81 ideas
13567 | Ontology should give insight into or an explanation of the world revealed by science [Ellis] |
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] |
13710 | In D we add that 'what is necessary is possible'; then tautologies are possible, and contradictions not necessary [Sider] |
13706 | Intuitively, deontic accessibility seems not to be reflexive, but to be serial [Sider] |
13711 | System B introduces iterated modalities [Sider] |
13604 | Real possibility and necessity has the logic of S5, which links equivalence classes of worlds of the same kind [Ellis] |
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] |
13680 | Maybe logical consequence is a primitive notion [Sider] |
13679 | Maybe logical consequence is more a matter of provability than of truth-preservation [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] |
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] |
13606 | Humean conceptions of reality drive the adoption of extensional logic [Ellis] |
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] |
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] |
13683 | A relation is a feature of multiple objects taken together [Sider] |
13584 | The extension of a property is a contingent fact, so cannot be the essence of the property [Ellis] |
13587 | There is no property of 'fragility', as things are each fragile in a distinctive way [Ellis] |
13577 | Typical 'categorical' properties are spatio-temporal, such as shape [Ellis] |
9436 | The property of 'being an electron' is not of anything, and only electrons could have it [Ellis] |
13582 | 'Being a methane molecule' is not a property - it is just a predicate [Ellis] |
13580 | Causal powers must necessarily act the way they do [Ellis] |
13598 | Causal powers are often directional (e.g. centripetal, centrifugal, circulatory) [Ellis] |
13568 | Basic powers may not be explained by structure, if at the bottom level there is no structure [Ellis] |
13586 | Maybe dispositions can be explained by intrinsic properties or structures [Ellis] |
13585 | The most fundamental properties of nature (mass, charge, spin ...) all seem to be dispositions [Ellis] |
13596 | A causal power is a disposition to produce forces [Ellis] |
13599 | Powers are dispositions of the essences of kinds that involve them in causation [Ellis] |
13572 | There are 'substantive' (objects of some kind), 'dynamic' (events of some kind) and 'property' universals [Ellis] |
13573 | Universals are all types of natural kind [Ellis] |
13571 | Scientific essentialism doesn't really need Kripkean individual essences [Ellis] |
13578 | The old idea that identity depends on essence and behaviour is rejected by the empiricists [Ellis] |
13702 | The identity of indiscernibles is necessarily true, if being a member of some set counts as a property [Sider] |
13576 | Necessities are distinguished by their grounds, not their different modalities [Ellis] |
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] |
13570 | Individual essences necessitate that individual; natural kind essences necessitate kind membership [Ellis] |
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] |
13607 | If events are unconnected, then induction cannot be solved [Ellis] |
13597 | Good explanations unify [Ellis] |
13601 | Explanations of particular events are not essentialist, as they don't reveal essential structures [Ellis] |
13569 | To give essentialist explanations there have to be natural kinds [Ellis] |
13600 | The point of models in theories is not to idealise, but to focus on what is essential [Ellis] |
22511 | Some reasonings are stronger than we are [Philolaus] |
13583 | There might be uninstantiated natural kinds, such as transuranic elements which have never occurred [Ellis] |
13574 | Natural kinds are distinguished by resting on essences [Ellis] |
13575 | If there are borderline cases between natural kinds, that makes them superficial [Ellis] |
13595 | Laws don't exist in the world; they are true of the world [Ellis] |
13566 | A proton must have its causal role, because without it it wouldn't be a proton [Ellis] |
13579 | What is most distinctive of scientific essentialism is regarding processes as natural kinds [Ellis] |
13581 | Scientific essentialism is more concerned with explanation than with identity (Locke, not Kripke) [Ellis] |
13594 | The ontological fundamentals are dispositions, and also categorical (spatio-temporal and structural) properties [Ellis] |
13603 | A primary aim of science is to show the limits of the possible [Ellis] |