40 ideas
6548 | Physicalism requires the naturalisation or rejection of set theory [Lycan] |
Full Idea: Eventually set theory will have to be either naturalised or rejected, if a thoroughgoing physicalism is to be maintained. | |
From: William Lycan (Consciousness [1987], 8.4) | |
A reaction: Personally I regard Platonism as a form of naturalism (though a rather bold and dramatic one). The central issue seems to be the ability of the human main/brain to form 'abstract' notions about the physical world in which it lives. |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
Full Idea: Intuitionists in mathematics deny excluded middle, because it is symptomatic of faith in the transcendent existence of mathematical objects and/or the truth of mathematical statements. | |
From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2) | |
A reaction: There are other problems with excluded middle, such as vagueness, but on the whole I, as a card-carrying 'realist', am committed to the law of excluded middle. |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
Full Idea: It is surely wise to identify the positions in the natural numbers structure with their counterparts in the integer, rational, real and complex number structures. | |
From: Stewart Shapiro (Thinking About Mathematics [2000], 10.2) | |
A reaction: The point is that this might be denied, since 3, 3/1, 3.00.., and -3*i^2 are all arrived at by different methods of construction. Natural 3 has a predecessor, but real 3 doesn't. I agree, intuitively, with Shapiro. Russell (1919) disagreed. |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
Full Idea: A sequence a1,a2,... of rational numbers is 'Cauchy' if for each rational number ε>0 there is a natural number N such that for all natural numbers m, n, if m>N and n>N then -ε < am - an < ε. | |
From: Stewart Shapiro (Thinking About Mathematics [2000], 7.2 n4) | |
A reaction: The sequence is 'Cauchy' if N exists. |
8764 | Categories are the best foundation for mathematics [Shapiro] |
Full Idea: There is a dedicated contingent who hold that the category of 'categories' is the proper foundation for mathematics. | |
From: Stewart Shapiro (Thinking About Mathematics [2000], 10.3 n7) | |
A reaction: He cites Lawvere (1966) and McLarty (1993), the latter presenting the view as a form of structuralism. I would say that the concept of a category will need further explication, and probably reduce to either sets or relations or properties. |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
Full Idea: Zermelo said that for each number n, its successor is the singleton of n, so 3 is {{{null}}}, and 1 is not a member of 3. Von Neumann said each number n is the set of numbers less than n, so 3 is {null,{null},{null,{null}}}, and 1 is a member of 3. | |
From: Stewart Shapiro (Thinking About Mathematics [2000], 10.2) | |
A reaction: See Idea 645 - Zermelo could save Plato from the criticisms of Aristotle! These two accounts are cited by opponents of the set-theoretical account of numbers, because it seems impossible to arbitrate between them. |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
Full Idea: The structuralist vigorously rejects any sort of ontological independence among the natural numbers; the essence of a natural number is its relations to other natural numbers. | |
From: Stewart Shapiro (Thinking About Mathematics [2000], 10.1) | |
A reaction: This seems to place the emphasis on ordinals (what order?) rather than on cardinality (how many?). I am strongly inclined to think that this is the correct view, though you can't really have relations if there is nothing to relate. |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
Full Idea: A 'system' is a collection of objects with certain relations among them; a 'pattern' or 'structure' is the abstract form of a system, highlighting the interrelationships and ignoring any features they do not affect how they relate to other objects. | |
From: Stewart Shapiro (Thinking About Mathematics [2000], 10.1) | |
A reaction: Note that 'ignoring' features is a psychological account of abstraction, which (thanks to Frege and Geach) is supposed to be taboo - but which I suspect is actually indispensable in any proper account of thought and concepts. |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
Full Idea: The thesis that principles of arithmetic are derivable from the laws of logic runs against a now common view that logic itself has no ontology. There are no particular logical objects. From this perspective logicism is a non-starter. | |
