61 ideas
2056 | Philosophers are always switching direction to something more interesting [Plato] |
Full Idea: Philosophers are always ready to change direction, if a topic crops up which is more attractive than the one to hand. | |
From: Plato (Theaetetus [c.368 BCE], 172d) | |
A reaction: Which sounds trivial, but it may be what God does. |
2086 | Understanding mainly involves knowing the elements, not their combinations [Plato] |
Full Idea: A perfect grasp of any subject depends far more on knowing elements than on knowing complexes. | |
From: Plato (Theaetetus [c.368 BCE], 206b) |
2083 | Either a syllable is its letters (making parts as knowable as whole) or it isn't (meaning it has no parts) [Plato] |
Full Idea: Either a syllable is not the same as its letters, in which case it cannot have the letters as parts of itself, or it is the same as its letters, in which case these basic elements are just as knowable as it is. | |
From: Plato (Theaetetus [c.368 BCE], 205b) |
2082 | A rational account is essentially a weaving together of things with names [Plato] |
Full Idea: Just as primary elements are woven together, so their names may be woven together to produce a spoken account, because an account is essentially a weaving together of names. | |
From: Plato (Theaetetus [c.368 BCE], 202b) | |
A reaction: If justification requires 'logos', and logos is a 'weaving together of names', then Plato might be taken as endorsing the coherence account of justification. Or do the two 'weavings' correspond? |
2052 | Eristic discussion is aggressive, but dialectic aims to help one's companions in discussion [Plato] |
Full Idea: Eristic discussions involve as many tricks and traps as possible, but dialectical discussions involve being serious and correcting the interlocutor's mistakes only when they are his own fault or the result of past conditioning. | |
From: Plato (Theaetetus [c.368 BCE], 167e) |
15854 | A primary element has only a name, and no logos, but complexes have an account, by weaving the names [Plato] |
Full Idea: A primary element cannot be expressed in an account; it can only be named, for a name is all that it has. But with the things composed of these ...just as the elements are woven together, so the names can woven to become an account. | |
From: Plato (Theaetetus [c.368 BCE], 202b01-3) | |
A reaction: This is the beginning of what I see as Aristotle's metaphysics, as derived from his epistemology, that is, ontology is what explains, and what we can give an account [logos] of. Aristotle treats this under 'definitions'. |
9570 | In Field's Platonist view, set theory is false because it asserts existence for non-existent things [Field,H, by Chihara] |
Full Idea: Field commits himself to a Platonic view of mathematics. The theorems of set theory are held to imply or presuppose the existence of things that don't in fact exist. That is why he believes that these theorems are false. | |
From: report of Hartry Field (Science without Numbers [1980]) by Charles Chihara - A Structural Account of Mathematics 11.1 | |
A reaction: I am sympathetic to Field, but this sounds wrong. A response that looks appealing is that maths is hypothetical ('if-thenism') - the truth is in the logical consequences, not in the ontological presuppositions. |
9358 | There are several logics, none of which will ever derive falsehoods from truth [Lewis,CI] |
Full Idea: The fact is that there are several logics, markedly different, each self-consistent in its own terms and such that whoever, using it, avoids false premises, will never reach a false conclusion. | |
From: C.I. Lewis (A Pragmatic Conception of the A Priori [1923], p.366) | |
A reaction: As the man who invented modal logic in five different versions, he speaks with some authority. Logicians now debate which version is the best, so how could that be decided? You could avoid false conclusions by never reasoning at all. |
10260 | Logical consequence is defined by the impossibility of P and ¬q [Field,H, by Shapiro] |
Full Idea: Field defines logical consequence by taking the notion of 'logical possibility' as primitive. Hence q is a consequence of P if the conjunction of the items in P with the negation of q is not possible. | |
From: report of Hartry Field (Science without Numbers [1980]) by Stewart Shapiro - Philosophy of Mathematics 7.2 | |
A reaction: The question would then be whether it is plausible to take logical possibility as primitive. Presumably only intuition could support it. But then intuition will equally support natural and metaphysical possibilities. |
9357 | Excluded middle is just our preference for a simplified dichotomy in experience [Lewis,CI] |
