18 ideas
| 10631 | If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological [Hale/Wright] |
| Full Idea: If we stipulate that 'x is heterological' iff it does not apply to itself, we speedily arrive at the contradiction that 'heterological' is itself heterological just in case it is not. | |
| From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2) |
| 10624 | The incompletability of formal arithmetic reveals that logic also cannot be completely characterized [Hale/Wright] |
| Full Idea: The incompletability of formal arithmetic reveals, not arithmetical truths which are not truths of logic, but that logical truth likewise defies complete deductive characterization. ...Gödel's result has no specific bearing on the logicist project. | |
| From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], §2 n5) | |
| A reaction: This is the key defence against the claim that Gödel's First Theorem demolished logicism. |
| 10629 | If structures are relative, this undermines truth-value and objectivity [Hale/Wright] |
| Full Idea: The relativization of ontology to theory in structuralism can't avoid carrying with it a relativization of truth-value, which would compromise the objectivity which structuralists wish to claim for mathematics. | |
| From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2 n26) | |
| A reaction: This is the attraction of structures which grow out of the physical world, where truth-value is presumably not in dispute. |
| 10628 | The structural view of numbers doesn't fit their usage outside arithmetical contexts [Hale/Wright] |
| Full Idea: It is not clear how the view that natural numbers are purely intra-structural 'objects' can be squared with the widespread use of numerals outside purely arithmetical contexts. | |
| From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2 n26) | |
| A reaction: I don't understand this objection. If they refer to quantity, they are implicitly cardinal. If they name things in a sequence they are implicitly ordinal. All users of numbers have a grasp of the basic structure. |
| 10622 | The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright] |
| Full Idea: The neo-Fregean takes a more optimistic view than Frege of the prospects for the kind of contextual explanation of the fundamental concepts of arithmetic and analysis (cardinals and reals), which he rejected in 'Grundlagen' 60-68. | |
| From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], §1) |
| 10626 | Objects just are what singular terms refer to [Hale/Wright] |
| Full Idea: Objects, as distinct from entities of other types (properties, relations or, more generally, functions of different types and levels), just are what (actual or possible) singular terms refer to. | |
| From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.1) | |
| A reaction: I find this view very bizarre and hard to cope with. It seems either to preposterously accept the implications of the way we speak into our ontology ('sakes'?), or preposterously bend the word 'object' away from its normal meaning. |
| 1556 | By nature people are close to one another, but culture drives them apart [Hippias] |
| Full Idea: I regard you all as relatives - by nature, not by convention. By nature like is akin to like, but convention is a tyrant over humankind and often constrains people to act contrary to nature. | |
| From: Hippias (fragments/reports [c.430 BCE]), quoted by Plato - Protagoras 337c8 |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 10630 | Abstracted objects are not mental creations, but depend on equivalence between given entities [Hale/Wright] |
| Full Idea: The new kind of abstract objects are not creations of the human mind. ...The existence of such objects depends upon whether or not the relevant equivalence relation holds among the entities of the presupposed kind. | |
| From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2) | |
| A reaction: It seems odd that we no longer have any choice about what abstract objects we use, and that we can't evade them if the objects exist, and can't have them if the objects don't exist - and presumably destruction of the objects kills the concept? |
| 10627 | Many conceptual truths ('yellow is extended') are not analytic, as derived from logic and definitions [Hale/Wright] |
| Full Idea: There are many statements which are plausibly viewed as conceptual truths (such as 'what is yellow is extended') which do not qualify as analytic under Frege's definition (as provable using only logical laws and definitions). | |
| From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2) | |
| A reaction: Presumably this is because the early assumptions of Frege were mathematical and logical, and he was trying to get away from Kant. That yellow is extended is a truth for non-linguistic beings. |
| 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. |