75 ideas
16539 | A definition of a circle will show what it is, and show its generating principle [Lowe] |
16540 | Defining an ellipse by conic sections reveals necessities, but not the essence of an ellipse [Lowe] |
16548 | An essence is what an entity is, revealed by a real definition; this is not an entity in its own right [Lowe] |
16549 | Simple things like 'red' can be given real ostensive definitions [Lowe] |
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] |
13679 | Maybe logical consequence is more a matter of provability than of truth-preservation [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] |
13722 | A 'theorem' is an axiom, or the last line of a legitimate proof [Sider] |
8195 | Undecidable statements result from quantifying over infinites, subjunctive conditionals, and the past tense [Dummett] |
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] |
13690 | Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms [Sider] |
13691 | Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step' [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] |
8194 | Surely there is no exact single grain that brings a heap into existence [Dummett] |
13701 | A single second-order sentence validates all of arithmetic - but this can't be proved axiomatically [Sider] |
8190 | Intuitionists rely on the proof of mathematical statements, not their truth [Dummett] |
8198 | A 'Cambridge Change' is like saying 'the landscape changes as you travel east' [Dummett] |
8192 | I no longer think what a statement about the past says is just what can justify it [Dummett] |
13692 | A 'precisification' of a trivalent interpretation reduces it to a bivalent interpretation [Sider] |
13695 | Supervaluational logic is classical, except when it adds the 'Definitely' operator [Sider] |
13693 | A 'supervaluation' assigns further Ts and Fs, if they have been assigned in every precisification [Sider] |
13694 | We can 'sharpen' vague terms, and then define truth as true-on-all-sharpenings [Sider] |
13683 | A relation is a feature of multiple objects taken together [Sider] |
16545 | The essence of lumps and statues shows that two objects coincide but are numerically distinct [Lowe] |
16546 | The essence of a bronze statue shows that it could be made of different bronze [Lowe] |
16551 | Grasping an essence is just grasping a real definition [Lowe] |
16542 | Explanation can't give an account of essence, because it is too multi-faceted [Lowe] |
16552 | If we must know some entity to know an essence, we lack a faculty to do that [Lowe] |
13702 | The identity of indiscernibles is necessarily true, if being a member of some set counts as a property [Sider] |
16533 | Logical necessities, based on laws of logic, are a proper sub-class of metaphysical necessities [Lowe] |
13721 | 'Strong' necessity in all possible worlds; 'weak' necessity in the worlds where the relevant objects exist [Sider] |
16531 | 'Metaphysical' necessity is absolute and objective - the strongest kind of necessity [Lowe] |
13707 | Maybe metaphysical accessibility is intransitive, if a world in which I am a frog is impossible [Sider] |
13709 | Logical truths must be necessary if anything is [Sider] |
16532 | 'Epistemic' necessity is better called 'certainty' [Lowe] |
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] |
16543 | If an essence implies p, then p is an essential truth, and hence metaphysically necessary [Lowe] |
16544 | Metaphysical necessity is either an essential truth, or rests on essential truths [Lowe] |
16538 | We could give up possible worlds if we based necessity on essences [Lowe] |
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] |
8199 | The existence of a universe without sentience or intelligence is an unintelligible fantasy [Dummett] |
16534 | 'Intuitions' are just unreliable 'hunches'; over centuries intuitions change enormously [Lowe] |
16535 | A concept is a way of thinking of things or kinds, whether or not they exist [Lowe] |
8193 | Verification is not an individual but a collective activity [Dummett] |
16550 | Direct reference doesn't seem to require that thinkers know what it is they are thinking about [Lowe] |
8189 | Truth-condition theorists must argue use can only be described by appeal to conditions of truth [Dummett] |
8191 | The truth-conditions theory must get agreement on a conception of truth [Dummett] |
16547 | H2O isn't necessary, because different laws of nature might affect how O and H combine [Lowe] |
8197 | Maybe past (which affects us) and future (which we can affect) are both real [Dummett] |
8196 | The present cannot exist alone as a mere boundary; past and future truths are rendered meaningless [Dummett] |