23 ideas
| 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. |
| 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? |
| 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. |
| 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? |
| 2584 | Lobotomised patients can cease to care about a pain [Block] |
| Full Idea: After frontal lobotomies, patients typically report that they still have pains, though the pains no longer bother them. | |
| From: Ned Block (Troubles with Functionalism [1978], p. 83) | |
| A reaction: I take this to be an endorsement of reductive physicalism, because what matters about pains is that they bother us, not how they feel, so frog pain could do the job, if it felt different from ours, but was disliked by the frog. |
| 2582 | A brain looks no more likely than anything else to cause qualia [Block] |
| Full Idea: NO physical mechanism seems very intuitively plausible as a seat of qualia, least of all a brain. | |
| From: Ned Block (Troubles with Functionalism [1978], p. 78) | |
| A reaction: I'm not sure about "least of all", given the mind-boggling complexity of the brain's connections. Certainly, though, nothing in either folk physics or academic physics suggests that any physical object is likely to be aware of anything. |
| 2574 | Behaviour requires knowledge as well as dispositions [Block] |
| Full Idea: A desire cannot be identified with a disposition to act, since the agent might not know that a particular act leads to the thing desired, and thus might not be disposed to do it. | |
| From: Ned Block (Troubles with Functionalism [1978], p. 69) | |
| A reaction: One might have a disposition to act, but not in a particular way. "Something must be done". To get to the particular act, it seems that indeed a belief must be added to the desire. |
| 2576 | In functionalism, desires are internal states with causal relations [Block] |
| Full Idea: According to functionalism, a system might have the behaviouristic input-output relations, yet not desire something, as this requires internal states with certain causal relations. | |
| From: Ned Block (Troubles with Functionalism [1978], p. 69) | |
| A reaction: Such a system might be Putnam's 'superactor', who only behaves as if he desires something. Of course, the internal states might need more than just 'causal relations'. |
| 2575 | Functionalism is behaviourism, but with mental states as intermediaries [Block] |
| Full Idea: Functionalism is a new incarnation of behaviourism, replacing sensory inputs with sensory inputs plus mental states, and replacing dispositions to act with dispositions plus certain mental states. | |
| From: Ned Block (Troubles with Functionalism [1978], p. 69) | |
| A reaction: I think of functionalism as behaviourism which extends inside the 'black box' between stimulus and response. It proposes internal stimuli and responses. Consequently functionalism inherits some behaviourist problems. |
| 2583 | You might invert colours, but you can't invert beliefs [Block] |
| Full Idea: It is hard to see how to make sense of the analog of color spectrum inversion with respect to non-qualitative states such a beliefs (where they are functionally equivalent but have different beliefs). | |
| From: Ned Block (Troubles with Functionalism [1978], p. 81) | |
| A reaction: I would suggest that beliefs can be 'inverted', because there are all sorts of ways to implement a belief, but colour can't be inverted, because that depends on a particular brain state. It makes good sense to me... |
| 2578 | Could a creature without a brain be in the right functional state for pain? [Block] |
| Full Idea: If pain is a functional state, it cannot be a brain state, because creatures without brains could realise the same Turing machine as creatures with brains. | |
| From: Ned Block (Troubles with Functionalism [1978], p. 70) | |
| A reaction: This strikes me as being a poorly grounded claim. There may be some hypothetical world where brainless creatures implement all our functions, but from here brains look the only plausible option. |
| 2585 | Not just any old functional network will have mental states [Block] |
| Full Idea: If there are any fixed points in the mind-body problem, one of them is that the economy of Bolivia could not have mental states, no matter how it is distorted. | |
| From: Ned Block (Troubles with Functionalism [1978], p. 86) | |
| A reaction: It is hard to disagree with this, but then it can hardly be a serious suggestion that anyone could see how to reconfigure an economy so that it mapped the functional state of the human brain. This is not a crucial problem. |
| 2586 | In functionalism, what are the special inputs and outputs of conscious creatures? [Block] |
| Full Idea: In functionalism, it is very hard to see how there could be a single physical characterization of the inputs and outputs of all and only creatures with mentality. | |
| From: Ned Block (Troubles with Functionalism [1978], p. 87) | |
| A reaction: It would be theoretically possible if the only way to achieve mentality was to have a particular pattern of inputs and outputs. I don't think, though, that 'mentality' is an all-or-nothing concept. |
| 2579 | Physicalism is prejudiced in favour of our neurology, when other systems might have minds [Block] |
| Full Idea: Physicalism is a chauvinist theory: it withholds mental properties from systems that in fact have them. | |
| From: Ned Block (Troubles with Functionalism [1978], p. 71) | |
| A reaction: This criticism interprets physicalism too rigidly. There may be several ways to implement a state. My own view is that other systems might implement our functions, but they won't experience them in a human way. |
| 2577 | Simple machine-functionalism says mind just is a Turing machine [Block] |
| Full Idea: In the simplest Turing-machine version of functionalism (Putnam 1967), mental states are identified with the total Turing-machine state, involving a machine table and its inputs and outputs. | |
| From: Ned Block (Troubles with Functionalism [1978], p. 70) | |
| A reaction: This obviously invites the question of why mental states would be conscious and phenomenal, given that modern computers are devoid of same, despite being classy Turing machines. |
| 2580 | A Turing machine, given a state and input, specifies an output and the next state [Block] |
| Full Idea: In a Turing machine, given any state and input, the machine table specifies an output and the next state. …To have full power the tape must be infinite in at least one direction, and be movable in both directions. | |
| From: Ned Block (Troubles with Functionalism [1978], p. 71) | |
| A reaction: In retrospect, the proposal that this feeble item should be taken as a model for the glorious complexity and richness of human consciousness doesn't look too plausible. |
| 2581 | Intuition may say that a complex sentence is ungrammatical, but linguistics can show that it is not [Block] |
| Full Idea: Linguistics rejects (on theoretical grounds) the intuition that the sentence "the boy the girl the cat bit scratched died" is ungrammatical. | |
| From: Ned Block (Troubles with Functionalism [1978], p. 78) | |
| A reaction: Once we have disentangled it, we practical speakers have no right to say it is ungrammatical. It isn't only theory. The sentence is just stylistically infelicitous. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |