9 ideas
| 13407 | All worthwhile philosophy is synthetic theorizing, evaluated by experience [Papineau] |
| Full Idea: I would say that all worthwhile philosophy consists of synthetic theorizing, evaluated against experience. | |
| From: David Papineau (Philosophical Insignificance of A Priori Knowledge [2010], §1) | |
| A reaction: This is the view that philosophy is just science at a high level of abstraction, and he explicitly rejects 'conceptual analysis' as a fruitful activity. I need to take a stance on this one, but find I am in a state of paralysis. Welcome to philosophy... |
| 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) |
| 13409 | Our best theories may commit us to mathematical abstracta, but that doesn't justify the commitment [Papineau] |
| Full Idea: Our empirically best-supported theories may commit us to certain abstract mathematical entities, but this does not necessarily mean that this is what justifies our commitment. That we are committed doesn't explain why we should be. | |
| From: David Papineau (Philosophical Insignificance of A Priori Knowledge [2010], §4) | |
| A reaction: A nice point. It is only a slightly gormless scientism which would say that we have to accept whatever scientists demand. Who's in charge here - scientists, mathematicians or philosophers? Don't answer that... |
| 18431 | Internal relations combine some tropes into a nucleus, which bears the non-essential tropes [Simons, by Edwards] |
| Full Idea: Simons's 'nuclear' option blends features of the substratum and bundle theories. First we have tropes collected by virtue of their internal relations, forming the essential kernel or nucleus. This nucleus then bears the non-essential tropes. | |
| From: report of Peter Simons (Particulars in Particular Clothing [1994], p.567) by Douglas Edwards - Properties 3.5 | |
| A reaction: [compression of Edwards's summary] This strikes me as being a remarkably good theory. I am not sure of the ontological status of properties, such that they can (unaided) combine to make part of an object. What binds the non-essentials? |
| 13406 | A priori knowledge is analytic - the structure of our concepts - and hence unimportant [Papineau] |
| Full Idea: I am a fully paid up-naturalist, but I see no reason to deny that a priori knowledge is possible. My view is that a priori knowledge is unimportant (esp to philosophy). If there is a priori knowledge, it is analytic, true by the structure of our concepts. | |
| From: David Papineau (Philosophical Insignificance of A Priori Knowledge [2010], §1) | |
| A reaction: It is one thing to say it is the structure of our concepts, and another to infer that it is unimportant. I take the structure of our concepts to be a shadow cast by the structure of the world. E.g. the structure of numbers reveals the world. |
| 13408 | Intuition and thought-experiments embody substantial information about the world [Papineau] |
| Full Idea: Naturalists can allow for thought-experiments in philosophy. Intuitions play an important role, but only because they embody substantial information about the world. | |
| From: David Papineau (Philosophical Insignificance of A Priori Knowledge [2010], §3) | |
| A reaction: In this sense, intuitions are just memories which are too complex for us to articulate. They are not the intuitions of 'pure reason'. It is hard to connect the intuitive spotting of a proof with memories of the physical world. |
| 13410 | Verificationism about concepts means you can't deny a theory, because you can't have the concept [Papineau] |
| Full Idea: Verificationism about concepts implies that thinkers will not share concepts with adherents of theories they reject. Those who reject the phlogiston theory will not possess the same concept as adherents, so cannot say 'there is no phlogiston'. | |
| From: David Papineau (Philosophical Insignificance of A Priori Knowledge [2010], §6) | |
| A reaction: The point seems to be more general - that it is hard to see how you can have a concept of anything which doesn't actually exist, if the concept is meant to rest on some sort of empirical verification. |