22 ideas
| 14086 | 'Modal' structuralism studies all possible concrete models for various mathematical theories [Linnebo] |
| Full Idea: The 'modal' version of eliminativist structuralism lifts the deductivist ban on modal notions. It studies what necessarily holds in all concrete models which are possible for various theories. | |
| From: Øystein Linnebo (Structuralism and the Notion of Dependence [2008], I) | |
| A reaction: [He cites Putnam 1967, and Hellman 1989] If mathematical truths are held to be necessary (which seems to be right), then it seems reasonable to include modal notions, about what is possible, in its study. |
| 14087 | 'Set-theoretic' structuralism treats mathematics as various structures realised among the sets [Linnebo] |
| Full Idea: 'Set-theoretic' structuralism rejects deductive nominalism in favour of a background theory of sets, and mathematics as the various structures realized among the sets. This is often what mathematicians have in mind when they talk about structuralism. | |
| From: Øystein Linnebo (Structuralism and the Notion of Dependence [2008], I) | |
| A reaction: This is the big shift from 'mathematics can largely be described in set theory' to 'mathematics just is set theory'. If it just is set theory, then which version of set theory? Which axioms? The safe iterative conception, or something bolder? |
| 14085 | 'Deductivist' structuralism is just theories, with no commitment to objects, or modality [Linnebo] |
| Full Idea: The 'deductivist' version of eliminativist structuralism avoids ontological commitments to mathematical objects, and to modal vocabulary. Mathematics is formulations of various (mostly categorical) theories to describe kinds of concrete structures. | |
| From: Øystein Linnebo (Structuralism and the Notion of Dependence [2008], 1) | |
| A reaction: 'Concrete' is ambiguous here, as mathematicians use it for the actual working maths, as opposed to the metamathematics. Presumably the structures are postulated rather than described. He cites Russell 1903 and Putnam. It is nominalist. |
| 14084 | Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo] |
| Full Idea: The 'non-eliminative' version of mathematical structuralism takes it to be a fundamental insight that mathematical objects are really just positions in abstract mathematical structures. | |
| From: Øystein Linnebo (Structuralism and the Notion of Dependence [2008], I) | |
| A reaction: The point here is that it is non-eliminativist because it is committed to the existence of mathematical structures. I oppose this view, since once you are committed to the structures, you may as well admit a vast implausible menagerie of abstracta. |
| 14089 | Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure [Linnebo] |
| Full Idea: Structuralism can be distinguished from traditional Platonism in that it denies that mathematical objects from the same structure are ontologically independent of one another | |
| From: Øystein Linnebo (Structuralism and the Notion of Dependence [2008], III) | |
| A reaction: My instincts strongly cry out against all versions of this. If you are going to be a platonist (rather as if you are going to be religious) you might as well go for it big time and have independent objects, which will then dictate a structure. |
| 14083 | Structuralism is right about algebra, but wrong about sets [Linnebo] |
| Full Idea: Against extreme views that all mathematical objects depend on the structures to which they belong, or that none do, I defend a compromise view, that structuralists are right about algebraic objects (roughly), but anti-structuralists are right about sets. | |
| From: Øystein Linnebo (Structuralism and the Notion of Dependence [2008], Intro) |
| 14090 | In mathematical structuralism the small depends on the large, which is the opposite of physical structures [Linnebo] |
| Full Idea: If objects depend on the other objects, this would mean an 'upward' dependence, in that they depend on the structure to which they belong, where the physical realm has a 'downward' dependence, with structures depending on their constituents. | |
| From: Øystein Linnebo (Structuralism and the Notion of Dependence [2008], III) | |
| A reaction: This nicely captures an intuition I have that there is something wrong with a commitment primarily to 'structures'. Our only conception of such things is as built up out of components. Not that I am committing to mathematical 'components'! |
| 14091 | There may be a one-way direction of dependence among sets, and among natural numbers [Linnebo] |
| Full Idea: We can give an exhaustive account of the identity of the empty set and its singleton without mentioning infinite sets, and it might be possible to defend the view that one natural number depends on its predecessor but not vice versa. | |
| From: Øystein Linnebo (Structuralism and the Notion of Dependence [2008], V) | |
| A reaction: Linnebo uses this as one argument against mathematical structuralism, where the small seems to depend on the large. The view of sets rests on the iterative conception, where each level is derived from a lower level. He dismisses structuralism of sets. |
| 3523 | Shadows are supervenient on their objects, but not reducible [Maslin] |
| Full Idea: Shadows are distinct from the physical objects casting the shadows and irreducible to them; any attempt at reduction would be incoherent, as it would entail identifying a shadow with the object of which it is a shadow. | |
| From: Keith T. Maslin (Introduction to the Philosophy of Mind [2001], 6.3) | |
| A reaction: Another failure to find a decent analogy for what is claimed in property dualism. A 'shadow' is a reification of the abstract concept of an absence of light. Objects lose their shadows at dusk, but the object itself doesn't change. |
| 3517 | 'Ontology' means 'study of things which exist' [Maslin] |
| Full Idea: The word 'ontology' is derived from the Greek word 'ontia', which means 'things which exist'. | |
| From: Keith T. Maslin (Introduction to the Philosophy of Mind [2001], 1.1) |
| 14088 | An 'intrinsic' property is either found in every duplicate, or exists independent of all externals [Linnebo] |