Full Idea: The law of excluded middle formulates our decision that whatever is not designated by a certain term shall be designated by its negative. It declares our purpose to make a complete dichotomy of experience, ..which is only our penchant for simplicity. | |
From: C.I. Lewis (A Pragmatic Conception of the A Priori [1923], p.365) | |
A reaction: I find this view quite appealing. 'Look, it's either F or it isn't!' is a dogmatic attitude which irritates a lot of people, and appears to be dispensible. Intuitionists in mathematics dispense with the principle, and vagueness threatens it. |
9364 | Names represent a uniformity in experience, or they name nothing [Lewis,CI] |
Full Idea: A name must represent some uniformity in experience or it names nothing. | |
From: C.I. Lewis (A Pragmatic Conception of the A Priori [1923], p.368) | |
A reaction: I like this because, in the quintessentially linguistic debate about the exact logical role of names, it reminds us that names arise because of the way reality is; they are not sui generis private games for logicians. |
8958 | In Field's version of science, space-time points replace real numbers [Field,H, by Szabó] |
Full Idea: Field's nominalist version of science develops a version of Newtonian gravitational theory, where no quantifiers range over mathematical entities, and space-time points and regions play the role of surrogates for real numbers. | |
From: report of Hartry Field (Science without Numbers [1980]) by Zoltán Gendler Szabó - Nominalism 5.1 | |
A reaction: This seems to be a very artificial contrivance, but Field has launched a programme for rewriting science so that numbers can be omitted. All of this is Field's rebellion against the Indispensability Argument for mathematics. I sympathise. |
18221 | 'Metric' axioms uses functions, points and numbers; 'synthetic' axioms give facts about space [Field,H] |
Full Idea: There are two approaches to axiomatising geometry. The 'metric' approach uses a function which maps a pair of points into the real numbers. The 'synthetic' approach is that of Euclid and Hilbert, which does without real numbers and functions. | |
From: Hartry Field (Science without Numbers [1980], 5) |
10216 | We master arithmetic by knowing all the numbers in our soul [Plato] |
Full Idea: It must surely be true that a man who has completely mastered arithmetic knows all numbers? Because there are pieces of knowledge covering all numbers in his soul. | |
From: Plato (Theaetetus [c.368 BCE], 198b) | |
A reaction: This clearly views numbers as objects. Expectation of knowing them all is a bit startling! They also appear to be innate in us, and hence they appear to be Forms. See Aristotle's comment in Idea 645. |
8757 | The Indispensability Argument is the only serious ground for the existence of mathematical entities [Field,H] |
Full Idea: There is one and only one serious argument for the existence of mathematical entities, and that is the Indispensability Argument of Putnam and Quine. | |
From: Hartry Field (Science without Numbers [1980], p.5), quoted by Stewart Shapiro - Thinking About Mathematics 9.1 | |
A reaction: Personally I don't believe (and nor does Field) that this gives a good enough reason to believe in such things. Quine (who likes 'desert landscapes' in ontology) ends up believing that sets are real because of his argument. Not for me. |
18212 | Nominalists try to only refer to physical objects, or language, or mental constructions [Field,H] |
Full Idea: The most popular approach of nominalistically inclined philosophers is to try to reinterpret mathematics, so that its terms and quantifiers only make reference to, say, physical objects, or linguistic expressions, or mental constructions. | |
From: Hartry Field (Science without Numbers [1980], Prelim) | |
A reaction: I am keen on naturalism and empiricism, but only referring to physical objects is a non-starter. I think I favour constructions, derived from the experience of patterns, and abstracted, idealised and generalised. Field says application is the problem. |
10261 | The application of mathematics only needs its possibility, not its truth [Field,H, by Shapiro] |
Full Idea: Field argues that to account for the applicability of mathematics, we need to assume little more than the possibility of the mathematics, not its truth. | |
From: report of Hartry Field (Science without Numbers [1980]) by Stewart Shapiro - Philosophy of Mathematics 7.2 | |
A reaction: Very persuasive. We can apply chess to real military situations, provided that chess isn't self-contradictory (or even naturally impossible?). |
18218 | Hilbert explains geometry, by non-numerical facts about space [Field,H] |
