48 ideas
| 18730 | The history of philosophy only matters if the subject is a choice between rival theories [Wittgenstein] |
| Full Idea: If philosophy were a matter of choice between rival theories, then it would be sound to teach it historically. But if it is not, then it is a fault to teach it historically, because it is quite unnecessary; we can tackle the subject direct. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], C V A) | |
| A reaction: Wittgenstein was a bit notorious for not knowing the history of the subject terribly well, and this explains why. Presumably our tackling the subject direct will not have the dreadful consequence of producing yet another theory. |
| 18704 | Philosophy tries to be rid of certain intellectual puzzles, irrelevant to daily life [Wittgenstein] |
| Full Idea: Philosophy is the attempt to be rid of a particular kind of puzzlement. This 'philosophical' puzzlement is one of the intellect and not of instinct. Philosophical puzzles are irrelevant to our every-day life. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], A I.1) | |
| A reaction: All enquiry begins with puzzles, and they are cured by explanations, which result in understanding. In that sense he is right. I entirely disagree that the puzzles are irrelevant to daily life. |
| 18710 | Philosophers express puzzlement, but don't clearly state the puzzle [Wittgenstein] |
| Full Idea: Philosophers as 'Why?' and 'What?' without knowing clearly what their questions are. They are expressing a feeling of mental uneasiness. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], B I.1) | |
| A reaction: He suggests it is childish to express puzzlement, instead of asking for precise information. How odd. All enquiries start with vague puzzlement, which gradually comes into focus, or else is abandoned. |
| 18732 | We don't need a theory of truth, because we use the word perfectly well [Wittgenstein] |
| Full Idea: It is nonsense to try to find a theory of truth, because we can see that in everyday life we use the word quite clearly and definitely in various different senses. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], C V B) | |
| A reaction: This was a year before Tarski published his famous theory of truth for formal languages. Prior to that, most philosophers were giving up on truth. Would he say the same about 'gravity' or 'inflation'? |
| 18714 | We already know what we want to know, and analysis gives us no new facts [Wittgenstein] |
| Full Idea: In philosophy we know already all that we want to know; philosophical analysis does not give us any new facts. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], B V.1) |
| 8623 | Proof reveals the interdependence of truths, as well as showing their certainty [Euclid, by Frege] |
| Full Idea: Euclid gives proofs of many things which anyone would concede to him without question. ...The aim of proof is not merely to place the truth of a proposition beyond doubt, but also to afford us insight into the dependence of truths upon one another. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by Gottlob Frege - Grundlagen der Arithmetik (Foundations) §02 | |
| A reaction: This connects nicely with Shoemaker's view of analysis (Idea 8559), which I will adopt as my general view. I've always thought of philosophy as the aspiration to wisdom through the cartography of concepts. |
| 18706 | Words of the same kind can be substituted in a proposition without producing nonsense [Wittgenstein] |
| Full Idea: 'Blue' and 'brown' are of the same kind, for the substitution of one for the other, though it may falsify the proposition, does not make nonsense of it. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], A I.4) | |
| A reaction: He chooses an easy example, because they are determinates of the determinable 'coloured'. What if I say 'the sky is blue', and then substitute 'frightening' for 'blue'? |
| 18735 | Talking nonsense is not following the rules [Wittgenstein] |
| Full Idea: Talking nonsense is not following the rules. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], C X) | |
| A reaction: He doesn't seem to distinguish between syntax and semantics, and makes it sound as if all nonsense is syntactic, which it isn't. |
| 18719 | Grammar says that saying 'sound is red' is not false, but nonsense [Wittgenstein] |
| Full Idea: If grammar says that you cannot say that a sound is red, it means not that it is false to say so but that it is nonsense - i.e. not a language at all. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], B IX.6) | |
| A reaction: I am baffled as to why he thinks 'grammar' is what prohibits such a statement. Surely the world, the nature of sound and colour, is what makes the application of the predicate wrong. Sounds aren't coloured, so they can't be red. False, not nonsense. |
