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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23647
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Objects have an essential constitution, producing its qualities, which we are too ignorant to define [Reid]
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Full Idea:
Individuals and objects have a real essence, or constitution of nature, from which all their qualities flow: but this essence our faculties do not comprehend. They are therefore incapable of definition.
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From:
Thomas Reid (Essays on Intellectual Powers 4: Conception [1785], 1)
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A reaction:
Aha - he's one of us! I prefer the phrase 'essential nature' of an object, which is understood, I think, by everyone. I especially like the last bit, directed at those who mistakenly think that Aristotle identified the essence with the definition.
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23646
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Reference is by name, or a term-plus-circumstance, or ostensively, or by description [Reid]
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Full Idea:
An individual is expressed by a proper name, or by a general word joined to distinguishing circumstances; if unknown, it may be pointed out to the senses; when beyond the reach of the senses it may be picked out by an imperfect but true description.
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From:
Thomas Reid (Essays on Intellectual Powers 4: Conception [1785], 1)
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A reaction:
[compressed] If Putnam, Kripke and Donnellan had read this paragraph they could have save themselves a lot of work! I take reference to be the activity of speakers and writers, and these are the main tools of the trade.
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