Combining Texts

All the ideas for 'Deflationary Metaontology of Thomasson', 'What Numbers Are' and 'A Theory of Conditionals'

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6 ideas

5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
17813 Löwenheim-Skolem says any theory with a true interpretation has a model in the natural numbers [White,NP]
     Full Idea: The Löwenheim-Skolem theorem tells us that any theory with a true interpretation has a model in the natural numbers.
     From: Nicholas P. White (What Numbers Are [1974], V)
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17812 Finite cardinalities don't need numbers as objects; numerical quantifiers will do [White,NP]
     Full Idea: Statements involving finite cardinalities can be made without treating numbers as objects at all, simply by using quantification and identity to define numerically definite quantifiers in the manner of Frege.
     From: Nicholas P. White (What Numbers Are [1974], IV)
     A reaction: [He adds Quine 1960:268 as a reference]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
14082 No sortal could ever exactly pin down which set of particles count as this 'cup' [Schaffer,J]
     Full Idea: Many decent candidates could the referent of this 'cup', differing over whether outlying particles are parts. No further sortal I could invoke will be selective enough to rule out all but one referent for it.
     From: Jonathan Schaffer (Deflationary Metaontology of Thomasson [2009], 3.1 n8)
     A reaction: I never had much faith in sortals for establishing individual identity, so this point comes as no surprise. The implication is strongly realist - that the cup has an identity which is permanently beyond our capacity to specify it.
9. Objects / F. Identity among Objects / 6. Identity between Objects
14081 Identities can be true despite indeterminate reference, if true under all interpretations [Schaffer,J]
     Full Idea: There can be determinately true identity claims despite indeterminate reference of the terms flanking the identity sign; these will be identity claims true under all admissible interpretations of the flanking terms.
     From: Jonathan Schaffer (Deflationary Metaontology of Thomasson [2009], 3.1)
     A reaction: In informal contexts there might be problems with the notion of what is 'admissible'. Is 'my least favourite physical object' admissible?
10. Modality / B. Possibility / 8. Conditionals / a. Conditionals
14286 In nearby worlds where A is true, 'if A,B' is true or false if B is true or false [Stalnaker]
     Full Idea: Consider a possible world in which A is true and otherwise differs minimally from the actual world. 'If A, then B' is true (false) just in case B is true (false) in that possible world.
     From: Robert C. Stalnaker (A Theory of Conditionals [1968], p.34), quoted by Dorothy Edgington - Conditionals (Stanf) 4.1
     A reaction: This is the first proposal to give a possible worlds semantics for conditional statements. Edgington observes that worlds which are nearby for me may not be nearby for you.
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
14285 A possible world is the ontological analogue of hypothetical beliefs [Stalnaker]
     Full Idea: A possible world is the ontological analogue of a stock of hypothetical beliefs.
     From: Robert C. Stalnaker (A Theory of Conditionals [1968], p.34), quoted by Dorothy Edgington - Conditionals (Stanf) 4.1
     A reaction: Sounds neat and persuasive. What is the ontological analogue of a stock of hopes? Heaven!