56 ideas
| 23728 | Analysis aims to express the full set of platitudes surrounding a given concept [Smith,M] |
| 23744 | Defining a set of things by paradigms doesn't pin them down enough [Smith,M] |
| 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] |
| 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] |
| 23743 | Capturing all the common sense facts about rationality is almost impossible [Smith,M] |
| 23739 | Goals need desires, and so only desires can motivate us [Smith,M] |
| 23724 | A pure desire could be criticised if it were based on a false belief [Smith,M] |
| 23736 | A person can have a desire without feeling it [Smith,M] |
| 23723 | In the Humean account, desires are not true/false, or subject to any rational criticism [Smith,M] |
| 23735 | Subjects may be fallible about the desires which explain their actions [Smith,M] |
| 23738 | Humeans (unlike their opponents) say that desires and judgements can separate [Smith,M] |
| 23742 | If first- and second-order desires conflict, harmony does not require the second-order to win [Smith,M] |
| 23746 | Objective reasons to act might be the systematic desires of a fully rational person [Smith,M] |
| 23733 | Motivating reasons are psychological, while normative reasons are external [Smith,M] |
| 23740 | Humeans take maximising desire satisfaction as the normative reasons for actions [Smith,M] |
| 23745 | We cannot expect even fully rational people to converge on having the same desires for action [Smith,M] |
| 23731 | 'Externalists' say moral judgements are not reasons, and maybe not even motives [Smith,M] |
| 23732 | A person could make a moral judgement without being in any way motivated by it [Smith,M] |
| 23729 | Moral internalism says a judgement of rightness is thereby motivating [Smith,M] |
| 23730 | 'Rationalism' says the rightness of an action is a reason to perform it [Smith,M] |
| 23727 | Expressivists count attitudes as 'moral' if they concern features of things, rather than their mere existence [Smith,M] |
| 23741 | Is valuing something a matter of believing or a matter of desiring? [Smith,M] |
| 22745 | Pherecydes said the first principle and element is earth [Pherecydes, by Sext.Empiricus] |
| 5883 | Pherecydes was the first to say that the soul is eternal [Pherecydes, by Cicero] |