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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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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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6217
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Natural law is supplied to the human mind by reality and human nature [Cumberland]
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Full Idea:
Some truths of natural law, concerning guides to moral good and evil, and duties not laid down by civil law and government, are necessarily supplied ot the human mind by the nature of things and of men.
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From:
Richard Cumberland (De Legibus Naturae [1672], Ch.I.I)
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A reaction:
I agree that some moral truths have the power of self-evidence. If you say they are built into the mind, we now ask what did the building, and evolution is the only answer, and hence we distance ourselves from the truths, seeing them as strategies.
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6221
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If there are different ultimate goods, there will be conflicting good actions, which is impossible [Cumberland]
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Full Idea:
If there be posited different ultimate ends, whose causes are opposed to each other, then there will be truly good actions likewise opposed to each other, which is impossible.
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From:
Richard Cumberland (De Legibus Naturae [1672], Ch.V.XVI)
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A reaction:
A very interesting argument for there being one good rather than many, and an argument which I don't recall in any surviving Greek text. A response might be to distinguish between what is 'right' and what is 'good'. See David Ross.
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6220
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The happiness of all contains the happiness of each, and promotes it [Cumberland]
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Full Idea:
The common happiness of all contains the greatest happiness for each, and most effectively promotes it. …There is no path leading anyone to his own happiness, other than the path which leads all to the common happiness.
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From:
Richard Cumberland (De Legibus Naturae [1672], Ch.I.VI)
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A reaction:
I take this as a revolutionary idea, which leads to utilitarianism. It is doing what seemed to the Greeks unthinkable, which is combining hedonism with altruism. There is no proof for it, but it is a wonderful clarion call for building a civil society.
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6216
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Natural law is immutable truth giving moral truths and duties independent of society [Cumberland]
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Full Idea:
Natural law is certain propositions of immutable truth, which guide voluntary actions about the choice of good and avoidance of evil, and which impose an obligation to act, even without regard to civil laws, and ignoring compacts of governments.
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From:
Richard Cumberland (De Legibus Naturae [1672], Ch.I.I)
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A reaction:
Not a popular view, but I am sympathetic. If you are in a foreign country and find a person lying in pain, there is a terrible moral deficiency in anyone who just ignores such a thing. No legislation can take away a person's right of self-defence.
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