74 ideas
| 15945 | Second-order set theory just adds a version of Replacement that quantifies over functions [Lavine] |
| Full Idea: Second-order set theory is just like first-order set-theory, except that we use the version of Replacement with a universal second-order quantifier over functions from set to sets. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VII.4) |
| 15914 | An 'upper bound' is the greatest member of a subset; there may be several of these, so there is a 'least' one [Lavine] |
| Full Idea: A member m of M is an 'upper bound' of a subset N of M if m is not less than any member of N. A member m of M is a 'least upper bound' of N if m is an upper bound of N such that if l is any other upper bound of N, then m is less than l. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.4) | |
| A reaction: [if you don't follow that, you'll have to keep rereading it till you do] |
| 15921 | Collections of things can't be too big, but collections by a rule seem unlimited in size [Lavine] |
| Full Idea: Since combinatorial collections are enumerated, some multiplicities may be too large to be gathered into combinatorial collections. But the size of a multiplicity seems quite irrelevant to whether it forms a logical connection. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], IV.2) |
| 15937 | Those who reject infinite collections also want to reject the Axiom of Choice [Lavine] |
| Full Idea: Many of those who are skeptical about the existence of infinite combinatorial collections would want to doubt or deny the Axiom of Choice. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VI.2) |
| 15936 | The Power Set is just the collection of functions from one collection to another [Lavine] |
| Full Idea: The Power Set is just he codification of the fact that the collection of functions from a mathematical collection to a mathematical collection is itself a mathematical collection that can serve as a domain of mathematical study. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VI.1) |
| 15899 | Replacement was immediately accepted, despite having very few implications [Lavine] |
| Full Idea: The Axiom of Replacement (of Skolem and Fraenkel) was remarkable for its universal acceptance, though it seemed to have no consequences except for the properties of the higher reaches of the Cantorian infinite. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], I) |
| 15930 | Foundation says descending chains are of finite length, blocking circularity, or ungrounded sets [Lavine] |
| Full Idea: The Axiom of Foundation (Zermelo 1930) says 'Every (descending) chain in which each element is a member of the previous one is of finite length'. ..This forbids circles of membership, or ungrounded sets. ..The iterative conception gives this centre stage. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.4) |
| 15920 | Pure collections of things obey Choice, but collections defined by a rule may not [Lavine] |
| Full Idea: Combinatorial collections (defined just by the members) obviously obey the Axiom of Choice, while it is at best dubious whether logical connections (defined by a rule) do. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], IV.2) |
| 15898 | The controversy was not about the Axiom of Choice, but about functions as arbitrary, or given by rules [Lavine] |
| Full Idea: The controversy was not about Choice per se, but about the correct notion of function - between advocates of taking mathematics to be about arbitrary functions and advocates of taking it to be about functions given by rules. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], I) |
| 15919 | The 'logical' notion of class has some kind of definition or rule to characterise the class [Lavine] |
| Full Idea: The Peano-Russell notion of class is the 'logical' notion, where each collection is associated with some kind of definition or rule that characterises the members of the collection. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], IV.1) |
| 15900 | The iterative conception of set wasn't suggested until 1947 [Lavine] |
| Full Idea: The iterative conception of set was not so much as suggested, let alone advocated by anyone, until 1947. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], I) |
| 15931 | The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine] |
| Full Idea: The iterative conception of sets does not tell us how far to iterate, and so we must start with an Axiom of Infinity. It also presupposes the notion of 'transfinite iteration'. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.5) |
| 15932 | The iterative conception doesn't unify the axioms, and has had little impact on mathematical proofs [Lavine] |
