71 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) |
| 17774 | Definitions make our intuitions mathematically useful [Mayberry] |
| Full Idea: Definition provides us with the means for converting our intuitions into mathematically usable concepts. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.405-1) |
| 17773 | Proof shows that it is true, but also why it must be true [Mayberry] |
| Full Idea: When you have proved something you know not only that it is true, but why it must be true. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.405-2) | |
| A reaction: Note the word 'must'. Presumably both the grounding and the necessitation of the truth are revealed. |
| 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. |
| 17795 | Set theory can't be axiomatic, because it is needed to express the very notion of axiomatisation [Mayberry] |
| Full Idea: Set theory cannot be an axiomatic theory, because the very notion of an axiomatic theory makes no sense without it. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.413-2) | |
| A reaction: This will come as a surprise to Penelope Maddy, who battles with ways to accept the set theory axioms as the foundation of mathematics. Mayberry says that the basic set theory required is much more simple and intuitive. |
| 17796 | There is a semi-categorical axiomatisation of set-theory [Mayberry] |
| Full Idea: We can give a semi-categorical axiomatisation of set-theory (all that remains undetermined is the size of the set of urelements and the length of the sequence of ordinals). The system is second-order in formalisation. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.413-2) | |
| A reaction: I gather this means the models may not be isomorphic to one another (because they differ in size), but can be shown to isomorphic to some third ingredient. I think. Mayberry says this shows there is no such thing as non-Cantorian set theory. |
| 17800 | The misnamed Axiom of Infinity says the natural numbers are finite in size [Mayberry] |
| Full Idea: The (misnamed!) Axiom of Infinity expresses Cantor's fundamental assumption that the species of natural numbers is finite in size. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.414-2) |
| 17801 | The set hierarchy doesn't rely on the dubious notion of 'generating' them [Mayberry] |
| Full Idea: The idea of 'generating' sets is only a metaphor - the existence of the hierarchy is established without appealing to such dubious notions. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.414-2) | |
| A reaction: Presumably there can be a 'dependence' or 'determination' relation which does not involve actual generation. |
| 17803 | Limitation of size is part of the very conception of a set [Mayberry] |
| Full Idea: Our very notion of a set is that of an extensional plurality limited in size. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.415-2) |
| 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. |
| 17786 | The mainstream of modern logic sees it as a branch of mathematics [Mayberry] |
| Full Idea: In the mainstream tradition of modern logic, beginning with Boole, Peirce and Schröder, descending through Löwenheim and Skolem to reach maturity with Tarski and his school ...saw logic as a branch of mathematics. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.410-1) | |
| A reaction: [The lesser tradition, of Frege and Russell, says mathematics is a branch of logic]. Mayberry says the Fregean tradition 'has almost died out'. |
| 17788 | First-order logic only has its main theorems because it is so weak [Mayberry] |
| Full Idea: First-order logic is very weak, but therein lies its strength. Its principle tools (Compactness, Completeness, Löwenheim-Skolem Theorems) can be established only because it is too weak to axiomatize either arithmetic or analysis. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.411-2) | |
| A reaction: He adds the proviso that this is 'unless we are dealing with structures on whose size we have placed an explicit, finite bound' (p.412-1). |
| 17791 | Only second-order logic can capture mathematical structure up to isomorphism [Mayberry] |
| Full Idea: Second-order logic is a powerful tool of definition: by means of it alone we can capture mathematical structure up to isomorphism using simple axiom systems. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.412-1) |
| 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'. |
| 17787 | Big logic has one fixed domain, but standard logic has a domain for each interpretation [Mayberry] |
| Full Idea: The 'logica magna' [of the Fregean tradition] has quantifiers ranging over a fixed domain, namely everything there is. In the Boolean tradition the domains differ from interpretation to interpretation. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.410-2) | |
| A reaction: Modal logic displays both approaches, with different systems for global and local domains. |
| 17790 | No Löwenheim-Skolem logic can axiomatise real analysis [Mayberry] |
| Full Idea: No logic which can axiomatize real analysis can have the Löwenheim-Skolem property. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.412-1) |
| 17778 | Axiomatiation relies on isomorphic structures being essentially the same [Mayberry] |
| Full Idea: The central dogma of the axiomatic method is this: isomorphic structures are mathematically indistinguishable in their essential properties. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.406-2) | |
| A reaction: Hence it is not that we have to settle for the success of a system 'up to isomorphism', since that was the original aim. The structures must differ in their non-essential properties, or they would be the same system. |
