92 ideas
| 20388 | 'Necessary' conditions are requirements, and 'sufficient' conditions are guarantees [Davies,S] |
| Full Idea: A 'necessary' condition for something's being an X is condition that all Xs must satisfy. ...A 'sufficient' condition for something's being an X is a condition that, when satisfied, guarantees that what satisfies it is an X. | |
| From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 2.1) | |
| A reaction: By summarising this I arrive at the requirement/guarantee formulation, which I am rather pleased with. What is required for rain, and what guarantees rain? |
| 224 | When questions are doubtful we should concentrate not on objects but on ideas of the intellect [Plato] |
| Full Idea: Doubtful questions should not be discussed in terms of visible objects or in relation to them, but only with reference to ideas conceived by the intellect. | |
| From: Plato (Parmenides [c.364 BCE], 135e) |
| 232 | Opposites are as unlike as possible [Plato] |
| Full Idea: Opposites are as unlike as possible. | |
| From: Plato (Parmenides [c.364 BCE], 159a) |
| 8937 | Plato's 'Parmenides' is the greatest artistic achievement of the ancient dialectic [Hegel on Plato] |
| Full Idea: Plato's 'Parmenides' is the greatest artistic achievement of the ancient dialectic. | |
| From: comment on Plato (Parmenides [c.364 BCE]) by Georg W.F.Hegel - Phenomenology of Spirit Pref 71 | |
| A reaction: It is a long way from the analytic tradition of philosophy to be singling out a classic text for its 'artistic' achievement. Eventually we may even look back on, say, Kripke's 'Naming and Necessity' and see it in that light. |
| 20389 | A definition of a thing gives all the requirements which add up to a guarantee of it [Davies,S] |
| Full Idea: If we specify the 'necessary' conditions that are 'sufficient' for something's being an X, that is a combination of conditions such that all and only Xs meet them, which is the hallmark of a definition of X-hood. | |
| From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 2.1) | |
| A reaction: There are, of course, many other ways to define something, as shown in the 2.D Reason | Definition section of this database. This nicely summarises the classical view. |
| 20391 | Feminists warn that ideologies use timeless objective definitions as a tool of repression [Davies,S] |
| Full Idea: According to the feminist critique, ideologies that operate as tools of political repression are falsely represented as definitions possessing a timeless, natural, asocial, universal objectivity. | |
| From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 2.2) | |
| A reaction: I suppose this does not just apply to definitions, but to all expressions of ideologically repressive strategy. I'm trying to think of an example of a specifically feminist problem case. Davies doesn't cite anyone. |
| 18074 | Intuitionists rely on assertability instead of truth, but assertability relies on truth [Kitcher] |
| Full Idea: Though it may appear that the intuitionist is providing an account of the connectives couched in terms of assertability conditions, the notion of assertability is a derivative one, ultimately cashed out by appealing to the concept of truth. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.5) | |
| A reaction: I have quite a strong conviction that Kitcher is right. All attempts to eliminate truth, as some sort of ideal at the heart of ordinary talk and of reasoning, seems to me to be doomed. |
| 13986 | Plato found antinomies in ideas, Kant in space and time, and Bradley in relations [Plato, by Ryle] |
| Full Idea: Plato (in 'Parmenides') shows that the theory that 'Eide' are substances, and Kant that space and time are substances, and Bradley that relations are substances, all lead to aninomies. | |
| From: report of Plato (Parmenides [c.364 BCE]) by Gilbert Ryle - Are there propositions? 'Objections' |
| 14150 | Plato's 'Parmenides' is perhaps the best collection of antinomies ever made [Russell on Plato] |
| Full Idea: Plato's 'Parmenides' is perhaps the best collection of antinomies ever made. | |
| From: comment on Plato (Parmenides [c.364 BCE]) by Bertrand Russell - The Principles of Mathematics §337 |
| 6298 | Kitcher says maths is an idealisation of the world, and our operations in dealing with it [Kitcher, by Resnik] |
| Full Idea: Kitcher says maths is an 'idealising theory', like some in physics; maths idealises features of the world, and practical operations, such as segregating and matching (numbering), measuring, cutting, moving, assembling (geometry), and collecting (sets). | |
| From: report of Philip Kitcher (The Nature of Mathematical Knowledge [1984]) by Michael D. Resnik - Maths as a Science of Patterns One.4.2.2 | |
| A reaction: This seems to be an interesting line, which is trying to be fairly empirical, and avoid basing mathematics on purely a priori understanding. Nevertheless, we do not learn idealisation from experience. Resnik labels Kitcher an anti-realist. |
| 12392 | Mathematical a priorism is conceptualist, constructivist or realist [Kitcher] |
| Full Idea: Proposals for a priori mathematical knowledge have three main types: conceptualist (true in virtue of concepts), constructivist (a construct of the human mind) and realist (in virtue of mathematical facts). | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 02.3) | |
| A reaction: Realism is pure platonism. I think I currently vote for conceptualism, with the concepts deriving from the concrete world, and then being extended by fictional additions, and shifts in the notion of what 'number' means. |