| Full Idea: The iterative conception does not provide a conception that unifies the axioms of set theory, ...and it has had very little impact on what theorems can be proved. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.5) | |
| A reaction: He says he would like to reject the iterative conception, but it may turn out that Foundation enables new proofs in mathematics (though it hasn't so far). |
| 15933 | Limitation of Size: if it's the same size as a set, it's a set; it uses Replacement [Lavine] |
| Full Idea: Limitation of Size has it that if a collection is the same size as a set, then it is a set. The Axiom of Replacement is characteristic of limitation of size. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.5) |
| 15913 | A collection is 'well-ordered' if there is a least element, and all of its successors can be identified [Lavine] |
| Full Idea: A collection M is 'well-ordered' by a relation < if < linearly orders M with a least element, and every subset of M that has an upper bound not in it has an immediate successor. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.4) |
| 15926 | Second-order logic presupposes a set of relations already fixed by the first-order domain [Lavine] |
| Full Idea: The distinctive feature of second-order logic is that it presupposes that, given a domain, there is a fact of the matter about what the relations on it are, so that the range of the second-order quantifiers is fixed as soon as the domain is fixed. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.3) | |
| A reaction: This sounds like a rather large assumption, which is open to challenge. I am not sure whether it was the basis of Quine's challenge to second-order logic. He seems to have disliked its vagueness, because it didn't stick with 'objects'. |
| 15934 | Mathematical proof by contradiction needs the law of excluded middle [Lavine] |
| Full Idea: The Law of Excluded Middle is (part of) the foundation of the mathematical practice of employing proofs by contradiction. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VI.1) | |
| A reaction: This applies in a lot of logic, as well as in mathematics. Come to think of it, it applies in Sudoku. |
| 15907 | Mathematics is nowadays (thanks to set theory) regarded as the study of structure, not of quantity [Lavine] |
| Full Idea: Mathematics is today thought of as the study of abstract structure, not the study of quantity. That point of view arose directly out of the development of the set-theoretic notion of abstract structure. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.2) | |
| A reaction: It sounds as if Structuralism, which is a controversial view in philosophy, is a fait accompli among mathematicians. |
| 15942 | Every rational number, unlike every natural number, is divisible by some other number [Lavine] |
| Full Idea: One reason to introduce the rational numbers is that it simplifes the theory of division, since every rational number is divisible by every nonzero rational number, while the analogous statement is false for the natural numbers. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VI.3) | |
| A reaction: That is, with rations every division operation has an answer. |
| 15922 | For the real numbers to form a set, we need the Continuum Hypothesis to be true [Lavine] |
| Full Idea: The chief importance of the Continuum Hypothesis for Cantor (I believe) was that it would show that the real numbers form a set, and hence that they were encompassed by his theory. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], IV.2) |
| 18250 | Cauchy gave a necessary condition for the convergence of a sequence [Lavine] |
| Full Idea: The Cauchy convergence criterion for a sequence: the sequence S0,S1,... has a limit if |S(n+r) - S(n)| is less than any given quantity for every value of r and sufficiently large values of n. He proved this necessary, but not sufficient. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], 2.5) |
| 15904 | The two sides of the Cut are, roughly, the bounding commensurable ratios [Lavine] |
| Full Idea: Roughly speaking, the upper and lower parts of the Dedekind cut correspond to the commensurable ratios greater than and less than a given incommensurable ratio. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], II.6) | |
| A reaction: Thus there is the problem of whether the contents of the gap are one unique thing, or many. |
| 15912 | Counting results in well-ordering, and well-ordering makes counting possible [Lavine] |
| Full Idea: Counting a set produces a well-ordering of it. Conversely, if one has a well-ordering of a set, one can count it by following the well-ordering. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.4) | |
| A reaction: Cantor didn't mean that you could literally count the set, only in principle. |
