75 ideas
12223 | It is a fallacy to explain the obscure with the even more obscure [Hale/Wright] |
17926 | Rejecting double negation elimination undermines reductio proofs [Colyvan] |
17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan] |
17924 | Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan] |
12230 | Singular terms refer if they make certain atomic statements true [Hale/Wright] |
17929 | Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan] |
17930 | Axioms are 'categorical' if all of their models are isomorphic [Colyvan] |
10631 | If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological [Hale/Wright] |
17928 | Ordinal numbers represent order relations [Colyvan] |
17923 | Intuitionists only accept a few safe infinities [Colyvan] |
17941 | Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan] |
17922 | Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan] |
17936 | Transfinite induction moves from all cases, up to the limit ordinal [Colyvan] |
10624 | The incompletability of formal arithmetic reveals that logic also cannot be completely characterized [Hale/Wright] |
8784 | Neo-logicism founds arithmetic on Hume's Principle along with second-order logic [Hale/Wright] |
8787 | The Julius Caesar problem asks for a criterion for the concept of a 'number' [Hale/Wright] |
17940 | Most mathematical proofs are using set theory, but without saying so [Colyvan] |
17931 | Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan] |
10629 | If structures are relative, this undermines truth-value and objectivity [Hale/Wright] |
10628 | The structural view of numbers doesn't fit their usage outside arithmetical contexts [Hale/Wright] |
17932 | If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan] |
8788 | Logicism is only noteworthy if logic has a privileged position in our ontology and epistemology [Hale/Wright] |
10622 | The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright] |
8783 | Logicism might also be revived with a quantificational approach, or an abstraction-free approach [Hale/Wright] |
12225 | Neo-Fregeanism might be better with truth-makers, rather than quantifier commitment [Hale/Wright] |
12224 | Are neo-Fregeans 'maximalists' - that everything which can exist does exist? [Hale/Wright] |
12226 | The identity of Pegasus with Pegasus may be true, despite the non-existence [Hale/Wright] |
12229 | Maybe we have abundant properties for semantics, and sparse properties for ontology [Hale/Wright] |
18443 | A successful predicate guarantees the existence of a property - the way of being it expresses [Hale/Wright] |
10626 | Objects just are what singular terms refer to [Hale/Wright] |
17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
17939 | Mathematics can reveal structural similarities in diverse systems [Colyvan] |
17938 | Mathematics can show why some surprising events have to occur [Colyvan] |
17934 | Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan] |
17933 | Reductio proofs do not seem to be very explanatory [Colyvan] |
17935 | If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan] |
17942 | Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan] |
17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
4363 | The word 'person' is useless in ethics, because what counts as a good or bad self-conscious being? [Hursthouse] |
10630 | Abstracted objects are not mental creations, but depend on equivalence between given entities [Hale/Wright] |
8786 | One first-order abstraction principle is Frege's definition of 'direction' in terms of parallel lines [Hale/Wright] |
12227 | Abstractionism needs existential commitment and uniform truth-conditions [Hale/Wright] |
12228 | Equivalence abstraction refers to objects otherwise beyond our grasp [Hale/Wright] |
12231 | Reference needs truth as well as sense [Hale/Wright] |
10627 | Many conceptual truths ('yellow is extended') are not analytic, as derived from logic and definitions [Hale/Wright] |
4355 | There may be inverse akrasia, where the agent's action is better than their judgement recommends [Hursthouse] |
4325 | Must all actions be caused in part by a desire, or can a belief on its own be sufficient? [Hursthouse] |
4351 | It is a fantasy that only through the study of philosophy can one become virtuous [Hursthouse] |
4340 | You are not a dishonest person if a tragic dilemma forces you to do something dishonest [Hursthouse] |
4329 | After a moral dilemma is resolved there is still a 'remainder', requiring (say) regret [Hursthouse] |
4330 | Deontologists resolve moral dilemmas by saying the rule conflict is merely apparent [Hursthouse] |
4341 | Involuntary actions performed in tragic dilemmas are bad because they mar a good life [Hursthouse] |
4358 | Virtue may be neither sufficient nor necessary for eudaimonia [Hursthouse] |
4337 | Teenagers are often quite wise about ideals, but rather stupid about consequences [Hursthouse] |
4324 | Animals and plants can 'flourish', but only rational beings can have eudaimonia [Hursthouse] |
4359 | When it comes to bringing up children, most of us think that the virtues are the best bet [Hursthouse] |
20195 | Eudaimonia first; virtue is a trait which promotes it; right acts are what virtues produce [Hursthouse, by Zagzebski] |
4336 | Any strict ranking of virtues or rules gets abandoned when faced with particular cases [Hursthouse] |
4334 | Virtue ethics is open to the objection that it fails to show priority among the virtues [Hursthouse] |
4361 | Good animals can survive, breed, feel characteristic pleasure and pain, and contribute to the group [Hursthouse] |
4349 | Virtuous people may not be fully clear about their reasons for action [Hursthouse] |
4352 | Performing an act simply because it is virtuous is sufficient to be 'morally motivated' or 'dutiful' [Hursthouse] |
4353 | If moral motivation is an all-or-nothing sense of duty, how can children act morally? [Hursthouse] |
4346 | The emotions of sympathy, compassion and love are no guarantee of right action or acting well [Hursthouse] |
4339 | According to virtue ethics, two agents may respond differently, and yet both be right [Hursthouse] |
4354 | Maybe in a deeply poisoned character none of their milder character traits could ever be a virtue [Hursthouse] |
4364 | Being unusually virtuous in some areas may entail being less virtuous in others [Hursthouse] |
4356 | We are puzzled by a person who can show an exceptional virtue and also behave very badly [Hursthouse] |
4327 | Deontologists do consider consequences, because they reveal when a rule might apply [Hursthouse] |
4335 | 'Codifiable' morality give rules for decisions which don't require wisdom [Hursthouse] |
4328 | Preference utilitarianism aims to be completely value-free, or empirical [Hursthouse] |
4343 | We are torn between utilitarian and deontological views of lying, depending on the examples [Hursthouse] |
4338 | Deontologists usually accuse utilitarians of oversimplifying hard cases [Hursthouse] |
4365 | We are distinct from other animals in behaving rationally - pursuing something as good, for reasons [Hursthouse] |
4350 | If people are virtuous in obedience to God, would they become wicked if they lost their faith? [Hursthouse] |