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All the ideas for 'Philosophy of Mathematics', 'A World of Dispositions' and 'Beauty: a very short introduction'

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19 ideas

2. Reason / A. Nature of Reason / 7. Status of Reason
Do aesthetic reasons count as reasons, if they are rejectable without contradiction? [Scruton]
     Full Idea: The judgement of beauty makes a claim about its object, and can be supported by reasons. But the reasons do not compel the judgement and can be rejected without contradiction. So are they reasons or aren't they?
     From: Roger Scruton (Beauty: a very short introduction [2011], 1)
     A reaction: I suspect that what he is really referring to is evidence rather than reasons.
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)
3. Truth / A. Truth Problems / 2. Defining Truth
Defining truth presupposes that there can be a true definition [Scruton]
     Full Idea: How can you define truth, without already assuming the distinction between a true definition and a false one?
     From: Roger Scruton (Beauty: a very short introduction [2011], 1)
     A reaction: Don't say we have to accept truth as yet another primitive! Philosophers are out of business if all the basic concepts are primitive. The axiomatic approach to truth is an alternative - by specifying how the primitive should be used.
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)
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)
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / e. Dispositions as potential
All structures are dispositional, objects are dispositions sets, and events manifest dispositions [Fetzer]
     Full Idea: I propose a dispositional ontology for the physical world, according to which a) every structural property is a dispositional one, b) a physical object is an ordered set of dispositions, and c) every event manifests a dispositional property of the world.
     From: J.H. Fetzer (A World of Dispositions [1977], Intro)
     A reaction: Mumford says this is consistent with ontology as a way of describing the world, rather than being facts about the world. I like Fetzer's sketch, which sounds to have a lot in common with 'process philosophy'.
9. Objects / C. Structure of Objects / 1. Structure of an Object
All events and objects are dispositional, and hence all structural properties are dispositional [Fetzer]
     Full Idea: Every atomic event in the world's history is a manifestation of some dispositional property of the world and every physical object is an instantiation of some set of dispositions; hence, every structural property is dispositional in kind.
     From: J.H. Fetzer (A World of Dispositions [1977], 5)
     A reaction: I quite like this drastic view, but there remains the intuition that there must always be something which has the disposition. That may be because I have not yet digested the lessons of modern physics.
21. Aesthetics / A. Aesthetic Experience / 2. Aesthetic Attitude
The pleasure taken in beauty also aims at understanding and valuing [Scruton]
     Full Idea: Like the pleasure in friendship, the pleasure in beauty is curious: it aims to understand its object, and to value what it finds.
     From: Roger Scruton (Beauty: a very short introduction [2011], 1)
     A reaction: At least he is trying to pin down the way in which aesthetic pleasure is phenomenologically different from other kinds of pleasure.
Art gives us imaginary worlds which we can view impartially [Scruton]
     Full Idea: One aim of art is to present imaginary worlds, towards which we can adopt, as part of the integral aesthetic attitude, a posture of impartial concern.
     From: Roger Scruton (Beauty: a very short introduction [2011], 5)
     A reaction: It connects to the pleasure of watching people when they don't know they are being watched (such as watching the street from a restaurant window). Scruton's suggestion makes art resemble examples in philosophy. Cf the Frege-Geach problem in ethics.
21. Aesthetics / A. Aesthetic Experience / 4. Beauty
Maybe 'beauty' is too loaded, and we should talk of fittingness or harmony [Scruton]
     Full Idea: Maybe we can understand the 'beauty' of a building better if we describe it in another and less loaded way, as a form of fittingness or harmony.
     From: Roger Scruton (Beauty: a very short introduction [2011], 1)
     A reaction: Almost everyone accepts the word 'beauty' for some things, such as a beautiful face, or goal, or steak. I remember a female interviewer writing that, reluctantly, the only appropriate word she could find for Nureyev's face was 'beautiful'.
Beauty shows us what we should want in order to achieve human fulfilment [Scruton]
     Full Idea: Beauty speaks to us of human fulfilment: not of things that we want, but of things that we ought to want, because human nature requires them. Such, at least, is my belief.