| 18078 | The interest or beauty of mathematics is when it uses current knowledge to advance undestanding [Kitcher] |
| Full Idea: What makes a question interesting or gives it aesthetic appeal is its focussing of the project of advancing mathematical understanding, in light of the concepts and systems of beliefs already achieved. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 09.3) | |
| A reaction: Kitcher defends explanation (the source of understanding, presumably) in terms of unification with previous theories (the 'concepts and systems'). I always have the impression that mathematicians speak of 'beauty' when they see economy of means. |
| 12426 | The 'beauty' or 'interest' of mathematics is just explanatory power [Kitcher] |
| Full Idea: Insofar as we can honor claims about the aesthetic qualities or the interest of mathematical inquiries, we should do so by pointing to their explanatory power. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 09.4) | |
| A reaction: I think this is a good enough account for me (but probably not for my friend Carl!). Beautiful cars are particularly streamlined. Beautiful people look particularly healthy. A beautiful idea is usually wide-ranging. |
| 12395 | Real numbers stand to measurement as natural numbers stand to counting [Kitcher] |
| Full Idea: The real numbers stand to measurement as the natural numbers stand to counting. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.4) |
| 12425 | Complex numbers were only accepted when a geometrical model for them was found [Kitcher] |
| Full Idea: An important episode in the acceptance of complex numbers was the development by Wessel, Argand, and Gauss, of a geometrical model of the numbers. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 07.5) | |
| A reaction: The model was in terms of vectors and rotation. New types of number are spurned until they can be shown to integrate into a range of mathematical practice, at which point mathematicians change the meaning of 'number' (without consulting us). |
| 18071 | A one-operation is the segregation of a single object [Kitcher] |
| Full Idea: We perform a one-operation when we perform a segregative operation in which a single object is segregated. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.3) | |
| A reaction: This is part of Kitcher's empirical but constructive account of arithmetic, which I find very congenial. He avoids the word 'unit', and goes straight to the concept of 'one' (which he treats as more primitive than zero). |
| 18066 | The old view is that mathematics is useful in the world because it describes the world [Kitcher] |
| Full Idea: There is an old explanation of the utility of mathematics. Mathematics describes the structural features of our world, features which are manifested in the behaviour of all the world's inhabitants. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.1) | |
| A reaction: He only cites Russell in modern times as sympathising with this view, but Kitcher gives it some backing. I think the view is totally correct. The digression produced by Cantorian infinities has misled us. |
| 18083 | With infinitesimals, you divide by the time, then set the time to zero [Kitcher] |
| Full Idea: The method of infinitesimals is that you divide by the time, and then set the time to zero. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 10.2) |
| 16150 | One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato] |
| Full Idea: If one is, there must also necessarily be number - Necessarily - But if there is number, there would be many, and an unlimited multitude of beings. ..So if all partakes of being, each part of number would also partake of it. | |
| From: Plato (Parmenides [c.364 BCE], 144a) | |
| A reaction: This seems to commit to numbers having being, then to too many numbers, and hence to too much being - but without backing down and wondering whether numbers had being after all. Aristotle disagreed. |
| 18061 | Mathematical intuition is not the type platonism needs [Kitcher] |
| Full Idea: The intuitions of which mathematicians speak are not those which Platonism requires. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 03.3) | |
| A reaction: The point is that it is not taken to be a 'special' ability, but rather a general insight arising from knowledge of mathematics. I take that to be a good account of intuition, which I define as 'inarticulate rationality'. |
| 12420 | If mathematics comes through intuition, that is either inexplicable, or too subjective [Kitcher] |
| Full Idea: If mathematical statements are don't merely report features of transient and private mental entities, it is unclear how pure intuition generates mathematical knowledge. But if they are, they express different propositions for different people and times. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 03.1) | |
| A reaction: This seems to be the key dilemma which makes Kitcher reject intuition as an a priori route to mathematics. We do, though, just seem to 'see' truths sometimes, and are unable to explain how we do it. |
| 12393 | Intuition is no basis for securing a priori knowledge, because it is fallible [Kitcher] |
| Full Idea: The process of pure intuition does not measure up to the standards required of a priori warrants not because it is sensuous but because it is fallible. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 03.2) |
| 12387 | Mathematical knowledge arises from basic perception [Kitcher] |
| Full Idea: Mathematical knowledge arises from rudimentary knowledge acquired by perception. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], Intro) | |
