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All the ideas for 'The Philosophy of Philosophy', 'Creating the Kingdom of Ends' and 'Philosophy of Arithmetic'

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21 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
Progress in philosophy is incremental, not an immature seeking after drama [Williamson]
     Full Idea: The incremental progress which I envisage for philosophy lacks the drama after which some philosophers still hanker, and that hankering is itself a symptom of the intellectual immaturity that helps hold philosophy back.
     From: Timothy Williamson (The Philosophy of Philosophy [2007], Intro)
     A reaction: This could stand as a motto for the whole current profession of analytical philosophy. It means that if anyone attempts to be dramatic they can make their own way out. They'll find Kripke out there, smoking behind the dustbins.
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
Correspondence to the facts is a bad account of analytic truth [Williamson]
     Full Idea: Even if talk of truth as correspondence to the facts is metaphorical, it is a bad metaphor for analytic truth in a way that it is not for synthetic truth.
     From: Timothy Williamson (The Philosophy of Philosophy [2007], 3.1)
     A reaction: A very simple and rather powerful point. Maybe the word 'truth' should be withheld from such cases. You might say that accepted analytic truths are 'conventional'. If that is wrong, then they correspond to natural facts at a high level of abstraction.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
0 is not a number, as it answers 'how many?' negatively [Husserl, by Dummett]
     Full Idea: Husserl contends that 0 is not a number, on the grounds that 'nought' is a negative answer to the question 'how many?'.
     From: report of Edmund Husserl (Philosophy of Arithmetic [1894], p.144) by Michael Dummett - Frege philosophy of mathematics Ch.8
     A reaction: I seem to be in a tiny minority in thinking that Husserl may have a good point. One apple is different from one orange, but no apples are the same as no oranges. That makes 0 a very peculiar number. See Idea 9838.
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
Multiplicity in general is just one and one and one, etc. [Husserl]
     Full Idea: Multiplicity in general is no more than something and something and something, etc.; ..or more briefly, one and one and one, etc.
     From: Edmund Husserl (Philosophy of Arithmetic [1894], p.85), quoted by Gottlob Frege - Review of Husserl's 'Phil of Arithmetic'
     A reaction: Frege goes on to attack this idea fairly convincingly. It seems obvious that it is hard to say that you have seventeen items, if the only numberical concept in your possession is 'one'. How would you distinguish 17 from 16? What makes the ones 'multiple'?
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
Husserl said counting is more basic than Frege's one-one correspondence [Husserl, by Heck]
     Full Idea: Husserl famously argued that one should not explain number in terms of equinumerosity (or one-one correspondence), but should explain equinumerosity in terms of sameness of number, which should be characterised in terms of counting.
     From: report of Edmund Husserl (Philosophy of Arithmetic [1894]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3
     A reaction: [Heck admits he hasn't read the Husserl] I'm very sympathetic to Husserl, though nearly all modern thinking favours Frege. Counting connects numbers to their roots in the world. Mathematicians seem oblivious of such things.
7. Existence / D. Theories of Reality / 4. Anti-realism
The realist/anti-realist debate is notoriously obscure and fruitless [Williamson]
     Full Idea: The debate between realism and anti-realism has become notorious in the rest of philosophy for its obscurity, convolution, and lack of progress.
     From: Timothy Williamson (The Philosophy of Philosophy [2007], After)
     A reaction: I find this reassuring, because fairly early on I decided that this problem was not of great interest, and quietly tiptoed away. I take the central issue to be whether nature has 'joints', to which the answer appears to be 'yes'. End of story.
7. Existence / D. Theories of Reality / 10. Vagueness / b. Vagueness of reality
There cannot be vague objects, so there may be no such thing as a mountain [Williamson]
     Full Idea: It is sometimes argued that if there is such a thing as a mountain it would be a vague object, but it is logically impossible for an object to be vague, so there is no such thing as a mountain.
     From: Timothy Williamson (The Philosophy of Philosophy [2007], 7.2)
     A reaction: I don't take this to be a daft view. No one is denying the existence of the solid rock that is involved, but allowing such a vague object may be a slippery slope to the acceptance of almost anything as an 'object'.
