display all the ideas for this combination of philosophers
4 ideas
| 18883 | Any equivalence relation among similar things allows the creation of an abstractum [Simons] |
| Full Idea: Whenever we have an equivalence relation among things - such as similarity in a certain respect - we can abstract under the equivalence and consider the abstractum. | |
| From: Peter Simons (Modes of Extension: comment on Fine [2008], p.19) | |
| A reaction: This strikes me as dressing up old-fashioned psychological abstractionism in the respectable clothing of Fregean equivalences (such as 'directions'). We can actually do what Simons wants without the precision of partitioned equivalence classes. |
| 18884 | Abstraction is usually seen as producing universals and numbers, but it can do more [Simons] |
| Full Idea: Abstraction as a cognitive tool has been associated predominantly with the metaphysics of universals and of mathematical objects such as numbers. But it is more widely applicable beyond this standard range. I commend its judicious use. | |
| From: Peter Simons (Modes of Extension: comment on Fine [2008], p.21) | |
| A reaction: Personally I think our view of the world is founded on three psychological principles: abstraction, idealisation and generalisation. You can try to give them rigour, as 'equivalence classes', or 'universal quantifications', if it makes you feel better. |
| 9819 | Psychologism blunders in focusing on concept-formation instead of delineating the concepts [Dummett on Husserl] |
| Full Idea: Husserl substitutes his account of the process of concept-formation for a delineation of the concept. It is above all in making this substitution that psychologism is objectionable (and Frege opposed it so vehemently). | |
| From: comment on Edmund Husserl (Philosophy of Arithmetic [1894]) by Michael Dummett - Frege philosophy of mathematics Ch.2 | |
| A reaction: While this is a powerful point which is a modern orthodoxy, it hardly excludes a study of concept-formation from being of great interest for other reasons. It may not appeal to logicians, but it is crucial part of the metaphysics of nature. |
| 9851 | Husserl wanted to keep a shadowy remnant of abstracted objects, to correlate them [Dummett on Husserl] |
| Full Idea: Husserl saw that abstracted units, though featureless, must in some way retain their distinctness, some shadowy remnant of their objects. So he wanted to correlate like-numbered sets, not just register their identity, but then abstractionism fails. | |
| From: comment on Edmund Husserl (Philosophy of Arithmetic [1894]) by Michael Dummett - Frege philosophy of mathematics Ch.12 | |
| A reaction: Abstractionism is held to be between the devil and the deep blue sea, of depending on units which are identifiable, when they are defined as devoid of all individuality. We seem forced to say that the only distinction between them is countability. |