From: Stewart Shapiro (Thinking About Mathematics [2000], 5.1) | |
A reaction: This criticism strikes me as utterly devastating. There are two routes to go: prove that logic does have an ontology of objects (what would they be?), or - better - deny that arithmetic contains any 'objects'. Or give up logicism. |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
Full Idea: Term Formalism is the view that mathematics is just about characters or symbols - the systems of numerals and other linguistic forms. ...This will cover integers and rational numbers, but what are real numbers supposed to be, if they lack names? | |
From: Stewart Shapiro (Thinking About Mathematics [2000], 6.1.1) | |
A reaction: Real numbers (such as pi and root-2) have infinite decimal expansions, so we can start naming those. We could also start giving names like 'Harry' to other reals, though it might take a while. OK, I give up. |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
Full Idea: Game Formalism likens mathematics to chess, where the 'content' of mathematics is exhausted by the rules of operating with its language. ...This, however, leaves the problem of why the mathematical games are so useful to the sciences. | |
From: Stewart Shapiro (Thinking About Mathematics [2000], 6.1.2) | |
A reaction: This thought pushes us towards structuralism. It could still be a game, but one we learned from observing nature, which plays its own games. Chess is, after all, modelled on warfare. |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
Full Idea: The Deductivist version of formalism (sometimes called 'if-thenism') says that the practice of mathematics consists of determining logical consequences of otherwise uninterpreted axioms. | |
From: Stewart Shapiro (Thinking About Mathematics [2000], 6.2) | |
A reaction: [Hilbert is the source] More plausible than Term or Game Formalism (qv). It still leaves the question of why it seems applicable to nature, and why those particular axioms might be chosen. In some sense, though, it is obviously right. |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
Full Idea: Critics commonly complain that the intuitionist restrictions cripple the mathematician. On the other hand, intuitionist mathematics allows for many potentially important distinctions not available in classical mathematics, and is often more subtle. | |
From: Stewart Shapiro (Thinking About Mathematics [2000], 7.1) | |
A reaction: The main way in which it cripples is its restriction on talk of infinity ('Cantor's heaven'), which was resented by Hilbert. Since high-level infinities are interesting, it would be odd if we were not allowed to discuss them. |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
Full Idea: I classify conceptualists according to what they say about properties or concepts. If someone classified properties as existing independent of language I would classify her as a realist in ontology of mathematics. Or they may be idealists or nominalists. | |
From: Stewart Shapiro (Thinking About Mathematics [2000], 2.2.1) | |
A reaction: In other words, Shapiro wants to eliminate 'conceptualist' as a useful label in philosophy of mathematics. He's probably right. All thought involves concepts, but that doesn't produce a conceptualist theory of, say, football. |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
Full Idea: A definition of a mathematical entity is 'impredicative' if it refers to a collection that contains the defined entity. The definition of 'least upper bound' is impredicative as it refers to upper bounds and characterizes a member of this set. | |
From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2) | |
A reaction: The big question is whether mathematics can live with impredicative definitions, or whether they threaten to be viciously circular, and undermine the whole enterprise. |
6532 | Types cannot be reduced, but levels of reduction are varied groupings of the same tokens [Lycan] |
Full Idea: If types cannot be reduced to more physical levels, this is not an embarrassment, as long as our institutional categories, our physiological categories, and our physical categories are just alternative groupings of the same tokens. | |
From: William Lycan (Consciousness [1987], 4.3) | |
A reaction: This is a self-evident truth about a car engine, so I don't see why it wouldn't apply equally to a brain. Lycan's identification of the type as the thing which cannot be reduced seems a promising explanation of much confusion among philosophers. |
