|
10180
|
Mathematicians do not study objects, but relations between objects [Poincaré]
|
|
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.
|
|
From:
Henri Poincaré (Science and Hypothesis [1902], p.20), quoted by E Reck / M Price - Structures and Structuralism in Phil of Maths §6
|
|
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.
|
|
23279
|
It is important that a person can change their character, and not just be successive 'selves' [Williams,B]
|
|
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'.
|
|
From:
Bernard Williams (Persons, Character and Morality [1976], II)
|
|
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.
|
|
23278
|
For utilitarians states of affairs are what have value, not matter who produced them [Williams,B]
|
|
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.
|
|
From:
Bernard Williams (Persons, Character and Morality [1976], I)
|
|
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?
|