Full Idea: Facts about geometric laws receive satisfying explanations, by the intrinsic facts about physical space, i.e. those laid down without reference to numbers in Hilbert's axioms. | |
From: Hartry Field (Science without Numbers [1980], 3) | |
A reaction: Hilbert's axioms mention points, betweenness, segment-congruence and angle-congruence (Field 25-26). Field cites arithmetic and geometry (as well as Newtonian mechanics) as not being dependent on number. |
9623 | Field needs a semantical notion of second-order consequence, and that needs sets [Brown,JR on Field,H] |
Full Idea: Field needs the notion of logical consequence in second-order logic, but (since this is not recursively axiomatizable) this is a semantical notion, which involves the idea of 'true in all models', a set-theoretic idea if there ever was one. | |
From: comment on Hartry Field (Science without Numbers [1980], Ch.4) by James Robert Brown - Philosophy of Mathematics | |
A reaction: Brown here summarises a group of critics. Field was arguing for modern nominalism, that actual numbers could (in principle) be written out of the story, as useful fictions. Popper's attempt to dump induction seemed to need induction. |
18215 | It seems impossible to explain the idea that the conclusion is contained in the premises [Field,H] |
Full Idea: No clear explanation of the idea that the conclusion was 'implicitly contained in' the premises was ever given, and I do not believe that any clear explanation is possible. | |
From: Hartry Field (Science without Numbers [1980], 1) |
18216 | Abstractions can form useful counterparts to concrete statements [Field,H] |
Full Idea: Abstract entities are useful because we can use them to formulate abstract counterparts of concrete statements. | |
From: Hartry Field (Science without Numbers [1980], 3) | |
A reaction: He defends the abstract statements as short cuts. If the concrete statements were 'true', then it seems likely that the abstract counterparts will also be true, which is not what fictionalism claims. |
18214 | Mathematics is only empirical as regards which theory is useful [Field,H] |
Full Idea: Mathematics is in a sense empirical, but only in the rather Pickwickian sense that is an empirical question as to which mathematical theory is useful. | |
From: Hartry Field (Science without Numbers [1980], 1) | |
A reaction: Field wants mathematics to be fictions, and not to be truths. But can he give an account of 'useful' that does not imply truth? Only in a rather dubiously pragmatist way. A novel is not useful. |
18210 | Why regard standard mathematics as truths, rather than as interesting fictions? [Field,H] |
Full Idea: Why regard the axioms of standard mathematics as truths, rather than as fictions that for a variety of reasons mathematicians have become interested in? | |
From: Hartry Field (Science without Numbers [1980], p.viii) |
2060 | There seem to be two sorts of change: alteration and motion [Plato] |
Full Idea: There are two kinds of change, I think: alteration and motion. | |
From: Plato (Theaetetus [c.368 BCE], 181d) | |
A reaction: Idea 1700 is better than this. |
18211 | You can reduce ontological commitment by expanding the logic [Field,H] |
Full Idea: One can often reduce one's ontological commitments by expanding one's logic. | |
From: Hartry Field (Science without Numbers [1980], p.ix) | |
A reaction: I don't actually understand this idea, but that's never stopped me before. Clearly, this sounds like an extremely interesting thought, and hence I should aspire to understand it. So I do aspire to understand it. First, how do you 'expand' a logic? |
8959 | Field presumes properties can be eliminated from science [Field,H, by Szabó] |
Full Idea: Field regards the eliminability of apparent reference to properties from the language of science as a foregone result. | |
From: report of Hartry Field (Science without Numbers [1980]) by Zoltán Gendler Szabó - Nominalism 5.1 n50 | |
A reaction: Field is a nominalist who also denies the existence of mathematics as part of science. He has a taste for ontological 'desert landscapes'. I have no idea what a property really is, so I think he is on to something. |
18213 | Abstract objects are only applicable to the world if they are impure, and connect to the physical [Field,H] |
Full Idea: To be able to apply any postulated abstract entities to the physical world, we need impure abstact entities, e.g. functions that map physical objects into pure abstract objects. | |
From: Hartry Field (Science without Numbers [1980], 1) | |
A reaction: I am a fan of 'impure metaphysics', and this pinpoints my reason very nicely. |
2084 | If a word has no parts and has a single identity, it turns out to be the same kind of thing as a letter [Plato] |
