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All the ideas for 'Three Varieties of Knowledge', 'Philosophy of Mathematics' and 'Db (ideas)'

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27 ideas

1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
Note that "is" can assert existence, or predication, or identity, or classification [PG]
     Full Idea: There are four uses of the word "is" in English: as existence ('he is at home'), as predication ('he is tall'), as identity ('he is the man I saw'), and as classification ('he is British').
     From: PG (Db (ideas) [2031])
     A reaction: This seems a nice instance of the sort of point made by analytical philosophy, which can lead to horrible confusion in other breeds of philosophy when it is overlooked.
2. Reason / A. Nature of Reason / 5. Objectivity
Objective truth arises from interpersonal communication [Davidson]
     Full Idea: The source of the concept of objective truth is interpersonal communication.
     From: Donald Davidson (Three Varieties of Knowledge [1991], p.209)
     A reaction: This is a distinctively Davidsonian idea, arising out of Wittgenstein's Private Language Argument. We could go a step further, and just say that 'objectivity is a social concept'. Davidson more or less pleads guilty to pragmatism in this essay.
2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions only refer to entities outside the defined collection [Horsten]
     Full Idea: Definitions are called 'predicative', and are considered sound, if they only refer to entities which exist independently from the defined collection.
     From: Leon Horsten (Philosophy of Mathematics [2007], §2.4)
2. Reason / F. Fallacies / 1. Fallacy
Fallacies are errors in reasoning, 'formal' if a clear rule is breached, and 'informal' if more general [PG]
     Full Idea: Fallacies are errors in reasoning, labelled as 'formal' if a clear rule has been breached, and 'informal' if some less precise error has been made.
     From: PG (Db (ideas) [2031])
     A reaction: Presumably there can be a grey area between the two.
2. Reason / F. Fallacies / 3. Question Begging
Question-begging assumes the proposition which is being challenged [PG]
     Full Idea: To beg the question is to take for granted in your argument that very proposition which is being challenged
     From: PG (Db (ideas) [2031])
     A reaction: An undoubted fallacy, and a simple failure to engage in the rational enterprise. I suppose one might give a reason for something, under the mistaken apprehension that it didn't beg the question; analysis of logical form is then needed.
2. Reason / F. Fallacies / 6. Fallacy of Division
What is true of a set is also true of its members [PG]
     Full Idea: The fallacy of division is the claim that what is true of a set must therefore be true of its members.
     From: PG (Db (ideas) [2031])
     A reaction: Clearly a fallacy, but if you only accept sets which are rational, then there is always a reason why a particular is a member of a set, and you can infer facts about particulars from the nature of the set
2. Reason / F. Fallacies / 7. Ad Hominem
The Ad Hominem Fallacy criticises the speaker rather than the argument [PG]
     Full Idea: The Ad Hominem Fallacy is to criticise the person proposing an argument rather than the argument itself, as when you say "You would say that", or "Your behaviour contradicts what you just said".
     From: PG (Db (ideas) [2031])
     A reaction: Nietzsche is very keen on ad hominem arguments, and cheerfully insults great philosophers, but then he doesn't believe there is such a thing as 'pure argument', and he is a relativist.
3. Truth / H. Deflationary Truth / 3. Minimalist Truth
Minimal theories of truth avoid ontological commitment to such things as 'facts' or 'reality' [PG]
     Full Idea: Minimalist theories of truth are those which involve minimum ontological commitment, avoiding references to 'reality' or 'facts' or 'what works', preferring to refer to formal relationships within language.
     From: PG (Db (ideas) [2031])
     A reaction: Personally I am suspicious of minimal theories, which seem to be designed by and for anti-realists. They seem too focused on language, when animals can obviously formulate correct propositions. I'm quite happy with the 'facts', even if that is vague.
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
     Full Idea: If a theory has, up to isomorphism, exactly one model, then it is said to be 'categorical'.
