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All the ideas for 'Lectures 1930-32 (student notes)', 'The Sophist' and 'Mathematics: Form and Function'

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52 ideas

1. Philosophy / C. History of Philosophy / 1. History of Philosophy
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.
1. Philosophy / D. Nature of Philosophy / 2. Invocation to Philosophy
We must fight fiercely for knowledge, understanding and intelligence [Plato]
     Full Idea: We need to use every argument we can to fight against anyone who does away with knowledge, understanding, and intelligence, but at the same time asserts anything at all about anything.
     From: Plato (The Sophist [c.359 BCE], 249c)
     A reaction: Thus showing that reason is only central if you want to put a high value on it?
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / d. Philosophy as puzzles
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.
1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
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.
1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
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'?
1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
The desire to split everything into its parts is unpleasant and unphilosophical [Plato]
     Full Idea: To try to set apart everything from everything is not only especially jangling, but it is the mark of someone altogether unmusical and unphilosophic.
     From: Plato (The Sophist [c.359 BCE], 259e)
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)
2. Reason / C. Styles of Reason / 1. Dialectic
Good analysis involves dividing things into appropriate forms without confusion [Plato]
     Full Idea: It takes expertise in dialectic to divide things by kinds and not to think that the same form is a different one or that a different form is the same.
     From: Plato (The Sophist [c.359 BCE], 253d)
Dialectic should only be taught to those who already philosophise well [Plato]
     Full Idea: The dialectical capacity - you won't give it to anyone else, I suspect, except to whoever philosophises purely and justly.
     From: Plato (The Sophist [c.359 BCE], 253e)
2. Reason / C. Styles of Reason / 2. Elenchus
In discussion a person's opinions are shown to be in conflict, leading to calm self-criticism [Plato]
     Full Idea: They collect someone's opinions together during the discussion, put them side by side, and show that they conflict with each other at the same time on the same subjects.... The person sees this, gets angry at themselves, and calmer towards others.
     From: Plato (The Sophist [c.359 BCE], 230b)
     A reaction: He goes on to say that the process is like a doctor purging a patient of internal harms. If anyone talks for long enough (even a good philosopher), their opinions will probably be seen to be in conflict. But which opinions do you abandon?
2. Reason / F. Fallacies / 8. Category Mistake / a. Category mistakes
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'?
2. Reason / F. Fallacies / 8. Category Mistake / b. Category mistake as syntactic
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.
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.
3. Truth / A. Truth Problems / 2. Defining Truth
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.
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
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.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZFC could contain a contradiction, and it can never prove its own consistency [MacLane]
     Full Idea: We have at hand no proof that the axioms of ZFC for set theory will never yield a contradiction, while Gödel's second theorem tells us that such a consistency proof cannot be conducted within ZFC.
     From: Saunders MacLane (Mathematics: Form and Function [1986], p.406), quoted by Penelope Maddy - Naturalism in Mathematics
     A reaction: Maddy quotes this, while defending set theory as the foundation of mathematics, but it clearly isn't the most secure foundation that could be devised. She says the benefits of set theory do not need guaranteed consistency (p.30).
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
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.
5. Theory of Logic / C. Ontology of Logic / 4. Logic by Convention
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'.
5. Theory of Logic / D. Assumptions for Logic / 3. Contradiction
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?
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
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)
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and
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)
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
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'.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
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)
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
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)
7. Existence / A. Nature of Existence / 3. Being / d. Non-being
What does 'that which is not' refer to? [Plato]
     Full Idea: What should the name 'that which is not' be applied to?
     From: Plato (The Sophist [c.359 BCE], 237c)
     A reaction: This leads into a discussion of the problem, in The Sophist. It became a large issue when modern logic was being developed by Frege and Russell.
7. Existence / A. Nature of Existence / 3. Being / e. Being and nothing
If statements about non-existence are logically puzzling, so are statements about existence [Plato]
     Full Idea: When the question was put to us as to the name of 'that which is not', to whatever one must apply it, we got stuck in every kind of perplexity. Are we now in any less perplexity about 'that which is'?
     From: Plato (The Sophist [c.359 BCE], 250d)
     A reaction: Nice. This precapitulates the whole story of modern philosophy of language. What started as a nagging doubt about reference to non-existents ends as bewilderment about everything we say.
7. Existence / A. Nature of Existence / 6. Criterion for Existence
To be is to have a capacity, to act on other things, or to receive actions [Plato]
     Full Idea: A thing really is if it has any capacity, either by nature to do something to something else or to have even the smallest thing done to it by the most trivial thing, even if it only happens once. I'll define those which are as nothing other than capacity.
