78 ideas
| 18390 | All metaphysical discussion should be guided by a quest for truthmakers [Armstrong] |
| 18467 | Truth-making can't be entailment, because truthmakers are portions of reality [Armstrong] |
| 18468 | Armstrong says truthmakers necessitate their truth, where 'necessitate' is a primitive relation [Armstrong, by MacBride] |
| 18377 | Negative truths have as truthmakers all states of affairs relevant to the truth [Armstrong] |
| 18382 | The nature of arctic animals is truthmaker for the absence of penguins there [Armstrong] |
| 18394 | In mathematics, truthmakers are possible instantiations of structures [Armstrong] |
| 18384 | One truthmaker will do for a contingent truth and for its contradictory [Armstrong] |
| 18387 | The truthmakers for possible unicorns are the elements in their combination [Armstrong] |
| 18386 | What is the truthmaker for 'it is possible that there could have been nothing'? [Armstrong] |
| 18381 | Necessitating general truthmakers must also specify their limits [Armstrong] |
| 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] |
| 18396 | The set theory brackets { } assert that the member is a unit [Armstrong] |
| 18393 | For 'there is a class with no members' we don't need the null set as truthmaker [Armstrong] |
| 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] |
| 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] |
| 18392 | Classes have cardinalities, so their members must all be treated as units [Armstrong] |
| 13701 | A single second-order sentence validates all of arithmetic - but this can't be proved axiomatically [Sider] |
| 18385 | Logical atomism builds on the simple properties, but are they the only possible properties? [Armstrong] |
| 18391 | 'Naturalism' says only the world of space-time exists [Armstrong] |
| 18374 | Truthmaking needs states of affairs, to unite particulars with tropes or universals. [Armstrong] |
| 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] |
| 18372 | We need properties, as minimal truthmakers for the truths about objects [Armstrong] |
| 18379 | The determinates of a determinable must be incompatible with each other [Armstrong] |
| 18378 | Length is a 'determinable' property, and one mile is one its 'determinates' [Armstrong] |
| 18373 | If tropes are non-transferable, then they necessarily belong to their particular substance [Armstrong] |
| 18400 | Properties are not powers - they just have powers [Armstrong] |
| 18397 | Powers must result in some non-powers, or there would only be potential without result [Armstrong] |
| 18399 | How does the power of gravity know the distance it acts over? [Armstrong] |
| 18371 | The class of similar things is much too big a truthmaker for the feature of a particular [Armstrong] |
| 18389 | When entities contain entities, or overlap with them, there is 'partial' identity [Armstrong] |
| 13702 | The identity of indiscernibles is necessarily true, if being a member of some set counts as a property [Sider] |
| 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] |
| 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] |
| 18388 | Possible worlds don't fix necessities; intrinsic necessities imply the extension in worlds [Armstrong] |
| 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] |
| 18375 | General truths are a type of negative truth, saying there are no more ravens than black ones [Armstrong] |
| 18368 | For all being, there is a potential proposition which expresses its existence and nature [Armstrong] |
| 18370 | A realm of abstract propositions is causally inert, so has no explanatory value [Armstrong] |
| 18380 | Negative causations supervene on positive causations plus their laws? [Armstrong] |
| 18401 | The pure present moment is too brief to be experienced [Armstrong] |
| 16713 | Philosophers are the forefathers of heretics [Tertullian] |
| 6610 | I believe because it is absurd [Tertullian] |