| 18731 | There is no theory of truth, because it isn't a concept [Wittgenstein] |
| Full Idea: It is wrong to say that there is any one theory of truth, for truth is not a concept. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], C V B) | |
| A reaction: This makes you wonder how he understood the word 'concept'. In most modern discussions truth seems to be a concept, and in Frege it can be an unsaturated predicate which is satisfied by sentences or thoughts. |
| 18707 | All thought has the logical form of reality [Wittgenstein] |
| Full Idea: Thought must have the logical form of reality if it is to be thought at all. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], A V.1) | |
| A reaction: This links nicely the idea that true thoughts somehow share the structure of what they refer to, with the idea of logical form in logic. But maybe logical form is a fiction we offer in order to obtain a spurious map of reality. |
| 13907 | If you pick an arbitrary triangle, things proved of it are true of all triangles [Euclid, by Lemmon] |
| Full Idea: Euclid begins proofs about all triangles with 'let ABC be a triangle', but ABC is not a proper name. It names an arbitrarily selected triangle, and if that has a property, then we can conclude that all triangles have the property. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by E.J. Lemmon - Beginning Logic 3.2 | |
| A reaction: Lemmon adds the proviso that there must be no hidden assumptions about the triangle we have selected. You must generalise the properties too. Pick a triangle, any triangle, say one with three angles of 60 degrees; now generalise from it. |
| 18724 | In logic nothing is hidden [Wittgenstein] |
| Full Idea: In logic nothing is hidden. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], B XII.3) | |
| A reaction: If so, then the essence of logic must be there for all to see. The rules of natural deduction are a good shot at showing this. |
| 18709 | Laws of logic are like laws of chess - if you change them, it's just a different game [Wittgenstein] |
| Full Idea: I might as well question the laws of logic as the laws of chess. If I change the rules it is a different game and there is an end of it. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], A XI.3) | |
| A reaction: No, that isn't the end of it, because there are meta-criteria for preferring one game to another. Why don't we just give up classical logic? It would be such fun to have a wild wacky logic. We can start with 'tonk'. |
| 18736 | Contradiction is between two rules, not between rule and reality [Wittgenstein] |
| Full Idea: Contradiction is between one rule and another, not between rule and reality. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], C XIII) | |
| A reaction: If I say 'he is sitting' and 'he is standing', it seems to be reality which produces the contradiction. What 'rule' could possibly do it? The rule which says sitting and standing are incompatible? But what makes that so? |
| 18723 | We may correctly use 'not' without making the rule explicit [Wittgenstein] |
| Full Idea: Correct use does not imply the ability to make the rules explicit. Understanding 'not' is like understanding a move in chess. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], B XII.1) |
| 18718 | Saying 'and' has meaning is just saying it works in a sentence [Wittgenstein] |
| Full Idea: When we say that the word 'and' has meaning what we mean is that it works in a sentence and is not just a flourish. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], B VIII.2) |
| 18727 | A person's name doesn't mean their body; bodies don't sit down, and their existence can be denied [Wittgenstein] |
| Full Idea: The meaning of the words 'Professor Moore' is not a certain human body, because we do not say that the meaning sits on the sofa, and the words occur in the proposition 'Professor Moore does not exist'. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], B Easter) | |
| A reaction: Brilliant. Love it. Kripke ending up denying the existence of 'meanings'. |
| 6297 | Euclid's geometry is synthetic, but Descartes produced an analytic version of it [Euclid, by Resnik] |
| Full Idea: Euclid's geometry is a synthetic geometry; Descartes supplied an analytic version of Euclid's geometry, and we now have analytic versions of the early non-Euclidean geometries. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by Michael D. Resnik - Maths as a Science of Patterns One.4 | |
| A reaction: I take it that the original Euclidean axioms were observations about the nature of space, but Descartes turned them into a set of pure interlocking definitions which could still function if space ceased to exist. |
