7 ideas
| 9159 | You can't simply convert geometry into algebra, as some spatial content is lost [Burge] |
| Full Idea: Although one can translate geometrical propositions into algebraic ones and produce equivalent models, the meaning of geometrical propositions seems to me to be thereby lost. Pure geometry involves spatial content, even if abstracted from physical space. | |
| From: Tyler Burge (Frege on Apriority [2000], IV) | |
| A reaction: This supports Frege's view (against Quine) that geometry won't easily fit into the programme of logicism. I agree with Burge. You would be focusing on the syntax of geometry, and leaving out the semantics. |
| 3626 | Knowing the attributes is enough to reveal a substance [Descartes] |
| Full Idea: I have never thought that anything more is required to reveal a substance than its various attributes. | |
| From: René Descartes (Reply to Fifth Objections [1641], 360) |
| 3630 | Our thinking about external things doesn't disprove the existence of innate ideas [Descartes] |
| Full Idea: You can't prove that Praxiteles never made any statues on the grounds that he did not get from within himself the marble from which he sculpted them. | |
| From: René Descartes (Reply to Fifth Objections [1641], 362) |
| 3631 | A blind man may still contain the idea of colour [Descartes] |
| Full Idea: How do you know that there is no idea of colour in a man born blind? | |
| From: René Descartes (Reply to Fifth Objections [1641], 363) |
| 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? |
| 3640 | Possible existence is a perfection in the idea of a triangle [Descartes] |
| Full Idea: Possible existence is a perfection in the idea of a triangle, just as necessary existence is a perfection in the idea of God. | |
| From: René Descartes (Reply to Fifth Objections [1641], 383) |
| 3639 | Necessary existence is a property which is uniquely part of God's essence [Descartes] |
| Full Idea: In the case of God necessary existence is in fact a property in the strictest sense of the term, since it applies to him alone and forms a part of his essence as it does of no other thing | |
| From: René Descartes (Reply to Fifth Objections [1641], 383) |