| A reaction: This is an empiricist manifesto, which asserts his allegiance to Mill, and he gives a sophisticated account of how higher mathematics can be accounted for in this way. Well, he tries to. |
| 12412 | My constructivism is mathematics as an idealization of collecting and ordering objects [Kitcher] |
| Full Idea: The constructivist position I defend claims that mathematics is an idealized science of operations which can be performed on objects in our environment. It offers an idealized description of operations of collecting and ordering. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], Intro) | |
| A reaction: I think this is right. What is missing from Kitcher's account (and every other account I've met) is what is meant by 'idealization'. How do you go about idealising something? Hence my interest in the psychology of abstraction. |
| 18065 | We derive limited mathematics from ordinary things, and erect powerful theories on their basis [Kitcher] |
| Full Idea: I propose that a very limited amount of our mathematical knowledge can be obtained by observations and manipulations of ordinary things. Upon this small base we erect the powerful general theories of modern mathematics. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 05.2) | |
| A reaction: I agree. The three related processes that take us from the experiential base of mathematics to its lofty heights are generalisation, idealisation and abstraction. |
| 18077 | The defenders of complex numbers had to show that they could be expressed in physical terms [Kitcher] |
| Full Idea: Proponents of complex numbers had ultimately to argue that the new operations shared with the original paradigms a susceptibility to construal in physical terms. The geometrical models of complex numbers answered to this need. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 07.5) | |
| A reaction: [A nice example of the verbose ideas which this website aims to express in plain English!] The interest is not that they had to be described physically (which may pander to an uninformed audience), but that they could be so described. |
| 12423 | Analyticity avoids abstract entities, but can there be truth without reference? [Kitcher] |
| Full Idea: Philosophers who hope to avoid commitment to abstract entities by claiming that mathematical statements are analytic must show how analyticity is, or provides a species of, truth not requiring reference. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 04.I) | |
| A reaction: [the last part is a quotation from W.D. Hart] Kitcher notes that Frege has a better account, because he provides objects to which reference can be made. I like this idea, which seems to raise a very large question, connected to truthmakers. |
| 18069 | Arithmetic is an idealizing theory [Kitcher] |
| Full Idea: I construe arithmetic as an idealizing theory. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.2) | |
| A reaction: I find 'generalising' the most helpful word, because everyone seems to understand and accept the idea. 'Idealisation' invokes 'ideals', which lots of people dislike, and lots of philosophers seem to have trouble with 'abstraction'. |
| 18068 | Arithmetic is made true by the world, but is also made true by our constructions [Kitcher] |
| Full Idea: I want to suggest both that arithmetic owes its truth to the structure of the world and that arithmetic is true in virtue of our constructive activity. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.2) | |
| A reaction: Well said, but the problem seems no more mysterious to me than the fact that trees grow in the woods and we build houses out of them. I think I will declare myself to be an 'empirical constructivist' about mathematics. |
| 18070 | We develop a language for correlations, and use it to perform higher level operations [Kitcher] |
| Full Idea: The development of a language for describing our correlational activity itself enables us to perform higher level operations. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.2) | |
| A reaction: This is because all language itself (apart from proper names) is inherently general, idealised and abstracted. He sees the correlations as the nested collections expressed by set theory. |
| 18072 | Constructivism is ontological (that it is the work of an agent) and epistemological (knowable a priori) [Kitcher] |
| Full Idea: The constructivist ontological thesis is that mathematics owes its truth to the activity of an actual or ideal subject. The epistemological thesis is that we can have a priori knowledge of this activity, and so recognise its limits. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.5) | |
| A reaction: The mention of an 'ideal' is Kitcher's personal view. Kitcher embraces the first view, and rejects the second. |
| 18063 | Conceptualists say we know mathematics a priori by possessing mathematical concepts [Kitcher] |
| Full Idea: Conceptualists claim that we have basic a priori knowledge of mathematical axioms in virtue of our possession of mathematical concepts. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 04.1) | |
| A reaction: I sympathise with this view. If concepts are reasonably clear, they will relate to one another in certain ways. How could they not? And how else would you work out those relations other than by thinking about them? |
| 18064 | If meaning makes mathematics true, you still need to say what the meanings refer to [Kitcher] |
| Full Idea: Someone who believes that basic truths of mathematics are true in virtue of meaning is not absolved from the task of saying what the referents of mathematical terms are, or ...what mathematical reality is like. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 04.6) | |
