102 ideas
21959 | Metaphysics is the most general attempt to make sense of things [Moore,AW] |
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] |
9738 | Each line of a truth table is a model [Fitting/Mendelsohn] |
9727 | Modal logic adds □ (necessarily) and ◊ (possibly) to classical logic [Fitting/Mendelsohn] |
9726 | We let 'R' be the accessibility relation: xRy is read 'y is accessible from x' [Fitting/Mendelsohn] |
9737 | The symbol ||- is the 'forcing' relation; 'Γ ||- P' means that P is true in world Γ [Fitting/Mendelsohn] |
13136 | The prefix σ names a possible world, and σ.n names a world accessible from that one [Fitting/Mendelsohn] |
13727 | A 'constant' domain is the same for all worlds; 'varying' domains can be entirely separate [Fitting/Mendelsohn] |
9734 | Modern modal logic introduces 'accessibility', saying xRy means 'y is accessible from x' [Fitting/Mendelsohn] |
9736 | A 'model' is a frame plus specification of propositions true at worlds, written < G,R,||- > [Fitting/Mendelsohn] |
9735 | A 'frame' is a set G of possible worlds, with an accessibility relation R, written < G,R > [Fitting/Mendelsohn] |
9741 | Accessibility relations can be 'reflexive' (self-referring), 'transitive' (carries over), or 'symmetric' (mutual) [Fitting/Mendelsohn] |
13149 | S5: a) if n ◊X then kX b) if n ¬□X then k ¬X c) if n □X then k X d) if n ¬◊X then k ¬X [Fitting/Mendelsohn] |
13141 | Negation: if σ ¬¬X then σ X [Fitting/Mendelsohn] |
13138 | Disj: a) if σ ¬(X∨Y) then σ ¬X and σ ¬Y b) if σ X∨Y then σ X or σ Y [Fitting/Mendelsohn] |
13142 | Existential: a) if σ ◊X then σ.n X b) if σ ¬□X then σ.n ¬X [n is new] [Fitting/Mendelsohn] |
13144 | T reflexive: a) if σ □X then σ X b) if σ ¬◊X then σ ¬X [Fitting/Mendelsohn] |
13145 | D serial: a) if σ □X then σ ◊X b) if σ ¬◊X then σ ¬□X [Fitting/Mendelsohn] |
13146 | B symmetric: a) if σ.n □X then σ X b) if σ.n ¬◊X then σ ¬X [n occurs] [Fitting/Mendelsohn] |
13147 | 4 transitive: a) if σ □X then σ.n □X b) if σ ¬◊X then σ.n ¬◊X [n occurs] [Fitting/Mendelsohn] |
13148 | 4r rev-trans: a) if σ.n □X then σ □X b) if σ.n ¬◊X then σ ¬◊X [n occurs] [Fitting/Mendelsohn] |
9740 | If a proposition is possibly true in a world, it is true in some world accessible from that world [Fitting/Mendelsohn] |
9739 | If a proposition is necessarily true in a world, it is true in all worlds accessible from that world [Fitting/Mendelsohn] |
13137 | Conj: a) if σ X∧Y then σ X and σ Y b) if σ ¬(X∧Y) then σ ¬X or σ ¬Y [Fitting/Mendelsohn] |
13140 | Bicon: a)if σ(X↔Y) then σ(X→Y) and σ(Y→X) b) [not biconditional, one or other fails] [Fitting/Mendelsohn] |
13139 | Implic: a) if σ ¬(X→Y) then σ X and σ ¬Y b) if σ X→Y then σ ¬X or σ Y [Fitting/Mendelsohn] |
13143 | Universal: a) if σ ¬◊X then σ.m ¬X b) if σ □X then σ.m X [m exists] [Fitting/Mendelsohn] |
9742 | The system K has no accessibility conditions [Fitting/Mendelsohn] |
13114 | □P → P is not valid in D (Deontic Logic), since an obligatory action may be not performed [Fitting/Mendelsohn] |
9743 | The system D has the 'serial' conditon imposed on its accessibility relation [Fitting/Mendelsohn] |
9744 | The system T has the 'reflexive' conditon imposed on its accessibility relation [Fitting/Mendelsohn] |
9746 | The system K4 has the 'transitive' condition on its accessibility relation [Fitting/Mendelsohn] |
9745 | The system B has the 'reflexive' and 'symmetric' conditions on its accessibility relation [Fitting/Mendelsohn] |
9747 | The system S4 has the 'reflexive' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn] |
9748 | System S5 has the 'reflexive', 'symmetric' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn] |
9404 | Modality affects content, because P→◊P is valid, but ◊P→P isn't [Fitting/Mendelsohn] |
13112 | In epistemic logic knowers are logically omniscient, so they know that they know [Fitting/Mendelsohn] |
13111 | Read epistemic box as 'a knows/believes P' and diamond as 'for all a knows/believes, P' [Fitting/Mendelsohn] |
13113 | F: will sometime, P: was sometime, G: will always, H: was always [Fitting/Mendelsohn] |
13728 | The Barcan says nothing comes into existence; the Converse says nothing ceases; the pair imply stability [Fitting/Mendelsohn] |
13729 | The Barcan corresponds to anti-monotonicity, and the Converse to monotonicity [Fitting/Mendelsohn] |
9725 | 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn] |
13730 | The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn] |
13725 | □ must be sensitive as to whether it picks out an object by essential or by contingent properties [Fitting/Mendelsohn] |
13731 | Objects retain their possible properties across worlds, so a bundle theory of them seems best [Fitting/Mendelsohn] |
13726 | Counterpart relations are neither symmetric nor transitive, so there is no logic of equality for them [Fitting/Mendelsohn] |
16814 | Understanding is not mysterious - it is just more knowledge, of causes [Lipton] |
21958 | Appearances are nothing beyond representations, which is transcendental ideality [Moore,AW] |
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] |
16799 | Inductive inference is not proof, but weighing evidence and probability [Lipton] |
16798 | We infer from evidence by working out what would explain that evidence [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] |
16800 | An inductive inference is underdetermined, by definition [Lipton] |
16858 | We can argue to support our beliefs, so induction will support induction, for believers in induction [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] |
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] |
16801 | A hypothesis is confirmed if an unlikely prediction comes true [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] |
16846 | A cause may not be an explanation [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] |
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] |
16819 | IBE is inferring that the best potential explanation is the actual explanation [Lipton] |
16820 | Finding the 'loveliest' potential explanation links truth to understanding [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] |