43 ideas
| 14179 | The finest branch of wisdom is justice and moderation in ordering states and families [Plato] |
| Full Idea: By far the greatest and fairest branch of wisdom is that which is concerned with the due ordering of states and families, whose name is moderation and justice. | |
| From: Plato (The Symposium [c.384 BCE], 209a) | |
| A reaction: ['Justice' is probably 'dikaiosune'] It is hard to disagree with this, and it relegates ivory tower philosophical contemplation to second place, unlike the late books of Aristotle's Ethics. |
| 17621 | What matters in mathematics is its objectivity, not the existence of the objects [Dummett] |
| Full Idea: As Kreisel has remarked, what is important is not the existence of mathematical objects, but the objectivity of mathematical statements. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: [see Maddy 2011:115 for the history of this idea] It seems rather unclear where Frege stands on objectivity. Maddy embraces it, following up this idea, and Tyler Burge's fat book on objectivity. |
| 10537 | The ordered pairs <x,y> can be reduced to the class of sets of the form {{x},{x,y}} [Dummett] |
| Full Idea: A classic reduction is the class of ordered pairs <x,y> being reduced to the class of sets of the form {{x},{x,y}}. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) |
| 10542 | To associate a cardinal with each set, we need the Axiom of Choice to find a representative [Dummett] |
| Full Idea: We may suppose that with each set is associated an object as its cardinal number, but we have no systematic way, without appeal to the Axiom of Choice, of selecting a representative set of each cardinality. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) |
| 10554 | Intuitionists find the Incompleteness Theorem unsurprising, since proof is intuitive, not formal [Dummett] |
| Full Idea: In the intuitionist view, the notion of an intuitive proof cannot be expected to coincide with that of a proof in a formal system, and Gödel's incompleteness theorem is thus unsurprising from an intuitionist point of view. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) |
| 10552 | Intuitionism says that totality of numbers is only potential, but is still determinate [Dummett] |
| Full Idea: From the intuitionist point of view natural numbers are mental constructions, so their totality is only potential, but it is neverthless a fully determinate totality. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: This could only be if the means of constructing the numbers was fully determinate, so how does that situation come about? |
| 10515 | Ostension is possible for concreta; abstracta can only be referred to via other objects [Dummett, by Hale] |
| Full Idea: Dummett distinguishes, roughly, between those concrete objects which can be possible objects of ostension, and abstract objects which can only be referred to by functional expressions whose argument is some other object. | |
| From: report of Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) by Bob Hale - Abstract Objects Ch.3.II | |
| A reaction: At least someone has proposed a theory! Hale gives a nice critical discussion of the proposal. It is a moot point whether in the second case, when you pick out the 'other object', you are thereby able to refer to some new abstract object. |
| 10544 | The concrete/abstract distinction seems crude: in which category is the Mistral? [Dummett] |
| Full Idea: The dichotomy between concrete and abstract objects comes to seem far too crude: to which of the two categories should we assign the Mistral, for instance? | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: He has previously given colours and points as difficult borderline cases. We can generalise this particular problem case as the question of whether a potentiality or possibility is abstract or concrete. |
| 10546 | We don't need a sharp concrete/abstract distinction [Dummett] |
| Full Idea: There is no reason for wanting a sharp distinction between concrete and abstract objects. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: This rather depends on your ontology. If you are happy for reality to be full of weird non-physical entities, then the blurring won't bother you. If the boundary is blurred but still real, it is a very interesting one. |
| 10540 | We can't say that light is concrete but radio waves abstract [Dummett] |
| Full Idea: If abstractions were defined by whether they could affect human sense-organs, light-waves would be concrete but radio waves abstract. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: This is a pretty good baseline example. No account should draw an abstract/concrete line through the electromagnetic spectrum. |
| 10548 | The context principle for names rules out a special philosophical sense for 'existence' [Dummett] |
