21 ideas
| 10482 | The logic of ZF is classical first-order predicate logic with identity [Boolos] |
| Full Idea: The logic of ZF Set Theory is classical first-order predicate logic with identity. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.121) | |
| A reaction: This logic seems to be unable to deal with very large cardinals, precisely those that are implied by set theory, so there is some sort of major problem hovering here. Boolos is fairly neutral. |
| 10492 | A few axioms of set theory 'force themselves on us', but most of them don't [Boolos] |
| Full Idea: Maybe the axioms of extensionality and the pair set axiom 'force themselves on us' (Gödel's phrase), but I am not convinced about the axioms of infinity, union, power or replacement. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.130) | |
| A reaction: Boolos is perfectly happy with basic set theory, but rather dubious when very large cardinals come into the picture. |
| 10485 | Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos] |
| Full Idea: The naïve view of set theory (that any zero or more things form a set) is natural, but inconsistent: the things that do not belong to themselves are some things that do not form a set. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.127) | |
| A reaction: As clear a summary of Russell's Paradox as you could ever hope for. |
| 10484 | The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos] |
| Full Idea: According to the iterative conception, every set is formed at some stage. There is a relation among stages, 'earlier than', which is transitive. A set is formed at a stage if and only if its members are all formed before that stage. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.126) | |
| A reaction: He gives examples of the early stages, and says the conception is supposed to 'justify' Zermelo set theory. It is also supposed to make the axioms 'natural', rather than just being selected for convenience. And it is consistent. |
| 17505 | Using proper names properly doesn't involve necessary and sufficient conditions [Putnam] |
| Full Idea: The important thing about proper names is that it would be ridiculous to think that having linguistic competence can be equated in their case with knowledge of a necessary and sufficient condition. | |
| From: Hilary Putnam (Explanation and Reference [1973], II B) |
| 10491 | Infinite natural numbers is as obvious as infinite sentences in English [Boolos] |
| Full Idea: The existence of infinitely many natural numbers seems to me no more troubling than that of infinitely many computer programs or sentences of English. There is, for example, no longest sentence, since any number of 'very's can be inserted. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.129) | |
| A reaction: If you really resisted an infinity of natural numbers, presumably you would also resist an actual infinity of 'very's. The fact that it is unclear what could ever stop a process doesn't guarantee that the process is actually endless. |
| 10483 | Mathematics and science do not require very high orders of infinity [Boolos] |
| Full Idea: To the best of my knowledge nothing in mathematics or science requires the existence of very high orders of infinity. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.122) | |
| A reaction: He is referring to particular high orders of infinity implied by set theory. Personally I want to wield Ockham's Razor. Is being implied by set theory a sufficient reason to accept such outrageous entities into our ontology? |
| 10490 | Mathematics isn't surprising, given that we experience many objects as abstract [Boolos] |
| Full Idea: It is no surprise that we should be able to reason mathematically about many of the things we experience, for they are already 'abstract'. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.129) | |
| A reaction: He has just given a list of exemplary abstract objects (Idea 10489), but I think there is a more interesting idea here - that our experience of actual physical objects is to some extent abstract, as soon as it is conceptualised. |
| 10488 | It is lunacy to think we only see ink-marks, and not word-types [Boolos] |
| Full Idea: It's a kind of lunacy to think that sound scientific philosophy demands that we think that we see ink-tracks but not words, i.e. word-types. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.128) | |
| A reaction: This seems to link him with Armstrong's mockery of 'ostrich nominalism'. There seems to be some ambiguity with the word 'see' in this disagreement. When we look at very ancient scratches on stones, why don't we always 'see' if it is words? |
| 10487 | I am a fan of abstract objects, and confident of their existence [Boolos] |
| Full Idea: I am rather a fan of abstract objects, and confident of their existence. Smaller numbers, sets and functions don't offend my sense of reality. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.128) | |
| A reaction: The great Boolos is rather hard to disagree with, but I disagree. Logicians love abstract objects, indeed they would almost be out of a job without them. It seems to me they smuggle them into our ontology by redefining either 'object' or 'exists'. |
| 10489 | We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos] |
| Full Idea: We twentieth century city dwellers deal with abstract objects all the time, such as bank balances, radio programs, software, newspaper articles, poems, mistakes, triangles. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.129) | |
| A reaction: I find this claim to be totally question-begging, and typical of a logician. The word 'object' gets horribly stretched in these discussions. We can create concepts which have all the logical properties of objects. Maybe they just 'subsist'? |
| 11908 | Putnam bases essences on 'same kind', but same kinds may not share properties [Mackie,P on Putnam] |
