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19463
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Induction assumes some uniformity in nature, or that in some respects the future is like the past [Ayer]
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Full Idea:
In all inductive reasoning we make the assumption that there is a measure of uniformity in nature; or, roughly speaking, that the future will, in the appropriate respects, resemble the past.
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From:
A.J. Ayer (The Problem of Knowledge [1956], 2.viii)
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A reaction:
I would say that nature is 'stable'. Nature changes, so a global assumption of total uniformity is daft. Do we need some global uniformity assumptions, if the induction involved is local? I would say yes. Are all inductions conditional on this?
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10180
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Mathematicians do not study objects, but relations between objects [Poincaré]
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Full Idea:
Mathematicians do not study objects, but relations between objects; it is a matter of indifference if the objects are replaced by others, provided the relations do not change. They are interested in form alone, not matter.
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From:
Henri Poincaré (Science and Hypothesis [1902], p.20), quoted by E Reck / M Price - Structures and Structuralism in Phil of Maths §6
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A reaction:
This connects modern structuralism with Aritotle's interest in the 'form' of things. Contrary to the views of the likes of Frege, it is hard to see that the number '7' has any properties at all, apart from its relations. A daffodil would do just as well.
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19459
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To say 'I am not thinking' must be false, but it might have been true, so it isn't self-contradictory [Ayer]
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Full Idea:
To say 'I am not thinking' is self-stultifying since if it is said intelligently it must be false: but it is not self-contradictory. The proof that it is not self-contradictory is that it might have been false.
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From:
A.J. Ayer (The Problem of Knowledge [1956], 2.iii)
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A reaction:
If it doesn't imply a contradiction, then it is not a necessary truth, which is what it is normally taken to be. Is 'This is a sentence' necessarily true? It might not have been one, if the rules of English syntax changed recently.
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19460
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'I know I exist' has no counterevidence, so it may be meaningless [Ayer]
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Full Idea:
If there is no experience at all of finding out that one is not conscious, or that one does not exist, ..it is tempting to say that sentences like 'I exist', 'I am conscious', 'I know that I exist' do not express genuine propositions.
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From:
A.J. Ayer (The Problem of Knowledge [1956], 2.iii)
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A reaction:
This is, of course, an application of the somewhat discredited verification principle, but the fact that strictly speaking the principle has been sort of refuted does not mean that we should not take it seriously, and be influenced by it.
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19462
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Induction passes from particular facts to other particulars, or to general laws, non-deductively [Ayer]
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Full Idea:
Inductive reasoning covers all cases in which we pass from a particular statement of fact, or set of them, to a factual conclusion which they do not formally entail. The inference may be to a general law, or by analogy to another particular instance.
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From:
A.J. Ayer (The Problem of Knowledge [1956], 2.viii)
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A reaction:
My preferred definition is 'learning from experience' - which I take to be the most rational behaviour you could possibly imagine. I don't think a definition should be couched in terms of 'objects' or 'particulars'.
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