| A reaction: Nice question! He's a fan of getting at the explanatory in mathematics. |
| 229 | The one was and is and will be and was becoming and is becoming and will become [Plato] |
| Full Idea: The one was and is and will be and was becoming and is becoming and will become. | |
| From: Plato (Parmenides [c.364 BCE], 155d) |
| 21821 | Plato's Parmenides has a three-part theory, of Primal One, a One-Many, and a One-and-Many [Plato, by Plotinus] |
| Full Idea: The Platonic Parmenides is more exact [than Parmenides himself]; the distinction is made between the Primal One, a strictly pure Unity, and a secondary One which is a One-Many, and a third which is a One-and-Many. | |
| From: report of Plato (Parmenides [c.364 BCE]) by Plotinus - The Enneads 5.1.08 | |
| A reaction: Plotinus approves of this three-part theory. Parmenides has the problem that the highest Being contains no movement. By placing the One outside Being you can give it powers which an existent thing cannot have. Cf the concept of God. |
| 221 | Absolute ideas, such as the Good and the Beautiful, cannot be known by us [Plato] |
| Full Idea: The absolute good and the beautiful and all which we conceive to be absolute ideas are unknown to us. | |
| From: Plato (Parmenides [c.364 BCE], 134c) |
| 223 | If you deny that each thing always stays the same, you destroy the possibility of discussion [Plato] |
| Full Idea: If a person denies that the idea of each thing is always the same, he will utterly destroy the power of carrying on discussion. | |
| From: Plato (Parmenides [c.364 BCE], 135c) |
| 227 | You must always mean the same thing when you utter the same name [Plato] |
| Full Idea: You must always mean the same thing when you utter the same name. | |
| From: Plato (Parmenides [c.364 BCE], 147d) |
| 210 | It would be absurd to think there were abstract Forms for vile things like hair, mud and dirt [Plato] |
| Full Idea: Are there abstract ideas for such things as hair, mud and dirt, which are particularly vile and worthless? That would be quite absurd. | |
| From: Plato (Parmenides [c.364 BCE], 130d) |
| 220 | The concept of a master includes the concept of a slave [Plato] |
| Full Idea: Mastership in the abstract is mastership of slavery in the abstract. | |
| From: Plato (Parmenides [c.364 BCE], 133e) |
| 211 | If admirable things have Forms, maybe everything else does as well [Plato] |
| Full Idea: It is troubling that if admirable things have abstract ideas, then perhaps everything else must have ideas as well. | |
| From: Plato (Parmenides [c.364 BCE], 130d) |
| 219 | If absolute ideas existed in us, they would cease to be absolute [Plato] |
| Full Idea: None of the absolute ideas exists in us, because then it would no longer be absolute. | |
| From: Plato (Parmenides [c.364 BCE], 133c) |
| 228 | Greatness and smallness must exist, to be opposed to one another, and come into being in things [Plato] |
| Full Idea: These two ideas, greatness and smallness, exist, do they not? For if they did not exist, they could not be opposites of one another, and could not come into being in things. | |
| From: Plato (Parmenides [c.364 BCE], 149e) |
| 16151 | Plato moves from Forms to a theory of genera and principles in his later work [Plato, by Frede,M] |
| Full Idea: It seems to me that Plato in the later dialogues, beginning with the second half of 'Parmenides', wants to substitute a theory of genera and theory of principles that constitute these genera for the earlier theory of forms. | |
| From: report of Plato (Parmenides [c.364 BCE]) by Michael Frede - Title, Unity, Authenticity of the 'Categories' V | |
| A reaction: My theory is that the later Plato came under the influence of the brilliant young Aristotle, and this idea is a symptom of it. The theory of 'principles' sounds like hylomorphism to me. |
| 218 | Participation is not by means of similarity, so we are looking for some other method of participation [Plato] |
| Full Idea: Participation is not by means of likeness, so we must seek some other method of participation. | |
| From: Plato (Parmenides [c.364 BCE], 133a) |
| 215 | If things partake of ideas, this implies either that everything thinks, or that everything actually is thought [Plato] |
| Full Idea: If all things partake of ideas, must either everything be made of thoughts and everything thinks, or everything is thought, and so can't think? | |
| From: Plato (Parmenides [c.364 BCE], 132c) |
| 213 | Each idea is in all its participants at once, just as daytime is a unity but in many separate places at once [Plato] |
| Full Idea: Just as day is in many places at once, but not separated from itself, so each idea might be in all its participants at once. | |
| From: Plato (Parmenides [c.364 BCE], 131b) |
| 216 | If things are made alike by participating in something, that thing will be the absolute idea [Plato] |
| Full Idea: That by participation in which like things are made like, will be the absolute idea, will it not? | |
| From: Plato (Parmenides [c.364 BCE], 132e) |
| 212 | The whole idea of each Form must be found in each thing which participates in it [Plato] |
| Full Idea: The whole idea of each form (of beauty, justice etc) must be found in each thing which participates in it. | |
| From: Plato (Parmenides [c.364 BCE], 131a) |
| 217 | Nothing can be like an absolute idea, because a third idea intervenes to make them alike (leading to a regress) [Plato] |
