17 ideas
| 6007 | If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R] |
| Full Idea: The 'undetected' or 'veiled' paradox of Eubulides says: if you know your father, and don't know the veiled person before you, but that person is your father, you both know and don't know the same person. | |
| From: report of Eubulides (fragments/reports [c.390 BCE]) by R.M. Dancy - Megarian School | |
| A reaction: Essentially an uninteresting equivocation on two senses of "know", but this paradox comes into its own when we try to give an account of how linguistic reference works. Frege's distinction of sense and reference tried to sort it out (Idea 4976). |
| 13931 | By using aporiai as his start, Aristotle can defer to the wise, as well as to the many [Haslanger] |
| Full Idea: The Aristotelian method of working form aporia allows one to use as starting points not only what is said by 'the many', but also what is said by 'the wise', including philosophers. | |
| From: Sally Haslanger (Persistence, Change and Explanation [1989], 1 n2) | |
| A reaction: [She mentions Nussbaum 1986:ch 7 for the opposing view] I like this thought a lot. Aristotle's democratic respect for widespread views can be a bit puzzling sometimes. |
| 6006 | If you say truly that you are lying, you are lying [Eubulides, by Dancy,R] |
| Full Idea: The liar paradox of Eubulides says 'if you state that you are lying, and state the truth, then you are lying'. | |
| From: report of Eubulides (fragments/reports [c.390 BCE]) by R.M. Dancy - Megarian School | |
| A reaction: (also Cic. Acad. 2.95) Don't say it, then. These kind of paradoxes of self-reference eventually lead to Russell's 'barber' paradox and his Theory of Types. |
| 6008 | Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R] |
| Full Idea: The 'sorites' paradox of Eubulides says: if you take one grain of sand from a heap (soros), what is left is still a heap; so no matter how many grains of sand you take one by one, the result is always a heap. | |
| From: report of Eubulides (fragments/reports [c.390 BCE]) by R.M. Dancy - Megarian School | |
| A reaction: (also Cic. Acad. 2.49) This is a very nice paradox, which goes to the heart of our bewilderment when we try to fully understand reality. It homes in on problems of identity, as best exemplified in the Ship of Theseus (Ideas 1212 + 1213). |
| 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. |
| 15923 | Poincaré rejected the actual infinite, claiming definitions gave apparent infinity to finite objects [Poincaré, by Lavine] |
| Full Idea: Poincaré rejected the actual infinite. He viewed mathematics that is apparently concerned with the actual infinite as actually concerning the finite linguistic definitions the putatively describe actually infinite objects. | |
| From: report of Henri Poincaré (On the Nature of Mathematical Reasoning [1894]) by Shaughan Lavine - Understanding the Infinite |
| 10180 | Mathematicians do not study objects, but relations between objects [Poincaré] |
| Full Idea: Mathematicians do not study objects, but relations between objects; it is a matter of indifference if the objects are replaced by others, provided the relations do not change. They are interested in form alone, not matter. | |
| From: Henri Poincaré (Science and Hypothesis [1902], p.20), quoted by E Reck / M Price - Structures and Structuralism in Phil of Maths §6 | |
| A reaction: This connects modern structuralism with Aritotle's interest in the 'form' of things. Contrary to the views of the likes of Frege, it is hard to see that the number '7' has any properties at all, apart from its relations. A daffodil would do just as well. |
| 9916 | Convention, yes! Arbitrary, no! [Poincaré, by Putnam] |
| Full Idea: Poincaré once exclaimed, 'Convention, yes! Arbitrary, no!'. | |
| From: report of Henri Poincaré (talk [1901]) by Hilary Putnam - Models and Reality | |
| A reaction: An interesting view. It mustn't be assumed that conventions are not rooted in something. Maybe a sort of pragmatism is implied. |
| 18203 | Avoid non-predicative classifications and definitions [Poincaré] |
| Full Idea: Never consider any objects but those capable of being defined in a finite number of word ...Avoid non-predicative classifications and definitions. | |
| From: Henri Poincaré (The Logic of Infinity [1909], p.63), quoted by Penelope Maddy - Naturalism in Mathematics II.4 |
| 13925 | Ontology disputes rest on more basic explanation disputes [Haslanger] |
| Full Idea: Disputes over ontology derive from more fundamental disputes over forms of explanation. | |