     From: Leon Horsten (Philosophy of Mathematics [2007], §5.2)
5. Theory of Logic / L. Paradox / 1. Paradox
Monty Hall Dilemma: do you abandon your preference after Monty eliminates one of the rivals? [PG]
     Full Idea: The Monty Hall Dilemma: Three boxes, one with a big prize; pick one to open. Monty Hall then opens one of the other two, which is empty. You may, if you wish, switch from your box to the other unopened box. Should you?
     From: PG (Db (ideas) [2031])
     A reaction: The other two boxes, as a pair, are more likely contain the prize than your box. Monty Hall has eliminated one of them for you, so you should choose the other one. Your intuition that the two remaining boxes are equal is incorrect!
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Computer proofs don't provide explanations [Horsten]
     Full Idea: Mathematicians are uncomfortable with computerised proofs because a 'good' proof should do more than convince us that a certain statement is true. It should also explain why the statement in question holds.
     From: Leon Horsten (Philosophy of Mathematics [2007], §5.3)
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
     Full Idea: The notion of an ordinal number is a set-theoretic, and hence non-arithmetical, concept.
     From: Leon Horsten (Philosophy of Mathematics [2007], §2.3)
10. Modality / B. Possibility / 6. Probability
Everything has a probability, something will happen, and probabilities add up [PG]
     Full Idea: The three Kolgorov axioms of probability: the probability of an event is a non-negative real number; it is certain that one of the 'elementary events' will occur; and the unity of probabilities is the sum of probability of parts ('additivity').
     From: PG (Db (ideas) [2031])
     A reaction: [My attempt to verbalise them; they are normally expressed in terms of set theory]. Got this from a talk handout, and Wikipedia.
11. Knowledge Aims / A. Knowledge / 4. Belief / e. Belief holism
A belief requires understanding the distinctions of true-and-false, and appearance-and-reality [Davidson]
     Full Idea: Having a belief demands in addition appreciating the contrast between true belief and false, between appearance and reality, mere seeming and being.
     From: Donald Davidson (Three Varieties of Knowledge [1991], p.209)
     A reaction: This sets the bar very high for belief (never mind knowledge), and seems to imply that animals don't have beliefs. How should we describe their cognitive states then? I would say these criteria only apply to actual knowledge.
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / a. Naïve realism
If reality is just what we perceive, we would have no need for a sixth sense [PG]
     Full Idea: Reality must be more than merely what we perceive, because a sixth sense would enhance our current knowledge, and a seventh, and so on.
     From: PG (Db (ideas) [2031])
12. Knowledge Sources / A. A Priori Knowledge / 5. A Priori Synthetic
If my team is losing 3-1, I have synthetic a priori knowledge that they need two goals for a draw [PG]
     Full Idea: If my football team is losing 3-1, I seem to have synthetic a priori knowledge that they need two goals to achieve a draw
     From: PG (Db (ideas) [2031])
13. Knowledge Criteria / E. Relativism / 2. Knowledge as Convention
Objectivity is intersubjectivity [Davidson]
     Full Idea: An entity is objective in so far as it is intersubjective.
     From: Donald Davidson (Three Varieties of Knowledge [1991]), quoted by Martin Kusch - Knowledge by Agreement Ch.10
     A reaction: This thought baffled me until I saw it in the context of socialised epistemology. Effectively objectivity is subsumed under justification, which in turn is seen in a social context, not private to individuals.
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / b. Scepticism of other minds
If we know other minds through behaviour, but not our own, we should assume they aren't like me [Davidson]
     Full Idea: If the mental states of others are known only through their behavioral and other outward manifestations, while this is not true of our own mental states, why should we think our own mental states are anything like those of others?
     From: Donald Davidson (Three Varieties of Knowledge [1991], p.207)
     A reaction: His point is that if you seriously doubt other minds, you should follow through on the implications. But that is to treat it as a theory about other minds, rather an a sceptical worry. Descartes didn't walk into walls while writing Meditation 1.
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / c. Knowing other minds
Knowing other minds rests on knowing both one's own mind and the external world [Davidson, by Dummett]
     Full Idea: Davidson argues that knowledge of other minds presupposes knowledge of one's own mind, and that there is no knowledge of other minds without knowledge of the external world.
