3 ideas
| 13166 | Essences are no use in mathematics, if all mathematical truths are necessary [Mancosu] |
| Full Idea: Essences and essential properties do not seem to be useful in mathematical contexts, since all mathematical truths are regarded as necessary (though Kit Fine distinguishes between essential and necessary properties). | |
| From: Paolo Mancosu (Explanation in Mathematics [2008], §6.1) | |
| A reaction: I take the proviso in brackets to be crucial. This represents a distortion of notion of an essence. There is a world of difference between the central facts about the nature of a square and the peripheral inferences derivable from it. |
| 19216 | Propositions (such as 'that dog is barking') only exist if their items exist [Williamson] |
| Full Idea: A proposition about an item exists only if that item exists... how could something be the proposition that that dog is barking in circumstances in which that dog does not exist? | |
| From: Timothy Williamson (Necessary Existents [2002], p.240), quoted by Trenton Merricks - Propositions | |
| A reaction: This is a view of propositions I can't make sense of. If I'm under an illusion that there is a dog barking nearby, when there isn't one, can I not say 'that dog is barking'? If I haven't expressed a proposition, what have I done? |
| 12702 | Causes can be inferred from perfect knowledge of their effects [Leibniz] |
| Full Idea: Whoever understands some effect perfectly will also arrive at the knowledge of its cause. | |
| From: Gottfried Leibniz (Meditatio de principio individui [1676], A6.3.490), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 2 | |
| A reaction: This sounds highly improbable, given that you would have thought that there could be lots of ways to bring about the same effect. Predicting effects is rather more plausible. I suppose if you can record all the ripples in the pond before they fade... |