| 15949 | The theory of infinity must rest on our inability to distinguish between very large sizes [Lavine] |
| Full Idea: The indiscernibility of indefinitely large sizes will be a critical part of the theory of indefinitely large sizes. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VIII.2) |
| 15947 | The infinite is extrapolation from the experience of indefinitely large size [Lavine] |
| Full Idea: My proposal is that the concept of the infinite began with an extrapolation from the experience of indefinitely large size. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VIII.2) | |
| A reaction: I think it might be better to talk of an 'abstraction' than an 'extrapolition', since the latter is just more of the same, which doesn't get you to concept. Lavine spends 100 pages working out his proposal. |
| 15940 | The intuitionist endorses only the potential infinite [Lavine] |
| Full Idea: The intuitionist endorse the actual finite, but only the potential infinite. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VI.2) |
| 15909 | 'Aleph-0' is cardinality of the naturals, 'aleph-1' the next cardinal, 'aleph-ω' the ω-th cardinal [Lavine] |
| Full Idea: The symbol 'aleph-nought' denotes the cardinal number of the set of natural numbers. The symbol 'aleph-one' denotes the next larger cardinal number. 'Aleph-omega' denotes the omega-th cardinal number. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.3) |
| 15915 | Ordinals are basic to Cantor's transfinite, to count the sets [Lavine] |
| Full Idea: The ordinals are basic because the transfinite sets are those that can be counted, or (equivalently for Cantor), those that can be numbered by an ordinal or are well-ordered. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.4) | |
| A reaction: Lavine observes (p.55) that for Cantor 'countable' meant 'countable by God'! |
| 15917 | Paradox: the class of all ordinals is well-ordered, so must have an ordinal as type - giving a bigger ordinal [Lavine] |
| Full Idea: The paradox of the largest ordinal (the 'Burali-Forti') is that the class of all ordinal numbers is apparently well-ordered, and so it has an ordinal number as order type, which must be the largest ordinal - but all ordinals can be increased by one. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.5) |
| 15918 | Paradox: there is no largest cardinal, but the class of everything seems to be the largest [Lavine] |
| Full Idea: The paradox of the largest cardinal ('Cantor's Paradox') says the diagonal argument shows there is no largest cardinal, but the class of all individuals (including the classes) must be the largest cardinal number. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.5) |
| 15929 | Set theory will found all of mathematics - except for the notion of proof [Lavine] |
| Full Idea: Every theorem of mathematics has a counterpart with set theory - ...but that theory cannot serve as a basis for the notion of proof. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.3) |
| 15935 | Modern mathematics works up to isomorphism, and doesn't care what things 'really are' [Lavine] |
| Full Idea: In modern mathematics virtually all work is only up to isomorphism and no one cares what the numbers or points and lines 'really are'. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VI.1) | |
| A reaction: At least that leaves the field open for philosophers, because we do care what things really are. So should everybody else, but there is no persuading some people. |
| 15928 | Intuitionism rejects set-theory to found mathematics [Lavine] |
| Full Idea: Intuitionism in philosophy of mathematics rejects set-theoretic foundations. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.3 n33) |
| 7871 | Perceptual concepts can't just refer to what causes classification [Papineau] |
| Full Idea: We may say that a perceptual concept refers to that entity which normally causes classificatory uses of that concept...but this won't work because such deployments are often caused by things which the concept doesn't refer to. A model might cause 'bird'. | |
| From: David Papineau (Thinking about Consciousness [2002], 4.6) | |
| A reaction: This rejects the causal theory of perceptual concepts. I like the approach, because classifying things strikes me as absolutely basic to what brains do. To see that x is a bird is to place x in the class of birds. |
| 7852 | The only serious mind-brain theories now are identity, token identity, realization and supervenience [Papineau] |
| Full Idea: Anybody writing seriously about mind-brain issues nowadays needs to explain whether they think of materialism in terms of identity, token identity, realization, or supervenience. | |