| From: Sally Haslanger (Persistence, Change and Explanation [1989], 1) | |
| A reaction: It immediately strikes me that Haslanger has stolen my master idea, but unfortunately the dating suggests that she has priority. The tricky part is to combine this view with realism. |
| 13924 | The persistence of objects seems to be needed if the past is to explain the present [Haslanger] |
| Full Idea: The notion that things persist through change is deeply embedded in ideas we have about explanation, and in particular, in the idea that the present is constrained by the past. | |
| From: Sally Haslanger (Persistence, Change and Explanation [1989], 1) | |
| A reaction: I take this to be both an important and an attractive idea. Deniers of persistence (4D-ists) will presumably have some ability to explain the present, but it is the idea of the present being 'constrained' by the past which is a challenge. |
| 13930 | Persistence makes change and its products intelligible [Haslanger] |
| Full Idea: Persistence offers intelligibility: the possibility of understanding a change, and of understanding the products of it. | |
| From: Sally Haslanger (Persistence, Change and Explanation [1989], 8) | |
| A reaction: I think this is exactly right, and it is a powerful idea with wide implications for metaphysics. Haslanger claims that an understanding of 'substance' is needed, which leads towards my defence of essentialism. |
| 13927 | We must explain change amongst 'momentary entities', or else the world is inexplicable [Haslanger] |
| Full Idea: If the world of time-slices is to be explicable, then it must be possible to provide explanations of change understood as a continual generation and destruction of these 'momentary entities'. | |
| From: Sally Haslanger (Persistence, Change and Explanation [1989], 7) | |
| A reaction: While fans of time-slices can offer some sort of explanation, in the process of explaining a 'worm', there don't seem to be the sort of causal chains that we traditionally rely on. Maybe there are no explanations of anything? |
| 13928 | If the things which exist prior to now are totally distinct, they need not have existed [Haslanger] |
| Full Idea: How is the case in which A exists prior to B, but is distinct from B, different (especially from B's point of view) from the case in which nothing exists prior to B? | |
| From: Sally Haslanger (Persistence, Change and Explanation [1989], 7) | |
| A reaction: I sympathise with her view, but this isn't persuasive. For A substitute 'Sally's mother' and for B substitute 'Sally'. A 4D-ist could bite the bullet and say that, indeed, previous parts of my 'worm' need not have existed. |
| 13929 | Natural explanations give the causal interconnections [Haslanger] |
| Full Idea: Natural explanations work by showing the systematic causal interconnections between things. | |
| From: Sally Haslanger (Persistence, Change and Explanation [1989], 7) | |
| A reaction: On the whole I love this sort of idea, but I am wondering if this one prevents mathematical or logical explanations from being natural. |
| 13926 | Best explanations, especially natural ones, need grounding, notably by persistent objects [Haslanger] |
| Full Idea: I am not resting my ontology on a simple 'argument to the best explanation'. ..What I want to say is that there are general demands on a kind of explanation, in particular, natural explanation, which require that there are persisting things. | |
| From: Sally Haslanger (Persistence, Change and Explanation [1989], 5) | |
| A reaction: This is a really nice idea - that best explanation is not just about specific cases, but also about best foundations for explanations in general, which brings in our metaphysics. I defend the role of essences in these best explanations. |
| 15877 | The aim of science is just to create a comprehensive, elegant language to describe brute facts [Poincaré, by Harré] |
| Full Idea: In Poincaré's view, we try to construct a language within which the brute facts of experience are expressed as comprehensively and as elegantly as possible. The job of science is the forging of a language precisely suited to that purpose. | |
| From: report of Henri Poincaré (The Value of Science [1906], Pt III) by Rom Harré - Laws of Nature 2 | |
| A reaction: I'm often struck by how obscure and difficult our accounts of self-evident facts can be. Chairs are easy, and the metaphysics of chairs is hideous. Why is that? I'm a robust realist, but I like Poincaré's idea. He permits facts. |