Combining Texts

All the ideas for 'Abstract Objects: a Case Study', 'Does Conceivability Entail Possibility?' and 'Grounding, Transitivity and Contrastivity'

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11 ideas

6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
Mathematics is both necessary and a priori because it really consists of logical truths [Yablo]
     Full Idea: Mathematics seems necessary because the real contents of mathematical statements are logical truths, which are necessary, and it seems a priori because logical truths really are a priori.
     From: Stephen Yablo (Abstract Objects: a Case Study [2002], 10)
     A reaction: Yablo says his logicism has a Kantian strain, because numbers and sets 'inscribed on our spectacles', but he takes a different view (in the present Idea) from Kant about where the necessity resides. Personally I am tempted by an a posteriori necessity.
6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo]
     Full Idea: Saying 'the number of Fs is 5', instead of using five quantifiers, puts the numeral in quantifiable position, which brings expressive advantages. 'There are more sheep in the field than cows' is an infinite disjunction, expressible in finite compass.
     From: Stephen Yablo (Abstract Objects: a Case Study [2002], 08)
     A reaction: See Hofweber with similar thoughts. This idea I take to be a key one in explaining many metaphysical confusions. The human mind just has a strong tendency to objectify properties, relations, qualities, categories etc. - for expression and for reasoning.
7. Existence / C. Structure of Existence / 1. Grounding / a. Nature of grounding
As causation links across time, grounding links the world across levels [Schaffer,J]
     Full Idea: Grounding is something like metaphysical causation. Just as causation links the world across time, grounding links the world across levels. Grounding connects the more fundamental to the less fundamental, and thereby backs a certain form of explanation.
     From: Jonathan Schaffer (Grounding, Transitivity and Contrastivity [2012], Intro)
     A reaction: Obviously you need 'levels' for this, which we should take to be structural levels.
If ground is transitive and irreflexive, it has a strict partial ordering, giving structure [Schaffer,J]
     Full Idea: By treating grounding as transitive (and irreflexive), one generates a strict partial ordering that induces metaphysical structure.
     From: Jonathan Schaffer (Grounding, Transitivity and Contrastivity [2012], Intro)
     A reaction: Schaffer's paper goes on to attach the claim that grounding is transitive, but I didn't find his examples very convincing.
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
Concrete objects have few essential properties, but properties of abstractions are mostly essential [Yablo]
     Full Idea: Objects like me have a few essential properties, and numerous accidental ones. Abstract objects are a different story. The intrinsic properties of the empty set are mostly essential. The relations of numbers are also mostly essential.
     From: Stephen Yablo (Abstract Objects: a Case Study [2002], 01)
We are thought to know concreta a posteriori, and many abstracta a priori [Yablo]
     Full Idea: Our knowledge of concreta is a posteriori, but our knowledge of numbers, at least, has often been considered a priori.
     From: Stephen Yablo (Abstract Objects: a Case Study [2002], 02)
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
Modal Rationalism: conceivability gives a priori access to modal truths [Chalmers, by Stalnaker]
     Full Idea: Chalmers' 'modal rationalist' is one who identifies what is possible with what is conceivable; the central claim of the doctrine is that we have a priori access to modal truth.
     From: report of David J.Chalmers (Does Conceivability Entail Possibility? [2002]) by Robert C. Stalnaker - Mere Possibilities 5
     A reaction: A helpful clarification, as I can now see how hopelessly and utterly wrong Chalmers is (about almost everything), and I find my confidence in any sort of genuine a priori knowledge (except of conceptual relations) dwindling by the minute.
Evaluate primary possibility from some world, and secondary possibility from this world [Chalmers, by Vaidya]
     Full Idea: For Chalmers, that water is XYZ is 'primary possible' (a priori, or conceptually), because it is true in some world considered as actual. It is 'secondary impossible', when it is evaluated from the Earth as actual.
     From: report of David J.Chalmers (Does Conceivability Entail Possibility? [2002]) by Anand Vaidya - Understanding and Essence Intro
     A reaction: [compressed] This is Chalmers' account of how we can know possibility from conceivability, via his two-dimensional semantics (see alphabetical themes).
14. Science / D. Explanation / 2. Types of Explanation / b. Contrastive explanations
Explaining 'Adam ate the apple' depends on emphasis, and thus implies a contrast [Schaffer,J]
     Full Idea: Explaining why ADAM ate the apple is a different matter from explaining why he ATE the apple, and from why he ate THE APPLE. ...In my view the best explanations incorporate ....contrastive information.
     From: Jonathan Schaffer (Grounding, Transitivity and Contrastivity [2012], 4.3.1)
     A reaction: But why are the contrasts Eve, or throwing it, or a pear? It occurs to me that this is wrong! The contrast is with anything else which could have gone in subject, verb or object position. It is a matter of categories, not of contrasts.
26. Natural Theory / A. Speculations on Nature / 1. Nature
I take what is fundamental to be the whole spatiotemporal manifold and its fields [Schaffer,J]
     Full Idea: I myself would prefer to speak of what is fundamental in terms of the whole spatiotemporal manifold and the fields that permeate it, with parts counting as derivative of the whole.
     From: Jonathan Schaffer (Grounding, Transitivity and Contrastivity [2012], 4.1.1)
     A reaction: Not quite the Parmenidean One, since it has parts, but a nice try at updating the great man. Note the reference to 'fields', suggesting that this view is grounded in the physics rather than metaphysics. How many fields has it got?
26. Natural Theory / C. Causation / 1. Causation
Nowadays causation is usually understood in terms of equations and variable ranges [Schaffer,J]
     Full Idea: The leading treatments of causation work within 'structural equation models', with events represented via variables each of which is allotted a range of permitted values, which constitute a 'contrast space'.
     From: Jonathan Schaffer (Grounding, Transitivity and Contrastivity [2012], 4.3.1)
     A reaction: Like Woodward's idea that causation is a graph, this seems to be a matter of plotting or formalising correlations between activities, which is a very Humean approach to causation.