11 ideas
| 17807 | To study formal systems, look at the whole thing, and not just how it is constructed in steps [Curry] |
| Full Idea: In the study of formal systems we do not confine ourselves to the derivation of elementary propositions step by step. Rather we take the system, defined by its primitive frame, as datum, and then study it by any means at our command. | |
| From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'The formalist') | |
| A reaction: This is what may potentially lead to an essentialist view of such things. Focusing on bricks gives formalism, focusing on buildings gives essentialism. |
| 17806 | It is untenable that mathematics is general physical truths, because it needs infinity [Curry] |
| Full Idea: According to realism, mathematical propositions express the most general properties of our physical environment. This is the primitive view of mathematics, yet on account of the essential role played by infinity in mathematics, it is untenable today. | |
| From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'The problem') | |
| A reaction: I resist this view, because Curry's view seems to imply a mad metaphysics. Hilbert resisted the role of the infinite in essential mathematics. If the physical world includes its possibilities, that might do the job. Hellman on structuralism? |
| 17808 | Saying mathematics is logic is merely replacing one undefined term by another [Curry] |
| Full Idea: To say that mathematics is logic is merely to replace one undefined term by another. | |
| From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'Mathematics') |
| 17499 | Theoretical models can represent, by mapping onto the data-models [Portides] |
| Full Idea: The semantic approach contends that theoretical models ...are candidates for representing physical systems by virtue of the fact that they stand in mapping relations to corresponding data-models. | |
| From: Demetris Portides (Models [2008], 'Current') | |
| A reaction: Sounds like a neat and satisfying picture. |
| 17498 | In the 'received view' models are formal; the 'semantic view' emphasises representation [Portides, by PG] |
| Full Idea: The 'received view' of models is that they are Tarskian formal axiomatic calculi interpreted by meta-mathematical models. The 'semantic' view of models gives equal importance to their representational capacity. | |
| From: report of Demetris Portides (Models [2008], 'background') by PG - Db (ideas) | |
| A reaction: The Tarskian view is the one covered in my section on Model Theory. Portides favours the semantic account, and I am with him all the way. Should models primarily integrate with formal systems, or with the world? Your choice... |
| 17501 | Representational success in models depends on success of their explanations [Portides] |
| Full Idea: Models are representational, independently of the strength of their relation to theory, depending on how well they achieve the purpose of providing explanations for what occurs in physical systems. | |
| From: Demetris Portides (Models [2008], 'Current') | |
| A reaction: This doesn't sound quite right. It seems possible to have a perfect representation of a system which remains quite baffling (because too complex, or with obscure ingredients). Does the stylised London tube map explain well but represent badly? |
| 17502 | The best model of the atomic nucleus is the one which explains the most results [Portides] |
| Full Idea: The unified model can be considered a better representation of the atomic nucleus in comparison to the liquid-drop and shell models, because it explains most of the known results about the nucleus. | |
| From: Demetris Portides (Models [2008], 'Current') | |
| A reaction: The point here is that models are evaluated not just by their accuracy, but by their explanatory power. Presumably a great model is satisfying and illuminating. Do the best models capture the essence of a thing? |
| 17496 | 'Model' belongs in a family of concepts, with representation, idealisation and abstraction [Portides] |
| Full Idea: A better understanding of 'model', as used in science, could be achieved if we examine it as a member of the triad of concepts of representation, idealisation and abstraction. | |
| From: Demetris Portides (Models [2008], 'Intro') | |
| A reaction: Abstraction seems to have a bad name in philosophy, and yet when you come to discuss things like models, you can't express it any other way. |
| 17497 | Models are theory-driven, or phenomenological (more empirical and specific) [Portides] |
| Full Idea: 'Theory-driven' models are constructed in a systematic theory-regulated way by supplementing the theoretical calculus with locally operative hypotheses. 'Phenomenological' models deploy semi-empirical results, with ad hoc hypotheses, and extra concepts. | |
| From: Demetris Portides (Models [2008], 'Intro') | |
| A reaction: [compressed] I am not at all clear about this distinction, even after reading his whole article. The first type of model seems more general, while the second seems tuned to particular circumstances. He claims the second type is more explanatory. |
| 17500 | General theories may be too abstract to actually explain the mechanisms [Portides] |
| Full Idea: If theoretical models are highly abstract and idealised descriptions of phenomena, they may only represent general features, and fail to explain the specific mechanisms at work in physical systems. | |
| From: Demetris Portides (Models [2008], 'Current') | |
| A reaction: [compressed] While there may be an ideal theory that explains everything, it sounds right capturing the actual mechanism (such as the stirrup bone in the ear) is not at all theoretical. |
| 8338 | A phenomenalist about objects has to be a regularity theorist about causation [Strawson,G] |
| Full Idea: If you are a phenomenalist about objects, then there is an important sense in which you ought to be a Regularity theorist about what causation is, in such objects. | |
| From: Galen Strawson (The Secret Connexion [1989], App C) | |
| A reaction: Strawson is denying that Hume is a phenomenalist. One might go a little further, and say that a phenomenalist should abandon the idea of causation (as Russell did). |