33 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) |
| 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] |
| 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) |
| 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'. |
| 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. |
| 3016 | Even the gods cannot strive against necessity [Pittacus, by Diog. Laertius] |
| Full Idea: Even the gods cannot strive against necessity. | |
| From: report of Pittacus (reports [c.610 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 01.5.4 |
| 2584 | Lobotomised patients can cease to care about a pain [Block] |
| Full Idea: After frontal lobotomies, patients typically report that they still have pains, though the pains no longer bother them. | |
| From: Ned Block (Troubles with Functionalism [1978], p. 83) | |
| A reaction: I take this to be an endorsement of reductive physicalism, because what matters about pains is that they bother us, not how they feel, so frog pain could do the job, if it felt different from ours, but was disliked by the frog. |
| 6172 | The Inverted Earth example shows that phenomenal properties are not representational [Block, by Rowlands] |
| Full Idea: Block's Inverted Earth example (with matching inversion of both colours and colour-language) tries to show a variation of representational properties without a variation of phenomenal properties, so that the latter are not constituted by the former. | |
| From: report of Ned Block (Inverted Earth [1990]) by Mark Rowlands - Externalism Ch.7 | |
| A reaction: (The example is actually quite complex). This type of argument - a thought experiment in which qualia are held steady while everything else varies, or vice versa - seems to be the only way that we can possibly get at an assessment of the role of qualia. |
| 2582 | A brain looks no more likely than anything else to cause qualia [Block] |
| Full Idea: NO physical mechanism seems very intuitively plausible as a seat of qualia, least of all a brain. | |
| From: Ned Block (Troubles with Functionalism [1978], p. 78) | |
| A reaction: I'm not sure about "least of all", given the mind-boggling complexity of the brain's connections. Certainly, though, nothing in either folk physics or academic physics suggests that any physical object is likely to be aware of anything. |
| 2574 | Behaviour requires knowledge as well as dispositions [Block] |
| Full Idea: A desire cannot be identified with a disposition to act, since the agent might not know that a particular act leads to the thing desired, and thus might not be disposed to do it. | |
| From: Ned Block (Troubles with Functionalism [1978], p. 69) | |
| A reaction: One might have a disposition to act, but not in a particular way. "Something must be done". To get to the particular act, it seems that indeed a belief must be added to the desire. |
| 2575 | Functionalism is behaviourism, but with mental states as intermediaries [Block] |
| Full Idea: Functionalism is a new incarnation of behaviourism, replacing sensory inputs with sensory inputs plus mental states, and replacing dispositions to act with dispositions plus certain mental states. | |
| From: Ned Block (Troubles with Functionalism [1978], p. 69) | |
| A reaction: I think of functionalism as behaviourism which extends inside the 'black box' between stimulus and response. It proposes internal stimuli and responses. Consequently functionalism inherits some behaviourist problems. |
| 2576 | In functionalism, desires are internal states with causal relations [Block] |
| Full Idea: According to functionalism, a system might have the behaviouristic input-output relations, yet not desire something, as this requires internal states with certain causal relations. | |
| From: Ned Block (Troubles with Functionalism [1978], p. 69) | |
| A reaction: Such a system might be Putnam's 'superactor', who only behaves as if he desires something. Of course, the internal states might need more than just 'causal relations'. |
| 2583 | You might invert colours, but you can't invert beliefs [Block] |
| Full Idea: It is hard to see how to make sense of the analog of color spectrum inversion with respect to non-qualitative states such a beliefs (where they are functionally equivalent but have different beliefs). | |
| From: Ned Block (Troubles with Functionalism [1978], p. 81) | |
| A reaction: I would suggest that beliefs can be 'inverted', because there are all sorts of ways to implement a belief, but colour can't be inverted, because that depends on a particular brain state. It makes good sense to me... |
| 2578 | Could a creature without a brain be in the right functional state for pain? [Block] |