| Full Idea: It is impossible for anything to be like an absolute idea, because a third idea will appear to make them alike, and if that is like anything, it will lead to another idea, and so on. | |
| From: Plato (Parmenides [c.364 BCE], 133a) |
| 214 | If absolute greatness and great things are seen as the same, another thing appears which makes them seem great [Plato] |
| Full Idea: If you regard the absolute great and the many great things in the same way, will not another appear beyond, by which all these must appear to be great? | |
| From: Plato (Parmenides [c.364 BCE], 132a) |
| 18067 | Abstract objects were a bad way of explaining the structure in mathematics [Kitcher] |
| Full Idea: The original introduction of abstract objects was a bad way of doing justice to the insight that mathematics is concerned with structure. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.1) | |
| A reaction: I'm a fan of explanations in metaphysics, and hence find the concept of 'bad' explanations in metaphysics particularly intriguing. |
| 15851 | Parts must belong to a created thing with a distinct form [Plato] |
| Full Idea: The part would not be the part of many things or all, but of some one character ['ideas'] and of some one thing, which we call a 'whole', since it has come to be one complete [perfected] thing composed [created] of all. | |
| From: Plato (Parmenides [c.364 BCE], 157d) | |
| A reaction: A serious shot by Plato at what identity is. Harte quotes it (125) and shows that 'character' is Gk 'idea', and 'composed' will translate as 'created'. 'Form' links this Platonic passage to Aristotle's hylomorphism. |
| 15846 | In Parmenides, if composition is identity, a whole is nothing more than its parts [Plato, by Harte,V] |
| Full Idea: At the heart of the 'Parmenides' puzzles about composition is the thesis that composition is identity. Considered thus, a whole adds nothing to an ontology that already includes its parts | |
| From: report of Plato (Parmenides [c.364 BCE]) by Verity Harte - Plato on Parts and Wholes 2.5 | |
| A reaction: There has to be more to a unified identity that mere proximity of the parts. When do parts come together, and when do they actually 'compose' something? |
| 15849 | Plato says only a one has parts, and a many does not [Plato, by Harte,V] |
| Full Idea: In 'Parmenides' it is argued that a part cannot be part of a many, but must be part of something one. | |
| From: report of Plato (Parmenides [c.364 BCE], 157c) by Verity Harte - Plato on Parts and Wholes 3.2 | |
| A reaction: This looks like the right way to go with the term 'part'. We presuppose a unity before we even talk of its parts, so we can't get into contradictions and paradoxes about their relationships. |
| 15850 | Anything which has parts must be one thing, and parts are of a one, not of a many [Plato] |
| Full Idea: The whole of which the parts are parts must be one thing composed of many; for each of the parts must be part, not of a many, but of a whole. | |
| From: Plato (Parmenides [c.364 BCE], 157c) | |
| A reaction: This is a key move of metaphysics, and we should hang on to it. The other way madness lies. |
| 13259 | It seems that the One must be composed of parts, which contradicts its being one [Plato] |
| Full Idea: The One must be composed of parts, both being a whole and having parts. So on both grounds the One would thus be many and not one. But it must be not many, but one. So if the One will be one, it will neither be a whole, nor have parts. | |
| From: Plato (Parmenides [c.364 BCE], 137c09), quoted by Kathrin Koslicki - The Structure of Objects 5.2 | |
| A reaction: This is the starting point for Plato's metaphysical discussion of objects. It seems to begin a line of thought which is completed by Aristotle, surmising that only an essential structure can bestow identity on a bunch of parts. |
| 15847 | Two things relate either as same or different, or part of a whole, or the whole of the part [Plato] |
| Full Idea: Everything is surely related to everything as follows: either it is the same or different; or, if it is not the same or different, it would be related as part to whole or as whole to part. | |
| From: Plato (Parmenides [c.364 BCE], 146b) | |
| A reaction: This strikes me as a really helpful first step in trying to analyse the nature of identity. Two things are either two or (actually) one, or related mereologically. |
| 12390 | A priori knowledge comes from available a priori warrants that produce truth [Kitcher] |
| Full Idea: X knows a priori that p iff the belief was produced with an a priori warrant, which is a process which is available to X, and this process is a warrant, and it makes p true. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 01.4) | |
| A reaction: [compression of a formal spelling-out] This is a modified version of Goldman's reliabilism, for a priori knowledge. It sounds a bit circular and uninformative, but it's a start. |
| 12418 | In long mathematical proofs we can't remember the original a priori basis [Kitcher] |
| Full Idea: When we follow long mathematical proofs we lose our a priori warrants for their beginnings. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 02.2) | |
| A reaction: Kitcher says Descartes complains about this problem several times in his 'Regulae'. The problem runs even deeper into all reasoning, if you become sceptical about memory. You have to remember step 1 when you do step 2. |
| 12389 | Knowledge is a priori if the experience giving you the concepts thus gives you the knowledge [Kitcher] |
| Full Idea: Knowledge is independent of experience if any experience which would enable us to acquire the concepts involved would enable us to have the knowledge. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 01.3) | |