Full Idea: If a complex or a syllable has no parts and is a single identity, hasn't it turned out to be the same kind of thing as an element or letter? | |
From: Plato (Theaetetus [c.368 BCE], 205d) |
15844 | A sum is that from which nothing is lacking, which is a whole [Plato] |
Full Idea: But this sum now - isn't it just when there is nothing lacking that it is a sum? Yes, necessarily. And won't this very same thing - that from which nothing is lacking - be a whole? | |
From: Plato (Theaetetus [c.368 BCE], 205a) | |
A reaction: This seems to be right, be rather too vague and potentially circular to be of much use. What is the criterion for deciding that nothing is lacking? |
15843 | The whole can't be the parts, because it would be all of the parts, which is the whole [Plato] |
Full Idea: The whole does not consist of parts; for it did, it would be all the parts and so would be the sum. | |
From: Plato (Theaetetus [c.368 BCE], 204e) | |
A reaction: That is, 'the whole is the sum of its parts' is a tautology! The claim that 'the whole is more than the sum of its parts' gets into similar trouble. See Verity Harte on this. |
9362 | Necessary truths are those we will maintain no matter what [Lewis,CI] |
Full Idea: Those laws and those laws only have necessary truth which we are prepared to maintain, no matter what. | |
From: C.I. Lewis (A Pragmatic Conception of the A Priori [1923], p.367) | |
A reaction: This bold and simple claim has famously been torpedoed by a well-known counterexample - that virtually every human being will cling on to the proposition "dogs have at some time existed" no matter what, but it clearly isn't a necessary truth. |
2080 | Things are only knowable if a rational account (logos) is possible [Plato] |
Full Idea: Things which are susceptible to a rational account are knowable. | |
From: Plato (Theaetetus [c.368 BCE], 201d) |
16126 | Expertise is knowledge of the whole by means of the parts [Plato] |
Full Idea: A man has passed from mere judgment to expert knowledge of the being of a wagon when he has done so in virtue of having gone over the whole by means of the elements. | |
From: Plato (Theaetetus [c.368 BCE], 207c) | |
A reaction: Plato is emphasising that the expert must know the hundred parts of a wagon, and not just the half dozen main components, but here the point is to go over the whole via the parts, and not just list the parts. |
2050 | It is impossible to believe something which is held to be false [Plato] |
Full Idea: It is impossible to believe something which is not the case. | |
From: Plato (Theaetetus [c.368 BCE], 167a) |
2076 | How can a belief exist if its object doesn't exist? [Plato] |
Full Idea: If the object of a belief is what is not, the object of this belief is nothing; but if there is no object to a belief, then that is not belief at all. | |
From: Plato (Theaetetus [c.368 BCE], 189a) |
9365 | We can maintain a priori principles come what may, but we can also change them [Lewis,CI] |
Full Idea: The a priori contains principles which can be maintained in the face of all experience, representing the initiative of the mind. But they are subject to alteration on pragmatic grounds, if expanding experience shows their intellectual infelicity. | |
From: C.I. Lewis (A Pragmatic Conception of the A Priori [1923], p.373) | |
A reaction: [compressed] This simply IS Quine's famous 'web of belief' picture, showing how firmly Quine is in the pragmatist tradition. Lewis treats a priori principles as a pragmatic toolkit, which can be refined to be more effective. Not implausible... |
2045 | Perception is infallible, suggesting that it is knowledge [Plato] |
Full Idea: Perception is always of something that is, and it is infallible, which suggests that it is knowledge. | |
From: Plato (Theaetetus [c.368 BCE], 152c) |
2067 | Our senses could have been separate, but they converge on one mind [Plato] |
Full Idea: It would be peculiar if each of us were like a Trojan horse, with a whole bunch of senses sitting inside us, rather than that all these perceptions converge onto a single identity (mind, or whatever one ought to call it). | |
From: Plato (Theaetetus [c.368 BCE], 184d) |
2068 | With what physical faculty do we perceive pairs of opposed abstract qualities? [Plato] |
Full Idea: With what physical faculty do we perceive being and not-being, similarity and dissimilarity, identity and difference, oneness and many, odd and even and other maths, ….fineness and goodness? | |
From: Plato (Theaetetus [c.368 BCE], 185d) |
2069 | Thought must grasp being itself before truth becomes possible [Plato] |