| Full Idea: There are two main ways of spelling out an 'intrinsic' property: if and only if it is shared by every duplicate of an object, ...and if and only if the object would have this property even if the rest of the universe were removed or disregarded. | |
| From: Øystein Linnebo (Structuralism and the Notion of Dependence [2008], II) | |
| A reaction: [He cites B.Weatherson's Stanford Encyclopaedia article] How about an intrinsic property being one which explains its identity, or behaviour, or persistence conditions? |
| 3538 | Analogy to other minds is uncheckable, over-confident and chauvinistic [Maslin] |
| Full Idea: The argument from analogy makes it impossible to check my inductive inferences because of the privacy of other minds; it also seems irresponsible to generalise from a single case; and it seems like a case of human chauvinism. | |
| From: Keith T. Maslin (Introduction to the Philosophy of Mind [2001], 8.2) | |
| A reaction: Privacy of other minds need not imply scepticism about them. I'm a believer, so I have no trouble checking my theories. Solipsists can't 'check' anything. It isn't 'irresponsible' to generalise from one case if that is all you have. |
| 3540 | If we are brains then we never meet each other [Maslin] |
| Full Idea: If I am my brain this leads to the odd result that you have never met me because you have never seen my brain. | |
| From: Keith T. Maslin (Introduction to the Philosophy of Mind [2001], 10.7) | |
| A reaction: 'Star Trek' is full of aliens who appear beautiful, and turn out to be ugly grey lumps. 'I am my face' would be just as odd, particularly if I were in a coma, or dead. |
| 3518 | I'm not the final authority on my understanding of maths [Maslin] |
| Full Idea: I may be the final authority on whether my shoe pinches, but I am manifestly not the final authority on whether I understand some mathematical theorem. | |
| From: Keith T. Maslin (Introduction to the Philosophy of Mind [2001], 1.7) | |
| A reaction: However, it doesn't follow that his teachers are the final authority either, because he may get correct answers by an algorithm, and bluff his way when demonstrating his understanding. Who knows whether anyone really understands anything? |
| 3530 | Denial of purely mental causation will lead to epiphenomenalism [Maslin] |
| Full Idea: If mental events are causally efficacious only by virtue of their physical features and not their mental ones, …then anomalous monism leads straight to ephiphenomenalism. | |
| From: Keith T. Maslin (Introduction to the Philosophy of Mind [2001], 7.6) | |
| A reaction: As epiphenomenalism strikes me as being incoherent (see Idea 7379), what this amounts to is that either mental effects are causally efficacious, or they are not worth mentioning. I take them to be causally efficacious because they are brain events. |
| 3520 | Token-identity removes the explanatory role of the physical [Maslin] |
| Full Idea: In token-identity mental and physical features seem as unrelated as colour and shape, which is very weak physicalism because it does not allow physical states an explanatory role in accounting for mental states. | |
| From: Keith T. Maslin (Introduction to the Philosophy of Mind [2001], 3.8.6) | |
| A reaction: Colour and shape are not totally unrelated, as they can both be totally explained by a full knowledge of the physical substance involved. ...But maybe if we fully understood Spinoza's single substance...? See Idea 4834. |
| 17371 | Some kinds are very explanatory, but others less so, and some not at all [Devitt] |
| Full Idea: Explanatory significance, hence naturalness, comes in degrees: positing some kinds may be very explanatory, positing others, only a little bit explanatory, positing others still, not explanatory at all. | |
| From: Michael Devitt (Natural Kinds and Biological Realism [2009], 4) | |
| A reaction: He mentions 'cousin' as a natural kind that is not very explanatory of anything. It interests us as humans, but not at all in other animals, it seems. ...Nice thought, though, that two squirrels might be cousins... |
| 3528 | Causality may require that a law is being followed [Maslin] |
| Full Idea: The principle of nomological causality says that if two events are intrinsically causally related, there must be a strict physical law under which they can be subsumed. | |
| From: Keith T. Maslin (Introduction to the Philosophy of Mind [2001], 7.5) |
| 3525 | Strict laws make causation logically necessary [Maslin] |
| Full Idea: 'Deductive-nomological' explanation consists of two premises - a strict law with no exceptions and supporting deterministic counterfactuals, and a statement of an event which falls under the law - which together logically require the effect. | |
| From: Keith T. Maslin (Introduction to the Philosophy of Mind [2001], 7.4) |
| 3527 | Strict laws allow no exceptions and are part of a closed system [Maslin] |
| Full Idea: 'Strict' laws of nature contain no ceteris paribus clauses ('all things being equal'), and are part of a closed system (so that whatever affects the system must be included within the system). | |
| From: Keith T. Maslin (Introduction to the Philosophy of Mind [2001], 7.5) |
| 17372 | The higher categories are not natural kinds, so the Linnaean hierarchy should be given up [Devitt] |
| Full Idea: The signs are that the higher categories are not natural kinds and so the Linnaean hierarchy must be abandoned. ...This is not abandoning a hierarchy altogether, it is not abandoning a tree of life. | |
| From: Michael Devitt (Natural Kinds and Biological Realism [2009], 6) | |
| A reaction: Devitt's underlying point is that the higher and more general kinds do not have an essence (a specific nature), which is the qualification to be a natural kind. They explain nothing. Essence is the hallmark of natural kinds. Hmmm. |
| 17373 | Species pluralism says there are several good accounts of what a species is [Devitt] |
| Full Idea: Species pluralism is the view that there are several equally good accounts of what it is to be a species. | |
| From: Michael Devitt (Natural Kinds and Biological Realism [2009], 7) | |
| A reaction: Devitt votes for it, and cites Dupré, among many other. Given the existence of rival accounts, all making good points, it is hard to resist this view. |