| 17779 | 'Classificatory' axioms aim at revealing similarity in morphology of structures [Mayberry] |
| Full Idea: The purpose of a 'classificatory' axiomatic theory is to single out an otherwise disparate species of structures by fixing certain features of morphology. ...The aim is to single out common features. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.406-2) |
| 17780 | 'Eliminatory' axioms get rid of traditional ideal and abstract objects [Mayberry] |
| Full Idea: The purpose of what I am calling 'eliminatory' axiomatic theories is precisely to eliminate from mathematics those peculiar ideal and abstract objects that, on the traditional view, constitute its subject matter. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.407-1) | |
| A reaction: A very interesting idea. I have a natural antipathy to 'abstract objects', because they really mess up what could otherwise be a very tidy ontology. What he describes might be better called 'ignoring' axioms. The objects may 'exist', but who cares? |
| 17789 | No logic which can axiomatise arithmetic can be compact or complete [Mayberry] |
| Full Idea: No logic which can axiomatise arithmetic can be compact or complete. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.412-1) | |
| A reaction: I take this to be because there are new truths in the transfinite level (as well as the problem of incompleteness). |
| 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) |
| 17784 | Real numbers can be eliminated, by axiom systems for complete ordered fields [Mayberry] |
| Full Idea: We eliminate the real numbers by giving an axiomatic definition of the species of complete ordered fields. These axioms are categorical (mutually isomorphic), and thus are mathematically indistinguishable. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.408-2) | |
| A reaction: Hence my clever mathematical friend says that it is a terrible misunderstanding to think that mathematics is about numbers. Mayberry says the reals are one ordered field, but mathematics now studies all ordered fields together. |
| 17782 | Greek quantities were concrete, and ratio and proportion were their science [Mayberry] |
| Full Idea: Quantities for Greeks were concrete things - lines, surfaces, solids, times, weights. At the centre of their science of quantity was the beautiful theory of ratio and proportion (...in which the notion of number does not appear!). | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.407-2) | |
| A reaction: [He credits Eudoxus, and cites Book V of Euclid] |
| 17781 | Real numbers were invented, as objects, to simplify and generalise 'quantity' [Mayberry] |
| Full Idea: The abstract objects of modern mathematics, the real numbers, were invented by the mathematicians of the seventeenth century in order to simplify and to generalize the Greek science of quantity. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.407-2) |
| 17799 | Cantor's infinite is an absolute, of all the sets or all the ordinal numbers [Mayberry] |
| Full Idea: In Cantor's new vision, the infinite, the genuine infinite, does not disappear, but presents itself in the guise of the absolute, as manifested in the species of all sets or the species of all ordinal numbers. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.414-2) |
| 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) |
| 17797 | Cantor extended the finite (rather than 'taming the infinite') [Mayberry] |
| Full Idea: We may describe Cantor's achievement by saying, not that he tamed the infinite, but that he extended the finite. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.414-2) |
| 17775 | If proof and definition are central, then mathematics needs and possesses foundations [Mayberry] |
| Full Idea: If we grant, as surely we must, the central importance of proof and definition, then we must also grant that mathematics not only needs, but in fact has, foundations. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.405-1) |
| 17776 | The ultimate principles and concepts of mathematics are presumed, or grasped directly [Mayberry] |
| Full Idea: The ultimate principles upon which mathematics rests are those to which mathematicians appeal without proof; and the primitive concepts of mathematics ...themselves are grasped directly, if grasped at all, without the mediation of definition. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.405-1) | |
| A reaction: This begs the question of whether the 'grasping' is purely a priori, or whether it derives from experience. I defend the latter, and Jenkins puts the case well. |
| 17777 | Foundations need concepts, definition rules, premises, and proof rules [Mayberry] |
| Full Idea: An account of the foundations of mathematics must specify four things: the primitive concepts for use in definitions, the rules governing definitions, the ultimate premises of proofs, and rules allowing advance from premises to conclusions. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.405-2) |
| 17804 | Axiom theories can't give foundations for mathematics - that's using axioms to explain axioms [Mayberry] |
| Full Idea: No axiomatic theory, formal or informal, of first or of higher order can logically play a foundational role in mathematics. ...It is obvious that you cannot use the axiomatic method to explain what the axiomatic method is. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.415-2) |
| 17792 | 1st-order PA is only interesting because of results which use 2nd-order PA [Mayberry] |
| Full Idea: The sole theoretical interest of first-order Peano arithmetic derives from the fact that it is a first-order reduct of a categorical second-order theory. Its axioms can be proved incomplete only because the second-order theory is categorical. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.412-1) |