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
Common sense and classical logic are often simultaneously abandoned in debates on vagueness [Williamson]
     Full Idea: The constraints of common sense and classical logic are often simultaneously abandoned in debates on vagueness.
     From: Timothy Williamson (The Philosophy of Philosophy [2007], After)
     A reaction: Wiliamson has described himself (in my hearing) as a 'rottweiller realist', but presumably the problem of vagueness interests a lot of people precisely because it pushes us away from common sense and classical logic.
10. Modality / D. Knowledge of Modality / 1. A Priori Necessary
Modal thinking isn't a special intuition; it is part of ordinary counterfactual thinking [Williamson]
     Full Idea: The epistemology of metaphysical modality requires no dedicated faculty of intuition. It is simply a special case of the epistemology of counterfactual thinking, a kind of thinking tightly integrated with our thinking about the spatio-temporal world.
     From: Timothy Williamson (The Philosophy of Philosophy [2007], 5.6)
     A reaction: This seems to me to be spot-on, though it puts the focus increasingly on the faculty of imagination, as arguably an even more extraordinary feature of brains than the much-vaunted normal consciousness.
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
Williamson can't base metaphysical necessity on the psychology of causal counterfactuals [Lowe on Williamson]
     Full Idea: The psychological mechanism that Williamson proposes as the supposedly reliable source of our knowledge of necessities only seems applicable to counterfactuals that are distinctively causal, not metaphysical, in character.
     From: comment on Timothy Williamson (The Philosophy of Philosophy [2007]) by E.J. Lowe - What is the Source of Knowledge of Modal Truths? 5
     A reaction: My rough impression of Williamson's account is that it is correct but unilluminating. We have to assess necessities by counterfactual thinking, because nothing else is available (apart from evaluating the coherence of the findings).
We scorn imagination as a test of possibility, forgetting its role in counterfactuals [Williamson]
     Full Idea: The epistemology of modality often focuses on (and pours scorn on) imagination or conceivability as a test of possibility, while ignoring the role of the imagination in the assessment of mundane counterfactuals.
     From: Timothy Williamson (The Philosophy of Philosophy [2007], 5.4)
     A reaction: Good point. I've been guilty of this easy scorn myself. Williamson gives our modal capacities an evolutionary context. What is needed is well-informed imagination, rather than wild fantasy.
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
There are 'armchair' truths which are not a priori, because experience was involved [Williamson]
     Full Idea: There is extensive 'armchair knowledge' in which experience plays no strictly evidential role, but it may not fit the stereotype of the a priori, because the contribution of experience was more than enabling, such as armchair truths about our environment.
     From: Timothy Williamson (The Philosophy of Philosophy [2007], 5.5)
     A reaction: Once this point is conceded we have no idea where to draw the line. Does 'if it is red it can't be green' derive from experience? I think it might.
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
Intuition is neither powerful nor vacuous, but reveals linguistic or conceptual competence [Williamson]
     Full Idea: Crude rationalists postulate a special knowledge-generating faculty of rational intuition. Crude empiricists regard intuition as an obscurantist term of folk psychology. Linguistic/conceptual philosophy says it reveals linguistic or conceptual competence.
     From: Timothy Williamson (The Philosophy of Philosophy [2007], Intro)
     A reaction: Kripke seems to think that it is the basis of logical competence. I would use it as a blank term for any insight in which we have considerable confidence, and yet are unable to articulate its basis; roughly, for rational thought that evades logic.
When analytic philosophers run out of arguments, they present intuitions as their evidence [Williamson]
     Full Idea: 'Intuition' plays a major role in contemporary analytic philosophy's self-understanding. ...When contemporary analytic philosophers run out of arguments, they appeal to intuitions. ...Thus intuitions are presented as our evidence in philosophy.
     From: Timothy Williamson (The Philosophy of Philosophy [2007], p.214-5), quoted by Herman Cappelen - Philosophy without Intuitions 01.1
     A reaction: Williamson says we must investigate this 'scandal', but Cappelen's book says analytic philosophy does not rely on intuition.
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
Husserl identifies a positive mental act of unification, and a negative mental act for differences [Husserl, by Frege]
     Full Idea: Husserl identifies a 'unitary mental act' where several contents are connected or related to one another, and also a difference-relation where two contents are related to one another by a negative judgement.
