117 ideas
| 7911 | Theory vanishes when one has obtained wisdom [Rahulabhadra] |
| 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] |
| 12075 | An Aristotelian definition is causal [Aristotle, by Witt] |
| 12384 | Definition by division needs predicates, which are well ordered and thorough [Aristotle] |
| 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] |
| 1668 | An axiom is a principle which must be understood if one is to learn anything [Aristotle] |
| 9738 | Each line of a truth table is a model [Fitting/Mendelsohn] |
| 9727 | Modal logic adds □ (necessarily) and ◊ (possibly) to classical logic [Fitting/Mendelsohn] |
| 9726 | We let 'R' be the accessibility relation: xRy is read 'y is accessible from x' [Fitting/Mendelsohn] |
| 9737 | The symbol ||- is the 'forcing' relation; 'Γ ||- P' means that P is true in world Γ [Fitting/Mendelsohn] |
| 13136 | The prefix σ names a possible world, and σ.n names a world accessible from that one [Fitting/Mendelsohn] |
| 13727 | A 'constant' domain is the same for all worlds; 'varying' domains can be entirely separate [Fitting/Mendelsohn] |
| 9734 | Modern modal logic introduces 'accessibility', saying xRy means 'y is accessible from x' [Fitting/Mendelsohn] |
| 9736 | A 'model' is a frame plus specification of propositions true at worlds, written < G,R,||- > [Fitting/Mendelsohn] |
| 9735 | A 'frame' is a set G of possible worlds, with an accessibility relation R, written < G,R > [Fitting/Mendelsohn] |
| 9741 | Accessibility relations can be 'reflexive' (self-referring), 'transitive' (carries over), or 'symmetric' (mutual) [Fitting/Mendelsohn] |
| 9740 | If a proposition is possibly true in a world, it is true in some world accessible from that world [Fitting/Mendelsohn] |
| 9739 | If a proposition is necessarily true in a world, it is true in all worlds accessible from that world [Fitting/Mendelsohn] |
| 13137 | Conj: a) if σ X∧Y then σ X and σ Y b) if σ ¬(X∧Y) then σ ¬X or σ ¬Y [Fitting/Mendelsohn] |
| 13140 | Bicon: a)if σ(X↔Y) then σ(X→Y) and σ(Y→X) b) [not biconditional, one or other fails] [Fitting/Mendelsohn] |
| 13139 | Implic: a) if σ ¬(X→Y) then σ X and σ ¬Y b) if σ X→Y then σ ¬X or σ Y [Fitting/Mendelsohn] |
| 13143 | Universal: a) if σ ¬◊X then σ.m ¬X b) if σ □X then σ.m X [m exists] [Fitting/Mendelsohn] |
| 13141 | Negation: if σ ¬¬X then σ X [Fitting/Mendelsohn] |
| 13138 | Disj: a) if σ ¬(X∨Y) then σ ¬X and σ ¬Y b) if σ X∨Y then σ X or σ Y [Fitting/Mendelsohn] |
| 13142 | Existential: a) if σ ◊X then σ.n X b) if σ ¬□X then σ.n ¬X [n is new] [Fitting/Mendelsohn] |
| 13144 | T reflexive: a) if σ □X then σ X b) if σ ¬◊X then σ ¬X [Fitting/Mendelsohn] |
| 13145 | D serial: a) if σ □X then σ ◊X b) if σ ¬◊X then σ ¬□X [Fitting/Mendelsohn] |
| 13146 | B symmetric: a) if σ.n □X then σ X b) if σ.n ¬◊X then σ ¬X [n occurs] [Fitting/Mendelsohn] |
| 13147 | 4 transitive: a) if σ □X then σ.n □X b) if σ ¬◊X then σ.n ¬◊X [n occurs] [Fitting/Mendelsohn] |
| 13148 | 4r rev-trans: a) if σ.n □X then σ □X b) if σ.n ¬◊X then σ ¬◊X [n occurs] [Fitting/Mendelsohn] |
| 13149 | S5: a) if n ◊X then kX b) if n ¬□X then k ¬X c) if n □X then k X d) if n ¬◊X then k ¬X [Fitting/Mendelsohn] |
| 9742 | The system K has no accessibility conditions [Fitting/Mendelsohn] |
| 13114 | □P → P is not valid in D (Deontic Logic), since an obligatory action may be not performed [Fitting/Mendelsohn] |
| 9743 | The system D has the 'serial' conditon imposed on its accessibility relation [Fitting/Mendelsohn] |
| 9744 | The system T has the 'reflexive' conditon imposed on its accessibility relation [Fitting/Mendelsohn] |
| 9746 | The system K4 has the 'transitive' condition on its accessibility relation [Fitting/Mendelsohn] |
