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Full Idea
Even in cases (such as Goldbach's Conjecture) which, if true, are logically necessary, we may be able to conceive the opposite. We can conceive of there being a number which is not the sum of two primes.
Gist of Idea
If Goldbach's Conjecture is true (and logically necessary), we may be able to conceive its opposite
Source
Harré,R./Madden,E.H. (Causal Powers [1975], 3.II)
Book Ref
Harré,R/Madden,E.H.: 'Causal Powers: A Theory of Natural Necessity' [Blackwell 1975], p.66
A Reaction
[attributed to Kneale] Ah, but can we conceive this (as Descartes would say) 'clearly and distinctly'? I can conceive circular squares, as long as I don't concentrate too hard.
| 3642 | Pythagoras' Theorem doesn't cease to be part of the essence of triangles just because we doubt it [Arnauld on Descartes] |
| 16582 | We can imagine a point swelling and contracting - but not how this could be done [Hobbes] |
| 11958 | Impossibilites are easily conceived in mathematics and geometry [Reid, by Molnar] |
| 8562 | It is possible to conceive what is not possible [Shoemaker] |
| 15252 | If Goldbach's Conjecture is true (and logically necessary), we may be able to conceive its opposite [Harré/Madden] |
| 9660 | The impossible can be imagined as long as it is a bit vague [Lewis] |
| 2407 | One can wrongly imagine two things being non-identical even though they are the same (morning/evening star) [Chalmers] |
| 3106 | If claims of metaphysical necessity are based on conceivability, we should be cautious [Segal] |
| 10652 | Conceivability may indicate possibility, but literary fantasy does not [Varzi] |
| 14714 | Contradictory claims about a necessary god both seem apriori coherent [Schroeter] |