Combining Texts

Ideas for 'fragments/reports', 'The Possibility of Metaphysics' and 'Remarks on the definition and nature of mathematics'

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2 ideas

18. Thought / E. Abstraction / 1. Abstract Thought
Abstractions are non-spatial, or dependent, or derived from concepts [Lowe]
     Full Idea: There are three conceptions of abstractness: 1) non-spatial entities, the opposite of 'concrete' (e.g. numbers and universals); 2) an entity logically incapable of a separate existence (e.g. an apple's colour); 3) Fregean abstractions from concepts.
     From: E.J. Lowe (The Possibility of Metaphysics [1998], 10.1)
     A reaction: [Lowe p.218 explains the third one] Lowe rejects the third one, and it is a moot point whether the second one could actually be classed as an entity (do they have identity-conditions?), so the big issue is the first one.
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
You can think of a direction without a line, but a direction existing with no lines is inconceivable [Lowe]
     Full Idea: Although one can separate 'in thought' a direction from any line of which it is the direction, one cannot conceive of a direction existing in the absence of any line possessing that direction.
     From: E.J. Lowe (The Possibility of Metaphysics [1998], 10.3)
     A reaction: Intriguing. If I ask you to imagine a line going in a certain direction, don't you need the direction before you can think of the line? 'That line is going in the wrong direction'. Maybe abstract ideas only exist 'in thought'. Lowe is a realist here.