| From: David Papineau (Thinking about Consciousness [2002], Intro §6) | |
| A reaction: Dualists are not invited. Functionalists are attending a different party. I wonder if his four categories collapse into two: the token/supervenience view, and the identity/realization view? |
| 7864 | Maybe mind and body do overdetermine acts, but are linked (for some reason) [Papineau] |
| Full Idea: Maybe physical effects of mental causes are always overdetermined by distinct causes (the 'belt and braces' view). Defenders say the two are still counterfactually dependent - but that would raise the question of why, if they are ontologically distinct. | |
| From: David Papineau (Thinking about Consciousness [2002], 1.5) | |
| A reaction: [He cites D.H. Mellor as defending 'belt and braces'] This strikes me as the sort of theory that arises from desperation: traditional dualism won't work, but we MUST keep mind separate, so that we can have free will, and save morality. All very confused! |
| 7873 | Young children can see that other individuals sometimes have false beliefs [Papineau] |
| Full Idea: The classic manifestation of being able to think about other individuals' mental states is success on the 'false belief test', which requires attribution of mistaken representations to other agents. Children aged three or four can do this. | |
| From: David Papineau (Thinking about Consciousness [2002], 4.7) | |
| A reaction: There may be an other minds problem, but there is empirical evidence that we can 'read' the minds of others (from their behaviour) even if other animals can't. That seems to be clear, even if folk psychology is fiction, and we make mistakes. |
| 7874 | Do we understand other minds by simulation-theory, or by theory-theory? [Papineau] |
| Full Idea: There is debate about whether we attribute beliefs and desires to others, and predict their behaviour, by simulating the decisions we would make ourselves ('simulation-theory'), or by deducing them from some general theory ('theory-theory'). | |
| From: David Papineau (Thinking about Consciousness [2002], 4.7) | |
| A reaction: Could be both. If someone is hurt, empathy leads to direct mind-reading (which seems like simulation), but if someone is behaving strangely we may have to bring theories to bear, because this person seems to be different. |
| 7882 | Researching phenomenal consciousness is peculiar, because the concepts involved are peculiar [Papineau] |
| Full Idea: It is a mistake to suppose that research into phenomenal consciousness can proceed just like other kinds of scientific research. Phenomenal concepts are peculiar, and some of the questions they pose for empirical investigation are peculiar too. | |
| From: David Papineau (Thinking about Consciousness [2002], 7.01) | |
| A reaction: This arises from Papineau's Conceptual Dualism, that our concepts are deeply dualist, when the underlying ontology is not. Brain researchers are wise to ignore phenomenology, and creep slowly forward from the physical end, where the concepts are clear. |
| 7854 | Whether octopuses feel pain is unclear, because our phenomenal concepts are too vague [Papineau] |
| Full Idea: Our phenomenal concepts are irredeemably vague in certain dimensions, in ways that preclude there being any fact of the matter about whether octopuses feel phenomenal pain, or silicon-based humanoids would have any phenomenal consciousness. | |
| From: David Papineau (Thinking about Consciousness [2002], Intro §7) | |
| A reaction: It would be hard for Papineau to prove this point, but clearly our imagination finds it very hard to grasp the idea of a thing which is 'somewhat conscious'. The concept of being much more conscious than humans also bewilders us. |
| 7889 | Our concept of consciousness is crude, and lacks theoretical articulation [Papineau] |
| Full Idea: Our phenomenal concept of consciousness-as-such is a crude tool, lacking theoretical articulation | |
| From: David Papineau (Thinking about Consciousness [2002], 7.13) | |
| A reaction: This is a point well made. Given that the human brain is the most complex thing (for its size) in the known universe, we shouldn't expect it to divide up into three or four clear-cut activities. Compare the precision of 'geography' as a concept. |
| 7891 | We can’t decide what 'conscious' means, so it is undecidable whether cats are conscious [Papineau] |
| Full Idea: If consciousness is availability for HOT judgements, then cats are not conscious, but if it consists in attention, then they are. I say the concept of consciousness is indefinite between the two, so there is no fact about whether cats are conscious. | |
| From: David Papineau (Thinking about Consciousness [2002], 7.16) | |
