43 ideas
| 10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
| Full Idea: The main objection to the axiom of choice was that it had to be given by some law or definition, but since sets are arbitrary this seems irrelevant. Formalists consider it meaningless, but set-theorists consider it as true, and practically obvious. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §3) |
| 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. |
| 10766 | Logic is either for demonstration, or for characterizing structures [Tharp] |
| Full Idea: One can distinguish at least two quite different senses of logic: as an instrument of demonstration, and perhaps as an instrument for the characterization of structures. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: This is trying to capture the proof-theory and semantic aspects, but merely 'characterizing' something sounds like a rather feeble aspiration for the semantic side of things. Isn't it to do with truth, rather than just rule-following? |
| 10767 | Elementary logic is complete, but cannot capture mathematics [Tharp] |
| Full Idea: Elementary logic cannot characterize the usual mathematical structures, but seems to be distinguished by its completeness. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10769 | Second-order logic isn't provable, but will express set-theory and classic problems [Tharp] |
| Full Idea: The expressive power of second-order logic is too great to admit a proof procedure, but is adequate to express set-theoretical statements, and open questions such as the continuum hypothesis or the existence of big cardinals are easily stated. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10762 | In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp] |
| Full Idea: In sentential logic there is a simple proof that all truth functions, of any number of arguments, are definable from (say) 'not' and 'and'. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §0) | |
| A reaction: The point of 'say' is that it can be got down to two connectives, and these are just the usual preferred pair. |
| 10776 | The main quantifiers extend 'and' and 'or' to infinite domains [Tharp] |
| Full Idea: The symbols ∀ and ∃ may, to start with, be regarded as extrapolations of the truth functional connectives ∧ ('and') and ∨ ('or') to infinite domains. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §5) |
| 10774 | There are at least five unorthodox quantifiers that could be used [Tharp] |
| Full Idea: One might add to one's logic an 'uncountable quantifier', or a 'Chang quantifier', or a 'two-argument quantifier', or 'Shelah's quantifier', or 'branching quantifiers'. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §3) | |
| A reaction: [compressed - just listed for reference, if you collect quantifiers, like collecting butterflies] |
| 10777 | Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp] |
| Full Idea: Skolem deduced from the Löwenheim-Skolem theorem that 'the absolutist conceptions of Cantor's theory' are 'illusory'. I think it is clear that this conclusion would not follow even if elementary logic were in some sense the true logic, as Skolem assumed. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §7) | |
| A reaction: [Tharp cites Skolem 1962 p.47] Kit Fine refers to accepters of this scepticism about the arithmetic of infinities as 'Skolemites'. |
| 10773 | The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp] |
| Full Idea: The Löwenheim-Skolem property seems to be undesirable, in that it states a limitation concerning the distinctions the logic is capable of making, such as saying there are uncountably many reals ('Skolem's Paradox'). | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10765 | Soundness would seem to be an essential requirement of a proof procedure [Tharp] |
| Full Idea: Soundness would seem to be an essential requirement of a proof procedure, since there is little point in proving formulas which may turn out to be false under some interpretation. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10763 | Completeness and compactness together give axiomatizability [Tharp] |
| Full Idea: Putting completeness and compactness together, one has axiomatizability. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §1) |
| 10770 | If completeness fails there is no algorithm to list the valid formulas [Tharp] |
| Full Idea: In general, if completeness fails there is no algorithm to list the valid formulas. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: I.e. the theory is not effectively enumerable. |
| 10771 | Compactness is important for major theories which have infinitely many axioms [Tharp] |
| Full Idea: It is strange that compactness is often ignored in discussions of philosophy of logic, since the most important theories have infinitely many axioms. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: An example of infinite axioms is the induction schema in first-order Peano Arithmetic. |
| 10772 | Compactness blocks infinite expansion, and admits non-standard models [Tharp] |
| Full Idea: The compactness condition seems to state some weakness of the logic (as if it were futile to add infinitely many hypotheses). To look at it another way, formalizations of (say) arithmetic will admit of non-standard models. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10764 | A complete logic has an effective enumeration of the valid formulas [Tharp] |
| Full Idea: A complete logic has an effective enumeration of the valid formulas. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10768 | Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp] |
| Full Idea: Despite completeness, the mere existence of an effective enumeration of the valid formulas will not, by itself, provide knowledge. For example, one might be able to prove that there is an effective enumeration, without being able to specify one. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: The point is that completeness is supposed to ensure knowledge (of what is valid but unprovable), and completeness entails effective enumerability, but more than the latter is needed to do the key job. |
| 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. |
| 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. |
| 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'. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 20949 | Study the use of words, not their origins [Herder] |
| Full Idea: Not how an expression can be etymologically derived and determined analytically, but how it is used is the question. Origin and use are often very different. | |
| From: Johann Gottfried Herder (works [1784], p.153), quoted by Andrew Bowie - Introduction to German Philosophy 2 'Herder' | |
| A reaction: This doesn't quite say that meaning is use, and is basically an attack on the Etymological Fallacy (that origin gives meaning), but it is a strikingly modern view of language. |
| 7669 | We cannot attain all the ideals of every culture, so there cannot be a perfect life [Herder, by Berlin] |
| Full Idea: For Herder, we cannot attain to the highest ideals of all the centuries and all the places at once, and since we cannot do that, the whole notion of the perfect life collapses. | |
| From: report of Johann Gottfried Herder (works [1784]) by Isaiah Berlin - The Roots of Romanticism Ch.3 | |
| A reaction: Herder seems to be the father of modern cultural relativism. The idea is hard to challenge, but the ideals of some cultures should be ignored, if they diminish rather than enhance the good life for all. |
| 7668 | Herder invented the idea of being rooted in (or cut off from) a home or a group [Herder, by Berlin] |
| Full Idea: The whole notion of being at home, or being cut off from one's natural roots, the whole idea of roots, the whole idea of belonging to a group, a sect, a movement, was largely invented by Herder. | |
| From: report of Johann Gottfried Herder (works [1784], Ch.3) by Isaiah Berlin - The Roots of Romanticism | |
| A reaction: Hm. Broad generalisations are an awful temptation in the history of ideas. As a corrective to this, trying reading the two Anglo-Saxon poems 'The Wanderer' and 'The Seafarer'. Very Germanic, I suppose. Interesting, though. Leads to Hegel's politics. |
| 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. |