81 ideas
12274 | Begin examination with basics, and subdivide till you can go no further [Aristotle] |
12260 | Dialectic starts from generally accepted opinions [Aristotle] |
12291 | There can't be one definition of two things, or two definitions of the same thing [Aristotle] |
12292 | Definitions are easily destroyed, since they can contain very many assertions [Aristotle] |
12261 | Differentia are generic, and belong with genus [Aristotle] |
12263 | 'Genus' is part of the essence shared among several things [Aristotle] |
12272 | We describe the essence of a particular thing by means of its differentiae [Aristotle] |
12279 | The differentia indicate the qualities, but not the essence [Aristotle] |
12283 | In definitions the first term to be assigned ought to be the genus [Aristotle] |
12289 | The genera and the differentiae are part of the essence [Aristotle] |
12285 | The definition is peculiar to one thing, not common to many [Aristotle] |
13689 | 'Theorems' are formulas provable from no premises at all [Sider] |
13705 | Truth tables assume truth functionality, and are just pictures of truth functions [Sider] |
13706 | Intuitively, deontic accessibility seems not to be reflexive, but to be serial [Sider] |
13710 | In D we add that 'what is necessary is possible'; then tautologies are possible, and contradictions not necessary [Sider] |
13711 | System B introduces iterated modalities [Sider] |
13708 | S5 is the strongest system, since it has the most valid formulas, because it is easy to be S5-valid [Sider] |
13712 | Epistemic accessibility is reflexive, and allows positive and negative introspection (KK and K¬K) [Sider] |
13714 | We can treat modal worlds as different times [Sider] |
13720 | Converse Barcan Formula: □∀αφ→∀α□φ [Sider] |
13718 | The Barcan Formula ∀x□Fx→□∀xFx may be a defect in modal logic [Sider] |
13723 | System B is needed to prove the Barcan Formula [Sider] |
13715 | You can employ intuitionist logic without intuitionism about mathematics [Sider] |
13678 | The most popular account of logical consequence is the semantic or model-theoretic one [Sider] |
13682 | Maybe logical consequence is impossibility of the premises being true and the consequent false [Sider] |
13680 | Maybe logical consequence is a primitive notion [Sider] |
13679 | Maybe logical consequence is more a matter of provability than of truth-preservation [Sider] |
13722 | A 'theorem' is an axiom, or the last line of a legitimate proof [Sider] |
13696 | When a variable is 'free' of the quantifier, the result seems incapable of truth or falsity [Sider] |
13700 | A 'total' function must always produce an output for a given domain [Sider] |
13703 | λ can treat 'is cold and hungry' as a single predicate [Sider] |
13688 | Good axioms should be indisputable logical truths [Sider] |
13687 | No assumptions in axiomatic proofs, so no conditional proof or reductio [Sider] |
13691 | Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step' [Sider] |
13690 | Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms [Sider] |
13685 | Natural deduction helpfully allows reasoning with assumptions [Sider] |
13686 | We can build proofs just from conclusions, rather than from plain formulae [Sider] |
13697 | Valuations in PC assign truth values to formulas relative to variable assignments [Sider] |
13684 | The semantical notion of a logical truth is validity, being true in all interpretations [Sider] |
13704 | It is hard to say which are the logical truths in modal logic, especially for iterated modal operators [Sider] |
13724 | In model theory, first define truth, then validity as truth in all models, and consequence as truth-preservation [Sider] |
13698 | In a complete logic you can avoid axiomatic proofs, by using models to show consequences [Sider] |
13699 | Compactness surprisingly says that no contradictions can emerge when the set goes infinite [Sider] |
11261 | Puzzles arise when reasoning seems equal on both sides [Aristotle] |
12273 | Unit is the starting point of number [Aristotle] |
13701 | A single second-order sentence validates all of arithmetic - but this can't be proved axiomatically [Sider] |
13692 | A 'precisification' of a trivalent interpretation reduces it to a bivalent interpretation [Sider] |
13693 | A 'supervaluation' assigns further Ts and Fs, if they have been assigned in every precisification [Sider] |
13695 | Supervaluational logic is classical, except when it adds the 'Definitely' operator [Sider] |
13694 | We can 'sharpen' vague terms, and then define truth as true-on-all-sharpenings [Sider] |
12267 | There are ten categories: essence, quantity, quality, relation, place, time, position, state, activity, passivity [Aristotle] |
13683 | A relation is a feature of multiple objects taken together [Sider] |
12282 | An individual property has to exist (in past, present or future) [Aristotle] |
12264 | An 'accident' is something which may possibly either belong or not belong to a thing [Aristotle] |
12280 | Genus gives the essence better than the differentiae do [Aristotle] |
13269 | In the case of a house the parts can exist without the whole, so parts are not the whole [Aristotle] |
12284 | Everything that is has one single essence [Aristotle] |
13074 | Only natural kinds and their members have real essences [Suárez, by Cover/O'Leary-Hawthorne] |
12262 | An 'idion' belongs uniquely to a thing, but is not part of its essence [Aristotle] |
12290 | Destruction is dissolution of essence [Aristotle] |
12286 | If two things are the same, they must have the same source and origin [Aristotle] |
13702 | The identity of indiscernibles is necessarily true, if being a member of some set counts as a property [Sider] |
12266 | 'Same' is mainly for names or definitions, but also for propria, and for accidents [Aristotle] |
12287 | Two identical things have the same accidents, they are the same; if the accidents differ, they're different [Aristotle] |
12288 | Numerical sameness and generic sameness are not the same [Aristotle] |
13721 | 'Strong' necessity in all possible worlds; 'weak' necessity in the worlds where the relevant objects exist [Sider] |
13707 | Maybe metaphysical accessibility is intransitive, if a world in which I am a frog is impossible [Sider] |
12259 | Reasoning is when some results follow necessarily from certain claims [Aristotle] |
13709 | Logical truths must be necessary if anything is [Sider] |
13716 | 'If B hadn't shot L someone else would have' if false; 'If B didn't shoot L, someone else did' is true [Sider] |
13717 | Transworld identity is not a problem in de dicto sentences, which needn't identify an individual [Sider] |
13719 | Barcan Formula problem: there might have been a ghost, despite nothing existing which could be a ghost [Sider] |
12271 | Induction is the progress from particulars to universals [Aristotle] |
12293 | We say 'so in cases of this kind', but how do you decide what is 'of this kind'? [Aristotle] |
12276 | Justice and self-control are better than courage, because they are always useful [Aristotle] |
12277 | Friendship is preferable to money, since its excess is preferable [Aristotle] |
12275 | We value friendship just for its own sake [Aristotle] |
12281 | Man is intrinsically a civilized animal [Aristotle] |
12265 | All water is the same, because of a certain similarity [Aristotle] |
7563 | The old 'influx' view of causation says it is a flow of accidental properties from A to B [Suárez, by Jolley] |
12278 | 'Being' and 'oneness' are predicated of everything which exists [Aristotle] |