| Full Idea: The dictum that a name has meaning only in the context of a sentence repudiates the conception of a special philosophical sense of 'existence', which claims that numbers do not exist while affirming existential statements about them. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: He refers to Frege's Context Principle. Personally I would say you could make plenty of 'affirmations' about arithmetic without them having to be 'existential'. I can say there 'is' a number between 6 and 8, without huge existential claims. |
| 10281 | The objects we recognise the world as containing depends on the structure of our language [Dummett] |
| Full Idea: What objects we recognise the world as containing depends upon the structure of our language. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: The background to this claim is the Fregean idea that there are no objects for us if there are no concepts. Dummett is adding that there are no concepts if there is no language. I say animals have concepts and recognise objects. |
| 10532 | We can understand universals by studying predication [Dummett] |
| Full Idea: It is by the study of the character of predication that we shall come to understand the essential nature of universals. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: I haven't founded a clearer manifesto for linguistic philosophy than that! Personally I find it highly dubious, given the shifting nature of linguistic forms, and the enormous variation between remote languages. |
| 1607 | Diotima said the Forms are the objects of desire in philosophical discourse [Plato, by Roochnik] |
| Full Idea: According to Diotima, the Forms are the objects of desire operative in philosophical discourse. | |
| From: report of Plato (The Symposium [c.384 BCE], 210a4-) by David Roochnik - The Tragedy of Reason p.199 |
| 10534 | 'Nominalism' used to mean denial of universals, but now means denial of abstract objects [Dummett] |
| Full Idea: The original sense of 'nominalism' is the denial of universals, that is the denial of reference to either predicates or to abstract nouns. The modern sense (of Nelson Goodman) is the denial of the existence of abstract objects. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: This is why you find loads of modern philosophers vigorous attacking nominalism, only to gradually realise that they don't actually believe in universals, as traditionally understood. It's hard to keep up, when words shift their meaning. |
| 10541 | Concrete objects such as sounds and smells may not be possible objects of ostension [Dummett] |
| Full Idea: We cannot simply distinguish concrete objects as objects of ostension, if it literally involves a pointing gesture, as this would exclude a colourless gas, a sound or a smell. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: He shifts to verbal ostension as a result, since we can talk of 'this smell'. On p.491 he suggests that affecting our senses is a sufficient condition to be concrete, but not a necessary one. |
| 10545 | Abstract objects may not cause changes, but they can be the subject of change [Dummett] |
| Full Idea: To say that an abstract object cannot be the cause of change seems plausible enough, but the thesis that it cannot be the subject of change is problematic. The shape of an object can change, or the number of sheep on a hill. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: This seems a pretty crucial difficulty for the standard notion of abstracta as non-causal. I would say that it is an acid which could eat away the whole edifice if you thought about it for long enough. He shifts shape-change to the physical object. |
| 10555 | If we can intuitively apprehend abstract objects, this makes them observable and causally active [Dummett] |
| Full Idea: For intuitionists, it ceases to be true that abstract objects are not observable and cannot be involved in causal interaction, since such intuitive apprehension of them may be regarded as just such an interaction. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: I would say that since abstract objects can be involved in causal interactions, in the mind, and since the mind is entirely physical (oh yes), this makes abstract objects entirely physical, which may come as a shock to some people. |
| 10543 | Abstract objects must have names that fall within the range of some functional expression [Dummett] |
| Full Idea: For an object to be abstract, we require only that an understanding of any name of that object involves a recognition that the object is in the range of some functional expression. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: I'm not sure I understand this, but a function must involve a relation between some objects, such that a unique object is consequently picked out. |
| 10320 | If a genuine singular term needs a criterion of identity, we must exclude abstract nouns [Dummett, by Hale] |