     From: Plato (The Sophist [c.359 BCE], 247e)
     A reaction: If philosophy is footnotes to Plato, this should be the foundational remark in all discussions of existence (though Parmenides might claim priority). It seems to say 'to be is to have a causal role (active or passive)'. It also seems essentialist.
7. Existence / D. Theories of Reality / 6. Physicalism
Some alarming thinkers think that only things which you can touch exist [Plato]
     Full Idea: One group drags everything down to earth, insisting that only what offers tangible contact is, since they define being as the same as body, despising anyone who says that something without a body is. These are frightening men.
     From: Plato (The Sophist [c.359 BCE], 246b)
7. Existence / D. Theories of Reality / 8. Facts / b. Types of fact
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.
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
Whenever there's speech it has to be about something [Plato]
     Full Idea: Whenever there's speech it has to be about something. It's impossible for it not to be about something.
     From: Plato (The Sophist [c.359 BCE], 262e)
     A reaction: [Quoted by Marcus about ontological commitment] The interesting test case would be speech about the existence of circular squares.
8. Modes of Existence / D. Universals / 5. Universals as Concepts
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.
8. Modes of Existence / D. Universals / 6. Platonic Forms / a. Platonic Forms
Good thinkers spot forms spread through things, or included within some larger form [Plato]
     Full Idea: It takes dialectic to divide things by kinds...such a person can discriminate a single form spread through a lot of separate things…and forms included in a single outside form…or a form connected as a unit through many wholes.
     From: Plato (The Sophist [c.359 BCE], 253d)
     A reaction: [compressed] This is very helpful in indicating the complex structure of the Forms that Plato envisages. If you talk of the meanings of words (other than names), though, it comes to the same thing. Wise people fully understand their language.
The not-beautiful is part of the beautiful, though opposed to it, and is just as real [Plato]
     Full Idea: So 'the not beautiful' turns out to be ..both marked off within one kind of those that are, and also set over against one of those that are, ..and the beautiful is no more a being than the not beautiful.
     From: Plato (The Sophist [c.359 BCE], 257d)
     A reaction: [dialogue eliminated] This is a highly significant passage, for two reasons. It suggests that the Form of the beautiful can have parts, and also that the negations of Forms are Forms themselves (both of which come as a surprise).
9. Objects / A. Existence of Objects / 6. Nihilism about Objects
If we see everything as separate, we can then give no account of it [Plato]
     Full Idea: To dissociate each thing from everything else is to destroy totally everything there is to say. The weaving together of forms is what makes speech [logos] possible for us.
     From: Plato (The Sophist [c.359 BCE], 259e)
     A reaction: This I take to be the lynchpin of metaphysics. We are forced to see the world in a way which enables us to give some sort of account of it. Our metaphysics is 'inference to the best logos'.
10. Modality / C. Sources of Modality / 3. Necessity by Convention
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.
11. Knowledge Aims / A. Knowledge / 2. Understanding
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?
12. Knowledge Sources / B. Perception / 4. Sense Data / a. Sense-data theory
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.
12. Knowledge Sources / B. Perception / 4. Sense Data / d. Sense-data problems
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.
12. Knowledge Sources / C. Rationalism / 1. Rationalism
A soul without understanding is ugly [Plato]
     Full Idea: The soul that lacks understanding must be set down as ugly.
     From: Plato (The Sophist [c.359 BCE], 228d)
     A reaction: The teleological view of things understands their nature in things of their perfection. and the essence of beauty is perfection. It is the mind's nature to know. Failing to know is as ugly as allowing your crops to die.
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
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.
14. Science / D. Explanation / 1. Explanation / b. Aims of explanation
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.
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.
14. Science / D. Explanation / 2. Types of Explanation / i. Explanations by mechanism
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.
14. Science / D. Explanation / 3. Best Explanation / a. Best explanation
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.
18. Thought / A. Modes of Thought / 1. Thought
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.
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
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.
19. Language / A. Nature of Meaning / 5. Meaning as Verification
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.
19. Language / A. Nature of Meaning / 7. Meaning Holism / a. Sentence meaning
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?
19. Language / D. Propositions / 1. Propositions
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.
23. Ethics / A. Egoism / 1. Ethical Egoism
Wickedness is an illness of the soul [Plato]
     Full Idea: Wickedness is a sedition and illness of the soul.
     From: Plato (The Sophist [c.359 BCE], 228b)
25. Social Practice / E. Policies / 5. Education / c. Teaching
Didactic education is hard work and achieves little [Plato]
     Full Idea: With a lot of effort the admonitory species of education accomplishes little.
     From: Plato (The Sophist [c.359 BCE], 230a)
26. Natural Theory / D. Laws of Nature / 11. Against Laws of Nature
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.