| A reaction: Nice point. My personal view is that the question of whether cats are conscious is hopeless because philosophers insist on making consciousness all-or-nothing (e.g. Idea 5786). If I experienced cat mentality, I might say I was 'semi-conscious'. |
| 7890 | Maybe a creature is conscious if its mental states represent things in a distinct way [Papineau] |
| Full Idea: The thesis of 'representational theories of consciousness' is that a creature is conscious just in case it is in a certain kind of representational state, some state which represents in a certain way. | |
| From: David Papineau (Thinking about Consciousness [2002]) | |
| A reaction: [He cites Harman, Dretske and Tye] The immediate impediment I see to this view is the extreme difficulty of explaining what the special 'way' is that turns representations into consciousness. Some mental states are not representational, and vice versa. |
| 7885 | The 'actualist' HOT theory says consciousness comes from actual higher judgements of mental states [Papineau] |
| Full Idea: The 'actualist' HOT theory says that a state is conscious if the subject is 'aware' of it, where this is understood as a matter of the subject forming some actual Higher-Order judgement about it. | |
| From: David Papineau (Thinking about Consciousness [2002], 7.11) | |
| A reaction: As stated there seems an obvious regress problem. Is the consciousness in the mental state, or in the higher awareness of it? If the former, how does being observed make it conscious? If the latter, what gives the higher level its consciousness? |
| 7886 | Actualist HOT theories imply that a non-conscious mental event could become conscious when remembered [Papineau] |
| Full Idea: Actualist HOT theories face an awkward problem with memory judgements: ...how can an earlier mental state be rendered conscious by some later act of memory? As when I see a red pillar box with no higher-order judgement, and then recall it later. | |
| From: David Papineau (Thinking about Consciousness [2002], 7.11) | |
| A reaction: [See 7886 for 'Actualist' HOT theories] This is not altogether absurd. A red pillar box could be somewhere in my field of vision, and then I might suddenly become conscious of it (if it moved!). Police interrogation reminds me of what I only glimpsed. |
| 7887 | States are conscious if they could be the subject of higher-order mental judgements [Papineau] |
| Full Idea: The 'dispositional' HOT thesis says that a state is conscious just in case it could have been the subject of an introspective Higher-Order judgement, even if it wasn't actually so subject. | |
| From: David Papineau (Thinking about Consciousness [2002], 7.13) | |
| A reaction: [He cites Dennett and Carruthers for this view] This is designed to meet other problems, but it sounds odd. Does it really make no difference whether higher-judgement actually occurs? How can conscious events be distinguished once they've gone? |
| 7888 | Higher-order judgements may be possible where the subject denies having been conscious [Papineau] |
| Full Idea: Dispositional Higher-Order judgeability will be present in some cases which the empirical methodology catalogues as not conscious (as when a subject denies having heard a sound, or seen a bird). | |
| From: David Papineau (Thinking about Consciousness [2002], 7.13) | |
| A reaction: (This attacks Idea 7887) This confirms my intuition, that we can be quite unconscious of things which can still be recalled at a later date. Of course, one could always challenge the reliability of the subject's report in such a case. |
| 7860 | The epiphenomenal relation of mind and brain is a 'causal dangler', unlike anything else [Papineau] |
| Full Idea: If epiphenomenalism were true, then the relation between mind and brain would be like nothing else in nature. After all, science recognises no other examples of 'causal danglers', ontologically independent states with causes but no effects. | |
| From: David Papineau (Thinking about Consciousness [2002], 1.4) | |
| A reaction: This would be a good enough reason for me to reject the epiphenomenalist view, even if I thought it was a coherent proposal. Insofar as it proposes the existence of something (mind) with no causal powers at all, it strikes me as nonsense. |
| 7862 | Maybe minds do not cause actions, but do cause us to report our decisions [Papineau] |
| Full Idea: Even if conscious decisions did not contribute causally to the actions normally attributed to them, they would still presumably be the causes of the sounds I make when I later report my earlier conscious decisions. | |
| From: David Papineau (Thinking about Consciousness [2002], 1.4) | |
| A reaction: This is a good reply to my view (borrowed from Dennett - Idea 7379), that epiphenomalism proposes an absurdity (an entity with no causal powers). But if mind can cause speech, why could it not cause arm movements? |
