111 ideas
| 8952 | We reach 'reflective equilibrium' when intuitions and theory completely align [Fisher] |
| 16841 | Good inference has mechanism, precision, scope, simplicity, fertility and background fit [Lipton] |
| 16854 | Contrary pairs entail contradictions; one member entails negation of the other [Lipton] |
| 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] |
| 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] |
| 8943 | Three-valued logic says excluded middle and non-contradition are not tautologies [Fisher] |
| 8945 | Fuzzy logic has many truth values, ranging in fractions from 0 to 1 [Fisher] |
| 8951 | Classical logic is: excluded middle, non-contradiction, contradictions imply all, disjunctive syllogism [Fisher] |
| 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] |
| 8950 | Logic formalizes how we should reason, but it shouldn't determine whether we are realists [Fisher] |
| 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] |
| 13687 | No assumptions in axiomatic proofs, so no conditional proof or reductio [Sider] |
| 13688 | Good axioms should be indisputable logical truths [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] |
| 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] |
| 8946 | We could make our intuitions about heaps precise with a million-valued logic [Fisher] |
| 13683 | A relation is a feature of multiple objects taken together [Sider] |
| 8944 | Vagueness can involve components (like baldness), or not (like boredom) [Fisher] |
| 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] |
| 8941 | We can't explain 'possibility' in terms of 'possible' worlds [Fisher] |
| 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] |
| 8947 | If all truths are implied by a falsehood, then not-p might imply both q and not-q [Fisher] |
| 8949 | In relevance logic, conditionals help information to flow from antecedent to consequent [Fisher] |
| 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] |
| 16814 | Understanding is not mysterious - it is just more knowledge, of causes [Lipton] |
| 16825 | How do we distinguish negative from irrelevant evidence, if both match the hypothesis? [Lipton] |
| 16851 | The inference to observables and unobservables is almost the same, so why distinguish them? [Lipton] |
| 16798 | We infer from evidence by working out what would explain that evidence [Lipton] |
| 16799 | Inductive inference is not proof, but weighing evidence and probability [Lipton] |
| 16856 | It is more impressive that relativity predicted Mercury's orbit than if it had accommodated it [Lipton] |
| 16857 | Predictions are best for finding explanations, because mere accommodations can be fudged [Lipton] |
| 16827 | If we make a hypothesis about data, then a deduction, where does the hypothesis come from? [Lipton] |
| 16804 | Induction is repetition, instances, deduction, probability or causation [Lipton] |
| 16823 | Standard induction does not allow for vertical inferences, to some unobservable lower level [Lipton] |
| 16858 | We can argue to support our beliefs, so induction will support induction, for believers in induction [Lipton] |
| 16800 | An inductive inference is underdetermined, by definition [Lipton] |
| 16832 | If something in ravens makes them black, it may be essential (definitive of ravens) [Lipton] |
| 16836 | My shoes are not white because they lack some black essence of ravens [Lipton] |
| 16831 | A theory may explain the blackness of a raven, but say nothing about the whiteness of shoes [Lipton] |
| 16833 | We can't turn non-black non-ravens into ravens, to test the theory [Lipton] |
| 16834 | To pick a suitable contrast to ravens, we need a hypothesis about their genes [Lipton] |
| 16801 | A hypothesis is confirmed if an unlikely prediction comes true [Lipton] |
| 16802 | Bayes seems to rule out prior evidence, since that has a probability of one [Lipton] |
| 16803 | Bayes is too liberal, since any logical consequence of a hypothesis confirms it [Lipton] |
| 16837 | Bayes involves 'prior' probabilities, 'likelihood', 'posterior' probability, and 'conditionalising' [Lipton] |
| 16839 | Explanation may be an important part of implementing Bayes's Theorem [Lipton] |
| 16850 | Explanation may describe induction, but may not show how it justifies, or leads to truth [Lipton] |
| 16807 | An explanation gives the reason the phenomenon occurred [Lipton] |
| 16808 | An explanation is what makes the unfamiliar familiar to us [Lipton] |
| 16806 | An explanation is what is added to knowledge to yield understanding [Lipton] |
| 16822 | Seaching for explanations is a good way to discover the structure of the world [Lipton] |
| 16816 | In 'contrastive' explanation there is a fact and a foil - why that fact, rather than this foil? [Lipton] |
| 16826 | With too many causes, find a suitable 'foil' for contrast, and the field narrows right down [Lipton] |
| 16811 | An explanation unifies a phenomenon with our account of other phenomena [Lipton] |
| 16810 | Deduction explanation is too easy; any law at all will imply the facts - together with the facts! [Lipton] |
| 16829 | We reject deductive explanations if they don't explain, not if the deduction is bad [Lipton] |
| 16809 | Good explanations may involve no laws and no deductions [Lipton] |
| 16812 | An explanation shows why it was necessary that the effect occurred [Lipton] |
| 16813 | To explain is to give either the causal history, or the causal mechanism [Lipton] |
| 16815 | Mathematical and philosophical explanations are not causal [Lipton] |
| 16846 | A cause may not be an explanation [Lipton] |
| 16849 | Explanations may be easier to find than causes [Lipton] |
| 16848 | Causal inferences are clearest when we can manipulate things [Lipton] |
| 16842 | We want to know not just the cause, but how the cause operated [Lipton] |
| 16840 | To maximise probability, don't go beyond your data [Lipton] |
| 16824 | Is Inference to the Best Explanation nothing more than inferring the likeliest cause? [Lipton] |
| 16817 | Best Explanation as a guide to inference is preferable to best standard explanations [Lipton] |
| 16818 | The 'likeliest' explanation is the best supported; the 'loveliest' gives the most understanding [Lipton] |
| 16820 | Finding the 'loveliest' potential explanation links truth to understanding [Lipton] |
| 16819 | IBE is inferring that the best potential explanation is the actual explanation [Lipton] |
| 16828 | IBE is not passive treatment of data, but involves feedback between theory and data search [Lipton] |
| 16844 | A contrasting difference is the cause if it offers the best explanation [Lipton] |
| 16853 | We select possible explanations for explanatory reasons, as well as choosing among them [Lipton] |
| 16821 | Must we only have one explanation, and must all the data be made relevant? [Lipton] |
| 16838 | Bayesians say best explanations build up an incoherent overall position [Lipton] |
| 16855 | The best theory is boring: compare 'all planets move elliptically' with 'most of them do' [Lipton] |
| 16852 | Best explanation can't be a guide to truth, because the truth must precede explanation [Lipton] |
| 16847 | Counterfactual causation makes causes necessary but not sufficient [Lipton] |