6531 | Institutions are not reducible as types, but they are as tokens [Lycan] |
Full Idea: Institutional types are irreducible, though I assume that institutional tokens are reducible in the sense of strict identity, all the way down to the subatomic level. | |
From: William Lycan (Consciousness [1987], 4.3) | |
A reaction: This seems a promising distinction, as the boundaries of 'institutions' disappear when you begin to reduce them to lower levels (cf. Idea 4601), and yet plenty of institutions are self-evidently no more than physics. Plants are invisible as physics. |
6534 | One location may contain molecules, a metal strip, a key, an opener of doors, and a human tragedy [Lycan] |
Full Idea: One space-time slice may be occupied by a collection of molecules, a metal strip, a key, an allower of entry to hotel rooms, a facilitator of adultery, and a destroyer souls. | |
From: William Lycan (Consciousness [1987], 4.3) | |
A reaction: Desdemona's handkerchief is a nice example. This sort of remark seems to be felt by some philosophers to be heartless wickedness, and yet it so screamingly self-evident that it is impossible to deny. |
6529 | I see the 'role'/'occupant' distinction as fundamental to metaphysics [Lycan] |
Full Idea: I see the 'role'/'occupant' distinction as fundamental to metaphysics. | |
From: William Lycan (Consciousness [1987], 4.0) | |
A reaction: A passing remark in a discussion of functionalism about the mind, but I find it appealing. Causation is basic to materialistic metaphysics, and it creates networks of regular causes. It leaves open the essentialist question of WHY it has that role. |
6549 | I think greenness is a complex microphysical property of green objects [Lycan] |
Full Idea: Personally I favour direct realism regarding secondary qualities, and identify greenness with some complex microphysical property exemplified by green physical objects. | |
From: William Lycan (Consciousness [1987], 8.4) | |
A reaction: He cites D.M.Armstrong (1981) as his source. Personally I find this a bewildering proposal. Does he think there is greenness in grass AS WELL AS the emission of that wavelength of electro-magnetic radiation? Is greenness zooming through the air? |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
Full Idea: Rationalism is a long-standing school that can be characterized as an attempt to extend the perceived methodology of mathematics to all of knowledge. | |
From: Stewart Shapiro (Thinking About Mathematics [2000], 1.1) | |
A reaction: Sometimes called 'Descartes's Dream', or the 'Enlightenment Project', the dream of proving everything. Within maths, Hilbert's Programme aimed for the same certainty. Idea 22 is the motto for the opposition to this approach. |
6543 | Intentionality comes in degrees [Lycan] |
Full Idea: Intentionality comes in degrees. | |
From: William Lycan (Consciousness [1987], 5.4) | |
A reaction: I agree. A footprint is 'about' a foot, in the sense of containing concentrated information about it. Can we, though, envisage a higher degree than human thought? Is there a maximum degree? Everything is 'about' everything, in some respect. |
6537 | Teleological views allow for false intentional content, unlike causal and nomological theories [Lycan] |
Full Idea: The teleological view begins to explain intentionality, and in particular allows brain states and events to have false intentional content; causal and nomological theories of intentionality tend to falter on this last task. | |
From: William Lycan (Consciousness [1987], 4.4) | |
A reaction: Certainly if you say thought is 'caused' by the world, false thought become puzzling. I'm not sure I understand the rest of this, but it is an intriguing remark about a significant issue… |
6546 | Pain is composed of urges, desires, impulses etc, at different levels of abstraction [Lycan] |
Full Idea: Our phenomenal experience of pain has components - it is a complex, consisting (perhaps) of urges, desires, impulses, and beliefs, probably occurring at quite different levels of institutional abstraction. | |
From: William Lycan (Consciousness [1987], 5.5) | |
A reaction: This seems to be true, and offers the reductionist a strategy for making inroads into the supposed irreducable and fundamental nature of qualia. What's it like to be a complex hierarchically structured multi-functional organism? |
6547 | The right 'level' for qualia is uncertain, though top (behaviourism) and bottom (particles) are false [Lycan] |