Full Idea: If you can't apprehend being you can't apprehend truth, and so a thing could not be known. Therefore knowledge is not located in immediate experience but in thinking about it, since the latter makes it possible to grasp being and truth. | |
From: Plato (Theaetetus [c.368 BCE], 186c) |
2078 | You might mistake eleven for twelve in your senses, but not in your mind [Plato] |
Full Idea: Sight or touch might make someone take eleven for twelve, but he could never form this mistaken belief about the contents of his mind. | |
From: Plato (Theaetetus [c.368 BCE], 195e) |
2089 | An inadequate rational account would still not justify knowledge [Plato] |
Full Idea: If you don't know which letters belong together in the right syllables…it is possible for true belief to be accompanied by a rational account and still not be entitled to the name of knowledge. | |
From: Plato (Theaetetus [c.368 BCE], 208b) | |
A reaction: In each case of justification there is a 'clinching' stage, for which there is never going to be a strict rule. It might be foundational, but equally it might be massive coherence, or no alternative. |
2085 | Parts and wholes are either equally knowable or equally unknowable [Plato] |
Full Idea: Either a syllable and its letters are equally knowable and expressible in a rational account, or they are both equally unknowable and inexpressible. | |
From: Plato (Theaetetus [c.368 BCE], 205e) | |
A reaction: Presumably you could explain the syllable by the letters, but not vice versa, but he must mean that the explanation is worthless without the letters being explained too. So all explanation is worthless? |
2091 | Without distinguishing marks, how do I know what my beliefs are about? [Plato] |
Full Idea: If I only have beliefs about Theaetetus when I don't know his distinguishing mark, how on earth were my beliefs about you rather than anyone else? | |
From: Plato (Theaetetus [c.368 BCE], 209b) | |
A reaction: This is a rather intellectualist approach to mental activity. Presumably Theaetetus has lots of distinguishing marks, but they are not conscious. Must Socrates know everything? |
2087 | A rational account might be seeing an image of one's belief, like a reflection in a mirror [Plato] |
Full Idea: A rational account might be forming an image of one's belief, as in a mirror or a pond. | |
From: Plato (Theaetetus [c.368 BCE], 206d) | |
A reaction: Not promising, since the image is not going to be clearer than the original, or contain any new information. Maybe it would be clarified by being 'framed', instead of drifting in muddle. |
2090 | A rational account involves giving an image, or analysis, or giving a differentiating mark [Plato] |
Full Idea: A third sort of rational account (after giving an image, or analysing elements) is being able to mention some mark which differentiates the object in question ('the sun is the brightest heavenly body'). | |
From: Plato (Theaetetus [c.368 BCE], 208c) | |
A reaction: This is Plato's clearest statement of what would be involved in adding the necessary logos to your true belief. An image of it, or an analysis, or an individuation. How about a cause? |
2081 | Maybe primary elements can be named, but not receive a rational account [Plato] |
Full Idea: Maybe the primary elements of which things are composed are not susceptible to rational accounts. Each of them taken by itself can only be named, but nothing further can be said about it. | |
From: Plato (Theaetetus [c.368 BCE], 201e) | |
A reaction: This still seems to be more or less the central issue in philosophy - which things should be treated as 'primitive', and which other things are analysed and explained using the primitive tools? |
2088 | A rational account of a wagon would mean knowledge of its hundred parts [Plato] |
Full Idea: In the case of a wagon, we may only have correct belief, but someone who is able to explain what it is by going through its hundred parts has got hold of a rational account. | |
From: Plato (Theaetetus [c.368 BCE], 207b) | |
A reaction: A wonderful example. In science, you know smoking correlates with cancer, but you only know it when you know the mechanism, the causal structure. This may be a general truth. |
2047 | What evidence can be brought to show whether we are dreaming or not? [Plato] |
Full Idea: What evidence could be brought if we were asked at this very moment whether we are asleep and are dreaming all our thoughts? | |
From: Plato (Theaetetus [c.368 BCE], 158b) |
2054 | Clearly some people are superior to others when it comes to medicine [Plato] |
Full Idea: In medicine, at least, most people are not self-sufficient at prescribing and effecting cures for themselves, and here some people are superior to others. | |
From: Plato (Theaetetus [c.368 BCE], 171e) |
