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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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9216
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Each area of enquiry, and its source, has its own distinctive type of necessity [Fine,K]
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Full Idea:
The three sources of necessity - the identity of things, the natural order, and the normative order - have their own peculiar forms of necessity. The three main areas of human enquiry - metaphysics, science and ethics - each has its own necessity.
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From:
Kit Fine (The Varieties of Necessity [2002], 6)
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A reaction:
I would treat necessity in ethics with caution, if it is not reducible to natural or metaphysical necessity. Fine's proposal is interesting, but I did not find it convincing, especially in its view that metaphysical necessity doesn't intrude into nature.
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23279
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It is important that a person can change their character, and not just be successive 'selves' [Williams,B]
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Full Idea:
I want to emphasise the basic importance of the ordinary idea of a self or person which undergoes changes of character, as opposed to dissolving a changing person into a series of 'selves'.
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From:
Bernard Williams (Persons, Character and Morality [1976], II)
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A reaction:
[compressed] He mentions Derek Parfit for the rival view. Williams has the Aristotelian view, that a person has an essential nature, which endures through change, and explains that change. But that needs some non-essential character traits.
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23278
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For utilitarians states of affairs are what have value, not matter who produced them [Williams,B]
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Full Idea:
The basic bearer of value for Utilitarianism is the state of affairs, and hence, when the relevant causal differences have been allowed for, it cannot make any further difference who produces a given state of affairs.
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From:
Bernard Williams (Persons, Character and Morality [1976], I)
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A reaction:
Which is morally better, that I water your bed of flowers, or that it rains? Which is morally better, that I water them from love, or because you threaten me with a whip?
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9215
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Causation is easier to disrupt than logic, so metaphysics is part of nature, not vice versa [Fine,K]
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Full Idea:
It would be harder to break P-and-Q implying P than the connection between cause and effect. This difference in strictness means it is more plausible that natural necessities include metaphysical necessities, than vice versa.
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From:
Kit Fine (The Varieties of Necessity [2002], 6)
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A reaction:
I cannot see any a priori grounds for the claim that causation is more easily disrupted than logic. It seems to be based on the strategy of inferring possibilities from what can be imagined, which seems to me to lead to wild misunderstandings.
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