| 7870 | Role concepts either name the realising property, or the higher property constituting the role [Papineau] |
| Full Idea: Role concepts can be of two kinds: they can name whichever property realises the role, or they can name the higher property which constitutes the role. | |
| From: David Papineau (Thinking about Consciousness [2002], 4.2 n1) | |
| A reaction: This points strikes me as being crucial to discussions of mental functions. Perhaps labels of Realising Properties and Constituting Properties would help. Analytical philosophy rules. |
| 7858 | If causes are basic particulars, this doesn't make conscious and physical properties identical [Papineau] |
| Full Idea: If causes are basic particulars, then the causal argument won't carry you to the identity of conscious and physical properties, since this only requires them to be instantiated in the same particular, not that the properties are themselves identical. | |
| From: David Papineau (Thinking about Consciousness [2002], 1.3) | |
| A reaction: [See Idea 7857; Papineau is rejecting the Davidson view] This explains how Davidson reaches a token-token identity view. Can two events occur in the same particular at the same moment? Depends what you mean by a 'particular'. |
| 7865 | Supervenience can be replaced by identifying mind with higher-order or disjunctional properties [Papineau] |
| Full Idea: I would argue that any benefits offered by the notion of supervenience are more easily gained simply by identifying mental properties directly with higher-order properties or disjunctions of physical properties. | |
| From: David Papineau (Thinking about Consciousness [2002], 1.8) | |
| A reaction: Those who talk of supervenience seem to me to have retreated into a mystery that is not far from substance dualism. We want the explanation of a supervenience. If you accompany me everywhere, I think you are stalking me, or are tied to my ankle. |
| 7892 | The completeness of physics is needed for mind-brain identity [Papineau] |
| Full Idea: Without the completeness of physics, there is no compelling reason to identify the mind with the brain. | |
| From: David Papineau (Thinking about Consciousness [2002], App 7) | |
| A reaction: Papineau says the completeness of physics was accepted from the 1950s. Why were Epicurus and Hobbes physicalists? Do we have a circularity here? How do you establish the completeness of physics, without asserting mind to be physical? |
| 7879 | Mind-brain reduction is less explanatory, because phenomenal concepts lack causal roles [Papineau] |
| Full Idea: Mind-brain reductions are less explanatory than characteristic reductions in other areas of science, ...because phenomenal concepts have no special associations with causal roles. | |
| From: David Papineau (Thinking about Consciousness [2002], 5.3) | |
| A reaction: This may always have some truth in it, but I would expect reductive accounts in the far future to get much closer to giving explanations of phenomenal experience. We can't work down from the phenomenal end, but we can work up from the physical/causal end. |
| 20971 | Weak reduction of mind is to physical causes; strong reduction is also to physical laws [Papineau] |
| Full Idea: Weak reduction of mind requires only that mental causes be identified with physical causes. A strong reduction requires also that the laws by which such causes operate follow by composition from non-special laws. | |
| From: David Papineau (Thinking about Consciousness [2002], App 3 n8) | |
| A reaction: I'm cautious about laws, but I still vote for strong reduction. No new principles are needed to make a mind from a brain. |
| 7856 | It is absurd to think that physical effects are caused twice, so conscious causes must be physical [Papineau] |
| Full Idea: Many effects that we attribute to conscious causes have full physical causes. But it would be absurd to suppose that these effects are caused twice over. So the conscious causes must be identical to some part of those physical causes. | |
| From: David Papineau (Thinking about Consciousness [2002], 1.2) | |
| A reaction: [Papineau labelled this the Causal Argument] Of course two causes can combine to produce an effect, and there can be redundant physical overcausation, but in general I think this is a good argument. |
| 7881 | Accept ontological monism, but conceptual dualism; we think in a different way about phenomenal thought [Papineau] |
| Full Idea: We should be ontological monists, but we should be conceptual dualists. We need to recognise a special phenomenal way of thinking about conscious properties, if we are to dispel the confusions that persuade us that conscious properties cannot be material. | |