Full Idea: It is just arbitrary to choose a level of nature a priori as the locus of qualia, even though we can agree that high levels (such as behaviourism) and low-levels (such as the subatomic) can be ruled out as totally improbable. | |
From: William Lycan (Consciousness [1987], 5.6) | |
A reaction: Very good. People scream 'qualia!' whenever the behaviour level or the atomic level are proposed as the locations of the mind, but the suggestion that they are complex, and are spread across many functional levels in the middle sounds good. |
6527 | If energy in the brain disappears into thin air, this breaches physical conservation laws [Lycan] |
Full Idea: By interacting causally, Cartesian dualism seems to violate the conservation laws of physics (concerning matter and energy). This seems testable, and afferent and efferent pathways disappearing into thin air would suggest energy is not conserved. | |
From: William Lycan (Consciousness [1987], 1.1) | |
A reaction: It would seem to be no problem as long as outputs were identical in energy to inputs. If the experiment could actually be done, the result might astonish us. |
6528 | In lower animals, psychology is continuous with chemistry, and humans are continuous with animals [Lycan] |
Full Idea: Evolution has proceeded in all other known species by increasingly complex configurations of molecules and organs, which support primitive psychologies; our human psychologies are more advanced, but undeniably continuous with lower animals. | |
From: William Lycan (Consciousness [1987], 1.1) | |
A reaction: Personally I find the evolution objection to dualism highly persuasive. I don't see how anyone can take evolution seriously and be a dualist. If there is a dramatic ontological break at some point, a plausible reason would be needed for that. |
6554 | Two behaviourists meet. The first says,"You're fine; how am I?" [Lycan] |
Full Idea: Old joke: two Behaviourists meet in the street, and the first says,"You're fine; how am I?" | |
From: William Lycan (Consciousness [1987], n1.6) | |
A reaction: This invites the response that introspection is uniquely authoritative about 'how we are', but this has been challenged quite a lot recently, which pushes us to consider whether these stupid behaviourists might actually have a good point. |
6545 | If functionalism focuses on folk psychology, it ignores lower levels of function [Lycan] |
Full Idea: 'Analytical functionalists', who hold that meanings of mental terms are determined by the causal roles associated with them by 'folk psychology', deny themselves appeals to lower levels of functional organisation. | |
From: William Lycan (Consciousness [1987], 5.4) | |
A reaction: Presumably folk psychology can fit into the kind of empirical methodology favoured by behaviourists, whereas 'lower levels' are going to become rather speculative and unscientific. |
6541 | Functionalism must not be too abstract to allow inverted spectrum, or so structural that it becomes chauvinistic [Lycan] |
Full Idea: The functionalist must find a level of characterisation of mental states that is not so abstract or behaviouristic as to rule out the possibility of inverted spectrum etc., nor so specific and structural as to fall into chauvinism. | |
From: William Lycan (Consciousness [1987], 5.4) | |
A reaction: If too specific then animals and aliens won't be able to implement the necessary functions; if the theory becomes very behaviouristic, then it loses interest in the possibility of an inverted spectrum. He is certainly right to hunt for a middle ground. |
6539 | The distinction between software and hardware is not clear in computing [Lycan] |
Full Idea: Even the software/hardware distinction as it is literally applied within computer science is philosophically unclear. | |
From: William Lycan (Consciousness [1987], 4.4) | |
A reaction: This is true, and very important for functionalist theories of the mind. Even very volatile software is realised in 'hard' physics, and rewritable discs etc blur the distinction between 'programmable' and 'hardwired'. |
6535 | Teleological characterisations shade off smoothly into brutely physical ones [Lycan] |
Full Idea: Highly teleological characterisations, unlike naïve and explicated mental characterisations, have the virtue of shading off fairly smoothly into (more) brutely physical ones. | |
From: William Lycan (Consciousness [1987], 4.3) | |
A reaction: Thus the purpose of a car engine, and a spark plug, and the spark, and the temperature, and the vibration of molecules show a fading away of the overt purpose, disappearing into the pointless activity of electrons and quantum levels. |