| A reaction: This is the 'conceptualist' view of a priori knowledge, which Kitcher goes on to attack, preferring a 'constructivist' view. The formula here shows that we can't divorce experience entirely from a priori thought. I find conceptualism a congenial view. |
| 12416 | We have some self-knowledge a priori, such as knowledge of our own existence [Kitcher] |
| Full Idea: One can make a powerful case for supposing that some self-knowledge is a priori. At most, if not all, of our waking moments, each of us knows of herself that she exists. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 01.6) | |
| A reaction: This is a begrudging concession from a strong opponent to the whole notion of a priori knowledge. I suppose if you ask 'what can be known by thought alone?' then truths about thought ought to be fairly good initial candidates. |
| 12413 | A 'warrant' is a process which ensures that a true belief is knowledge [Kitcher] |
| Full Idea: A 'warrant' refers to those processes which produce belief 'in the right way': X knows that p iff p, and X believes that p, and X's belief that p was produced by a process which is a warrant for it. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 01.2) | |
| A reaction: That is, a 'warrant' is a justification which makes a belief acceptable as knowledge. Traditionally, warrants give you certainty (and are, consequently, rather hard to find). I would say, in the modern way, that warrants are agreed by social convention. |
| 20473 | If experiential can defeat a belief, then its justification depends on the defeater's absence [Kitcher, by Casullo] |
| Full Idea: According to Kitcher, if experiential evidence can defeat someone's justification for a belief, then their justification depends on the absence of that experiential evidence. | |
| From: report of Philip Kitcher (The Nature of Mathematical Knowledge [1984], p.89) by Albert Casullo - A Priori Knowledge 2.3 | |
| A reaction: Sounds implausible. There are trillions of possible defeaters for most beliefs, but to say they literally depend on trillions of absences seems a very odd way of seeing the situation |
| 18075 | Idealisation trades off accuracy for simplicity, in varying degrees [Kitcher] |
| Full Idea: To idealize is to trade accuracy in describing the actual for simplicity of description, and the compromise can sometimes be struck in different ways. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.5) | |
| A reaction: There is clearly rather more to idealisation than mere simplicity. A matchstick man is not an ideal man. |
| 20387 | Aesthetic experience involves perception, but also imagination and understanding [Davies,S] |
| Full Idea: It was suggested that aesthetic experience isn't solely perceptual. It's infused by a cognitive but non-conceptual process described by Kant as involving the free play of the imagination and the understanding. | |
| From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 1.2) | |
| A reaction: This fits literature very well, painting quite well, and music hardly at all. |
| 20385 | The faculty of 'taste' was posited to explain why only some people had aesthetic appreciation [Davies,S] |
| Full Idea: To explain why not everyone who is prepared to encounter a thing's aesthetic properties can recognise them, ...eighteenth century theorists posited the existence of a special faculty of aesthetic perception, that of taste. | |
| From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 1.2) | |
| A reaction: But there seem to be two aspects to taste - first the capacity to enjoy some sorts of art, and second the ability to discriminate the good from the bad. The latter is 'standards' of taste (Hume's title). Do non-musical people lack taste? |
| 20386 | The sublime is negative in awareness of insignificance, and positive in showing understanding [Davies,S] |
| Full Idea: An example of the sublime is the vastness of the night sky. ...It includes negative feelings of insignificance in the face of nature's indifference, power and magnitude, but is positive in that we are capable of comprehending such matters. | |
| From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 1.2) | |
| A reaction: The negative part seems to be a very intellectual experience, with close links to religion, and may be the experience that leads to deism (belief in God's indifference). |
| 20384 | The idea that art forms are linked into a single concept began in the 1740s [Davies,S] |
| Full Idea: The first to link the art forms together explicitly and to separate them from other disciplines and activities were the authors of encyclopedias and books in the 1740s and 1750s. | |
| From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 1.2) | |
| A reaction: Intriguing that no individual seems to get the credit (or blame). Presumably our modern Aesthetics (applied to art) couldn't exist before this move was made - and yet there is plenty of aesthetic discussion in early Greek philosophy. |
| 20390 | Defining art as representation or expression or form were all undermined by the avant-garde [Davies,S] |
| Full Idea: The avant-garde art of the twentieth century played a significant role in defeating definitions that had prevailed in earlier times, such as ones maintaining that art is representation, expression or significant form | |
| From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 2.2) | |
| A reaction: I really think the first rule of philosophical aesthetics is 'ignore Marcel Duchamp'. We wouldn't give up our idea of philosophy if someone managed to publish a long string of expletives in a philosophy journal. Would we?? |
