65 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) |
| 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'? |
| 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. |
| 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. |
| 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. |
| 15413 | With four tense operators, all complex tenses reduce to fourteen basic cases [Burgess] |
| Full Idea: Fand P as 'will' and 'was', G as 'always going to be', H as 'always has been', all tenses reduce to 14 cases: the past series, each implying the next, FH,H,PH,HP,P,GP, and the future series PG,G,FG,GF,F,HF, plus GH=HG implying all, FP=PF which all imply. | |
| From: John P. Burgess (Philosophical Logic [2009], 2.8) | |
| A reaction: I have tried to translate the fourteen into English, but am not quite confident enough to publish them here. I leave it as an exercise for the reader. |
| 15415 | The temporal Barcan formulas fix what exists, which seems absurd [Burgess] |
| Full Idea: In temporal logic, if the converse Barcan formula holds then nothing goes out of existence, and the direct Barcan formula holds if nothing ever comes into existence. These results highlight the intuitive absurdity of the Barcan formulas. | |
| From: John P. Burgess (Philosophical Logic [2009], 2.9) | |
| A reaction: This is my reaction to the modal cases as well - the absurdity of thinking that no actually nonexistent thing might possibly have existed, or that the actual existents might not have existed. Williamson seems to be the biggest friend of the formulas. |
| 15430 | Is classical logic a part of intuitionist logic, or vice versa? [Burgess] |
| Full Idea: From one point of view intuitionistic logic is a part of classical logic, missing one axiom, from another classical logic is a part of intuitionistic logic, missing two connectives, intuitionistic v and → | |
| From: John P. Burgess (Philosophical Logic [2009], 6.4) |
| 15431 | It is still unsettled whether standard intuitionist logic is complete [Burgess] |
| Full Idea: The question of the completeness of the full intuitionistic logic for its intended interpretation is not yet fully resolved. | |
| From: John P. Burgess (Philosophical Logic [2009], 6.9) |
| 15429 | Relevance logic's → is perhaps expressible by 'if A, then B, for that reason' [Burgess] |
| Full Idea: The relevantist logician's → is perhaps expressible by 'if A, then B, for that reason'. | |
| From: John P. Burgess (Philosophical Logic [2009], 5.8) |
| 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. |
| 15404 | Technical people see logic as any formal system that can be studied, not a study of argument validity [Burgess] |
| Full Idea: Among the more technically oriented a 'logic' no longer means a theory about which forms of argument are valid, but rather means any formalism, regardless of its applications, that resembles original logic enough to be studied by similar methods. | |
| From: John P. Burgess (Philosophical Logic [2009], Pref) | |
| A reaction: There doesn't seem to be any great intellectual obligation to be 'technical'. As far as pure logic is concerned, I am very drawn to the computer approach, since I take that to be the original dream of Aristotle and Leibniz - impersonal precision. |
| 15405 | Classical logic neglects the non-mathematical, such as temporality or modality [Burgess] |
| Full Idea: There are topics of great philosophical interest that classical logic neglects because they are not important to mathematics. …These include distinctions of past, present and future, or of necessary, actual and possible. | |
| From: John P. Burgess (Philosophical Logic [2009], 1.1) |
| 15421 | Classical logic neglects counterfactuals, temporality and modality, because maths doesn't use them [Burgess] |
| Full Idea: Classical logic neglects counterfactual conditionals for the same reason it neglects temporal and modal distinctions, namely, that they play no serious role in mathematics. | |
| From: John P. Burgess (Philosophical Logic [2009], 4.1) | |
| A reaction: Science obviously needs counterfactuals, and metaphysics needs modality. Maybe so-called 'classical' logic will be renamed 'basic mathematical logic'. Philosophy will become a lot clearer when that happens. |
| 15427 | The Cut Rule expresses the classical idea that entailment is transitive [Burgess] |
| Full Idea: The Cut rule (from A|-B and B|-C, infer A|-C) directly expresses the classical doctrine that entailment is transitive. | |
| From: John P. Burgess (Philosophical Logic [2009], 5.3) |
| 15403 | Philosophical logic is a branch of logic, and is now centred in computer science [Burgess] |
| Full Idea: Philosophical logic is a branch of logic, a technical subject. …Its centre of gravity today lies in theoretical computer science. | |
| From: John P. Burgess (Philosophical Logic [2009], Pref) | |
| A reaction: He firmly distinguishes it from 'philosophy of logic', but doesn't spell it out. I take it that philosophical logic concerns metaprinciples which compare logical systems, and suggest new lines of research. Philosophy of logic seems more like metaphysics. |
| 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? |
| 15407 | Formalising arguments favours lots of connectives; proving things favours having very few [Burgess] |
