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All the ideas for 'Katzav on limitations of dispositions', 'The Philosophy of Logic' and 'Modal Logic as Metaphysics'

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9 ideas

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
Very large sets should be studied in an 'if-then' spirit [Putnam]
     Full Idea: Sets of a very high type or very high cardinality (higher than the continuum, for example), should today be investigated in an 'if-then' spirit.
     From: Hilary Putnam (The Philosophy of Logic [1971], p.347), quoted by Penelope Maddy - Naturalism in Mathematics
     A reaction: Quine says the large sets should be regarded as 'uninterpreted'.
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
Indispensability strongly supports predicative sets, and somewhat supports impredicative sets [Putnam]
     Full Idea: We may say that indispensability is a pretty strong argument for the existence of at least predicative sets, and a pretty strong, but not as strong, argument for the existence of impredicative sets.
     From: Hilary Putnam (The Philosophy of Logic [1971], p.346), quoted by Penelope Maddy - Naturalism in Mathematics II.2
We must quantify over numbers for science; but that commits us to their existence [Putnam]
     Full Idea: Quantification over mathematical entities is indispensable for science..., therefore we should accept such quantification; but this commits us to accepting the existence of the mathematical entities in question.
     From: Hilary Putnam (The Philosophy of Logic [1971], p.57), quoted by Stephen Yablo - Apriority and Existence
     A reaction: I'm not surprised that Hartry Field launched his Fictionalist view of mathematics in response to such a counterintuitive claim. I take it we use numbers to slice up reality the way we use latitude to slice up the globe. No commitment to lines!
10. Modality / E. Possible worlds / 3. Transworld Objects / e. Possible Objects
If talking donkeys are possible, something exists which could be a talking donkey [Williamson, by Cameron]
     Full Idea: Williamson's view on modality is that everything that could exist does exist: since there could exist a talking donkey there actually exists some thing that could be a talking donkey.
     From: report of Timothy Williamson (Modal Logic as Metaphysics [2013], n20) by Ross P. Cameron - Truthmaking for Presentists n20
     A reaction: Well that thing certainly isn't me, or Tim Williamson. I'm guessing that the thing is an actual donkey, probably a rather bright one. Actually, I think this is one of those views that invites the incredulous stare. (Barcan formulae).
26. Natural Theory / B. Natural Kinds / 1. Natural Kinds
The natural kinds are objects, processes and properties/relations [Ellis]
     Full Idea: There are three hierarchies of natural kinds: objects or substances (substantive universals), events or processes (dynamic universals), and properties or relations (tropic universals).
     From: Brian Ellis (Katzav on limitations of dispositions [2005], 91)
     A reaction: Most interesting here is the identifying of natural kinds with universals, making universals into the families of nature. Universals are high-level sets of natural kinds. To grasp universals you must see patterns, and infer the underlying order.
26. Natural Theory / D. Laws of Nature / 2. Types of Laws
Least action is not a causal law, but a 'global law', describing a global essence [Ellis]
     Full Idea: The principle of least action is not a causal law, but is what I call a 'global law', which describes the essence of the global kind, which every object in the universe necessarily instantiates.
     From: Brian Ellis (Katzav on limitations of dispositions [2005])
     A reaction: As a fan of essentialism I find this persuasive. If I inherit part of my essence from being a mammal, I inherit other parts of my essence from being an object, and all objects would share that essence, so it would look like a 'law' for all objects.
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
A species requires a genus, and its essence includes the essence of the genus [Ellis]
     Full Idea: A specific universal can exist only if the generic universal of which it is a species exists, but generic universals don't depend on species; …the essence of any genus is included in its species, but not conversely.
     From: Brian Ellis (Katzav on limitations of dispositions [2005], 91)
     A reaction: Thus the species 'electron' would be part of the genus 'lepton', or 'human' part of 'mammal'. The point of all this is to show how individual items connect up with the rest of the universe, giving rise to universal laws, such as Least Action.
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / c. Essence and laws
A hierarchy of natural kinds is elaborate ontology, but needed to explain natural laws [Ellis]
     Full Idea: The hierarchy of natural kinds proposed by essentialism may be more elaborate than is strictly required for purposes of ontology, but it is necessary to explain the necessity of the laws of nature, and the universal applicability of global principles.
     From: Brian Ellis (Katzav on limitations of dispositions [2005], 91)
     A reaction: I am all in favour of elaborating ontology in the name of best explanation. There seem, though, to be some remaining ontological questions at the point where the explanations of essentialism run out.
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / d. Knowing essences
Without general principles, we couldn't predict the behaviour of dispositional properties [Ellis]
     Full Idea: It is objected to dispositionalism that without the principle of least action, or some general principle of equal power, the specific dispositional properties of things could tell us very little about how these things would be disposed to behave.
     From: Brian Ellis (Katzav on limitations of dispositions [2005], 90)
     A reaction: Ellis attempts to meet this criticism, by placing dispositional properties within a hierarchy of broader properties. There remains a nagging doubt about how essentialism can account for space, time, order, and the existence of essences.