17 ideas
| 2510 | Traditionally philosophy is an a priori enquiry into general truths about reality [Katz] |
| Full Idea: The traditional conception of philosophy is that it is an a priori enquiry into the most general facts about reality. | |
| From: Jerrold J. Katz (Realistic Rationalism [2000], Int.xi) | |
| A reaction: I think this still defines philosophy, though it also highlights the weakness of the subject, which is over-confidence about asserting necessary truths. How could the most god-like areas of human thought be about anything else? |
| 2516 | Most of philosophy begins where science leaves off [Katz] |
| Full Idea: Philosophy, or at least one large part of it, is subsequent to science; it begins where science leaves off. | |
| From: Jerrold J. Katz (Realistic Rationalism [2000], Int.xxi) | |
| A reaction: In some sense this has to be true. Without metaphysics there couldn't be any science. Rationalists should not forget, though, the huge impact which Darwin's science has (or should have) on fairly abstract philosophy (e.g. epistemology). |
| 6601 | Science rules the globe because of colonising power, not inherent rationality [Feyerabend] |
| Full Idea: Science now reigns supreme all over the globe; but the reason was not insight in its 'inherent rationality' but power play (the colonising nations imposed their way of living) and the need for weapons. | |
| From: Paul Feyerabend (Against Method [1975], 3), quoted by Robert Fogelin - Walking the Tightrope of Reason Ch.5 | |
| A reaction: A nice clear statement of ridiculous relativism about science. What gave the colonisers their power if it was not more accurate knowledge of how to manipulate nature? |
| 10185 | Set theory is the standard background for modern mathematics [Burgess] |
| Full Idea: In present-day mathematics, it is set theory that serves as the background theory in which other branches of mathematics are developed. | |
| From: John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §1) | |
| A reaction: [He cites Bourbaki as an authority for this] See Benacerraf for a famous difficulty here, when you actually try to derive an ontology from the mathematicians' working practices. |
| 10184 | Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure [Burgess] |
| Full Idea: On the structuralist interpretation, theorems of analysis concerning the real numbers R are about all complete ordered fields. So R, which appears to be the name of a specific structure, is taken to be a variable ranging over structures. | |
| From: John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §1) | |
| A reaction: Since I am beginning to think that nearly all linguistic expressions should be understood as variables, I find this very appealing, even if Burgess hates it. Terms slide and drift, and are vague, between variable and determinate reference. |
| 10189 | There is no one relation for the real number 2, as relations differ in different models [Burgess] |
| Full Idea: One might meet the 'Van Inwagen Problem' by saying that the intrinsic properties of the object playing the role of 2 will differ from one model to another, so that no statement about the intrinsic properties of 'the' real numbers will make sense. | |
| From: John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §5) | |
| A reaction: There seems to be a potential confusion among opponents of structuralism between relations at the level of actual mathematical operations, and generalisations about relations, which are captured in the word 'patterns'. Call them 'meta-relations'? |
| 10186 | If set theory is used to define 'structure', we can't define set theory structurally [Burgess] |
| Full Idea: It is to set theory that one turns for the very definition of 'structure', ...and this creates a problem of circularity if we try to impose a structuralist interpretation on set theory. | |
| From: John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §1) | |
| A reaction: This seems like a nice difficulty, especially if, like Shapiro, you wade in and try to give a formal account of structures and patterns. Resnik is more circumspect and vague. |
| 10187 | Abstract algebra concerns relations between models, not common features of all the models [Burgess] |
| Full Idea: Abstract algebra, such as group theory, is not concerned with the features common to all models of the axioms, but rather with the relationships among different models of those axioms (especially homomorphic relation functions). | |
| From: John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §1) | |
| A reaction: It doesn't seem to follow that structuralism can't be about the relations (or patterns) found when abstracting away and overviewing all the models. One can study family relations, or one can study kinship in general. |
| 10188 | How can mathematical relations be either internal, or external, or intrinsic? [Burgess] |
| Full Idea: The 'Van Inwagen Problem' for structuralism is of explaining how a mathematical relation (such as set membership, or the ratios of an ellipse) can fit into one of the three scholastics types of relations: are they internal, external, or intrinsic? | |
| From: John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §5) | |
| A reaction: The difficulty is that mathematical objects seem to need intrinsic properties to get any of these three versions off the ground (which was Russell's complaint against structures). |
| 2521 | 'Real' maths objects have no causal role, no determinate reference, and no abstract/concrete distinction [Katz] |
| Full Idea: Three objections to realism in philosophy of mathematics: mathematical objects have no space/time location, and so no causal role; that such objects are determinate, but reference to numbers aren't; and that there is no abstract/concrete distinction. | |
| From: Jerrold J. Katz (Realistic Rationalism [2000], Int.xxix) |
| 2513 | We don't have a clear enough sense of meaning to pronounce some sentences meaningless or just analytic [Katz] |
| Full Idea: Linguistic meaning is not rich enough to show either that all metaphysical sentences are meaningless or that all alleged synthetic a priori propositions are just analytic a priori propositions. | |
| From: Jerrold J. Katz (Realistic Rationalism [2000], Int.xx) |
| 2522 | Experience cannot teach us why maths and logic are necessary [Katz] |
| Full Idea: The Leibniz-Kant criticism of empiricism is that experience cannot teach us why mathematical and logical facts couldn't be otherwise than they are. | |
| From: Jerrold J. Katz (Realistic Rationalism [2000], Int.xxxi) |
| 2561 | For Feyerabend the meaning of a term depends on a whole theory [Feyerabend, by Rorty] |
| Full Idea: For Feyerabend the meaning of a term depends on a whole theory containing the term. | |
| From: report of Paul Feyerabend (Against Method [1975]) by Richard Rorty - Philosophy and the Mirror of Nature 6.3 |
| 2517 | Structuralists see meaning behaviouristically, and Chomsky says nothing about it [Katz] |
| Full Idea: In linguistics there are two schools of thought: Bloomfieldian structuralism (favoured by Quine) conceives of sentences acoustically and meanings behaviouristically; and Chomskian generative grammar (which is silent about semantics). | |
| From: Jerrold J. Katz (Realistic Rationalism [2000], Int.xxiv) | |
| A reaction: They both appear to be wrong, so there is (or was) something rotten in the state of linguistics. Are the only options for meaning either behaviourist or eliminativist? |
| 2519 | It is generally accepted that sense is defined as the determiner of reference [Katz] |
| Full Idea: There is virtually universal acceptance of Frege's definition of sense as the determiner of reference. | |
| From: Jerrold J. Katz (Realistic Rationalism [2000], Int.xxvi) | |
| A reaction: Not any more, since Kripke and Putnam. It is one thing to say sense determines reference, and quite another to say that this is the definition of sense. |
| 2520 | Sense determines meaning and synonymy, not referential properties like denotation and truth [Katz] |
| Full Idea: Pace Frege, sense determines sense properties and relations, like meaningfulness and synonymy, rather than determining referential properties, like denotation and truth. | |
| From: Jerrold J. Katz (Realistic Rationalism [2000], Int.xxvi) | |
| A reaction: This leaves room for Fregean 'sense', after Kripke has demolished the idea that sense determines reference. |
| 2518 | Sentences are abstract types (like musical scores), not individual tokens [Katz] |
| Full Idea: Sentences are types, not utterance tokens or mental/neural tokens, and hence sentences are abstract objects (like musical scores). | |
| From: Jerrold J. Katz (Realistic Rationalism [2000], Int.xxvi) | |
| A reaction: If sentences are abstract types, then two verbally indistinguishable sentences are the same sentence. But if I say 'I am happy', that isn't the same as you saying it. |