| 20392 | 'Aesthetic functionalism' says art is what is intended to create aesthetic experiences [Davies,S] |
| Full Idea: 'Aesthetic functionalism' maintains that something is an artwork if it is intended to provide the person who contemplates it for its own sake with an aesthetic experience of a significant magnitude on the basis of its aesthetic features. | |
| From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 2.5) | |
| A reaction: [Beardsley is cited as having this view] For this you need to know what an aesthetic 'feature' is, and you'd have to indepdently recognise aesthetic experience. |
| 20405 | Music may be expressive by being 'associated' with other emotional words or events [Davies,S] |
| Full Idea: One view explains music's expressiveness as 'associative'. Through being regularly associated with emotionally charged words or events, particular musical ideas become associated with emotions or moods. | |
| From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 6.4) | |
| A reaction: This is a more promising theory. I take the feeling in music to be parasitic on other feelings we have, and other triggers that evoke them. I'm particularly struck with story-telling (which Levinson and Robinson also like). |
| 20403 | It seems unlikely that sad music expresses a composer's sadness; it takes ages to write [Davies,S] |
| Full Idea: The 'expression theory' holds that if music is sad that is because it expresses the composer's sadness, ...but composers take a long time composing sad works, and may even been gleeful at receiving payment for it. | |
| From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 6.4) | |
| A reaction: [compressed] Pretty conclusive. I see composing as like acting. Just as you can put on a happy or sad face, so a composer can discover music that feels sad or happy. Three movement sonatas don't fit expression at all. |
| 20393 | The 'institutional' theory says art is just something appropriately placed in the 'artworld' [Davies,S] |
| Full Idea: The 'institutional' theory says to be an artwork, an artwork must be appropriately placed within a web of practices, roles and frameworks that comprise an informally organised institution, the artworld. | |
| From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 2.5) | |
| A reaction: [He cites George Dickie] This theory seems to entirely developed to cope with the defiant gesture of Marcel Duchamp. Once I am an established artist, I have the authority to label anything I like as a work of art. Silly. |
| 20402 | Music is too definite to be put into words (not too indefinite!) [Davies,S] |
| Full Idea: Mendelssohn said that what music expresses is not too indefinite to put into words but, on the contrary, it is too definite. | |
| From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 6.4) | |
| A reaction: Not sure whether that is true, but it is a lovely remark. It certainly challenges the naive philosophical view that words are the most precise mode of expression. |
| 20395 | The title of a painting can be vital, and the artist decrees who the portrait represents [Davies,S] |
| Full Idea: The title as given by the artist is something we might need to know (Brueghel's 'Icarus', for example), ...and if a painting depicts one of two twins, it will be the artist's intention that settles which one it is. | |
| From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 3.5) | |
| A reaction: Those two points strike me as conclusively in favour of the importance of an artist's perceived intentions. |
| 20396 | We must know what the work is meant to be, to evaluate the artist's achievement [Davies,S] |
| Full Idea: Learning that a work is a copy of an earlier work, or is done in the style of some other artist, is relevant to an evaluation of what its creator has achieved. | |
| From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 3.6) | |
| A reaction: A simple but powerful point. We evaluate a forgery as an achievement, and the original plate of a great print as the focus of the achievement. We can assess the achievement of a poem in any printed copy. But what about perfect painting replicas? |
| 20399 | Intentionalism says either meaning just is intention, or ('moderate') meaning is successful intention [Davies,S] |
| Full Idea: 'Actual intentionalism' holds that work's meaning is what its author intended, ...while 'moderate actual intentionalism' allows that the author's intention determines the work's meaning only if that intention is carried through successfully. | |
| From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 5.3) | |
| A reaction: [He cites Noel Carroll for the moderate version] D.H. Lawrence, probably with a dose of Freud, said 'trust the work, not the artist' (of Moby Dick, I think). The thought is that authors only half know intentions, and works reveal them. |
| 20401 | The meaning is given by the audience's best guess at the author's intentions [Davies,S] |
| Full Idea: According to the 'hypothetical intentionalist', the work's meaning is determined by the intentions the audience is best justified in attributing to the author, whether or not these are the ones the author actually had. | |
| From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 5.4) | |
| A reaction: [Nehamas, Levinson and Jenefer Robinson are cited] This opens the door for psychiatric interpretations of 'Hamlet', and so on. The experts disagree over the nature of the audience needed to do the job. |
| 20397 | If we could perfectly clone the Mona Lisa, the original would still be special [Davies,S] |