| 9603 | An assumption that there is a largest prime leads to a contradiction [Euclid, by Brown,JR] |
| Full Idea: Assume a largest prime, then multiply the primes together and add one. The new number isn't prime, because we assumed a largest prime; but it can't be divided by a prime, because the remainder is one. So only a larger prime could divide it. Contradiction. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by James Robert Brown - Philosophy of Mathematics Ch.1 | |
| A reaction: Not only a very elegant mathematical argument, but a model for how much modern logic proceeds, by assuming that the proposition is false, and then deducing a contradiction from it. |
| 18738 | We don't get 'nearer' to something by adding decimals to 1.1412... (root-2) [Wittgenstein] |
| Full Idea: We say we get nearer to root-2 by adding further figures after the decimal point: 1.1412.... This suggests there is something we can get nearer to, but the analogy is a false one. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], Notes) |
| 9894 | A unit is that according to which each existing thing is said to be one [Euclid] |
| Full Idea: A unit is that according to which each existing thing is said to be one. | |
| From: Euclid (Elements of Geometry [c.290 BCE], 7 Def 1) | |
| A reaction: See Frege's 'Grundlagen' §29-44 for a sustained critique of this. Frege is good, but there must be something right about the Euclid idea. If I count stone, paper and scissors as three, each must first qualify to be counted as one. Psychology creeps in. |
| 8738 | Postulate 2 says a line can be extended continuously [Euclid, by Shapiro] |
| Full Idea: Euclid's Postulate 2 says the geometer can 'produce a finite straight line continuously in a straight line'. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by Stewart Shapiro - Thinking About Mathematics 4.2 | |
| A reaction: The point being that this takes infinity for granted, especially if you start counting how many points there are on the line. The Einstein idea that it might eventually come round and hit you on the back of the head would have charmed Euclid. |
| 18708 | Infinity is not a number, so doesn't say how many; it is the property of a law [Wittgenstein] |
| Full Idea: 'Infinite' is not an answer to the question 'How many?', since the infinite is not a number. ...Infinity is the property of a law, not of an extension. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], A VII.2) |
| 22278 | Euclid relied on obvious properties in diagrams, as well as on his axioms [Potter on Euclid] |
| Full Idea: Euclid's axioms were insufficient to derive all the theorems of geometry: at various points in his proofs he appealed to properties that are obvious from the diagrams but do not follow from the stated axioms. | |
| From: comment on Euclid (Elements of Geometry [c.290 BCE]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 03 'aim' | |
| A reaction: I suppose if the axioms of a system are based on self-evidence, this would licence an appeal to self-evidence elsewhere in the system. Only pedants insist on writing down what is obvious to everyone! |
| 8673 | Euclid's parallel postulate defines unique non-intersecting parallel lines [Euclid, by Friend] |
| Full Idea: Euclid's fifth 'parallel' postulate says if there is an infinite straight line and a point, then there is only one straight line through the point which won't intersect the first line. This axiom is independent of Euclid's first four (agreed) axioms. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by Michèle Friend - Introducing the Philosophy of Mathematics 2.2 | |
| A reaction: This postulate was challenged in the nineteenth century, which was a major landmark in the development of modern relativist views of knowledge. |
| 10250 | Euclid needs a principle of continuity, saying some lines must intersect [Shapiro on Euclid] |
| Full Idea: Euclid gives no principle of continuity, which would sanction an inference that if a line goes from the outside of a circle to the inside of circle, then it must intersect the circle at some point. | |
| From: comment on Euclid (Elements of Geometry [c.290 BCE]) by Stewart Shapiro - Philosophy of Mathematics 6.1 n2 | |
| A reaction: Cantor and Dedekind began to contemplate discontinuous lines. |
| 10302 | Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays] |
| Full Idea: Euclid postulates: One can join two points by a straight line; Hilbert states the axiom: Given any two points, there exists a straight line on which both are situated. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by Paul Bernays - On Platonism in Mathematics p.259 |
| 14157 | Modern geometries only accept various parts of the Euclid propositions [Russell on Euclid] |