     From: Roger Scruton (Beauty: a very short introduction [2011], 7)
     A reaction: I'm not sure how this works with a beautiful natural landscape. And what should I see that I ought to desire after viewing a great Rembrandt self-portrait? That I don't want to end up looking as bleak as that? Hm. Lofty words.
Beauty is rationally founded, inviting meaning, comparison and self-reflection [Scruton]
     Full Idea: Beauty is rationally founded; it challenges us to find meaning in its object, to make critical comparisons, and to examine our own lives and emotions in the light of what we find.
     From: Roger Scruton (Beauty: a very short introduction [2011], 9)
     A reaction: This is the Kantian tradition, and I'm not finding it very persuasive. It seems to place the value of beauty in what we do with it afterwards, and he seems to make beauty a necessary stepping stone to virtue. I see beauty as more sui generis.
21. Aesthetics / A. Aesthetic Experience / 5. Natural Beauty
Natural beauty reassures us that the world is where we belong [Scruton]
     Full Idea: The experience of natural beauty is not a sense of 'how nice!' or 'how pleasant!' It contains a reassurance that this world is a right and fitting place to be - a home in which our human powers and prospects find confirmation.
     From: Roger Scruton (Beauty: a very short introduction [2011], 2)
     A reaction: To call it a 'reassurance' and 'confirmation' sounds like theism, anthropomorphism, or the pathetic fallacy. That said, this is certainly a heart-warming idea, and hence must contain a grain of truth.
21. Aesthetics / B. Nature of Art / 4. Art as Expression
Croce says art makes inarticulate intuitions conscious; rival views say the audience is the main concern [Scruton]
     Full Idea: The Croce model is of an inarticulate inner state (an 'intuition') becoming articulate and conscious through artistic expression. The rival model is fitting thing together so as to create links which resonate in the audience's feelings.
     From: Roger Scruton (Beauty: a very short introduction [2011], 5)
     A reaction: The first model tells you nothing about how the artist imagines the audience reacting. The second model tells you nothing about what matters personally to the artist. A good theory must do both!
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
Beauty (unlike truth and goodness) is questionable as an ultimate value [Scruton]
     Full Idea: The status of beauty as an ultimate value is questionable, in the way that the status of truth and goodness are not.
     From: Roger Scruton (Beauty: a very short introduction [2011], 1)
     A reaction: We suspect that a love of beauty may be a bit parochial, where it is hard to conceive of living creatures anywhere in the cosmos who don't value the other two.
25. Social Practice / F. Life Issues / 5. Sexual Morality
Prostitution is wrong because it hardens the soul, since soul and body are one [Scruton]
     Full Idea: The condemnation of prostitution was not just puritan bigotry; it was a recognition of a profound truth, that you and your body are not two things but one, and by selling the body you harden your soul.
     From: Roger Scruton (Beauty: a very short introduction [2011], 7)
     A reaction: No one, I imagine, who condones or even enthuses about prostitution would hope that their own daughter followed the profession, so there is something wrong with it. But must an enthusiastic and cheerful prostitute necessarily have a hard soul?
26. Natural Theory / B. Natural Kinds / 2. Defining Kinds
Kinds are arrangements of dispositions [Fetzer]
     Full Idea: Kinds of things are specific arrangements of dispositions.
     From: J.H. Fetzer (A World of Dispositions [1977], 2)
     A reaction: A 'disposition' doesn't seem quite the right word for what is basic to the physical world, though Harré and Madden make a good case for the 'fields' of physic being understood in that way. I prefer 'power', though that doesn't solve anything.
26. Natural Theory / D. Laws of Nature / 3. Laws and Generalities
Lawlike sentences are general attributions of disposition to all members of some class [Fetzer]
     Full Idea: Lawlike sentences are conceived as logically general dispositional statements attributing permanent dispositional properties to every member of a reference class. ...Their basic form is that of subjunctive generalizations.
     From: J.H. Fetzer (A World of Dispositions [1977], 3)
     A reaction: I much prefer talk of 'lawlike sentences' to talk of 'laws'. At least they imply that the true generalisations about nature are fairly fine-grained. Why not talk of 'generalisations' instead of 'laws'? Fetzer wants dispositions to explain everything.