     From: report of Edmund Husserl (Philosophy of Arithmetic [1894], p.73-74) by Gottlob Frege - Review of Husserl's 'Phil of Arithmetic' p.322
     A reaction: Frege is setting this up ready for a fairly vicious attack. Where Hume has a faculty for spotting resemblances, it is not implausible that we should also be hard-wired to spot differences. 'You look different; have you changed your hair style?'
18. Thought / D. Concepts / 4. Structure of Concepts / b. Analysis of concepts
We clarify concepts (e.g. numbers) by determining their psychological origin [Husserl, by Velarde-Mayol]
     Full Idea: Husserl said that the clarification of any concept is made by determining its psychological origin. He is concerned with the psychological origins of the operation of calculating cardinal numbers.
     From: report of Edmund Husserl (Philosophy of Arithmetic [1894]) by Victor Velarde-Mayol - On Husserl 2.2
     A reaction: This may not be the same as the 'psychologism' that Frege so despised, because Husserl is offering a clarification, rather than the intrinsic nature of number concepts. It is not a theory of the origin of numbers.
18. Thought / E. Abstraction / 8. Abstractionism Critique
Psychologism blunders in focusing on concept-formation instead of delineating the concepts [Dummett on Husserl]
     Full Idea: Husserl substitutes his account of the process of concept-formation for a delineation of the concept. It is above all in making this substitution that psychologism is objectionable (and Frege opposed it so vehemently).
     From: comment on Edmund Husserl (Philosophy of Arithmetic [1894]) by Michael Dummett - Frege philosophy of mathematics Ch.2
     A reaction: While this is a powerful point which is a modern orthodoxy, it hardly excludes a study of concept-formation from being of great interest for other reasons. It may not appeal to logicians, but it is crucial part of the metaphysics of nature.
Husserl wanted to keep a shadowy remnant of abstracted objects, to correlate them [Dummett on Husserl]
     Full Idea: Husserl saw that abstracted units, though featureless, must in some way retain their distinctness, some shadowy remnant of their objects. So he wanted to correlate like-numbered sets, not just register their identity, but then abstractionism fails.
     From: comment on Edmund Husserl (Philosophy of Arithmetic [1894]) by Michael Dummett - Frege philosophy of mathematics Ch.12
     A reaction: Abstractionism is held to be between the devil and the deep blue sea, of depending on units which are identifiable, when they are defined as devoid of all individuality. We seem forced to say that the only distinction between them is countability.
19. Language / A. Nature of Meaning / 6. Meaning as Use
You might know that the word 'gob' meant 'mouth', but not be competent to use it [Williamson]
     Full Idea: Someone who acquires the word 'gob' just by being reliably told that it is synonymous with 'mouth' knows what 'gob' means without being fully competent to use it.
     From: Timothy Williamson (The Philosophy of Philosophy [2007], 4.7)
     A reaction: Not exactly an argument against meaning-as-use, but a very nice cautionary example to show that 'knowing the meaning' of a word may be a rather limited, and dangerous, achievement.
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / b. Rational ethics
Maybe final value rests on the extrinsic property of being valued by a rational agent [Korsgaard, by Orsi]
     Full Idea: Korsgaard argues for the ultimate dependence of final value on the extrinsic property of being valued by a rational agent.
     From: report of Christine M. Korsgaard (Creating the Kingdom of Ends [1992]) by Francesco Orsi - Value Theory 2.3 n4
     A reaction: This hyper-Kantian view doesn't strike me as very plausible. Not philosophical theory which entirely cuts animals out of the story has much appeal for me.
24. Political Theory / B. Nature of a State / 5. Culture
If languages are intertranslatable, and cognition is innate, then cultures are all similar [Williamson]
     Full Idea: Given empirical evidence for the approximate intertranslatability of all human languages, and a universal innate basis of human cognition, we may wonder how 'other' any human culture really is.
     From: Timothy Williamson (The Philosophy of Philosophy [2007], 8.1)
     A reaction: This seems to be a fairly accurate account of the situation. In recent centuries people seem to have been over-impressed by superficial differences in cultural behaviour, but we increasingly see the underlying identity.