| From: David Papineau (Thinking about Consciousness [2002], 7.01) | |
| A reaction: This idea came to me as a revelation, and strikes me as spot on. We have developed conceptual dualism simply because humans cannot directly see that their thinking is actually physical brain activity. Thought seems ungrounded, and utterly different. |
| 7866 | Mary acquires new concepts; she previously thought about the same property using material concepts [Papineau] |
| Full Idea: While there is indeed a before-after difference in Mary, this is just a matter of coming to think in new ways, and acquiring a new concept. There is no new experiential property. She could think about the property perfectly well, using material concepts. | |
| From: David Papineau (Thinking about Consciousness [2002], 2.2) | |
| A reaction: I think it is better to talk of Mary encountering a new mode of experiencing something, just as experience becomes blurred when glasses are removed. No one acquires new 'knowledge' of blurred objects when they remove their glasses. |
| 7850 | Thinking about a thing doesn't require activating it [Papineau] |
| Full Idea: Thinking about something doesn't require activating some version of it. | |
| From: David Papineau (Thinking about Consciousness [2002], Intro §5) | |
| A reaction: E.g. I can discuss 'red' without visualising it. This observation strikes me as simple and basic to what thinking is. Papineau thinks that confusion about this simple point leads to major errors in the philosophy of mind. |
| 7851 | Consciousness affects bodily movement, so thoughts must be material states [Papineau] |
| Full Idea: Conscious states clearly affect our bodily movements. But surely anything that so produces a material effect must itself be a material state. | |
| From: David Papineau (Thinking about Consciousness [2002], Intro §6) | |
| A reaction: This is Papineau's simplest possible statement of what he calls the Causal Argument, which he considers to be a knock-down argument for materialism. I agree, but it is really only an intuition. You never know... |
| 7884 | Most reductive accounts of representation imply broad content [Papineau] |
| Full Idea: Broadness of content is sometimes defended purely on intuitive grounds, but it is also a corollary of most reductive accounts of representation, including standard teleosemantic and causal accounts. | |
| From: David Papineau (Thinking about Consciousness [2002]) | |
| A reaction: (For Causal and Teleosemantic views, see Idea 7871, Idea 7872) Presumably a causal/purposeful relationship would only make sense if both halves of the relationship were specified. I suspect this is obscured by over-simplifications. Cf Idea 6634! |
| 7863 | If content hinges on matters outside of you, how can it causally influence your actions? [Papineau] |
| Full Idea: How can 'broad contents', which hinge on matters outside your head, exert a causal influence on your bodily movements? Surely your bodily movements are causally influenced solely by matters inside your skin, not by how matters are outside you. | |
| From: David Papineau (Thinking about Consciousness [2002], 1.4) | |
| A reaction: This supports my suspicion that there are some extremely simplistic interpretations of the Twin Earth case floating around. If Putnam means by 'elm' whatever experts mean, it is still his idea of what counts as an expert view. |
| 7883 | Verificationists tend to infer indefinite answers from undecidable questions [Papineau] |
| Full Idea: The verificationist sin is to infer an indefiniteness of answers immediately from the undecidability of questions. | |
| From: David Papineau (Thinking about Consciousness [2002], 7.02) | |
| A reaction: This remark is aimed at Dummett's anti-realism. It strikes me that what is being described really is a sort of arrogance, in believing that reality can somehow be inferred from studying the epistemic apparatus of a few miserable little mammals. |
| 7872 | Teleosemantics equates meaning with the item the concept is intended to track [Papineau] |
| Full Idea: The teleosemantic view of perceptual concepts is that the referential value of the concept can be equated with those items which it is the biological function of the concept to track. | |
| From: David Papineau (Thinking about Consciousness [2002], 4.6) | |
| A reaction: This seems to work quite nicely for 'bird', which is concept which is used to track birds. It might even work for complex entities, or abstract entities, or even negative entities. Imagination must play a role in that last one. |
| 7869 | Truth conditions in possible worlds can't handle statements about impossibilities [Papineau] |