| Full Idea: When formalising arguments it is convenient to have as many connectives as possible available.; but when proving results about formulas it is convenient to have as few as possible. | |
| From: John P. Burgess (Philosophical Logic [2009], 1.4) | |
| A reaction: Illuminating. The fact that you can whittle classical logic down to two (or even fewer!) connectives warms the heart of technicians, but makes connection to real life much more difficult. Hence a bunch of extras get added. |
| 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) |
| 15424 | Asserting a disjunction from one disjunct seems odd, but can be sensible, and needed in maths [Burgess] |
| Full Idea: Gricean implicature theory might suggest that a disjunction is never assertable when a disjunct is (though actually the disjunction might be 'pertinent') - but the procedure is indispensable in mathematical practice. | |
| From: John P. Burgess (Philosophical Logic [2009], 5.2) | |
| A reaction: He gives an example of a proof in maths which needs it, and an unusual conversational occasion where it makes sense. |
| 15409 | All occurrences of variables in atomic formulas are free [Burgess] |
| Full Idea: All occurrences of variables in atomic formulas are free. | |
| From: John P. Burgess (Philosophical Logic [2009], 1.7) |
| 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'. |
| 15414 | The denotation of a definite description is flexible, rather than rigid [Burgess] |
| Full Idea: By contrast to rigidly designating proper names, …the denotation of definite descriptions is (in general) not rigid but flexible. | |
| From: John P. Burgess (Philosophical Logic [2009], 2.9) | |
| A reaction: This modern way of putting it greatly clarifies why Russell was interested in the type of reference involved in definite descriptions. Obviously some descriptions (such as 'the only person who could ever have…') might be rigid. |
| 15406 | 'Induction' and 'recursion' on complexity prove by connecting a formula to its atomic components [Burgess] |
| Full Idea: There are atomic formulas, and formulas built from the connectives, and that is all. We show that all formulas have some property, first for the atomics, then the others. This proof is 'induction on complexity'; we also use 'recursion on complexity'. | |
| From: John P. Burgess (Philosophical Logic [2009], 1.4) | |
| A reaction: That is: 'induction on complexity' builds a proof from atomics, via connectives; 'recursion on complexity' breaks down to the atomics, also via the connectives. You prove something by showing it is rooted in simple truths. |
| 15425 | The sequent calculus makes it possible to have proof without transitivity of entailment [Burgess] |
| Full Idea: It might be wondered how one could have any kind of proof procedure at all if transitivity of entailment is disallowed, but the sequent calculus can get around the difficulty. | |
| From: John P. Burgess (Philosophical Logic [2009], 5.3) | |
| A reaction: He gives examples where transitivity of entailment (so that you can build endless chains of deductions) might fail. This is the point of the 'cut free' version of sequent calculus, since the cut rule allows transitivity. |
| 15426 | We can build one expanding sequence, instead of a chain of deductions [Burgess] |
| Full Idea: Instead of demonstrations which are either axioms, or follow from axioms by rules, we can have one ever-growing sequence of formulas of the form 'Axioms |- ______', where the blank is filled by Axioms, then Lemmas, then Theorems, then Corollaries. | |
| From: John P. Burgess (Philosophical Logic [2009], 5.3) |
| 15408 | 'Tautologies' are valid formulas of classical sentential logic - or substitution instances in other logics [Burgess] |
| Full Idea: The valid formulas of classical sentential logic are called 'tautologically valid', or simply 'tautologies'; with other logics 'tautologies' are formulas that are substitution instances of valid formulas of classical sentential logic. | |
| From: John P. Burgess (Philosophical Logic [2009], 1.5) |
| 15418 | Validity (for truth) and demonstrability (for proof) have correlates in satisfiability and consistency [Burgess] |
| Full Idea: Validity (truth by virtue of logical form alone) and demonstrability (provability by virtue of logical form alone) have correlative notions of logical possibility, 'satisfiability' and 'consistency', which come apart in some logics. | |
| From: John P. Burgess (Philosophical Logic [2009], 3.3) |
| 15411 | We only need to study mathematical models, since all other models are isomorphic to these [Burgess] |
| Full Idea: In practice there is no need to consider any but mathematical models, models whose universes consist of mathematical objects, since every model is isomorphic to one of these. | |
| From: John P. Burgess (Philosophical Logic [2009], 1.8) | |
| A reaction: The crucial link is the technique of Gödel Numbering, which can translate any verbal formula into numerical form. He adds that, because of the Löwenheim-Skolem theorem only subsets of the natural numbers need be considered. |
| 15412 | Models leave out meaning, and just focus on truth values [Burgess] |
| Full Idea: Models generally deliberately leave out meaning, retaining only what is important for the determination of truth values. | |
| From: John P. Burgess (Philosophical Logic [2009], 2.2) | |
| A reaction: This is the key point to hang on to, if you are to avoid confusing mathematical models with models of things in the real world. |