2053 | If you claim that all beliefs are true, that includes beliefs opposed to your own [Plato] |
Full Idea: To say that everyone believes what is the case, is to concede the truth of the oppositions' beliefs; in other words, the person has to concede that he himself is wrong. | |
From: Plato (Theaetetus [c.368 BCE], 171a) |
2059 | How can a relativist form opinions about what will happen in the future? [Plato] |
Full Idea: Does a relativist have any authority to decide about things which will happen in the future? | |
From: Plato (Theaetetus [c.368 BCE], 178c) | |
A reaction: Nice question! It seems commonsense that such speculations are possible, but without a concept of truth they are ridiculous. |
18222 | Beneath every extrinsic explanation there is an intrinsic explanation [Field,H] |
Full Idea: A plausible methodological principle is that underlying every good extrinsic explanation there is an intrinsic explanation. | |
From: Hartry Field (Science without Numbers [1980], 5) | |
A reaction: I'm thinking that Hartry Field is an Aristotelian essentialist, though I bet he would never admit it. |
9361 | We have to separate the mathematical from physical phenomena by abstraction [Lewis,CI] |
Full Idea: Physical processes present us with phenomena in which the purely mathematical has to be separated out by abstraction. | |
From: C.I. Lewis (A Pragmatic Conception of the A Priori [1923], p.367) | |
A reaction: This is the father of modal logic endorsing traditional abstractionism, it seems. He is also, though, endorsing the view that a priori knowledge is created by us, with pragmatic ends in view. |
9917 | 'Abstract' is unclear, but numbers, functions and sets are clearly abstract [Field,H] |
Full Idea: The term 'abstract entities' may not be entirely clear, but one thing that does seem clear is that such alleged entities as numbers, functions and sets are abstract. | |
From: Hartry Field (Science without Numbers [1980], p.1), quoted by JP Burgess / G Rosen - A Subject with No Object I.A.1.a | |
A reaction: Field firmly denies the existence of such things. Sets don't seem a great problem, if the set is a herd of elephants, but the null and singleton sets show up the difficulties. |
9363 | Science seeks classification which will discover laws, essences, and predictions [Lewis,CI] |
Full Idea: The scientific search is for such classification as will make it possible to correlate appearance and behaviour, to discover law, to penetrate to the "essential nature" of things in order that behaviour may become predictable. | |
From: C.I. Lewis (A Pragmatic Conception of the A Priori [1923], p.368) | |
A reaction: Modern scientific essentialists no longer invoke scare quotes, and I think we should talk of the search for the 'mechanisms' which explain behaviour, but Lewis seems to have been sixty years ahead of his time. |
18223 | In theories of fields, space-time points or regions are causal agents [Field,H] |
Full Idea: According to theories that take the notion of a field seriously, space-time points or regions are fully-fledge causal agents. | |
From: Hartry Field (Science without Numbers [1980], n 23) |
18220 | Both philosophy and physics now make substantivalism more attractive [Field,H] |
Full Idea: In general, it seems to me that recent developments in both philosophy and physics have made substantivalism a much more attractive position than it once was. | |
From: Hartry Field (Science without Numbers [1980], 4) | |
A reaction: I'm intrigued as to what philosophical developments are involved in this. The arrival of fields is the development in physics. |
18219 | Relational space is problematic if you take the idea of a field seriously [Field,H] |
Full Idea: The problem of the relational view of space is especially acute in the context of physical theories that take the notion of a field seriously, e.g. classical electromagnetic theory. | |
From: Hartry Field (Science without Numbers [1980], 4) | |
A reaction: In the Leibniz-Clarke debate I sided with the Newtonian Clarke (defending absolute space), and it looks like modern science agrees with me. Nothing exists purely as relations. |
2058 | God must be the epitome of goodness, and we can only approach a divine state by being as good as possible [Plato] |
Full Idea: It is impossible for God to be immoral and not to be the acme of morality; and the only way any of us can approximate to God is to become as moral as possible. | |
From: Plato (Theaetetus [c.368 BCE], 176c) |
2057 | There must always be some force of evil ranged against good [Plato] |
Full Idea: The elimination of evil is impossible, Theodorus; there must always be some force ranged against good. | |
From: Plato (Theaetetus [c.368 BCE], 176a) |