66 ideas
| 15413 | With four tense operators, all complex tenses reduce to fourteen basic cases [Burgess] |
| 15415 | The temporal Barcan formulas fix what exists, which seems absurd [Burgess] |
| 15430 | Is classical logic a part of intuitionist logic, or vice versa? [Burgess] |
| 15431 | It is still unsettled whether standard intuitionist logic is complete [Burgess] |
| 15429 | Relevance logic's → is perhaps expressible by 'if A, then B, for that reason' [Burgess] |
| 15404 | Technical people see logic as any formal system that can be studied, not a study of argument validity [Burgess] |
| 15405 | Classical logic neglects the non-mathematical, such as temporality or modality [Burgess] |
| 15427 | The Cut Rule expresses the classical idea that entailment is transitive [Burgess] |
| 15421 | Classical logic neglects counterfactuals, temporality and modality, because maths doesn't use them [Burgess] |
| 15403 | Philosophical logic is a branch of logic, and is now centred in computer science [Burgess] |
| 15407 | Formalising arguments favours lots of connectives; proving things favours having very few [Burgess] |
| 15424 | Asserting a disjunction from one disjunct seems odd, but can be sensible, and needed in maths [Burgess] |
| 15409 | All occurrences of variables in atomic formulas are free [Burgess] |
| 15414 | The denotation of a definite description is flexible, rather than rigid [Burgess] |
| 15406 | 'Induction' and 'recursion' on complexity prove by connecting a formula to its atomic components [Burgess] |
| 15425 | The sequent calculus makes it possible to have proof without transitivity of entailment [Burgess] |
| 15426 | We can build one expanding sequence, instead of a chain of deductions [Burgess] |
| 15408 | 'Tautologies' are valid formulas of classical sentential logic - or substitution instances in other logics [Burgess] |
| 15418 | Validity (for truth) and demonstrability (for proof) have correlates in satisfiability and consistency [Burgess] |
| 15412 | Models leave out meaning, and just focus on truth values [Burgess] |
| 15411 | We only need to study mathematical models, since all other models are isomorphic to these [Burgess] |
| 15416 | We aim to get the technical notion of truth in all models matching intuitive truth in all instances [Burgess] |
| 15428 | The Liar seems like a truth-value 'gap', but dialethists see it as a 'glut' [Burgess] |
| 10185 | Set theory is the standard background for modern mathematics [Burgess] |
| 10184 | Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure [Burgess] |
| 10189 | There is no one relation for the real number 2, as relations differ in different models [Burgess] |
| 10186 | If set theory is used to define 'structure', we can't define set theory structurally [Burgess] |
| 10187 | Abstract algebra concerns relations between models, not common features of all the models [Burgess] |
| 10188 | How can mathematical relations be either internal, or external, or intrinsic? [Burgess] |
| 12887 | A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim] |
| 15420 | De re modality seems to apply to objects a concept intended for sentences [Burgess] |
| 15419 | General consensus is S5 for logical modality of validity, and S4 for proof [Burgess] |
| 15417 | Logical necessity has two sides - validity and demonstrability - which coincide in classical logic [Burgess] |
| 15422 | Three conditionals theories: Materialism (material conditional), Idealism (true=assertable), Nihilism (no truth) [Burgess] |
| 15423 | It is doubtful whether the negation of a conditional has any clear meaning [Burgess] |
| 4363 | The word 'person' is useless in ethics, because what counts as a good or bad self-conscious being? [Hursthouse] |
| 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] |