Combining Texts

All the ideas for 'The Metaontology of Abstraction', 'Apology for Raymond Sebond' and 'Proof that every set can be well-ordered'

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17 ideas

1. Philosophy / A. Wisdom / 2. Wise People
Why can't a wise man doubt everything? [Montaigne]
     Full Idea: Why cannot a wise man dare to doubt anything and everything?
     From: Michel de Montaigne (Apology for Raymond Sebond [1580], p.0562)
     A reaction: This question seems to be the start of the Enlightenment Project, of attempting to prove everything. MacIntyre warns of the dangers of this in ethical theory. The story of modern philosophy is the discovery of its impossibility. E.g. Davidson on truth.
1. Philosophy / A. Wisdom / 3. Wisdom Deflated
No wisdom could make us comfortably walk a wide beam if it was high in the air [Montaigne]
     Full Idea: Take a beam wide enough to walk along: suspend it between two towers: there is no philosophical wisdom, however firm, which could make us walk along it just as we would if we were on the ground.
     From: Michel de Montaigne (Apology for Raymond Sebond [1580], p.0672)
     A reaction: This proposes great scepticism about the practical application of philosophical wisdom, but if we talk in terms of the wise assessment of risk in any undertaking, our caution on the raised beam makes perfectly good sense.
2. Reason / F. Fallacies / 1. Fallacy
It is a fallacy to explain the obscure with the even more obscure [Hale/Wright]
     Full Idea: The fallacy of 'ad obscurum per obscurius' is to explain the obscure by appeal to what is more obscure.
     From: B Hale / C Wright (The Metaontology of Abstraction [2009], §3)
     A reaction: Not strictly a fallacy, so much as an example of inadequate explanation, along with circularity and infinite regresses.
3. Truth / A. Truth Problems / 3. Value of Truth
Virtue is the distinctive mark of truth, and its greatest product [Montaigne]
     Full Idea: The distinctive mark of the Truth we hold ought to be virtue, which is the most exacting mark of Truth, the closest one to heaven and the most worthy thing that Truth produces.
     From: Michel de Montaigne (Apology for Raymond Sebond [1580], p.0493)
     A reaction: A long way from Tarski and minimalist theories of truth! But not so far from pragmatism. Personally I think Montaigne is making an important claim, which virtue theorists should be attempting to incorporate into their theory. Aristotle would sympathise.
5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
Singular terms refer if they make certain atomic statements true [Hale/Wright]
     Full Idea: Anyone should agree that a justification for regarding a singular term as having objectual reference is provided just as soon as one has justification for regarding as true certain atomic statements in which it functions as a singular term.
     From: B Hale / C Wright (The Metaontology of Abstraction [2009], §9)
     A reaction: The meat of this idea is hidden in the word 'certain'. See Idea 10314 for Hale's explanation. Without that, the proposal strikes me as absurd.
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / e. Countable infinity
Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed [Zermelo, by Lavine]
     Full Idea: Zermelo realised that the Axiom of Choice (based on arbitrary functions) could be used to 'count', in the Cantorian sense, those collections that had given Cantor so much trouble, which restored a certain unity to set theory.
     From: report of Ernst Zermelo (Proof that every set can be well-ordered [1904]) by Shaughan Lavine - Understanding the Infinite I
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
Neo-Fregeanism might be better with truth-makers, rather than quantifier commitment [Hale/Wright]
     Full Idea: A third way has been offered to 'make sense' of neo-Fregeanism: we should reject Quine's well-known criterion of ontological commitment in favour of one based on 'truth-maker theory'.
     From: B Hale / C Wright (The Metaontology of Abstraction [2009], §4 n19)
     A reaction: [The cite Ross Cameron for this] They reject this proposal, on the grounds that truth-maker theory is not sufficient to fix the grounding truth-conditions of statements.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Are neo-Fregeans 'maximalists' - that everything which can exist does exist? [Hale/Wright]
     Full Idea: It is claimed that neo-Fregeans are committed to 'maximalism' - that whatever can exist does.
     From: B Hale / C Wright (The Metaontology of Abstraction [2009], §4)
     A reaction: [The cite Eklund] They observe that maximalism denies contingent non-existence (of the £20 note I haven't got). There seems to be the related problem of 'hyperinflation', that if abstract objects are generated logically, the process is unstoppable.
7. Existence / D. Theories of Reality / 3. Reality
We lack some sense or other, and hence objects may have hidden features [Montaigne]
     Full Idea: We may all lack some sense or other; because of that defect, most of the features of objects may be concealed from us.
     From: Michel de Montaigne (Apology for Raymond Sebond [1580], p.0666)
