17 ideas
| 12154 | Are 'word token' and 'word type' different sorts of countable objects, or two ways of counting? [Geach, by Perry] |
| Full Idea: If we list the words 'bull', 'bull' and 'cow', it is often said that there are three 'word tokens' but only two 'word types', but Geach says there are not two kinds of object to be counted, but two different ways of counting the same object. | |
| From: report of Peter Geach (Reference and Generality (3rd ed) [1980]) by John Perry - The Same F II | |
| A reaction: Insofar as the notion that a 'word type' is an 'object', my sympathies are entirely with Geach, to my surprise. Geach's point is that 'bull' and 'bull' are the same meaning, but different actual words. Identity is relative to a concept. |
| 18200 | 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'. |
| 18199 | 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 |
| 8857 | 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! |
| 8969 | We should abandon absolute identity, confining it to within some category [Geach, by Hawthorne] |
| Full Idea: Geach argued that the notion of absolute identity should be abandoned. ..We can only grasp the meaning of a count noun when we associate it with a criterion of identity, expressed by a particular relative identity sortal. | |
| From: report of Peter Geach (Reference and Generality (3rd ed) [1980]) by John Hawthorne - Identity | |
| A reaction: In other words, identity needs categorisation. Hawthorne concludes that Geach is wrong. Geach clearly has much common usage on his side. 'What's that?' usually invites a categorisation. Sameness of objects seems to need a 'respect'. |
| 16075 | Denial of absolute identity has drastic implications for logic, semantics and set theory [Wasserman on Geach] |
| Full Idea: Geach's denial of absolute identity has drastic implications for logic, semantics and set theory. He must deny the axiom of extensionality in set theory, for example. | |
| From: comment on Peter Geach (Reference and Generality (3rd ed) [1980]) by Ryan Wasserman - Material Constitution 6 | |
| A reaction: I'm beginning to think we have two entirely different concepts here - the logicians' and mathematicians' notion of when two things are identical, and the ordinary language concept of two things being 'the same'. 'We like the same music'. |
| 12152 | Identity is relative. One must not say things are 'the same', but 'the same A as' [Geach] |
| Full Idea: Identity is relative. When one says 'x is identical with y' this is an incomplete expression. It is short for 'x is the same A as y', where 'A' represents some count noun understood from the context of utterance. | |
| From: Peter Geach (Reference and Generality (3rd ed) [1980], p.39), quoted by John Perry - The Same F I | |
| A reaction: Perry notes that Geach's view is in conscious opposition to Frege, who had a pure notion of identity. We say 'they are the same insofar as they are animals', but not 'they are the same animal'. Perfect identity involves all possible A's. |
| 16073 | Leibniz's Law is incomplete, since it includes a non-relativized identity predicate [Geach, by Wasserman] |
| Full Idea: Geach rejects the standard formulation of Leibniz's Law as incomplete, since it includes a non-relativized identity predicate. | |
| From: report of Peter Geach (Reference and Generality (3rd ed) [1980]) by Ryan Wasserman - Material Constitution 6 | |
| A reaction: Not many people accept Geach's premiss that identity is a relative matter. I agree with Wiggins on this, that identity is an absolute (and possibly indefinable). The problem with the Law is what you mean by a 'property'. |
| 22189 | Why abandon a theory if you don't have a better one? [Gorham] |
| Full Idea: There is no sense in abandoning a successful theory if you have nothing to replace it with. | |
| From: Geoffrey Gorham (Philosophy of Science [2009], 2) | |
| A reaction: This is also a problem for infererence to the best explanation. What to do if your best explanation is not very good? The simple message is do not rush to dump a theory when faced with an anomaly. |
| 22190 | If a theory is more informative it is less probable [Gorham] |
| Full Idea: Popper's theory implies that more informative theories seem to be less probable. | |
| From: Geoffrey Gorham (Philosophy of Science [2009], 3) | |
| A reaction: [On p.75 Gorham replies to this objection] The point is that to be more testable they must be more detailed. He's not wrong. Theories are meant to be general, so they sweep up the details. But they need precise generalities and specifics. |
| 22192 | Is Newton simpler with universal simultaneity, or Einstein simpler without absolute time? [Gorham] |
| Full Idea: Is Newton's theory simpler than Einstein's, since there is only one relation of simultaneity in absolute time, or is Einstein's simpler because it dispenses with absolute time altogether? | |
| From: Geoffrey Gorham (Philosophy of Science [2009], 4) | |
| A reaction: A nice question, to which a good scientist might be willing to offer an answer. Since simultaneity is crucial but the existence of time is not, I would vote for Newton as the simpler. |
| 22194 | Structural Realism says mathematical structures persist after theory rejection [Gorham] |
| Full Idea: Structural Realists say that modern science achieves a true or 'truer' account of the world only with respect to its mathematical structure rather than its intrinsic qualities or nature. The structure carries over to new theories. | |
| From: Geoffrey Gorham (Philosophy of Science [2009], 4) | |
| A reaction: At first glance I am unconvinced that when an old theory is replaced it neverthess contains some sort of 'mathematical structure' which endures and is worth preserving. No doubt Worrall, French and co have examples. |
| 22195 | Structural Realists must show the mathematics is both crucial and separate [Gorham] |
| Full Idea: Structural Realists must show that it is the mathematical aspects of the theories, not their content, that account for their success ….and that their structure and content can be clearly separated. | |
| From: Geoffrey Gorham (Philosophy of Science [2009], 4) | |
| A reaction: Their approach certainly seems to rely on mathematical types of science, so it presumably fits biology, geology and even astronomy less well. |
| 22196 | For most scientists their concepts are not just useful, but are meant to be true and accurate [Gorham] |
| Full Idea: The main difficulty with instrumentalism is its implausible account ot the meaning of theoretical claims and concepts. Most scientists take them to be straightforward attempts to describe the world. Most say they are useful because they are accurate. | |
| From: Geoffrey Gorham (Philosophy of Science [2009], 4) | |
| A reaction: Instrumentalism is seen as a Pragmatist view, and Dewey is cited. |
| 22197 | Theories aren't just for organising present experience if they concern the past or future [Gorham] |
| Full Idea: The strangeness of interpreting theories as mere tools for organising present experience is brought out clearly in sciences like cosmology and paleontology, which largely concern events in the remote past or future. | |
| From: Geoffrey Gorham (Philosophy of Science [2009], 4) | |
| A reaction: Not conclusive. An anti-realist has to interpret those sciences in terms of the current observations that are available. |
| 22193 | Consilience makes the component sciences more likely [Gorham] |
| Full Idea: The more unification and integration is found among the modern sciences, the less likely it seems it will have all been a dream. | |
| From: Geoffrey Gorham (Philosophy of Science [2009], 4) | |
| A reaction: I believe this strongly. Ancient theories which were complex, wide ranging and false do not impress me. This is part of my coherence view of justification. |
| 22198 | Aristotelian physics has circular celestial motion and linear earthly motion [Gorham] |
| Full Idea: Aristotelian physics assumed that celestial motion is naturally circular and eternal while terrestrial motion is naturally toward the center of the earth and final. | |
| From: Geoffrey Gorham (Philosophy of Science [2009], 4) | |
| A reaction: The overthrow of this by Galileo and then Newton may have been the most dramatic revolution of the new science. It opened up the possibility of universal laws of physics. |