78 ideas
| 10482 | The logic of ZF is classical first-order predicate logic with identity [Boolos] |
| 10492 | A few axioms of set theory 'force themselves on us', but most of them don't [Boolos] |
| 18192 | Do the Replacement Axioms exceed the iterative conception of sets? [Boolos, by Maddy] |
| 7785 | The use of plurals doesn't commit us to sets; there do not exist individuals and collections [Boolos] |
| 10485 | Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos] |
| 10484 | The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos] |
| 13547 | Limitation of Size is weak (Fs only collect is something the same size does) or strong (fewer Fs than objects) [Boolos, by Potter] |
| 10699 | Does a bowl of Cheerios contain all its sets and subsets? [Boolos] |
| 14249 | Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley] |
| 10225 | Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro] |
| 10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
| 10736 | Boolos showed how plural quantifiers can interpret monadic second-order logic [Boolos, by Linnebo] |
| 10780 | Any sentence of monadic second-order logic can be translated into plural first-order logic [Boolos, by Linnebo] |
| 10829 | A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos] |
| 10697 | Identity is clearly a logical concept, and greatly enhances predicate calculus [Boolos] |
| 10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
| 13671 | Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology [Boolos, by Shapiro] |
| 10267 | We should understand second-order existential quantifiers as plural quantifiers [Boolos, by Shapiro] |
| 10698 | Plural forms have no more ontological commitment than to first-order objects [Boolos] |
| 7806 | Boolos invented plural quantification [Boolos, by Benardete,JA] |
| 10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos] |
| 13841 | Why should compactness be definitive of logic? [Boolos, by Hacking] |
| 10491 | Infinite natural numbers is as obvious as infinite sentences in English [Boolos] |
| 10483 | Mathematics and science do not require very high orders of infinity [Boolos] |
| 10833 | Many concepts can only be expressed by second-order logic [Boolos] |
| 10490 | Mathematics isn't surprising, given that we experience many objects as abstract [Boolos] |
| 10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
| 10488 | It is lunacy to think we only see ink-marks, and not word-types [Boolos] |
| 10487 | I am a fan of abstract objects, and confident of their existence [Boolos] |
| 10489 | We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos] |
| 6375 | The taste of chocolate is a 'finer-grained' sensation than the taste of sweetness [Polger] |
| 4669 | Persons are conscious, they relate, they think, they feel, and they are self-aware [Glover] |
| 6381 | The mind and the self are one, and the mind-self is a biological phenomenon [Polger] |
| 6378 | Teleological functions explain why a trait exists; causal-role functions say what it does [Polger] |
| 6380 | Identity theory says consciousness is an abstraction: a state, event, process or property [Polger] |
| 8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos] |
| 4656 | A problem arises in any moral system that allows more than one absolute right [Glover] |
| 4657 | Double Effect: no bad acts with good consequences, but possibly good acts despite bad consequences [Glover] |
| 4658 | Acts and Omissions: bad consequences are morally better if they result from an omission rather than an act [Glover] |
| 4659 | It doesn't seem worse to switch off a life-support machine than to forget to switch it on [Glover] |
| 4660 | Harmful omissions are unavoidable, while most harmful acts can be avoided [Glover] |
| 4661 | What matters is not intrinsic value of life or rights, but worthwhile and desired life, and avoidance of pain [Glover] |
| 4648 | 'Death' is best seen as irreversible loss of consciousness, since this is why we care about brain function [Glover] |
| 3785 | You can't separate acts from the people performing them [Glover] |
| 3786 | Aggression in defence may be beneficial but morally corrupting [Glover] |
| 4650 | The quality of a life is not altogether independent of its length [Glover] |
| 3784 | Duty prohibits some acts, whatever their consequences [Glover] |
| 3782 | Satisfaction of desires is not at all the same as achieving happiness [Glover, by PG] |
| 3787 | Rule-utilitarianism is either act-utilitarianism, or not really utilitarian [Glover] |
| 3783 | How can utilitarianism decide the ideal population size? [Glover] |
| 4675 | The sanctity of life doctrine implies a serious increase of abnormality among the population [Glover] |
| 4654 | Autonomy favours present opinions over future ones, and says nothing about the interests of potential people [Glover] |
| 4655 | If a whole community did not mind death, respect for autonomy suggests that you could kill them all [Glover] |
| 4680 | Autonomy seems to acquire greater weight when the decision is more important to a person [Glover] |
| 4670 | Being alive is not intrinsically good, and there is no 'right to life' [Glover] |
| 4668 | You can't have a right to something you can't desire, so a foetus has no 'right' to life [Glover] |
| 4649 | If someone's life is 'worth living', that gives one direct reason not to kill him [Glover] |
| 4651 | Utilitarians object to killing directly (pain, and lost happiness), and to side-effects (loss to others, and precedents) [Glover] |
| 4671 | What is wrong with killing someone, if another equally worthwhile life is substituted? [Glover] |
| 4676 | The 'no trade-off' position: killing is only justified if it prevents other deaths [Glover] |
| 4685 | Societies spend a lot to save known persons, but very little to reduce fatal accidents [Glover] |
| 4683 | Involuntary euthanasia is wrong because it violates autonomy, and it has appalling side-effects [Glover] |
| 4682 | Euthanasia is voluntary (patient's wish), or involuntary (ignore wish), or non-voluntary (no wish possible) [Glover] |
| 4684 | Maybe extreme treatment is not saving life, but prolonging the act of dying [Glover] |
| 4681 | The Nazi mass murders seem to have originated in their euthanasia programme [Glover] |
| 4665 | Conception isn't the fixed boundary for a person's beginning, because twins are possible within two weeks [Glover] |
| 4667 | How would we judge abortion if mothers had transparent wombs? [Glover] |
| 4652 | If killing is wrong because it destroys future happiness, not conceiving a happy child is also wrong [Glover] |
| 4662 | Defenders of abortion focus on early pregnancy, while opponents focus on later stages [Glover] |
| 4663 | If abortion is wrong, it is because a foetus is a human being or a person (or potentially so) [Glover] |
| 4664 | If abortion is wrong because of the 'potential' person, that makes contraception wrong too [Glover] |
| 4673 | Abortion differs morally from deliberate non-conception only in its side-effects [Glover] |
| 4666 | If viability is a test or boundary at the beginning of life, it should also be so for frail old people [Glover] |
| 4672 | Apart from side effects, it seems best to replace an inadequate foetus with one which has a better chance [Glover] |
| 4674 | It is always right for a qualified person to perform an abortion when requested by the mother [Glover] |
| 4679 | One test for a worthwhile life is to assess the amount of life for which you would rather be unconscious [Glover] |
| 6379 | A mummified heart has the teleological function of circulating blood [Polger] |
| 6377 | Teleological notions of function say what a thing is supposed to do [Polger] |