6408
|
Russell needed three extra axioms to reduce maths to logic: infinity, choice and reducibility [Grayling]
|
|
Full Idea:
In order to deduce the theorems of mathematics from purely logical axioms, Russell had to add three new axioms to those of standards logic, which were: the axiom of infinity, the axiom of choice, and the axiom of reducibility.
|
|
From:
A.C. Grayling (Russell [1996], Ch.2)
|
|
A reaction:
The third one was adopted to avoid his 'barber' paradox, but many thinkers do not accept it. The interesting question is why anyone would 'accept' or 'reject' an axiom.
|
23896
|
We see our character as a restricting limit, but also as an unshakable support [Weil]
|
|
Full Idea:
Our character appears to us as a limit by which we do not want to be imprisoned, …but also as a support that we want to believe is unshakable.
|
|
From:
Simone Weil (On the Concept of Character [1941], p.100)
|
|
A reaction:
A nice perception. It is fairly easy to criticise, or even laugh at, one's own actions, but extremely hard to criticise our own character. Maybe we all wish we were more determined in our projects, but not much else.
|
23893
|
We don't see character in a single moment, but only over a period of time [Weil]
|
|
Full Idea:
Character is constant over a period of time; the way a person is at a single moment does not at all reflect the character of this person. We do, however, concede that character changes.
|
|
From:
Simone Weil (On the Concept of Character [1941], p.98)
|
|
A reaction:
I do think, though, that there are moments in behaviour which are hugely revealing of character, even in a single remark. But I agree that most single moments do not show much.
|
23895
|
We modify our character by placing ourselves in situations, or by attending to what seems trivial [Weil]
|
|
Full Idea:
We can modify our character, by putting ourselves in circumstances that will act on us from the outside, …or by the orientation of our attention in the moments that appear most insignificant or indifferent in our lives.
|
|
From:
Simone Weil (On the Concept of Character [1941], p.99)
|
|
A reaction:
I've never seen anyone address this question (apart from Aristotle's emphasis on training habits). Choosing your source for current affairs information strikes me as very important. What you read, what you watch, who you spend time with…
|