62 ideas
| 1502 | Parmenides was much more cautious about accepting ideas than his predecessors [Simplicius on Parmenides] |
| 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] |
| 15421 | Classical logic neglects counterfactuals, temporality and modality, because maths doesn't use them [Burgess] |
| 15427 | The Cut Rule expresses the classical idea that entailment is transitive [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] |
| 15426 | We can build one expanding sequence, instead of a chain of deductions [Burgess] |
| 15425 | The sequent calculus makes it possible to have proof without transitivity of entailment [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] |
| 15411 | We only need to study mathematical models, since all other models are isomorphic to these [Burgess] |
| 15412 | Models leave out meaning, and just focus on truth values [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] |
| 449 | Being is not divisible, since it is all alike [Parmenides] |
| 448 | No necessity could produce Being either later or earlier, so it must exist absolutely or not at all [Parmenides] |
| 447 | Being must be eternal and uncreated, and hence it is timeless [Parmenides] |
| 445 | The realm of necessary non-existence cannot be explored, because it is unknowable [Parmenides] |
| 1503 | There is no such thing as nothing [Parmenides] |
| 21820 | Parmenides at least saw Being as the same as Nous, and separate from the sensed realm [Parmenides, by Plotinus] |
| 452 | All our concepts of change and permanence are just names, not the truth [Parmenides] |
| 1504 | Something must be unchanging to make recognition and knowledge possible [Aristotle on Parmenides] |
| 15420 | De re modality seems to apply to objects a concept intended for sentences [Burgess] |
| 444 | The first way of enquiry involves necessary existence [Parmenides] |
| 15417 | Logical necessity has two sides - validity and demonstrability - which coincide in classical logic [Burgess] |
| 15419 | General consensus is S5 for logical modality of validity, and S4 for proof [Burgess] |
| 450 | Necessity sets limits on being, in order to give it identity [Parmenides] |
| 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] |
| 451 | Thinking implies existence, because thinking depends on it [Parmenides] |
| 1506 | Parmenides treats perception and intellectual activity as the same [Theophrastus on Parmenides] |
| 3058 | Only reason can prove the truth of facts [Parmenides] |
| 6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |
| 555 | People who say that the cosmos is one forget that they must explain movement [Aristotle on Parmenides] |
| 226 | The one is without any kind of motion [Parmenides] |
| 5081 | There could be movement within one thing, as there is within water [Aristotle on Parmenides] |
| 1509 | The one can't be divisible, because if it was it could be infinitely divided down to nothing [Parmenides, by Simplicius] |
| 20900 | Defenders of the One say motion needs the void - but that is not part of Being [Parmenides, by Aristotle] |
| 1505 | Reason sees reality as one, the senses see it as many [Aristotle on Parmenides] |
| 453 | Reality is symmetrical and balanced, like a sphere, with no reason to be greater one way rather than another [Parmenides] |
| 1792 | He taught that there are two elements, fire the maker, and earth the matter [Parmenides, by Diog. Laertius] |
| 5115 | It is feeble-minded to look for explanations of everything being at rest [Aristotle on Parmenides] |
| 13217 | The void can't exist, and without the void there can't be movement or separation [Parmenides, by Aristotle] |
| 22918 | What could have triggered the beginning [of time and being]? [Parmenides] |
| 1794 | He was the first to discover the identity of the Morning and Evening Stars [Parmenides, by Diog. Laertius] |
| 1791 | He was the first person to say the earth is spherical [Parmenides, by Diog. Laertius] |