| Full Idea: Basing content on possible worlds that result in truth leaves no room for thoughts about genuine impossibilities, since there are not possible worlds whose actuality would make an 'impossible thought' true. | |
| From: David Papineau (Thinking about Consciousness [2002], 3.7) | |
| A reaction: Negative existentials like 'no rabbits in this room' and 'no snakes in this room' seem to have the same truth conditions as well. I suppose the sentences must be translated into a logical form which suits the theory, with negation stuck on the end. |
| 7868 | Thought content is possible worlds that make the thought true; if that includes the actual world, it's true [Papineau] |
| Full Idea: The content of our thoughts can be equated with those possible worlds whose actuality would make the thought true. On this model, a true thought is one whose content includes the actual world, while a false thought is one whose content does not. | |
| From: David Papineau (Thinking about Consciousness [2002], 3.7) | |
| A reaction: This is the possible worlds semantics version of truth conditions theories of meaning. Papineau offers a nice difficulty for the theory (Idea 7869). Dummett says the whole approach is circular, because content precedes truth. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 7853 | Causation is based on either events, or facts, or states of affairs [Papineau] |
| Full Idea: Any serious theory of the mind-brain must explain whether it thinks of causation in terms of events, facts, or states of affairs. | |
| From: David Papineau (Thinking about Consciousness [2002], Intro §6) | |
| A reaction: I instantly prefer events, simply because they can be specified a little more precisely than the other two. Since cause has a direction in time, it would be nice to specify the times of its components, and events have times. |
| 7857 | Causes are instantiations of properties by particulars, or they are themselves basic particulars [Papineau] |
| Full Idea: One view of causes is that they are facts, or instantiations of properties (maybe by particulars, making them 'Kim-events'); the alternative view is that causes themselves are basic particulars ('Davidson-events'). | |
| From: David Papineau (Thinking about Consciousness [2002], 1.3) | |
| A reaction: Like Papineau, I incline to the Kim view. It is too easy for philosophers to treat key ideas as unanalysable axioms of thought. An event typically has components and features. It is a contingent matter whether there are any events. |
| 20976 | The completeness of physics cannot be proved [Papineau] |
| Full Idea: There is no knock down argument for the completeness of physics. | |
| From: David Papineau (Thinking about Consciousness [2002], App 7) | |
| A reaction: This is commendably honest, given that he pins his view of the mind on it. He makes the case sound overwhelming, though. The thing which would breach the completeness is like the Loch Ness monster - you can't prove it isn't there, if it hides. |
| 20970 | Determinism is possible without a complete physics, if mental forces play a role [Papineau] |
| Full Idea: We can accept determinism without accepting physical determinism, and so without accepting the completeness of physics. ...We can have a deterministic model in which sui generis mental forces play an essential role. | |
| From: David Papineau (Thinking about Consciousness [2002], App 3) | |
| A reaction: Papineau cites (on p.241) the 18th century biologist Robert Whytt as an example of this view. |
| 20974 | Modern biological research, especially into the cell, has revealed no special new natural forces [Papineau] |
| Full Idea: In the 1950s a great deal became known about biochemical and neurophysiological processes, especially at the level of the cell, and none of it gave any evidence for the existence of special forces not found elsewhere in nature. | |
| From: David Papineau (Thinking about Consciousness [2002], A 6) | |
| A reaction: Papineau says that this plus the conservation of energy makes the closure of physics faily conclusive. I would think the similar failure of modern research into the brain to find evidence of weird forces strengthens the case. |
| 20975 | Quantum 'wave collapses' seem to violate conservation of energy [Papineau] |
| Full Idea: The conservation of energy is apparently violated by 'wave collapses' in quantum systems. | |
| From: David Papineau (Thinking about Consciousness [2002], A 7 n15) | |
| A reaction: One could imagine it being a little harder to verify the conservation of energy at the quantum levels, where particles and anti-particles pop in and out of existence. I've been wondering why there is some suspicion of collapses. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |