85 ideas
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] |
15413 | With four tense operators, all complex tenses reduce to fourteen basic cases [Burgess] |
15415 | The temporal Barcan formulas fix what exists, which seems absurd [Burgess] |
15430 | Is classical logic a part of intuitionist logic, or vice versa? [Burgess] |
15431 | It is still unsettled whether standard intuitionist logic is complete [Burgess] |
15429 | Relevance logic's → is perhaps expressible by 'if A, then B, for that reason' [Burgess] |
15404 | Technical people see logic as any formal system that can be studied, not a study of argument validity [Burgess] |
15405 | Classical logic neglects the non-mathematical, such as temporality or modality [Burgess] |
15421 | Classical logic neglects counterfactuals, temporality and modality, because maths doesn't use them [Burgess] |
15427 | The Cut Rule expresses the classical idea that entailment is transitive [Burgess] |
15403 | Philosophical logic is a branch of logic, and is now centred in computer science [Burgess] |
15407 | Formalising arguments favours lots of connectives; proving things favours having very few [Burgess] |
15424 | Asserting a disjunction from one disjunct seems odd, but can be sensible, and needed in maths [Burgess] |
15409 | All occurrences of variables in atomic formulas are free [Burgess] |
15414 | The denotation of a definite description is flexible, rather than rigid [Burgess] |
15406 | 'Induction' and 'recursion' on complexity prove by connecting a formula to its atomic components [Burgess] |
15426 | We can build one expanding sequence, instead of a chain of deductions [Burgess] |
15425 | The sequent calculus makes it possible to have proof without transitivity of entailment [Burgess] |
15408 | 'Tautologies' are valid formulas of classical sentential logic - or substitution instances in other logics [Burgess] |
15418 | Validity (for truth) and demonstrability (for proof) have correlates in satisfiability and consistency [Burgess] |
15411 | We only need to study mathematical models, since all other models are isomorphic to these [Burgess] |
15412 | Models leave out meaning, and just focus on truth values [Burgess] |
15416 | We aim to get the technical notion of truth in all models matching intuitive truth in all instances [Burgess] |
15428 | The Liar seems like a truth-value 'gap', but dialethists see it as a 'glut' [Burgess] |
15420 | De re modality seems to apply to objects a concept intended for sentences [Burgess] |
15417 | Logical necessity has two sides - validity and demonstrability - which coincide in classical logic [Burgess] |
15419 | General consensus is S5 for logical modality of validity, and S4 for proof [Burgess] |
15423 | It is doubtful whether the negation of a conditional has any clear meaning [Burgess] |
15422 | Three conditionals theories: Materialism (material conditional), Idealism (true=assertable), Nihilism (no truth) [Burgess] |
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] |
1556 | By nature people are close to one another, but culture drives them apart [Hippias] |
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] |