75 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] |
| 5937 | The goodness of opinions depends on their grounds, and corresponding degrees of conviction [Ross] |
| 5936 | Knowledge is superior to opinion because it is certain [Ross] |
| 5927 | I prefer the causal theory to sense data, because sensations are events, not apprehensions [Ross] |
| 5940 | Two goods may be comparable, although they are not commensurable [Ross] |
| 5924 | Identical objects must have identical value [Ross] |
| 5933 | Aesthetic enjoyment combines pleasure with insight [Ross] |
| 5928 | Beauty is neither objective nor subjective, but a power of producing certain mental events [Ross] |
| 5911 | Moral duties are as fundamental to the universe as the axioms of mathematics [Ross] |
| 5926 | The beauty of a patch of colour might be the most important fact about it [Ross] |
| 7259 | Ross said moral principles are self-evident from the facts, but not from pure thought [Ross, by Dancy,J] |
| 5913 | The moral convictions of thoughtful educated people are the raw data of ethics [Ross] |
| 5920 | Value is held to be either a quality, or a relation (usually between a thing and a mind) [Ross] |
| 5923 | The arguments for value being an objective or a relation fail, so it appears to be a quality [Ross] |
| 5918 | The thing is intrinsically good if it would be good when nothing else existed [Ross] |
| 5930 | All things being equal, we all prefer the virtuous to be happy, not the vicious [Ross] |
| 5922 | An instrumentally good thing might stay the same, but change its value because of circumstances [Ross] |
| 5921 | We can ask of pleasure or beauty whether they are valuable, but not of goodness [Ross] |
| 5932 | The four goods are: virtue, pleasure, just allocation of pleasure, and knowledge [Ross] |
| 5910 | The three intrinsic goods are virtue, knowledge and pleasure [Ross] |
| 5898 | 'Right' and 'good' differ in meaning, as in a 'right action' and a 'good man' [Ross] |
| 5899 | If there are two equally good acts, they may both be right, but neither a duty [Ross] |
| 5904 | In the past 'right' just meant what is conventionally accepted [Ross] |
| 5919 | Goodness is a wider concept than just correct ethical conduct [Ross] |
| 5941 | Motives decide whether an action is good, and what is done decides whether it was right [Ross] |
| 5938 | Virtue is superior to pleasure, as pleasure is never a duty, but goodness is [Ross] |
| 5931 | All other things being equal, a universe with more understanding is better [Ross] |
| 5939 | Morality is not entirely social; a good moral character should love truth [Ross] |
| 5905 | We clearly value good character or understanding, as well as pleasure [Ross] |
| 5929 | No one thinks it doesn't matter whether pleasure is virtuously or viciously acquired [Ross] |
| 5906 | Promise-keeping is bound by the past, and is not concerned with consequences [Ross] |
| 18622 | Promises create a new duty to a particular person; they aren't just a strategy to achieve well-being [Ross] |
| 5908 | Prima facie duties rest self-evidently on particular circumstance [Ross] |
| 5917 | People lose their rights if they do not respect the rights of others [Ross] |
| 5900 | We should do our duty, but not from a sense of duty [Ross] |
| 5942 | We like people who act from love, but admire more the people who act from duty [Ross] |
| 5909 | Be faithful, grateful, just, beneficent, non-malevolent, and improve yourself [Ross, by PG] |
| 5914 | An act may be described in innumerable ways [Ross] |
| 5912 | We should use money to pay debts before giving to charity [Ross] |
| 5916 | Rights were originally legal, and broadened to include other things [Ross] |
| 5915 | Rights can be justly claimed, so animals have no rights, as they cannot claim any [Ross] |