31 ideas
| 1642 | We must fight fiercely for knowledge, understanding and intelligence [Plato] |
| Full Idea: We need to use every argument we can to fight against anyone who does away with knowledge, understanding, and intelligence, but at the same time asserts anything at all about anything. | |
| From: Plato (The Sophist [c.359 BCE], 249c) | |
| A reaction: Thus showing that reason is only central if you want to put a high value on it? |
| 1645 | The desire to split everything into its parts is unpleasant and unphilosophical [Plato] |
| Full Idea: To try to set apart everything from everything is not only especially jangling, but it is the mark of someone altogether unmusical and unphilosophic. | |
| From: Plato (The Sophist [c.359 BCE], 259e) |
| 10571 | Concern for rigour can get in the way of understanding phenomena [Fine,K] |
| Full Idea: It is often the case that the concern for rigor gets in the way of a true understanding of the phenomena to be explained. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) | |
| A reaction: This is a counter to Timothy Williamson's love affair with rigour in philosophy. It strikes me as the big current question for analytical philosophy - of whether the intense pursuit of 'rigour' will actually deliver the wisdom we all seek. |
| 287 | Good analysis involves dividing things into appropriate forms without confusion [Plato] |
| Full Idea: It takes expertise in dialectic to divide things by kinds and not to think that the same form is a different one or that a different form is the same. | |
| From: Plato (The Sophist [c.359 BCE], 253d) |
| 1644 | Dialectic should only be taught to those who already philosophise well [Plato] |
| Full Idea: The dialectical capacity - you won't give it to anyone else, I suspect, except to whoever philosophises purely and justly. | |
| From: Plato (The Sophist [c.359 BCE], 253e) |
| 20478 | In discussion a person's opinions are shown to be in conflict, leading to calm self-criticism [Plato] |
| Full Idea: They collect someone's opinions together during the discussion, put them side by side, and show that they conflict with each other at the same time on the same subjects.... The person sees this, gets angry at themselves, and calmer towards others. | |
| From: Plato (The Sophist [c.359 BCE], 230b) | |
| A reaction: He goes on to say that the process is like a doctor purging a patient of internal harms. If anyone talks for long enough (even a good philosopher), their opinions will probably be seen to be in conflict. But which opinions do you abandon? |
| 10565 | There is no stage at which we can take all the sets to have been generated [Fine,K] |
| Full Idea: There is no stage at which we can take all the sets to have been generated, since the set of all those sets which have been generated at a given stage will itself give us something new. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
| 10564 | We might combine the axioms of set theory with the axioms of mereology [Fine,K] |
| Full Idea: We might combine the standard axioms of set theory with the standard axioms of mereology. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
| 10569 | If you ask what F the second-order quantifier quantifies over, you treat it as first-order [Fine,K] |
| Full Idea: We are tempted to ask of second-order quantifiers 'what are you quantifying over?', or 'when you say "for some F" then what is the F?', but these questions already presuppose that the quantifiers are first-order. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005]) |
| 10570 | Assigning an entity to each predicate in semantics is largely a technical convenience [Fine,K] |
| Full Idea: In doing semantics we normally assign some appropriate entity to each predicate, but this is largely for technical convenience. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) |
| 10573 | Dedekind cuts lead to the bizarre idea that there are many different number 1's [Fine,K] |
| Full Idea: Because of Dedekind's definition of reals by cuts, there is a bizarre modern doctrine that there are many 1's - the natural number 1, the rational number 1, the real number 1, and even the complex number 1. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) | |
| A reaction: See Idea 10572. |
| 10575 | Why should a Dedekind cut correspond to a number? [Fine,K] |
| Full Idea: By what right can Dedekind suppose that there is a number corresponding to any pair of irrationals that constitute an irrational cut? | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) |
| 10574 | Unless we know whether 0 is identical with the null set, we create confusions [Fine,K] |
| Full Idea: What is the union of the singleton {0}, of zero, and the singleton {φ}, of the null set? Is it the one-element set {0}, or the two-element set {0, φ}? Unless the question of identity between 0 and φ is resolved, we cannot say. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) |
| 10560 | Set-theoretic imperialists think sets can represent every mathematical object [Fine,K] |
| Full Idea: Set-theoretic imperialists think that it must be possible to represent every mathematical object as a set. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
| 10568 | Logicists say mathematics can be derived from definitions, and can be known that way [Fine,K] |
| Full Idea: Logicists traditionally claim that the theorems of mathematics can be derived by logical means from the relevant definitions of the terms, and that these theorems are epistemically innocent (knowable without Kantian intuition or empirical confirmation). | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) |
| 11278 | What does 'that which is not' refer to? [Plato] |
| Full Idea: What should the name 'that which is not' be applied to? | |
| From: Plato (The Sophist [c.359 BCE], 237c) | |
| A reaction: This leads into a discussion of the problem, in The Sophist. It became a large issue when modern logic was being developed by Frege and Russell. |
| 1643 | If statements about non-existence are logically puzzling, so are statements about existence [Plato] |
