3 ideas
18244 | I say the irrational is not the cut itself, but a new creation which corresponds to the cut [Dedekind] |
Full Idea: Of my theory of irrationals you say that the irrational number is nothing else than the cut itself, whereas I prefer to create something new (different from the cut), which corresponds to the cut. We have the right to claim such a creative power. | |
From: Richard Dedekind (Letter to Weber [1888], 1888 Jan), quoted by Stewart Shapiro - Philosophy of Mathematics 5.4 | |
A reaction: Clearly a cut will not locate a unique irrational number, so something more needs to be done. Shapiro remarks here that for Dedekind numbers are objects. |
7946 | The memory criterion has a problem when one thing branches into two things [Williams,B, by Macdonald,C] |
Full Idea: The memory criterion for personal identity permits 'branching' (where two things can later meet the criteria of persistence of a single earlier thing), which presents it with serious problems. | |
From: report of Bernard Williams (Personal Identity and Individuation [1956]) by Cynthia Macdonald - Varieties of Things Ch.4 | |
A reaction: Of course, any notion of personal identity would have serious problem if people could branch into two, like fissioning amoeba. If that happened, we probably wouldn't have had a strong notion of personal identity in the first place. See Parfit. |
5655 | Happiness is not satisfaction of desires, but fulfilment of values [Bradley, by Scruton] |
Full Idea: For Bradley, the happiness of the individual is not to be understood in terms of his desires and needs, but rather in terms of his values - which is to say, in terms of those of his desires which he incorporates into his self. | |
From: report of F.H. Bradley (Ethical Studies [1876]) by Roger Scruton - Short History of Modern Philosophy Ch.16 | |
A reaction: Good. Bentham will reduce the values to a further set of desires, so that a value is a complex (second-level?) desire. I prefer to think of values as judgements, but I like Scruton's phrase of 'incorporating into his self'. Kant take note (Idea 1452). |