6533 | Mental types are a subclass of teleological types at a high level of functional abstraction [Lycan] |
Full Idea: I am taking mental types to form a small subclass of teleological types occurring for the most part at a high level of functional abstraction. | |
From: William Lycan (Consciousness [1987], 4.3) | |
A reaction: He goes on to say that he understand teleology in evolutionary terms. There is always a gap between how you characterise or individuate something, and what it actually is. To say spanners are 'a small subclass of tools' is not enough. |
6544 | Identity theory is functionalism, but located at the lowest level of abstraction [Lycan] |
Full Idea: 'Neuron' may be understood as a physiological term or a functional term, so even the Identity Theorist is a Functionalist - one who locates mental entities at a very low level of abstraction. | |
From: William Lycan (Consciousness [1987], 5.4) | |
A reaction: This is a striking observation, and somewhat inclines me to switch from identity theory to functionalism. If you ask what is the correct level of abstraction, Lycan's teleological-homuncular version refers you to all the levels. |
6536 | Teleological functionalism helps us to understand psycho-biological laws [Lycan] |
Full Idea: Teleological functionalism helps us to understand the nature of biological and psychological laws, particularly in the face of Davidsonian scepticism about the latter. | |
From: William Lycan (Consciousness [1987], 4.4) | |
A reaction: Personally I doubt the existence of psycho-physical laws, but only because of the vast complexity. They would be like the laws of weather. 'Psycho-physical' laws seem to presuppose some sort of dualism. |
6530 | We reduce the mind through homuncular groups, described abstractly by purpose [Lycan] |
Full Idea: I am explicating the mental in a reductive way, by reducing mental characterizations to homuncular institutional ones, which are teleological characterizations at various levels of functional abstraction. | |
From: William Lycan (Consciousness [1987], 4.3) | |
A reaction: I think this is the germ of a very good physicalist account of the mind. More is needed than a mere assertion about what the mind reduces to at the very lowest level; this offers a decent account of the descending stages of reduction. |
6542 | A Martian may exhibit human-like behaviour while having very different sensations [Lycan] |
Full Idea: Quite possibly a Martian's humanoid behaviour is prompted by his having sensations somewhat unlike ours, despite his superficial behavioural similarities to us. | |
From: William Lycan (Consciousness [1987], 5.4) | |
A reaction: I think this firmly refutes the multiple realisability objection to type-type physicalism. Mental events are individuated by their phenomenal features (known only to the user), and by their causal role (publicly available). These are separate. |
19745 | The nature of people is decided by the government and politics of their society [Rousseau] |
Full Idea: Everything is rooted in politics, and whatever might be attempted, no people would ever be other than the nature of their government made them. | |
From: Jean-Jacques Rousseau (The Confessions [1770], 9-1756) | |
A reaction: A striking anticipation of one of Marx's most important ideas - that society is not created by individual minds, because the nature of consciousness is created by society. The central idea in the subject of sociology, I think. |
6538 | We need a notion of teleology that comes in degrees [Lycan] |
Full Idea: We need a notion of teleology that comes in degrees. | |
From: William Lycan (Consciousness [1987], 4.4) | |
A reaction: Anyone who says that key concepts, such as those concerning the mind, should come 'in degrees' wins my instant support. A whole car engine requires a very teleological explanation, the spark in the sparkplug far less so. |
6551 | 'Physical' means either figuring in physics descriptions, or just located in space-time [Lycan] |
Full Idea: An object is specifically physical if it figures in explanations and descriptions of features of ordinary non-living matter, as in current physics; it is more generally physical if it is simply located in space-time. | |
From: William Lycan (Consciousness [1987], 8.5) | |
A reaction: This gives a useful distinction when trying to formulate a 'physicalist' account of the mind, where type-type physicalism says only the 'postulates of physics' can be used, whereas 'naturalism' about the mind uses the more general concept. |