| Full Idea: When the question was put to us as to the name of 'that which is not', to whatever one must apply it, we got stuck in every kind of perplexity. Are we now in any less perplexity about 'that which is'? | |
| From: Plato (The Sophist [c.359 BCE], 250d) | |
| A reaction: Nice. This precapitulates the whole story of modern philosophy of language. What started as a nagging doubt about reference to non-existents ends as bewilderment about everything we say. |
| 7022 | To be is to have a capacity, to act on other things, or to receive actions [Plato] |
| Full Idea: A thing really is if it has any capacity, either by nature to do something to something else or to have even the smallest thing done to it by the most trivial thing, even if it only happens once. I'll define those which are as nothing other than capacity. | |
| From: Plato (The Sophist [c.359 BCE], 247e) | |
| A reaction: If philosophy is footnotes to Plato, this should be the foundational remark in all discussions of existence (though Parmenides might claim priority). It seems to say 'to be is to have a causal role (active or passive)'. It also seems essentialist. |
| 10563 | A generative conception of abstracts proposes stages, based on concepts of previous objects [Fine,K] |
| Full Idea: It is natural to have a generative conception of abstracts (like the iterative conception of sets). The abstracts are formed at stages, with the abstracts formed at any given stage being the abstracts of those concepts of objects formed at prior stages. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) | |
| A reaction: See 10567 for Fine's later modification. This may not guarantee 'levels', but it implies some sort of conceptual priority between abstract entities. |
| 1641 | Some alarming thinkers think that only things which you can touch exist [Plato] |
| Full Idea: One group drags everything down to earth, insisting that only what offers tangible contact is, since they define being as the same as body, despising anyone who says that something without a body is. These are frightening men. | |
| From: Plato (The Sophist [c.359 BCE], 246b) |
| 10784 | Whenever there's speech it has to be about something [Plato] |
| Full Idea: Whenever there's speech it has to be about something. It's impossible for it not to be about something. | |
| From: Plato (The Sophist [c.359 BCE], 262e) | |
| A reaction: [Quoted by Marcus about ontological commitment] The interesting test case would be speech about the existence of circular squares. |
| 16122 | Good thinkers spot forms spread through things, or included within some larger form [Plato] |
| Full Idea: It takes dialectic to divide things by kinds...such a person can discriminate a single form spread through a lot of separate things…and forms included in a single outside form…or a form connected as a unit through many wholes. | |
| From: Plato (The Sophist [c.359 BCE], 253d) | |
| A reaction: [compressed] This is very helpful in indicating the complex structure of the Forms that Plato envisages. If you talk of the meanings of words (other than names), though, it comes to the same thing. Wise people fully understand their language. |
| 10422 | The not-beautiful is part of the beautiful, though opposed to it, and is just as real [Plato] |
| Full Idea: So 'the not beautiful' turns out to be ..both marked off within one kind of those that are, and also set over against one of those that are, ..and the beautiful is no more a being than the not beautiful. | |
| From: Plato (The Sophist [c.359 BCE], 257d) | |
| A reaction: [dialogue eliminated] This is a highly significant passage, for two reasons. It suggests that the Form of the beautiful can have parts, and also that the negations of Forms are Forms themselves (both of which come as a surprise). |
| 15855 | If we see everything as separate, we can then give no account of it [Plato] |
| Full Idea: To dissociate each thing from everything else is to destroy totally everything there is to say. The weaving together of forms is what makes speech [logos] possible for us. | |
| From: Plato (The Sophist [c.359 BCE], 259e) | |
| A reaction: This I take to be the lynchpin of metaphysics. We are forced to see the world in a way which enables us to give some sort of account of it. Our metaphysics is 'inference to the best logos'. |
| 1637 | A soul without understanding is ugly [Plato] |
| Full Idea: The soul that lacks understanding must be set down as ugly. | |
| From: Plato (The Sophist [c.359 BCE], 228d) | |
| A reaction: The teleological view of things understands their nature in things of their perfection. and the essence of beauty is perfection. It is the mind's nature to know. Failing to know is as ugly as allowing your crops to die. |
| 10561 | Abstraction-theoretic imperialists think Fregean abstracts can represent every mathematical object [Fine,K] |
| Full Idea: Abstraction-theoretic imperialists think that it must be possible to represent every mathematical object as a Fregean abstract. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
| 10562 | We can combine ZF sets with abstracts as urelements [Fine,K] |
| Full Idea: I propose a unified theory which is a version of ZF or ZFC with urelements, where the urelements are taken to be the abstracts. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
| 10567 | We can create objects from conditions, rather than from concepts [Fine,K] |
| Full Idea: Instead of viewing the abstracts (or sums) as being generated from objects, via the concepts from which they are defined, we can take them to be generated from conditions. The number of the universe ∞ is the number of self-identical objects. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) | |
| A reaction: The point is that no particular object is now required to make the abstraction. |
| 1636 | Wickedness is an illness of the soul [Plato] |
| Full Idea: Wickedness is a sedition and illness of the soul. | |
| From: Plato (The Sophist [c.359 BCE], 228b) |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |
| 1638 | Didactic education is hard work and achieves little [Plato] |
| Full Idea: With a lot of effort the admonitory species of education accomplishes little. | |
| From: Plato (The Sophist [c.359 BCE], 230a) |