| 9745 | The system B has the 'reflexive' and 'symmetric' conditions on its accessibility relation [Fitting/Mendelsohn] |
| 9747 | The system S4 has the 'reflexive' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn] |
| 9748 | System S5 has the 'reflexive', 'symmetric' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn] |
| 9404 | Modality affects content, because P→◊P is valid, but ◊P→P isn't [Fitting/Mendelsohn] |
| 13112 | In epistemic logic knowers are logically omniscient, so they know that they know [Fitting/Mendelsohn] |
| 13111 | Read epistemic box as 'a knows/believes P' and diamond as 'for all a knows/believes, P' [Fitting/Mendelsohn] |
| 13113 | F: will sometime, P: was sometime, G: will always, H: was always [Fitting/Mendelsohn] |
| 13728 | The Barcan says nothing comes into existence; the Converse says nothing ceases; the pair imply stability [Fitting/Mendelsohn] |
| 13729 | The Barcan corresponds to anti-monotonicity, and the Converse to monotonicity [Fitting/Mendelsohn] |
| 12376 | Demonstrations by reductio assume excluded middle [Aristotle] |
| 12373 | Something holds universally when it is proved of an arbitrary and primitive case [Aristotle] |
| 12363 | Everything is either asserted or denied truly [Aristotle] |
| 9725 | 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn] |
| 13004 | Aristotle's axioms (unlike Euclid's) are assumptions awaiting proof [Aristotle, by Leibniz] |
| 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] |
| 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] |
| 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] |
| 13730 | The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn] |
| 12381 | What is necessary cannot be otherwise [Aristotle] |
| 1690 | A stone travels upwards by a forced necessity, and downwards by natural necessity [Aristotle] |
| 13725 | □ must be sensitive as to whether it picks out an object by essential or by contingent properties [Fitting/Mendelsohn] |
| 13731 | Objects retain their possible properties across worlds, so a bundle theory of them seems best [Fitting/Mendelsohn] |
| 13726 | Counterpart relations are neither symmetric nor transitive, so there is no logic of equality for them [Fitting/Mendelsohn] |
| 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] |
| 23309 | Aristotle's concepts of understanding and explanation mean he is not a pure empiricist [Aristotle, by Frede,M] |
| 1693 | Animals may have some knowledge if they retain perception, but understanding requires reasons to be given [Aristotle] |
| 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] |
| 1691 | Aim to get definitions of the primitive components, thus establishing the kind, and work towards the attributes [Aristotle] |
| 12383 | There must be definitions before demonstration is possible [Aristotle] |
| 1674 | All demonstration is concerned with existence, axioms and properties [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] |
| 1667 | Premises must be true, primitive and immediate, and prior to and explanatory of conclusions [Aristotle] |
| 12365 | We can know by demonstration, which is a scientific deduction leading to understanding [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] |
| 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] |
| 12147 | The principles of demonstrations are definitions [Aristotle] |
| 12371 | A demonstration is a deduction which proceeds from necessities [Aristotle] |
| 1683 | We learn universals from many particulars [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] |
| 12380 | Universals are valuable because they make the explanations plain [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] |
| 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] |
| 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] |