     A reaction: This strikes me as simple, straightforward common sense, and right. I cannot make sense of the claim that reality really is just the way it appears. We do not have a built-in neutrino detector, for example.
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
The identity of Pegasus with Pegasus may be true, despite the non-existence [Hale/Wright]
     Full Idea: Identity is sometimes read so that 'Pegasus is Pegasus' expresses a truth, the non-existence of any winged horse notwithstanding.
     From: B Hale / C Wright (The Metaontology of Abstraction [2009], §5)
     A reaction: This would give you ontological commitment to truth, without commitment to existence. It undercuts the use of identity statements as the basis of existence claims, which was Frege's strategy.
8. Modes of Existence / B. Properties / 3. Types of Properties
Maybe we have abundant properties for semantics, and sparse properties for ontology [Hale/Wright]
     Full Idea: There is a compatibilist view which says that it is for the abundant properties to play the role of 'bedeutungen' in semantic theory, and the sparse ones to address certain metaphysical concerns.
     From: B Hale / C Wright (The Metaontology of Abstraction [2009], §9)
     A reaction: Only a philosopher could live with the word 'property' having utterly different extensions in different areas of discourse. They similarly bifurcate words like 'object' and 'exist'. Call properties 'quasi-properties' and I might join in.
8. Modes of Existence / B. Properties / 10. Properties as Predicates
A successful predicate guarantees the existence of a property - the way of being it expresses [Hale/Wright]
     Full Idea: The good standing of a predicate is already trivially sufficient to ensure the existence of an associated property, a (perhaps complex) way of being which the predicate serves to express.
     From: B Hale / C Wright (The Metaontology of Abstraction [2009], §9)
     A reaction: 'Way of being' is interesting. Is 'being near Trafalgar Sq' a way of being? I take properties to be 'features', which seems to give a clearer way of demarcating them. They say they are talking about 'abundant' (rather than 'sparse') properties.
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
Sceptics say there is truth, but no means of making or testing lasting judgements [Montaigne]
     Full Idea: Pyrrhonians say that truth and falsehood exist; within us we have means of looking for them, but not of making any lasting judgements: we have no touchstone.
     From: Michel de Montaigne (Apology for Raymond Sebond [1580], p.0564)
     A reaction: This states the key difference between sceptics and relativists. The latter are more extreme as they say there is no such thing as truth. The former concede truth, and their scepticism is about the abilities of human beings. I am an anti-relativist.
15. Nature of Minds / A. Nature of Mind / 1. Mind / d. Location of mind
The soul is in the brain, as shown by head injuries [Montaigne]
     Full Idea: The seat of the powers of the soul is in the brain, as is clearly shown by the fact that wounds and accidents affecting the head immediately harm the faculties of the soul.
     From: Michel de Montaigne (Apology for Raymond Sebond [1580], p.0614)
     A reaction: At last someone has finally got the facts clear. It seems surprising that the Greeks never clearly grasped this piece of irrefutable evidence - even those Greeks who speculated that the brain was the key. Here we have a fixed fact of philosophy of mind.
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
Abstractionism needs existential commitment and uniform truth-conditions [Hale/Wright]
     Full Idea: Abstractionism needs a face-value, existentially committed reading of the terms occurring on the left-hand sides together with sameness of truth-conditions across the biconditional.
     From: B Hale / C Wright (The Metaontology of Abstraction [2009], §5)
     A reaction: They employ 'abstractionism' to mean their logical Fregean strategy for defining abstractions, not to mean the older psychological account. Thus the truth-conditions for being 'parallel' and for having the 'same direction' must be consistent.
Equivalence abstraction refers to objects otherwise beyond our grasp [Hale/Wright]
     Full Idea: Abstraction principles purport to introduce fundamental means of reference to a range of objects, to which there is accordingly no presumption that we have any prior or independent means of reference.
     From: B Hale / C Wright (The Metaontology of Abstraction [2009], §8)
     A reaction: There's the rub! They make it sound like a virtue, that we open up yet another heaven of abstract toys to play with. As fictions, they are indeed exciting new fun. As platonic discoveries they strike me as Cloud-Cuckoo Land.
19. Language / B. Reference / 4. Descriptive Reference / a. Sense and reference
Reference needs truth as well as sense [Hale/Wright]
     Full Idea: It takes, over and above the possession of sense, the truth of relevant contexts to ensure reference.
     From: B Hale / C Wright (The Metaontology of Abstraction [2009], §9)
     A reaction: Reference purely through sense was discredited by Kripke. The present idea challenges Kripke's baptismal realist approach. How do you 'baptise' an abstract object? But isn't reference needed prior to the establishment of truth?