6 ideas
| 10245 | One geometry cannot be more true than another [Poincaré] |
| Full Idea: One geometry cannot be more true than another; it can only be more convenient. | |
| From: Henri Poincaré (Science and Method [1908], p.65), quoted by Stewart Shapiro - Philosophy of Mathematics | |
| A reaction: This is the culminating view after new geometries were developed by tinkering with Euclid's parallels postulate. |
| 13160 | To exist and be understood, a multitude must first be reduced to a unity [Leibniz] |
| Full Idea: A plurality of things can neither be understood nor can exist unless one first understands the thing that is one, that to which the multitude necessarily reduces. | |
| From: Gottfried Leibniz (Notes on Comments by Fardella [1690], Prop 3) | |
| A reaction: Notice that it is our need to understand which imposes the unity on the multitude. It is not just some random fiction, or a meaningless mechanical act of thought. |
| 13161 | Substances are everywhere in matter, like points in a line [Leibniz] |
| Full Idea: There are substances everywhere in matter, just as points are everywhere in a line. | |
| From: Gottfried Leibniz (Notes on Comments by Fardella [1690], Clarif) | |
| A reaction: Since Leibniz is unlikely to believe in the reality of the points, we must wonder whether he was really committed to this infinity of substances. The more traditional notion of substance is always called 'substantial form' by Leibniz. |
| 8793 | If observation is knowledge, it is not just an experience; it is a justification in the space of reasons [Sellars] |
| Full Idea: In characterizing an observational episode or state as 'knowing', we are not giving an empirical description of it; we are placing it in the logical space of reasons, of justifying and being able to justify what one says. | |
| From: Wilfrid Sellars (Does Emp.Knowledge have Foundation? [1956], p.123) | |
| A reaction: McDowell has made the Kantian phrase 'the logical space of reasons' very popular. This is a very nice statement of the internalist view of justification, with which I sympathise more and more. It is a rationalist coherentist view. It needn't be mystical! |
| 8792 | Observations like 'this is green' presuppose truths about what is a reliable symptom of what [Sellars] |
| Full Idea: Observational knowledge of any particular fact, e.g. that this is green, presupposes that one knows general facts of the form 'X is a reliable symptom of Y'. | |
| From: Wilfrid Sellars (Does Emp.Knowledge have Foundation? [1956], p.123) | |
| A reaction: This is a nicely observed version of the regress problem with justification. I would guess that foundationalists would simply deny that this further knowledge is required; 'this is green' arises out of the experience, but it is not an inference. |
| 8791 | The concept of 'green' involves a battery of other concepts [Sellars] |
| Full Idea: One can only have the concept of green by having a whole battery of concepts of which it is one element. | |
| From: Wilfrid Sellars (Does Emp.Knowledge have Foundation? [1956], p.120) | |
| A reaction: This points in the direction of holism about language and thought, but need not imply it. It might be that concepts have to be learned in small families. It is not clear, though, what is absolutely essential to 'green', except that it indicates colour. |