoning of ordinary language, and we should rely a little less on purely formal accounts. |
11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
Full Idea: If 'and' and 'but' really are alike in sense, in what might that likeness consist? Some philosophers of classical logic will reply that they share a sense by virtue of sharing a truth table. | |
From: Ian Rumfitt ("Yes" and "No" [2000]) | |
A reaction: This is the standard view which Rumfitt sets out to challenge. |
11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
Full Idea: A connective will possess the sense that it has by virtue of its competent users' finding certain rules of inference involving it to be primitively obvious. | |
From: Ian Rumfitt ("Yes" and "No" [2000], III) | |
A reaction: Rumfitt cites Peacocke as endorsing this view, which characterises the logical connectives by their rules of usage rather than by their pure semantic value. |
11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |
Full Idea: The standard view is that affirming not-A is more complex than affirming the atomic sentence A itself, with the latter determining its sense. But we could learn 'not' directly, by learning at once how to either affirm A or reject A. | |
From: Ian Rumfitt ("Yes" and "No" [2000], IV) | |
A reaction: [compressed] This seems fairly anti-Fregean in spirit, because it looks at the psychology of how we learn 'not' as a way of clarifying what we mean by it, rather than just looking at its logical behaviour (and thus giving it a secondary role). |
21093 | Friendship without community spirit misses out on the main part of virtue [Hume] |
Full Idea: A man who is only susceptible of friendship, without public spirit or a regard to the community, is deficient in the most material part of virtue. | |
From: David Hume (That Politics may be reduced to a Science [1750], p.21) | |
A reaction: I think this is aimed at the epicureans. If the highest virtues are focused on one's friends that can easily lead to injustice, because it can tolerate prejudice against people who are very unlike one's friends. |
21091 | It would be absurd if even a free constitution did not impose restraints, for the public good [Hume] |
Full Idea: A republican and free form of government would be an obvious absurdity, if the particular checks and controls, provided by the constitution, had really no influence, and made it not the interest, even of bad men, to act for the public good. | |
From: David Hume (That Politics may be reduced to a Science [1750], p.14) | |
A reaction: Presumably if you attain absolute power you can write any old constitution you like (Clause 1: the presidency is for life). But there does seem much point in doing it - unless it is to facilitate the use of the law for persecutions. |
21092 | Nobility either share in the power of the whole, or they compose the power of the whole [Hume] |
Full Idea: A nobility may possess power in two different ways. Either every nobleman shares the power as part of the whole body, or the whole body enjoys the power as composed of parts, which each have a distinct power and authority. | |
From: David Hume (That Politics may be reduced to a Science [1750], p.15) | |
A reaction: He says the first type is found in Venice, and is preferable to the second type, which is found in Poland. Presumably in the shared version there is some restraint on depraved nobles. The danger is each noble being an autocrat. |