| Full Idea: In descriptive geometry the first 26 propositions of Euclid hold. In projective geometry the 1st, 7th, 16th and 17th require modification (as a straight line is not a closed series). Those after 26 depend on the postulate of parallels, so aren't assumed. | |
| From: comment on Euclid (Elements of Geometry [c.290 BCE]) by Bertrand Russell - The Principles of Mathematics §388 |
| 1600 | Euclid's common notions or axioms are what we must have if we are to learn anything at all [Euclid, by Roochnik] |
| Full Idea: The best known example of Euclid's 'common notions' is "If equals are subtracted from equals the remainders are equal". These can be called axioms, and are what "the man who is to learn anything whatever must have". | |
| From: report of Euclid (Elements of Geometry [c.290 BCE], 72a17) by David Roochnik - The Tragedy of Reason p.149 |
| 18737 | There are no positive or negative facts; these are just the forms of propositions [Wittgenstein] |
| Full Idea: There are no positive or negative facts. 'Positive' and 'negative' refer to the form of propositions, and not to the facts which verify or falsify them. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], C XIII) | |
| A reaction: Personally I think if we are going to allow the world to be full of 'facts', then there are negative, conjunctive, disjunctive and hypothetical facts. |
| 18715 | Using 'green' is a commitment to future usage of 'green' [Wittgenstein] |
| Full Idea: If I say this is green, I must say that other things are green too. I am committed to a future usage. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], B VI.2) | |
| A reaction: This seems to suggest that the eternal verity of a universal concept is just a convention of stability in a language. |
| 6215 | 'Contingent' means that the cause is unperceived, not that there is no cause [Hobbes] |
| Full Idea: For contingent, men do not mean that which hath no cause, but that which hath not for cause any thing that we perceive, as when a traveller meets a shower, they both had sufficient causes, but they didn't cause one another, so we say it was contingent. | |
| From: Thomas Hobbes (Of Liberty and Necessity [1654], §95) | |
| A reaction: Contingent nowadays means 'might not have happened', or 'does not happen in all possible worlds'. Personally I share Hobbes' doubts about the concept of contingency, and this is quite a good account of the misunderstanding. |
| 18726 | For each necessity in the world there is an arbitrary rule of language [Wittgenstein] |
| Full Idea: To a necessity in the world there corresponds an arbitrary rule in language. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], B XIV.2) | |
| A reaction: This seems to be hardcore logical positivism, making all necessities arbitrary. Compare Quine on the number of planets. |
| 18712 | Understanding is translation, into action or into other symbols [Wittgenstein] |
| Full Idea: Understanding is really translation, whether into other symbols or into action. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], B I.5) | |
| A reaction: The second part of this sounds like pure pragmatism. To do is to understand? I doubt it. Do animals understand anything? |
| 18280 | We live in sense-data, but talk about physical objects [Wittgenstein] |
| Full Idea: The world we live in is the world of sense-data, but the world we talk about is the world of physical objects. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], p.82), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 13 'Verif' | |
| A reaction: I really like that one. Even animals, I surmise, think of objects quite differently from the way they immediately experience them. |
| 18729 | Part of what we mean by stating the facts is the way we tend to experience them [Wittgenstein] |
| Full Idea: There is no need of a theory to reconcile what we know about sense data and what we believe about physical objects, because part of what we mean by saying that a penny is round is that we see it as elliptical in such and such conditions. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], C III) | |
| A reaction: This is an interesting and cunning move to bridge the gap between our representations and reallity. We may surmise how a thing really is, but then be surprised by the sense-data we get from it. |
| 18734 | If you remember wrongly, then there must be some other criterion than your remembering [Wittgenstein] |
| Full Idea: If you remember wrongly, then there must be some other criterion than your remembering. If you admit another test, then your memory itself is not the test. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], C VII) | |
| A reaction: If I fear that I am remembering some private solitary event wrongly, there is no other criterion to turn to, so I'm stuck. Sometimes dubious memories are all we have. |