| 15416 | We aim to get the technical notion of truth in all models matching intuitive truth in all instances [Burgess] |
| Full Idea: The aim in setting up a model theory is that the technical notion of truth in all models should agree with the intuitive notion of truth in all instances. A model is supposed to represent everything about an instance that matters for its truth. | |
| From: John P. Burgess (Philosophical Logic [2009], 3.2) |
| 15428 | The Liar seems like a truth-value 'gap', but dialethists see it as a 'glut' [Burgess] |
| Full Idea: It is a common view that the liar sentence ('This very sentence is not true') is an instance of a truth-value gap (neither true nor false), but some dialethists cite it as an example of a truth-value glut (both true and false). | |
| From: John P. Burgess (Philosophical Logic [2009], 5.7) | |
| A reaction: The defence of the glut view must be that it is true, then it is false, then it is true... Could it manage both at once? |
| 8923 | Numbers are identified by their main properties and relations, involving the successor function [MacBride] |
| Full Idea: The mathematically significant properties and relations of natural numbers arise from the successor function that orders them; the natural numbers are identified simply as the objects that answer to this basic function. | |
| From: Fraser MacBride (Structuralism Reconsidered [2007], §1) | |
| A reaction: So Julius Caesar would be a number if he was the successor of Pompey the Great? I would have thought that counting should be mentioned - cardinality as well as ordinality. Presumably Peano's Axioms are being referred to. |
| 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) |
| 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) |
| 8926 | For mathematical objects to be positions, positions themselves must exist first [MacBride] |
| Full Idea: The identification of mathematical objects with positions in structures rests upon the prior credibility of the thesis that positions are objects in their own right. | |
| From: Fraser MacBride (Structuralism Reconsidered [2007], §3) | |
| A reaction: Sounds devastating, but something has to get the whole thing off the ground. This is why Resnik's word 'patterns' is so appealing. Patterns stare you in the face, and they don't change if all the objects making it up are replaced by others. |
| 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. |
| 15420 | De re modality seems to apply to objects a concept intended for sentences [Burgess] |
| Full Idea: There is a problem over 'de re' modality (as contrasted with 'de dicto'), as in ∃x□x. What is meant by '"it is analytic that Px" is satisfied by a', given that analyticity is a notion that in the first instance applies to complete sentences? | |
| From: John P. Burgess (Philosophical Logic [2009], 3.9) | |
| A reaction: This is Burgess's summary of one of Quine's original objections. The issue may be a distinction between whether the sentence is analytic, and what makes it analytic. The necessity of bachelors being unmarried makes that sentence analytic. |
| 15419 | General consensus is S5 for logical modality of validity, and S4 for proof [Burgess] |
| Full Idea: To the extent that there is any conventional wisdom about the question, it is that S5 is correct for alethic logical modality, and S4 correct for apodictic logical modality. | |
| From: John P. Burgess (Philosophical Logic [2009], 3.8) | |
| A reaction: In classical logic these coincide, so presumably one should use the minimum system to do the job, which is S4 (?). |
| 15417 | Logical necessity has two sides - validity and demonstrability - which coincide in classical logic [Burgess] |
| Full Idea: Logical necessity is a genus with two species. For classical logic the truth-related notion of validity and the proof-related notion of demonstrability, coincide - but they are distinct concept. In some logics they come apart, in intension and extension. | |
| From: John P. Burgess (Philosophical Logic [2009], 3.3) | |
| A reaction: They coincide in classical logic because it is sound and complete. This strikes me as the correct approach to logical necessity, tying it to the actual nature of logic, rather than some handwavy notion of just 'true in all possible worlds'. |
| 15422 | Three conditionals theories: Materialism (material conditional), Idealism (true=assertable), Nihilism (no truth) [Burgess] |
| Full Idea: Three main theories of the truth of indicative conditionals are Materialism (the conditions are the same as for the material conditional), Idealism (identifying assertability with truth-value), and Nihilism (no truth, just assertability). | |
| From: John P. Burgess (Philosophical Logic [2009], 4.3) |
| 15423 | It is doubtful whether the negation of a conditional has any clear meaning [Burgess] |
| Full Idea: It is contentious whether conditionals have negations, and whether 'it is not the case that if A,B' has any clear meaning. | |
| From: John P. Burgess (Philosophical Logic [2009], 4.9) | |
| A reaction: This seems to be connected to Lewis's proof that a probability conditional cannot be reduced to a single proposition. If a conditional only applies to A-worlds, it is not surprising that its meaning gets lost when it leaves that world. |
| 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. |