15 ideas
| 16123 | Whenever you perceive a community of things, you should also hunt out differences in the group [Plato] |
| Full Idea: The rule is that when one perceives first the community between the members of a group of many things, one should not desist until one sees in it all those differences that are located in classes. | |
| From: Plato (The Statesman [c.356 BCE], 285b) | |
| A reaction: He goes on to recommend the opposite as well - see community even when there appears to be nothing but differences. I take this to be analysis, just as much as modern linguistic approaches are. Analyse the world, not language. |
| 16125 | To reveal a nature, divide down, and strip away what it has in common with other things [Plato] |
| Full Idea: Let's take the kind posited and cut it in two, .then follow the righthand part of what we've cut, and hold onto things that the sophist is associated with until we strip away everything he has in common with other things, then display his peculiar nature. | |
| From: Plato (The Statesman [c.356 BCE], 264e) | |
| A reaction: This seems to be close to Aristotle's account of definition, when he is trying to get at what-it-is-to-be some thing. But if you strip away everything the definiendum has in common with other things, will anything remain? |
| 16124 | No one wants to define 'weaving' just for the sake of weaving [Plato] |
| Full Idea: I don't suppose that anyone with any sense would want to hunt down the definition of 'weaving' for the sake of weaving itself. | |
| From: Plato (The Statesman [c.356 BCE], 285d) | |
| A reaction: The point seems to be that the definition brings out the connections between weaving and other activities and objects, thus enlarging our understanding. |
| 9148 | I think of variables as objects rather than as signs [Fine,K] |
| Full Idea: It is natural nowadays to think of variables as a certain kind of sign, but I wish to think of them as a certain kind of object. | |
| From: Kit Fine (Cantorian Abstraction: Recon. and Defence [1998], §2) | |
| A reaction: Fine has a theory based on 'arbitrary objects', which is a rather charming idea. The cell of a spreadsheet is a kind of object, I suppose. A variable might be analogous to a point in space, where objects can locate themselves. |
| 5961 | The soul gets its goodness from god, and its evil from previous existence. [Plato] |
| Full Idea: From its composer the soul possesses all beautiful things, but from its former condition, everything that proves to be harsh and unjust in heaven. | |
| From: Plato (The Statesman [c.356 BCE], 273b) | |
| A reaction: A neat move to explain the origins of evil (or rather, to shift the problem of evil to a long long way from here). This view presumably traces back to the views of Empedocles on good and evil. Can the soul acquire evil in its current existence? |
| 9152 | If green is abstracted from a thing, it is only seen as a type if it is common to many things [Fine,K] |
| Full Idea: In traditional abstraction, the colour green merely has the intrinsic property of being green, other properties of things being abstracted away. But why should that be regarded as a type? It must be because the property is common to the instances. | |
| From: Kit Fine (Cantorian Abstraction: Recon. and Defence [1998], §5) | |
| A reaction: A nice question which shows that the much-derided single act of abstraction is not sufficient to arrive at a concept, so that abstraction is a more complex matter (perhaps even a rational one) than simple empiricists believe. |
| 9149 | To obtain the number 2 by abstraction, we only want to abstract the distinctness of a pair of objects [Fine,K] |
| Full Idea: In abstracting from the elements of a doubleton to obtain 2, we do not wish to abstract away from all features of the objects. We wish to take account of the fact that the two objects are distinct; this alone should be preserved under abstraction. | |
| From: Kit Fine (Cantorian Abstraction: Recon. and Defence [1998], §3) | |
| A reaction: This is Fine's strategy for meeting Frege's objection to abstraction, summarised in Idea 9146. It seems to use the common sense idea that abstraction is not all-or-nothing. Abstraction has degrees (and levels). |
| 9150 | We should define abstraction in general, with number abstraction taken as a special case [Fine,K] |
| Full Idea: Number abstraction can be taken to be a special case of abstraction in general, which can then be defined without recourse to the concept of number. | |
| From: Kit Fine (Cantorian Abstraction: Recon. and Defence [1998], §3) | |
| A reaction: At last, a mathematical logician recognising that they don't have a monopoly on abstraction. It is perfectly obvious that abstractions of simple daily concepts must be chronologically and logically prior to number abstraction. Number of what? |
| 9146 | After abstraction all numbers seem identical, so only 0 and 1 will exist! [Fine,K] |
| Full Idea: In Cantor's abstractionist account there can only be two numbers, 0 and 1. For abs(Socrates) = abs(Plato), since their numbers are the same. So the number of {Socrates,Plato} is {abs(Soc),abs(Plato)}, which is the same number as {Socrates}! | |
| From: Kit Fine (Cantorian Abstraction: Recon. and Defence [1998], §1) | |
| A reaction: Fine tries to answer this objection, which arises from §45 of Frege's Grundlagen. Fine summarises that "indistinguishability without identity appears to be impossible". Maybe we should drop talk of numbers in terms of sets. |
| 283 | The question of whether or not to persuade comes before the science of persuasion [Plato] |
| Full Idea: The science of whether one must persuade or not must rule over the science capable of persuading. | |
| From: Plato (The Statesman [c.356 BCE], 304c) | |
| A reaction: Plato probably thinks that reason has to be top of the pyramid, but there is always the Nietzschean/romantic question of why we should place such a value on what is rational. |
| 282 | Non-physical beauty can only be shown clearly by speech [Plato] |
| Full Idea: The bodiless things, being the most beautiful and the greatest, are only shown with clarity by speech and nothing else. | |
| From: Plato (The Statesman [c.356 BCE], 286a) | |
| A reaction: Unfortunately this will be true of warped and ugly ideas as well. |
| 281 | The arts produce good and beautiful things by preserving the mean [Plato] |
| Full Idea: It is by preserving the mean that arts produce everything that is good and beautiful. | |
| From: Plato (The Statesman [c.356 BCE], 284b) |
| 22559 | Democracy is the worst of good constitutions, but the best of bad constitutions [Plato, by Aristotle] |
| Full Idea: Plato judged that when the constitution is decent, democracy is the worst of them, but when they are bad it is the best. | |
| From: report of Plato (The Statesman [c.356 BCE], 302e) by Aristotle - Politics 1289b07 | |
| A reaction: Aristotle denies that a good oligarchy is superior. What of technocracy? The challenge is to set up institutions which ensure the health of the democracy. The big modern problem is populists who lie. |
| 279 | Only divine things can always stay the same, and bodies are not like that [Plato] |
| Full Idea: It is fitting for only the most divine things of all to be always the same and in the same state and in the same respects, and the nature of body is not of this ordering. | |
| From: Plato (The Statesman [c.356 BCE], 269b) |
| 16711 | Heretics should be eradicated like wolves [Aquinas] |
| Full Idea: Heretics are wolves …and therefore ought to be eradicated. | |
| From: Thomas Aquinas (Sentences [1264], IV.13.2.3sc), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 20.2 |