| 18721 | Explanation and understanding are the same [Wittgenstein] |
| Full Idea: For us explanation and understanding are the same, understanding being the correlate of explanation. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], B XI.2) | |
| A reaction: I'm not convinced that they are 'the same', but they are almost interdependent ideas. Strevens has a nice paper on this. |
| 18720 | Explanation gives understanding by revealing the full multiplicity of the thing [Wittgenstein] |
| Full Idea: An explanation gives understanding, ...but it cannot teach you understanding, it cannot create understanding. It makes further distinctions i.e. it increases multiplicity. When multiplicity is complete, then there is no further misunderstanding. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], B X.3) | |
| A reaction: The thought seems to resemble Aristotle's idea of definition as gradual division of the subject. To understand is the dismantle the parts and lay them out before us. Wittgenstein was very interested in explanation at this time. |
| 18716 | A machine strikes us as being a rule of movement [Wittgenstein] |
| Full Idea: We are accustomed to look on a machine as the expression of a rule of movement. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], B VII.2) | |
| A reaction: What a beautiful definition of a machine! I like this because it connects the two halves of my view of the 'essence' of a thing, as derived from Aristotle, as both a causal mechanism and an underlying principle. Cf Turing machines. |
| 18713 | If an explanation is good, the symbol is used properly in the future [Wittgenstein] |
| Full Idea: The criterion of an explanation is whether the symbol explained is used properly in the future. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], B II.4) | |
| A reaction: This appears to be a pragmatic criterion for the best explanation. It presumably rests on his doctrine that meaning is use, so good explanation is understanding meanings. |
| 18717 | Thought is an activity which we perform by the expression of it [Wittgenstein] |
| Full Idea: Thought is an activity which we perform by the expression of it, and lasts as long as the expression. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], B VIII) | |
| A reaction: I take this to be an outmoded view of thought, which modern cognitive science has undermined, by showing how little of our thinking is actually conscious. |
| 18725 | A proposition draws a line around the facts which agree with it [Wittgenstein] |
| Full Idea: A proposition gives reality a degree of freedom; it draws a line round the facts which agree with it, and distinguishes them from those which do not. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], B XIII.2) | |
| A reaction: This seems to be the idea of meaning as the range of truth conditions. Propositions as sets of possible worlds extends this into possible facts which agree with the proposition. Most facts neither agree nor disagree with some proposition. |
| 18728 | The meaning of a proposition is the mode of its verification [Wittgenstein] |
| Full Idea: The meaning of a proposition is the mode of its verification (and two propositions cannot have the same verification). | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], C I) | |
| A reaction: Does this mean that if two sentences have the same mode of verification, then they must be expressing the same proposition? I guess so. |
| 18705 | Words function only in propositions, like levers in a machine [Wittgenstein] |
| Full Idea: Words function only in propositions, like the levers in a machine. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], A I.4) | |
| A reaction: Hm. Consider the word 'tree'. Did you manage to do it? Was it just a noise? |
| 18711 | A proposition is any expression which can be significantly negated [Wittgenstein] |
| Full Idea: Any affirmation can be negated: if it has sense to say p it also has sense to say ¬p. ...A proposition therefore is any expression which can be significantly negated. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], B I.2) | |
| A reaction: I'm not sure about 'therefore'. I'm thinking you would have to already grasp the proposition in order to apply his negation test. |
| 18733 | Laws of nature are an aspect of the phenomena, and are just our mode of description [Wittgenstein] |
| Full Idea: The laws of nature are not outside phenomena. They are part of language and of our way of describing things; you cannot discuss them apart from their physical manifestation. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], C V C) | |
| A reaction: I suppose this amounts to a Humean regularity theory - that the descriptions pick out patterns in the manifestations. I like the initial claim that they are not external to phenomena. |