11 ideas
| 2676 | Didactic argument starts from the principles of the subject, not from the opinions of the learner [Aristotle] |
| Full Idea: Didactic arguments are those which reason from the principles appropriate to each branch of learning and not from the opinions of the answerer (for he who is learning must take things on trust). | |
| From: Aristotle (Sophistical Refutations [c.331 BCE], 165b01) |
| 2675 | Reasoning is a way of making statements which makes them lead on to other statements [Aristotle] |
| Full Idea: Reasoning is based on certain statements made in such a way as necessarily to cause the assertion of things other than those statements and as a result of those statements. | |
| From: Aristotle (Sophistical Refutations [c.331 BCE], 165a01) |
| 2677 | Dialectic aims to start from generally accepted opinions, and lead to a contradiction [Aristotle] |
| Full Idea: Dialectical arguments are those which, starting from generally accepted opinions, reason to establish a contradiction. | |
| From: Aristotle (Sophistical Refutations [c.331 BCE], 165b03) |
| 2674 | Competitive argument aims at refutation, fallacy, paradox, solecism or repetition [Aristotle] |
| Full Idea: Those who compete and contend in argument aim at five objects: refutation, fallacy, paradox, solecism, and the reduction of one's opponent to a state of babbling, that is, making him say the same thing over and over again. | |
| From: Aristotle (Sophistical Refutations [c.331 BCE], 165b15) |
| 16967 | 'Are Coriscus and Callias at home?' sounds like a single question, but it isn't [Aristotle] |
| Full Idea: If you ask 'Are Coriscus and Callias at home or not at home?', whether they are both at home or not there, the number of propositions is more than one. For if the answer is true, it does not follow that the question is a single one. | |
| From: Aristotle (Sophistical Refutations [c.331 BCE], 176a08) | |
| A reaction: [compressed] Aristotle is saying that some questions should not receive a 'yes' or 'no' answer, because they are equivocal. Arthur Prior cites this passage, on 'and'. Ordinary use of 'and' need not be the logical use of 'and'. |
| 9935 | Mathematical truth is always compromising between ordinary language and sensible epistemology [Benacerraf] |
| Full Idea: Most accounts of the concept of mathematical truth can be identified with serving one or another of either semantic theory (matching it to ordinary language), or with epistemology (meshing with a reasonable view) - always at the expense of the other. | |
| From: Paul Benacerraf (Mathematical Truth [1973], Intro) | |
| A reaction: The gist is that language pulls you towards platonism, and epistemology pulls you towards empiricism. He argues that the semantics must give ground. He's right. |
| 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. |
| 17927 | Realists have semantics without epistemology, anti-realists epistemology but bad semantics [Benacerraf, by Colyvan] |
| Full Idea: Benacerraf argues that realists about mathematical objects have a nice normal semantic but no epistemology, and anti-realists have a good epistemology but an unorthodox semantics. | |
| From: report of Paul Benacerraf (Mathematical Truth [1973]) by Mark Colyvan - Introduction to the Philosophy of Mathematics 1.2 |
| 9936 | The platonist view of mathematics doesn't fit our epistemology very well [Benacerraf] |
| Full Idea: The principle defect of the standard (platonist) account of mathematical truth is that it appears to violate the requirement that our account be susceptible to integration into our over-all account of knowledge. | |
| From: Paul Benacerraf (Mathematical Truth [1973], III) | |
| A reaction: Unfortunately he goes on to defend a causal theory of justification (fashionable at that time, but implausible now). Nevertheless, his general point is well made. Your theory of what mathematics is had better make it knowable. |
| 16149 | Generic terms like 'man' are not substances, but qualities, relations, modes or some such thing [Aristotle] |
| Full Idea: 'Man', and every generic term, denotes not an individual substance but a quality or relation or mode or something of the kind. | |
| From: Aristotle (Sophistical Refutations [c.331 BCE], 179a01) | |
| A reaction: This is Aristotle's denial that species constitutes the essence of anything. I take 'man' to be a categorisation of individuals, and is ontologically nothing at all in its own right. |
| 11840 | Only if two things are identical do they have the same attributes [Aristotle] |
| Full Idea: It is only to things which are indistinguishable and one in essence [ousia] that all the same attributes are generally held to belong. | |
| From: Aristotle (Sophistical Refutations [c.331 BCE], 179a37) | |
| A reaction: This simply IS Leibniz's Law (to which I shall from now on quietly refer to as 'Aristotle's Law'). It seems that it just as plausible to translate 'ousia' as 'being' rather than 'essence'. 'Indistinguishable' and 'one in ousia' are not the same. |