Combining Texts

All the ideas for 'works', 'Conceptions of Consequence' and 'Grounding, Transitivity and Contrastivity'

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7 ideas

6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]
     Full Idea: Archimedes gave a sort of definition of 'straight line' when he said it is the shortest line between two points.
     From: report of Archimedes (fragments/reports [c.240 BCE]) by Gottfried Leibniz - New Essays on Human Understanding 4.13
     A reaction: Commentators observe that this reduces the purity of the original Euclidean axioms, because it involves distance and measurement, which are absent from the purest geometry.
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.
11. Knowledge Aims / A. Knowledge / 2. Understanding
Aristotle's proofs give understanding, so it can't be otherwise, so consequence is necessary [Smiley, by Rumfitt]
     Full Idea: The ingredient of necessity [in Aristotle's account of consequence] is required by his demand that proof should produce 'understanding' [episteme], coupled with his claim that understanding something involves seeing that it cannot be otherwise.
     From: report of Timothy Smiley (Conceptions of Consequence [1998], p.599) by Ian Rumfitt - The Boundary Stones of Thought 3.2
     A reaction: An intriguing reverse of the normal order. Not 'necessity in logic delivers understanding', but 'reaching understanding shows the logic was necessary'.
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.