| Full Idea: If we could duplicate 'Mona Lisa', we're likely to be concerned to track the original and keep it separate from its clones, even if we judge that the clone isn't inferior to the original when the goal is art appreciation. | |
| From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 4.3) | |
| A reaction: But why? Is it just a sentimental attachment to what Leonardo worked on? Does the original manuscript of a work of literature have the same importance? We treasure such things, but not for aesthetic reasons. |
| 20398 | Art that is multiply instanced may require at least one instance [Davies,S] |
| Full Idea: Some multiply instanced artworks, such as novel and poems, must have at least one instance. | |
| From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 4.4) | |
| A reaction: This is a comment on the idea that all artworks, even oil paintings and buildings are potentially multiply instanced (so the work is the type - Wollheim's view, not one of the tokens). |
| 20404 | Music isn't just sad because it makes the listener feel sad [Davies,S] |
| Full Idea: The 'arousal' theory says music is sad because it moves the hearer to sadness, ...but this seems to get things back to front, because we normally think it is because the music is sad that it moves the listener to sadness. | |
| From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 6.4) | |
| A reaction: The objection is right. If Beethoven's 'Ode to Joy' always makes me feel sad (because it is so hopelessly optimistic), then that makes the music sad. Is the theory saying that there are no feelings in the music? |
| 22705 | If the depiction of evil is glorified, that is an artistic flaw [Davies,S] |
| Full Idea: One case when the depiction of immorality becomes an artistic flaw …is when it is presented in brutal detail in a way that glorifies it. The celebration of evil corrodes the work's artistic value. | |
| From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 8.7) | |
| A reaction: This doesn't allow for the case where the evil is celebrated in one part of a novel, yet the novel as a whole does not endorse the evil. The Marquis de Sade seems to have fully celebrated what we take to be evil. |
| 22707 | It is an artistic defect if excessive moral outrage distorts the story, and narrows our sympathies [Davies,S] |
| Full Idea: The positive moral stance of a story can be an artistic defect where it shapes the story in an inappropriate fashion. If it displays disproportionate moral outrage, …it reveals a lack of toleration, compassion, or insight into its subject-matter. | |
| From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 8.7) | |
| A reaction: There could be narrative irony in a story told by an angry and puritanical person, which continually condemns wickedness, with the reader expected to have a more tolerant attitude. Hard to think of any examples of this problem. |
| 22706 | A work which seeks approval for immorality, but alienates the audience, is a failure [Davies,S] |
| Full Idea: A work that looks for the audience's sympathetic approval and alienates them instead, because it's both morally repulsive and incoherent in what it requires them to suppose, isn't an artistic success. | |
| From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 8.7) | |
| A reaction: The implication seems to be that works are only successful if they achieve what the creator consciously intended. Lawrence said trust the novel, not the novelist. Milton's Satan is a famous example of heroism not intended by the author. |
| 22704 | Immorality may or may not be an artistic defect [Davies,S] |
| Full Idea: Immorality in art is sometimes an artistic defect and sometimes not. | |
| From: Stephen Davies (The Philosophy of Art (2nd ed) [2016], 8.7) | |
| A reaction: Davies seems to avoid the 'immoralist' view, that immorality in a work of art can sometimes be a strength. A sharp distinction is needed, I think, between the morality of what is depicted, and the morality of the whole artwork. |
| 222 | Only a great person can understand the essence of things, and an even greater person can teach it [Plato] |
| Full Idea: Only a man of very great natural gifts will be able to understand that everything has a class and absolute essence, and an even more wonderful man can teach this. | |
| From: Plato (Parmenides [c.364 BCE], 135a) |
| 225 | The unlimited has no shape and is endless [Plato] |
| Full Idea: The unlimited partakes neither of the round nor of the straight, because it has no ends nor edges. | |
| From: Plato (Parmenides [c.364 BCE], 137e) |
| 233 | Some things do not partake of the One [Plato] |
| Full Idea: The others cannot partake of the one in any way; they can neither partake of it nor of the whole. | |
| From: Plato (Parmenides [c.364 BCE], 159d) | |
| A reaction: Compare Idea 231 |
| 2062 | The only movement possible for the One is in space or in alteration [Plato] |
| Full Idea: If the One moves it either moves spatially or it is altered, since these are the only motions. | |
| From: Plato (Parmenides [c.364 BCE], 138b) |
| 231 | Everything partakes of the One in some way [Plato] |
| Full Idea: The others are not altogether deprived of the one, for they partake of it in some way. | |
| From: Plato (Parmenides [c.364 BCE], 157c) | |
| A reaction: Compare Idea 233. |
| 234 | We couldn't discuss the non-existence of the One without knowledge of it [Plato] |
| Full Idea: There must be knowledge of the one, or else not even the meaning of the words 'if the one does not exist' would be known. | |
| From: Plato (Parmenides [c.364 BCE], 160d) |