32 ideas
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| Full Idea: One feature of the Axiom of Choice that troubled many mathematicians was the so-called Banach-Tarski paradox: using the Axiom, a sphere can be decomposed into finitely many parts and those parts reassembled into two spheres the same size as the original. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) | |
| A reaction: (The key is that the parts are non-measurable). To an outsider it is puzzling that the Axiom has been universally accepted, even though it produces such a result. Someone can explain that, I'm sure. |
| 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. |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| Full Idea: If-thenism denies that mathematics is in the business of discovering truths about abstracta. ...[their opponents] obviously don't regard any starting point, even a consistent one, as equally worthy of investigation. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.3) | |
| A reaction: I have some sympathy with if-thenism, in that you can obviously study the implications of any 'if' you like, but deep down I agree with the critics. |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| Full Idea: At the end of the nineteenth century there was a renewed emphasis on rigor, the central tool of which was axiomatization, along the lines of Hilbert's axioms for geometry and Dedekind's axioms for real numbers. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| Full Idea: The fact that two apparently fruitful mathematical themes turn out to coincide makes it all the more likely that they're tracking a genuine strain of mathematical depth. | |
| From: Penelope Maddy (Defending the Axioms [2011], 5.3ii) |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| Full Idea: One form of the Continuum Hypothesis is the claim that every infinite set of reals is either countable or of the same size as the full set of reals. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.4 n40) |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| Full Idea: Our set-theoretic methods track the underlying contours of mathematical depth. ...What sets are, most fundamentally, is markers for these contours ...they are maximally effective trackers of certain trains of mathematical fruitfulness. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.4) | |
| A reaction: This seems to make it more like a map of mathematics than the actual essence of mathematics. |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| Full Idea: Ordinary perceptual cognition is most likely involved in our grasp of elementary arithmetic, but ...this connection to the physical world has long since been idealized away in the infinitary structures of contemporary pure mathematics. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.3) | |
| A reaction: Despite this, Maddy's quest is for a 'naturalistic' account of mathematics. She ends up defending 'objectivity' (and invoking Tyler Burge), rather than even modest realism. You can't 'idealise away' the counting of objects. I blame Cantor. |
| 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? |
| 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. |
| 22393 | I don't understand the idea of a reason for acting, but it is probably the agent's interests or desires [Foot] |
| Full Idea: I am sure I do not understand the idea of a reason for acting, and I wonder whether anyone else does either. I incline to the view that all such reasons depend either on the agent's interests (meaning here what is in his interest) or else on his desires. | |
| From: Philippa Foot (Reasons for Actions and Desires [1972], p.156 Post) | |
| A reaction: It seems common to assume that a reason for an action must be something rational, but it makes sense to say that the reason for someone's action was an irrational whim. Is the reason for an action just the cause of the action? |
| 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. |