| Full Idea: Dummett's best argument for excluding abstract nouns relies upon the entirely Fregean requirement that with any genuine singular term there must be associated a criterion of identity. | |
| From: report of Michael Dummett (Frege Philosophy of Language (2nd ed) [1973]) by Bob Hale - Abstract Objects Ch.2.II | |
| A reaction: This sounds a rather rigid test. Must the criteria be logically precise, or must you just have some vague idea of what you are talking about? |
| 10547 | Abstract objects can never be confronted, and need verbal phrases for reference [Dummett] |
| Full Idea: An abstract object can be referred to only by means of a verbal phrase, ...and no confrontation with an abstract object is possible. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: So does this mean that animals are incapable of entertaining abstract concepts? Some research suggests otherwise. Does a dog understand what a 'walk' is, without use of the word? Dummett disgracefully neglects animals in his theories. |
| 10531 | There is a modern philosophical notion of 'object', first introduced by Frege [Dummett] |
| Full Idea: The notion of 'object', as it is now commonly used in philosophical contexts, is a modern notion, one first introduced by Frege. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: If we say 'objects exist', I think it is crucial that if we are going to introduce 'object' as a term of art, then 'exist' had better stick to normal usage. If that drifts into a term of art as well (incorporating 'subsist', or some such) we have no hope! |
| 174 | True opinion without reason is midway between wisdom and ignorance [Plato] |
| Full Idea: There is a state of mind half-way between wisdom and ignorance - having true opinions without being able to give reasons for them. | |
| From: Plato (The Symposium [c.384 BCE], 202a) | |
| A reaction: Compare Idea 2140, where Plato scorns this state of mind. What he describes could be split into two - purely lucky true beliefs, and 'externalist knowledge', with non-conscious justification. |
| 19699 | A Gettier case is a belief which is true, and its fallible justification involves some luck [Hetherington] |
| Full Idea: A Gettier case contains a belief which is true and well justified without being knowledge. Its justificatory support is also fallible, ...and there is considerable luck in how the belief combnes being true with being justified. | |
| From: Stephen Hetherington (The Gettier Problem [2011], 5) | |
| A reaction: This makes luck the key factor. 'Luck' is a rather vague concept, and so the sort of luck involved must first be spelled out. Or the varieties of luck that can produce this outcome. |
| 180 | We call a person the same throughout life, but all their attributes change [Plato] |
| Full Idea: During the period from boyhood to old age, man does not retain the same attributes, though he is called the same person. | |
| From: Plato (The Symposium [c.384 BCE], 207d) | |
| A reaction: This precisely identifies the basic problem of personal identity over time. If this is the problem, DNA looks more and more significant for the answer, though it would be an awful mistake to think a pattern of DNA was a person. |
| 181 | Only the gods stay unchanged; we replace our losses with similar acquisitions [Plato] |
| Full Idea: We retain identity not by staying the same (the preserve of gods) but by replacing losses with new similar acquisitions. | |
| From: Plato (The Symposium [c.384 BCE], 208b) | |
| A reaction: Any modern student of personal identity should be intrigued by this remark! It appears to take a rather physical view of the matter, and to be aware of human biology as a process. Are my continuing desires token-identical, or just 'similar'? |
| 19168 | Concepts only have a 'functional character', because they map to truth values, not objects [Dummett, by Davidson] |
| Full Idea: Real functions map objects onto objects, but concepts map objects onto truth value, ...so Dummett says that concepts are not functions, but that they have a 'functional character'. | |
| From: report of Michael Dummett (Frege Philosophy of Language (2nd ed) [1973]) by Donald Davidson - Truth and Predication 6 |
| 10549 | Since abstract objects cannot be picked out, we must rely on identity statements [Dummett] |
| Full Idea: Since we cannot pick an abstract object out from its surrounding, all that we need to master is the use of statements of identity between objects of a certain kind. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: This is the necessary Fregean preliminary to using a principle of abstraction to identify two objects which are abstract (when the two objects are in an equivalence relation). Presumably circular squares and square circles are identical? |
| 10516 | A realistic view of reference is possible for concrete objects, but not for abstract objects [Dummett, by Hale] |
