117 ideas
| 11283 | There is pure deductive reasoning, and explanatory demonstration reasoning [Aristotle, by Politis] |
| 1672 | Maybe everything could be demonstrated, if demonstration can be reciprocal or circular [Aristotle] |
| 1684 | Two falsehoods can be contrary to one another [Aristotle] |
| 12145 | Definitions are of what something is, and that is universal [Aristotle] |
| 12384 | Definition by division needs predicates, which are well ordered and thorough [Aristotle] |
| 12075 | An Aristotelian definition is causal [Aristotle, by Witt] |
| 9066 | You can define objects by progressively identifying what is the same and what is different [Aristotle] |
| 12382 | What it is and why it is are the same; screening defines and explains an eclipse [Aristotle] |
| 10987 | Three traditional names of rules are 'Simplification', 'Addition' and 'Disjunctive Syllogism' [Read] |
| 1668 | An axiom is a principle which must be understood if one is to learn anything [Aristotle] |
| 11004 | Necessity is provability in S4, and true in all worlds in S5 [Read] |
| 11018 | There are fuzzy predicates (and sets), and fuzzy quantifiers and modifiers [Read] |
| 11011 | Same say there are positive, negative and neuter free logics [Read] |
| 11020 | Realisms like the full Comprehension Principle, that all good concepts determine sets [Read] |
| 10986 | Not all validity is captured in first-order logic [Read] |
| 10972 | The non-emptiness of the domain is characteristic of classical logic [Read] |
| 12376 | Demonstrations by reductio assume excluded middle [Aristotle] |
| 11024 | Semantics must precede proof in higher-order logics, since they are incomplete [Read] |
| 10985 | We should exclude second-order logic, precisely because it captures arithmetic [Read] |
| 12373 | Something holds universally when it is proved of an arbitrary and primitive case [Aristotle] |
| 10970 | A theory of logical consequence is a conceptual analysis, and a set of validity techniques [Read] |
| 10984 | Logical consequence isn't just a matter of form; it depends on connections like round-square [Read] |
| 12363 | Everything is either asserted or denied truly [Aristotle] |
| 10973 | A theory is logically closed, which means infinite premisses [Read] |
| 11007 | Quantifiers are second-order predicates [Read] |
| 10978 | In second-order logic the higher-order variables range over all the properties of the objects [Read] |
| 10971 | A logical truth is the conclusion of a valid inference with no premisses [Read] |
| 10988 | Any first-order theory of sets is inadequate [Read] |
| 13004 | Aristotle's axioms (unlike Euclid's) are assumptions awaiting proof [Aristotle, by Leibniz] |
| 10975 | Compactness does not deny that an inference can have infinitely many premisses [Read] |
| 10974 | Compactness is when any consequence of infinite propositions is the consequence of a finite subset [Read] |
| 10977 | Compactness blocks the proof of 'for every n, A(n)' (as the proof would be infinite) [Read] |
| 10976 | Compactness makes consequence manageable, but restricts expressive power [Read] |
| 11014 | Self-reference paradoxes seem to arise only when falsity is involved [Read] |
| 12377 | Mathematics is concerned with forms, not with superficial properties [Aristotle] |
| 12372 | The essence of a triangle comes from the line, mentioned in any account of triangles [Aristotle] |
| 12369 | A unit is what is quantitatively indivisible [Aristotle] |
| 11025 | Infinite cuts and successors seems to suggest an actual infinity there waiting for us [Read] |
| 10979 | Although second-order arithmetic is incomplete, it can fully model normal arithmetic [Read] |
| 10980 | Second-order arithmetic covers all properties, ensuring categoricity [Read] |
| 10997 | Von Neumann numbers are helpful, but don't correctly describe numbers [Read] |
| 11016 | Would a language without vagueness be usable at all? [Read] |
| 11019 | Supervaluations say there is a cut-off somewhere, but at no particular place [Read] |
| 11012 | A 'supervaluation' gives a proposition consistent truth-value for classical assignments [Read] |
| 11013 | Identities and the Indiscernibility of Identicals don't work with supervaluations [Read] |
| 18910 | To seek truth, study the real connections between subjects and attributes [Aristotle] |
| 1675 | Separate Forms aren't needed for logic, but universals (one holding of many) are essential [Aristotle] |
| 1677 | We can forget the Forms, as they are irrelevant, and not needed in giving demonstrations [Aristotle] |
| 10995 | A haecceity is a set of individual properties, essential to each thing [Read] |
| 1687 | Why are being terrestrial and a biped combined in the definition of man, but being literate and musical aren't? [Aristotle] |
| 1681 | Units are positionless substances, and points are substances with position [Aristotle] |
| 12146 | Definitions recognise essences, so are not themselves essences [Aristotle] |
| 17039 | The predicates of a thing's nature are necessary to it [Aristotle] |
| 11994 | Aristotelian essences are properties mentioned at the starting point of a science [Aristotle, by Kung] |
| 12381 | What is necessary cannot be otherwise [Aristotle] |
| 11001 | Equating necessity with truth in every possible world is the S5 conception of necessity [Read] |
| 1690 | A stone travels upwards by a forced necessity, and downwards by natural necessity [Aristotle] |
| 10989 | The standard view of conditionals is that they are truth-functional [Read] |
| 10992 | The point of conditionals is to show that one will accept modus ponens [Read] |
| 11017 | Some people even claim that conditionals do not express propositions [Read] |