| Full Idea: If pain is a functional state, it cannot be a brain state, because creatures without brains could realise the same Turing machine as creatures with brains. | |
| From: Ned Block (Troubles with Functionalism [1978], p. 70) | |
| A reaction: This strikes me as being a poorly grounded claim. There may be some hypothetical world where brainless creatures implement all our functions, but from here brains look the only plausible option. |
| 2585 | Not just any old functional network will have mental states [Block] |
| Full Idea: If there are any fixed points in the mind-body problem, one of them is that the economy of Bolivia could not have mental states, no matter how it is distorted. | |
| From: Ned Block (Troubles with Functionalism [1978], p. 86) | |
| A reaction: It is hard to disagree with this, but then it can hardly be a serious suggestion that anyone could see how to reconfigure an economy so that it mapped the functional state of the human brain. This is not a crucial problem. |
| 2586 | In functionalism, what are the special inputs and outputs of conscious creatures? [Block] |
| Full Idea: In functionalism, it is very hard to see how there could be a single physical characterization of the inputs and outputs of all and only creatures with mentality. | |
| From: Ned Block (Troubles with Functionalism [1978], p. 87) | |
| A reaction: It would be theoretically possible if the only way to achieve mentality was to have a particular pattern of inputs and outputs. I don't think, though, that 'mentality' is an all-or-nothing concept. |
| 2579 | Physicalism is prejudiced in favour of our neurology, when other systems might have minds [Block] |
| Full Idea: Physicalism is a chauvinist theory: it withholds mental properties from systems that in fact have them. | |
| From: Ned Block (Troubles with Functionalism [1978], p. 71) | |
| A reaction: This criticism interprets physicalism too rigidly. There may be several ways to implement a state. My own view is that other systems might implement our functions, but they won't experience them in a human way. |
| 2577 | Simple machine-functionalism says mind just is a Turing machine [Block] |
| Full Idea: In the simplest Turing-machine version of functionalism (Putnam 1967), mental states are identified with the total Turing-machine state, involving a machine table and its inputs and outputs. | |
| From: Ned Block (Troubles with Functionalism [1978], p. 70) | |
| A reaction: This obviously invites the question of why mental states would be conscious and phenomenal, given that modern computers are devoid of same, despite being classy Turing machines. |
| 2580 | A Turing machine, given a state and input, specifies an output and the next state [Block] |
| Full Idea: In a Turing machine, given any state and input, the machine table specifies an output and the next state. …To have full power the tape must be infinite in at least one direction, and be movable in both directions. | |
| From: Ned Block (Troubles with Functionalism [1978], p. 71) | |
| A reaction: In retrospect, the proposal that this feeble item should be taken as a model for the glorious complexity and richness of human consciousness doesn't look too plausible. |
| 3178 | A fast machine could pass all behavioural tests with a vast lookup table [Block, by Rey] |
| Full Idea: Ned Block proposes a machine (a 'blockhead') which could pass the Turing Test just by looking up responses in a vast look-up table. | |
| From: report of Ned Block (works [1984]) by Georges Rey - Contemporary Philosophy of Mind 5.3 | |
| A reaction: Once you suspected you were talking to a blockhead, I think you could catch it out in a Turing Test. How can the lookup table keep up to date with immediate experience? Ask it about your new poem. |
| 18033 | The meaning of a representation is its role in thought, perception or decisions [Block] |
| Full Idea: According to conceptual role semantics, the meaning of a representation is the role of that representation in the cognitive life of the agent, for example, in perception, thought and decision-making. | |
| From: Ned Block (Semantics, Conceptual Role [1998]) | |
| A reaction: I never believe theories of this kind, because I always find myself asking 'what is the nature of this representation which enables it to play this role?'. |
| 2581 | Intuition may say that a complex sentence is ungrammatical, but linguistics can show that it is not [Block] |
| Full Idea: Linguistics rejects (on theoretical grounds) the intuition that the sentence "the boy the girl the cat bit scratched died" is ungrammatical. | |
| From: Ned Block (Troubles with Functionalism [1978], p. 78) | |
| A reaction: Once we have disentangled it, we practical speakers have no right to say it is ungrammatical. It isn't only theory. The sentence is just stylistically infelicitous. |