| Full Idea: Dummett claims that a realistic conception of reference can be sustained for concrete objects (possible objects of ostension), but breaks down for (putative) names of (pure) abstract objects. | |
| From: report of Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) by Bob Hale - Abstract Objects Ch.3.II | |
| A reaction: An extremely hard claim to evaluate, because a case must first be made for abstract objects which are fundamentally different in kind. Realistic reference must certainly deal with these hard cases. Field rejects Dummett's abstract points. |
| 4026 | Beauty is harmony with what is divine, and ugliness is lack of such harmony [Plato] |
| Full Idea: Ugliness is out of harmony with everything that is godly; beauty, however, is in harmony with the divine. | |
| From: Plato (The Symposium [c.384 BCE], 206d) | |
| A reaction: This remark shows how the concept of 'harmony' is at the centre of Greek thought (and is a potential bridge of the is/ought gap). |
| 172 | Love of ugliness is impossible [Plato] |
| Full Idea: There cannot be such a thing as love of ugliness. | |
| From: Plato (The Symposium [c.384 BCE], 201a) |
| 173 | Beauty and goodness are the same [Plato] |
| Full Idea: What is good is the same as what is beautiful. | |
| From: Plato (The Symposium [c.384 BCE], 201c) |
| 183 | Stage two is the realisation that beauty of soul is of more value than beauty of body [Plato] |
| Full Idea: The second stage of progress is to realise that beauty of soul is more valuable than beauty of body. | |
| From: Plato (The Symposium [c.384 BCE], 210b) |
| 184 | Progress goes from physical beauty, to moral beauty, to the beauty of knowledge, and reaches absolute beauty [Plato] |
| Full Idea: One should step up from physical beauty, to moral beauty, to the beauty of knowledge, until at last one knows what absolute beauty is. | |
| From: Plato (The Symposium [c.384 BCE], 211c) | |
| A reaction: Presumably this is why Socrates refused sexual favours to Alcibiades. The idea is inspiring, and yet it is a rejection of humanity. |
| 171 | Music is a knowledge of love in the realm of harmony and rhythm [Plato] |
| Full Idea: Music may be called a knowledge of the principles of love in the realm of harmony and rhythm. | |
| From: Plato (The Symposium [c.384 BCE], 187c) |
| 176 | Love follows beauty, wisdom is exceptionally beautiful, so love follows wisdom [Plato] |
| Full Idea: Wisdom is one of the most beautiful of things, and Love is love of beauty, so it follows that Love must be a love of wisdom. | |
| From: Plato (The Symposium [c.384 BCE], 204b) | |
| A reaction: Good, but wisdom isn't the only exceptionally beautiful thing. Music is beautiful partly because it is devoid of ideas. |
| 14177 | Love assists men in achieving merit and happiness [Plato] |
| Full Idea: Phaedrus: Love is not only the oldest and most honourable of the gods, but also the most powerful to assist men in the acquisition of merit and happiness, both here and hereafter. | |
| From: Plato (The Symposium [c.384 BCE], 180b) | |
| A reaction: Maybe we should talk less of love as a feeling, and more as a motivation, not just in human relationships, but in activities like gardening and database compilation. |
| 179 | Love is desire for perpetual possession of the good [Plato] |
| Full Idea: Love is desire for perpetual possession of the good. | |
| From: Plato (The Symposium [c.384 BCE], 206a) | |
| A reaction: Even the worst human beings often have lovers. 'Perpetual' is a nice observation. |
| 177 | If a person is good they will automatically become happy [Plato] |
| Full Idea: 'What will be gained by a man who is good?' 'That is easy - he will be happy'. | |
| From: Plato (The Symposium [c.384 BCE], 205a) | |
| A reaction: Suppose you tried to assassinate Hitler in 1944 (a good deed), but failed. Happiness presumably results from success, rather than mere good intentions. |
| 14178 | Happiness is secure enjoyment of what is good and beautiful [Plato] |
| Full Idea: By happy you mean in secure enjoyment of what is good and beautiful? - Certainly. | |
| From: Plato (The Symposium [c.384 BCE], 202c) | |
| A reaction: We seem to have lost track of the idea that beauty might be an essential ingredient of happiness. |
| 170 | The only slavery which is not dishonourable is slavery to excellence [Plato] |
| Full Idea: The only form of servitude which has no dishonour has for its object the acquisition of excellence. | |
| From: Plato (The Symposium [c.384 BCE], 184c) |
| 182 | The first step on the right path is the contemplation of physical beauty when young [Plato] |
| Full Idea: The man who would pursue the right way to his goal must begin, when he is young, by contemplating physical beauty. | |
| From: Plato (The Symposium [c.384 BCE], 210a) |
| 175 | Gods are not lovers of wisdom, because they are already wise [Plato] |
| Full Idea: No god is a lover of wisdom or desires to be wise, for he is wise already. | |
| From: Plato (The Symposium [c.384 BCE], 204a) |