| Full Idea: The only place for essentialism to come from in Putnam's semantic account is out of the 'same kind' relation. But if the same kind relation can be cashed out in terms that do not involve sharing properties (apart from 'being water') there is a gap. | |
| From: comment on Hilary Putnam (Explanation and Reference [1973]) by Penelope Mackie - How Things Might Have Been 10.4 | |
| A reaction: [This is the criticism of Salmon and Mellor] See Mackie's discussion for details. I would always have thought that relations result from essences, so could never be used to define them. |
| 17508 | Science aims at truth, not at 'simplicity' [Putnam] |
| Full Idea: Scientists are not trying to maximise some formal property of 'simplicity'; they are trying to maximise truth. | |
| From: Hilary Putnam (Explanation and Reference [1973], III B) | |
| A reaction: This seems to be aimed at the Mill-Ramsey-Lewis account of laws of nature, as the simplest axioms of experience. I'm with Putnam (as he was at this date). |
| 7658 | Obviously there can't be a functional anaylsis of qualia if they are defined by intrinsic properties [Dennett] |
| Full Idea: If you define qualia as intrinsic properties of experiences considered in isolation from all their causes and effects, logically independent of all dispositional properties, then they are logically guaranteed to elude all broad functional analysis. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.8) | |
| A reaction: This is a good point - it seems daft to reify qualia and imagine them dangling in mid-air with all their vibrant qualities - but that is a long way from saying there is nothing more to qualia than functional roles. Functions must be exlained too. |
| 7655 | The work done by the 'homunculus in the theatre' must be spread amongst non-conscious agencies [Dennett] |
| Full Idea: All the work done by the imagined homunculus in the Cartesian Theater must be distributed among various lesser agencies in the brain, none of which is conscious. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.3) | |
| A reaction: Dennett's account crucially depends on consciousness being much more fragmentary than most philosophers claim it to be. It is actually full of joints, which can come apart. He may be right. |
| 7657 | Intelligent agents are composed of nested homunculi, of decreasing intelligence, ending in machines [Dennett] |
| Full Idea: As long as your homunculi are more stupid and ignorant than the intelligent agent they compose, the nesting of homunculi within homunculi can be finite, bottoming out, eventually, with agents so unimpressive they can be replaced by machines. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.6) | |
| A reaction: [Dennett first proposed this in 'Brainstorms' 1978]. This view was developed well by Lycan. I rate it as one of the most illuminating ideas in the modern philosophy of mind. All complex systems (like aeroplanes) have this structure. |
| 7656 | I don't deny consciousness; it just isn't what people think it is [Dennett] |
| Full Idea: I don't maintain, of course, that human consciousness does not exist; I maintain that it is not what people often think it is. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.3) | |
| A reaction: I consider Dennett to be as near as you can get to an eliminativist, but he is not stupid. As far as I can see, the modern philosopher's bogey-man, the true total eliminativist, simply doesn't exist. Eliminativists usually deny propositional attitudes. |
| 7654 | What matters about neuro-science is the discovery of the functional role of the chemistry [Dennett] |
| Full Idea: Neuro-science matters because - and only because - we have discovered that the many different neuromodulators and other chemical messengers that diffuse throughout the brain have functional roles that make important differences. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.1) | |
| A reaction: I agree with Dennett that this is the true ground for pessimism about spectacular breakthroughs in artificial intelligence, rather than abstract concerns about irreducible features of the mind like 'qualia' and 'rationality'. |
| 17506 | I now think reference by the tests of experts is a special case of being causally connected [Putnam] |
| Full Idea: In previous papers I suggested that the reference is fixed by a test known to experts; it now seems to me that this is just a special case of my use being causally connected to an introducing event. | |
| From: Hilary Putnam (Explanation and Reference [1973], II C) | |
| A reaction: I think he was probably right the first time, and has now wandered off course. |
| 11904 | Express natural kinds as a posteriori predicate connections, not as singular terms [Putnam, by Mackie,P] |
| Full Idea: Putnam implies dispensing with the designation of natural kinds by singular terms in favour of the postulation of necessary but a posteriori connections between predicates. ...We might call this 'predicate essentialism', but not 'de re essentialism'. | |
| From: report of Hilary Putnam (Explanation and Reference [1973]) by Penelope Mackie - How Things Might Have Been 10.1 | |
| A reaction: It is characteristic of modern discussion that the logical form of natural kind statements is held to be crucial, rather than an account of nature in any old ways that do the job. So do I prefer singular terms, or predicate-connections. Hm. |
| 17507 | Natural kind stereotypes are 'strong' (obvious, like tiger) or 'weak' (obscure, like molybdenum) [Putnam] |
| Full Idea: Natural kinds can be associated with 'strong' stereotypes (giving a strong picture of a typical member, like a tiger), or with 'weak' stereotypes (with no idea of a sufficient condition, such as molybdenum or elm). | |
| From: Hilary Putnam (Explanation and Reference [1973], II C) |