| 17793 | It is only 2nd-order isomorphism which suggested first-order PA completeness [Mayberry] |
| Full Idea: If we did not know that the second-order axioms characterise the natural numbers up to isomorphism, we should have no reason to suppose, a priori, that first-order Peano Arithmetic should be complete. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.412-1) |
| 17794 | Set theory is not just first-order ZF, because that is inadequate for mathematics [Mayberry] |
| Full Idea: The idea that set theory must simply be identified with first-order Zermelo-Fraenkel is surprisingly widespread. ...The first-order axiomatic theory of sets is clearly inadequate as a foundation of mathematics. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.412-2) | |
| A reaction: [He is agreeing with a quotation from Skolem]. |
| 17802 | We don't translate mathematics into set theory, because it comes embodied in that way [Mayberry] |
| Full Idea: One does not have to translate 'ordinary' mathematics into the Zermelo-Fraenkel system: ordinary mathematics comes embodied in that system. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.415-1) | |
| A reaction: Mayberry seems to be a particular fan of set theory as spelling out the underlying facts of mathematics, though it has to be second-order. |
| 17805 | Set theory is not just another axiomatised part of mathematics [Mayberry] |
| Full Idea: The fons et origo of all confusion is the view that set theory is just another axiomatic theory and the universe of sets just another mathematical structure. ...The universe of sets ...is the world that all mathematical structures inhabit. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.416-1) |
| 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. |
| 17785 | Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry] |
| Full Idea: The abstractness of the old fashioned real numbers has been replaced by generality in the modern theory of complete ordered fields. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.408-2) | |
| A reaction: In philosophy, I'm increasingly thinking that we should talk much more of 'generality', and a great deal less about 'universals'. (By which I don't mean that redness is just the set of red things). |
| 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. |
| 7658 | Obviously there can't be a functional anaylsis of qualia if they are defined by intrinsic properties [Dennett] |
| Full Idea: If you define qualia as intrinsic properties of experiences considered in isolation from all their causes and effects, logically independent of all dispositional properties, then they are logically guaranteed to elude all broad functional analysis. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.8) | |
| A reaction: This is a good point - it seems daft to reify qualia and imagine them dangling in mid-air with all their vibrant qualities - but that is a long way from saying there is nothing more to qualia than functional roles. Functions must be exlained too. |
| 7655 | The work done by the 'homunculus in the theatre' must be spread amongst non-conscious agencies [Dennett] |
| Full Idea: All the work done by the imagined homunculus in the Cartesian Theater must be distributed among various lesser agencies in the brain, none of which is conscious. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.3) | |
| A reaction: Dennett's account crucially depends on consciousness being much more fragmentary than most philosophers claim it to be. It is actually full of joints, which can come apart. He may be right. |
| 7657 | Intelligent agents are composed of nested homunculi, of decreasing intelligence, ending in machines [Dennett] |
| Full Idea: As long as your homunculi are more stupid and ignorant than the intelligent agent they compose, the nesting of homunculi within homunculi can be finite, bottoming out, eventually, with agents so unimpressive they can be replaced by machines. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.6) | |
| A reaction: [Dennett first proposed this in 'Brainstorms' 1978]. This view was developed well by Lycan. I rate it as one of the most illuminating ideas in the modern philosophy of mind. All complex systems (like aeroplanes) have this structure. |
| 7656 | I don't deny consciousness; it just isn't what people think it is [Dennett] |
| Full Idea: I don't maintain, of course, that human consciousness does not exist; I maintain that it is not what people often think it is. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.3) | |
| A reaction: I consider Dennett to be as near as you can get to an eliminativist, but he is not stupid. As far as I can see, the modern philosopher's bogey-man, the true total eliminativist, simply doesn't exist. Eliminativists usually deny propositional attitudes. |
| 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. |
| 7654 | What matters about neuro-science is the discovery of the functional role of the chemistry [Dennett] |
| Full Idea: Neuro-science matters because - and only because - we have discovered that the many different neuromodulators and other chemical messengers that diffuse throughout the brain have functional roles that make important differences. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.1) | |
| A reaction: I agree with Dennett that this is the true ground for pessimism about spectacular breakthroughs in artificial intelligence, rather than abstract concerns about irreducible features of the mind like 'qualia' and 'rationality'. |
| 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. |