     From: report of Donald Davidson (Three Varieties of Knowledge [1991]) by Michael Dummett - Common Sense and Physics Ch.10
     A reaction: Davidson't argument is actually hard to swallow because it is so long and complex. Compressing the point makes it begin to sound like a variant of the argument from analogy.
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / b. Multiple realisability
Maybe a mollusc's brain events for pain ARE of the same type (broadly) as a human's [PG]
     Full Idea: To defend type-type identity against the multiple realisability objection, we might say that a molluscs's brain events that register pain ARE of the same type as humans, given that being 'of the same type' is a fairly flexible concept.
     From: PG (Db (ideas) [2031])
     A reaction: But this reduces 'of the same type' to such vagueness that it may become vacuous. You would be left with token-token identity, where the mental event is just identical to some brain event, with its 'type' being irrelevant.
Maybe a frog's brain events for fear are functionally like ours, but not phenomenally [PG]
     Full Idea: To defend type-type identity against the multiple realisability objection, we might (also) say that while a frog's brain events for fear are functionally identical to a human's (it runs away), that doesn't mean they are phenomenally identical.
     From: PG (Db (ideas) [2031])
     A reaction: I take this to be the key reply to the multiple realisability problem. If a frog flees from a loud noise, it is 'frightened' in a functional sense, but that still leaves the question 'What's it like to be a frightened frog?', which may differ from humans.
19. Language / F. Communication / 4. Private Language
Content of thought is established through communication, so knowledge needs other minds [Davidson]
     Full Idea: Until a baseline has been established by communication with someone else, there is no point is saying one's own thoughts have a propositional content. Hence knowledge of another mind is essential all thought and all knowledge.
     From: Donald Davidson (Three Varieties of Knowledge [1991], p.213)
     A reaction: This really is building a skyscraper on the slightly shaky claims of the Private Language Argument (e.g. Idea 4158). Animals are so important in discussions of this kind. Is an albatross more or less devoid of thought and belief?
19. Language / F. Communication / 6. Interpreting Language / c. Principle of charity
The principle of charity attributes largely consistent logic and largely true beliefs to speakers [Davidson]
     Full Idea: Concerning charity, the Principle of Coherence seeks logical consistency in the thought of the speaker, and the Principle of Correspondence seeks a similar response to features of the world to that of an interpreter. The speaker has logic and true belief.
     From: Donald Davidson (Three Varieties of Knowledge [1991], p.211)
     A reaction: Davidson adds a Kantian commitment to pure and universal reason to the very sceptical framework created by Quine. I agree with Davidson, but it seems more like faith than like an argument or an empirical observation.
23. Ethics / E. Utilitarianism / 4. Unfairness
Utilitarianism seems to justify the discreet murder of unhappy people [PG]
     Full Idea: If I discreetly murdered a gloomy and solitary tramp who was upsetting people in my village, if is hard to see how utilitarianism could demonstrate that I had done something wrong.
     From: PG (Db (ideas) [2031])
27. Natural Reality / G. Biology / 2. Life
Life is Movement, Respiration, Sensation, Nutrition, Excretion, Reproduction, Growth (MRS NERG) [PG]
     Full Idea: The biologists' acronym for the necessary conditions of life is MRS NERG: that is, Movement, Respiration, Sensation, Nutrition, Excretion, Reproduction, Growth.
     From: PG (Db (ideas) [2031])
     A reaction: How strictly necessary are each of these is a point for discussion. A notorious problem case is fire, which (at a stretch) may pass all seven tests.
28. God / A. Divine Nature / 4. Divine Contradictions
An omniscient being couldn't know it was omniscient, as that requires information from beyond its scope of knowledge [PG]
     Full Idea: God seems to be in the paradoxical situation that He may be omniscient, but can never know that He is, because that involves knowing that there is nothing outside his scope of knowledge (e.g. another God)
     From: PG (Db (ideas) [2031])
How could God know there wasn't an unknown force controlling his 'free' will? [PG]
     Full Idea: How could God be certain that he has free will (if He has), if He couldn't be sure that there wasn't an unknown force controlling his will?
     From: PG (Db (ideas) [2031])