9 ideas
| 13831 | Logic is based on transitions between sentences [Prawitz] |
| Full Idea: I agree entirely with Dummett that the right way to answer the question 'what is logic?' is to consider transitions between sentences. | |
| From: Dag Prawitz (Gentzen's Analysis of First-Order Proofs [1974], §04) | |
| A reaction: I always protest at this point that reliance on sentences is speciesism against animals, who are thereby debarred from reasoning. See the wonderful Idea 1875 of Chrysippus. Hacking's basic suggestion seems right. Transition between thoughts. |
| 13825 | Natural deduction introduction rules may represent 'definitions' of logical connectives [Prawitz] |
| Full Idea: With Gentzen's natural deduction, we may say that the introductions represent, as it were, the 'definitions' of the logical constants. The introductions are not literally understood as 'definitions'. | |
| From: Dag Prawitz (Gentzen's Analysis of First-Order Proofs [1974], 2.2.2) | |
| A reaction: [Hacking, in 'What is Logic? §9' says Gentzen had the idea that his rules actually define the constants; not sure if Prawitz and Hacking are disagreeing] |
| 13823 | In natural deduction, inferences are atomic steps involving just one logical constant [Prawitz] |
| Full Idea: In Gentzen's natural deduction, the inferences are broken down into atomic steps in such a way that each step involves only one logical constant. The steps are the introduction or elimination of the logical constants. | |
| From: Dag Prawitz (Gentzen's Analysis of First-Order Proofs [1974], 1.1) |
| 6613 | 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. |
| 10370 | Causal relata are individuated by coarse spacetime regions [Quine, by Schaffer,J] |
| Full Idea: Quine's view is that causal relata are individuated by spacetime regions, which is even less fine-grained than Davidson's account of events.... He says fine-grained events are poorly individuated and unfamiliar. | |
| From: report of Willard Quine (Events and Reification [1985]) by Jonathan Schaffer - The Metaphysics of Causation 1.2 | |
| A reaction: [Schaffer cites Davidson 1985 as accepting this view] This is a nice suggestion, if we are looking for a naturalistic account of causal relata. It makes a minimum ontological commitment (a Quine trait), and I would supplement it with active 'powers'. |
| 6616 | 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. |
| 6615 | 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. |
| 6614 | 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. |
| 6612 | 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. |