| 10983 | Knowledge of possible worlds is not causal, but is an ontology entailed by semantics [Read] |
| 10982 | How can modal Platonists know the truth of a modal proposition? [Read] |
| 10996 | Actualism is reductionist (to parts of actuality), or moderate realist (accepting real abstractions) [Read] |
| 10981 | A possible world is a determination of the truth-values of all propositions of a domain [Read] |
| 11000 | If worlds are concrete, objects can't be present in more than one, and can only have counterparts [Read] |
| 12072 | For Aristotle knowledge is explanatory, involving understanding, and principles or causes [Aristotle, by Witt] |
| 12073 | 'Episteme' means grasping causes, universal judgments, explanation, and teaching [Aristotle, by Witt] |
| 12378 | The reason why is the key to knowledge [Aristotle] |
| 12364 | We understand a thing when we know its explanation and its necessity [Aristotle] |
| 12370 | Some understanding, of immediate items, is indemonstrable [Aristotle] |
| 12366 | We only understand something when we know its explanation [Aristotle] |
| 1685 | No one has mere belief about something if they think it HAS to be true [Aristotle] |
| 1673 | Knowledge proceeds from principles, so it is hard to know if we know [Aristotle] |
| 12379 | You cannot understand anything through perception [Aristotle] |
| 16725 | Some knowledge is lost if you lose a sense, and there is no way the knowledge can be replaced [Aristotle] |
| 1693 | Animals may have some knowledge if they retain perception, but understanding requires reasons to be given [Aristotle] |
| 23309 | Aristotle's concepts of understanding and explanation mean he is not a pure empiricist [Aristotle, by Frede,M] |
| 9067 | Many memories of the same item form a single experience [Aristotle] |
| 1671 | Sceptics say justification is an infinite regress, or it stops at the unknowable [Aristotle] |
| 1670 | When you understand basics, you can't be persuaded to change your mind [Aristotle] |
| 12900 | How could 'S knows he has hands' not have a fixed content? [Bach] |
| 12901 | If contextualism is right, knowledge sentences are baffling out of their context [Bach] |
| 12902 | Sceptics aren't changing the meaning of 'know', but claiming knowing is tougher than we think [Bach] |
| 12147 | The principles of demonstrations are definitions [Aristotle] |
| 12383 | There must be definitions before demonstration is possible [Aristotle] |
| 24068 | Demonstration is more than entailment, as the explanatory order must match the causal order [Aristotle, by Koslicki] |
| 17310 | Aristotle gets asymmetric consequence from demonstration, which reflects real causal priority [Aristotle, by Koslicki] |
| 21359 | Aristotle doesn't actually apply his theory of demonstration to his practical science [Leroi on Aristotle] |
| 12365 | We can know by demonstration, which is a scientific deduction leading to understanding [Aristotle] |
| 1667 | Premises must be true, primitive and immediate, and prior to and explanatory of conclusions [Aristotle] |
| 10918 | Demonstrative understanding rests on necessary features of the thing in itself [Aristotle] |
| 12374 | Demonstrations must be necessary, and that depends on the middle term [Aristotle] |
| 12148 | Demonstrations are syllogisms which give explanations [Aristotle] |
| 1691 | Aim to get definitions of the primitive components, thus establishing the kind, and work towards the attributes [Aristotle] |
| 12371 | A demonstration is a deduction which proceeds from necessities [Aristotle] |
| 1674 | All demonstration is concerned with existence, axioms and properties [Aristotle] |
| 1679 | Universal demonstrations are about thought; particular demonstrations lead to perceptions [Aristotle] |
| 1680 | Demonstration is better with fewer presuppositions, and it is quicker if these are familiar [Aristotle] |
| 1683 | We learn universals from many particulars [Aristotle] |
| 12380 | Universals are valuable because they make the explanations plain [Aristotle] |
| 12367 | What is most universal is furthest away, and the particulars are nearest [Aristotle] |
| 12385 | Are particulars explained more by universals, or by other particulars? [Aristotle] |
| 1689 | Explanation is of the status of a thing, inferences to it, initiation of change, and purpose [Aristotle] |
| 1686 | What we seek and understand are facts, reasons, existence, and identity [Aristotle] |
| 12357 | Explanation and generality are inseparable [Aristotle, by Wedin] |
| 1669 | The foundation or source is stronger than the thing it causes [Aristotle] |
| 1678 | Universals give better explanations, because they are self-explanatory and primitive [Aristotle] |
| 10998 | The mind abstracts ways things might be, which are nonetheless real [Read] |
| 9068 | Perception creates primitive immediate principles by building a series of firm concepts [Aristotle] |
| 9069 | A perception lodging in the soul creates a primitive universal, which becomes generalised [Aristotle] |
| 9070 | We learn primitives and universals by induction from perceptions [Aristotle] |
| 11005 | Negative existentials with compositionality make the whole sentence meaningless [Read] |
| 10966 | A proposition objectifies what a sentence says, as indicative, with secure references [Read] |
| 12368 | Negation takes something away from something [Aristotle] |
| 1692 | If you shouldn't argue in metaphors, then you shouldn't try to define them either [Aristotle] |
| 12375 | Whatever holds of a kind intrinsically holds of it necessarily [Aristotle] |
| 1688 | Properties must be proved, but not essence; but existents are not a kind, so existence isn't part of essence [Aristotle] |