102 ideas
2797 | As coherence expands its interrelations become steadily tighter, culminating only in necessary truth [Dancy,J] |
2768 | The correspondence theory also has the problem that two sets of propositions might fit the facts equally well [Dancy,J] |
2769 | If one theory is held to be true, all the other theories appear false, because they can't be added to the true one [Dancy,J] |
2765 | Rescher says that if coherence requires mutual entailment, this leads to massive logical redundancy [Dancy,J] |
2766 | Even with a tight account of coherence, there is always the possibility of more than one set of coherent propositions [Dancy,J] |
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] |
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] |
13727 | A 'constant' domain is the same for all worlds; 'varying' domains can be entirely separate [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] |
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] |
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] |
13143 | Universal: a) if σ ¬◊X then σ.m ¬X b) if σ □X then σ.m X [m exists] [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] |
13141 | Negation: if σ ¬¬X then σ X [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] |
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] |
13144 | T reflexive: a) if σ □X then σ X b) if σ ¬◊X then σ ¬X [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] |
13147 | 4 transitive: a) if σ □X then σ.n □X b) if σ ¬◊X then σ.n ¬◊X [n occurs] [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] |
13145 | D serial: a) if σ □X then σ ◊X b) if σ ¬◊X then σ ¬□X [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] |
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] |
13111 | Read epistemic box as 'a knows/believes P' and diamond as 'for all a knows/believes, P' [Fitting/Mendelsohn] |
13112 | In epistemic logic knowers are logically omniscient, so they know that they know [Fitting/Mendelsohn] |
13113 | F: will sometime, P: was sometime, G: will always, H: was always [Fitting/Mendelsohn] |
13729 | The Barcan corresponds to anti-monotonicity, and the Converse to monotonicity [Fitting/Mendelsohn] |
13728 | The Barcan says nothing comes into existence; the Converse says nothing ceases; the pair imply stability [Fitting/Mendelsohn] |
9725 | 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn] |
2781 | Realism says that most perceived objects exist, and have some of their perceived properties [Dancy,J] |
12887 | A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim] |
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] |
2745 | A pupil who lacks confidence may clearly know something but not be certain of it [Dancy,J] |
2755 | If senses are fallible, then being open to correction is an epistemological virtue [Dancy,J] |
5677 | Naïve direct realists hold that objects retain all of their properties when unperceived [Dancy,J] |
5678 | Scientific direct realism says we know some properties of objects directly [Dancy,J] |
5681 | Maybe we are forced from direct into indirect realism by the need to explain perceptual error [Dancy,J] |
5683 | Indirect realism depends on introspection, the time-lag, illusions, and neuroscience [Dancy,J, by PG] |
5682 | Internal realism holds that we perceive physical objects via mental objects [Dancy,J] |
2778 | Phenomenalism includes possible experiences, but idealism only refers to actual experiences [Dancy,J] |
5684 | Eliminative idealists say there are no objects; reductive idealists say objects exist as complex experiences [Dancy,J] |
2777 | Extreme solipsism only concerns current experience, but it might include past and future [Dancy,J] |
2794 | Knowing that a cow is not a horse seems to be a synthetic a priori truth [Dancy,J] |
2780 | Perception is either direct realism, indirect realism, or phenomenalism [Dancy,J] |
5679 | We can't grasp the separation of quality types, or what a primary-quality world would be like [Dancy,J] |
5680 | For direct realists the secondary and primary qualities seem equally direct [Dancy,J] |
2782 | We can be looking at distant stars which no longer actually exist [Dancy,J] |
2775 | It is not clear from the nature of sense data whether we should accept them as facts [Dancy,J] |
2784 | Appearances don't guarantee reality, unless the appearance is actually caused by the reality [Dancy,J] |
2785 | Perceptual beliefs may be directly caused, but generalisations can't be [Dancy,J] |
2788 | If perception and memory are indirect, then two things stand between mind and reality [Dancy,J] |
2787 | Memories aren't directly about the past, because time-lags and illusions suggest representation [Dancy,J] |
2791 | Phenomenalism about memory denies the past, or reduces it to present experience [Dancy,J] |
2790 | I can remember plans about the future, and images aren't essential (2+3=5) [Dancy,J] |
2754 | Foundations are justified by non-beliefs, or circularly, or they need no justification [Dancy,J] |
2749 | For internalists we must actually know that the fact caused the belief [Dancy,J] |
2770 | Internalists tend to favour coherent justification, but not the coherence theory of truth [Dancy,J] |
2752 | Foundationalism requires inferential and non-inferential justification [Dancy,J] |
2771 | Foundationalists must accept not only the basic beliefs, but also rules of inference for further progress [Dancy,J] |
2756 | If basic beliefs can be false, falsehood in non-basic beliefs might by a symptom [Dancy,J] |
2753 | Beliefs can only be infallible by having almost no content [Dancy,J] |
2773 | Coherentism gives a possible justification of induction, and opposes scepticism [Dancy,J] |
2779 | Idealists must be coherentists, but coherentists needn't be idealists [Dancy,J] |
2786 | For coherentists justification and truth are not radically different things [Dancy,J] |
2767 | If it is empirical propositions which have to be coherent, this eliminates coherent fiction [Dancy,J] |
2776 | Externalism could even make belief unnecessary (e.g. in animals) [Dancy,J] |
2746 | How can a causal theory of justification show that all men die? [Dancy,J] |
2747 | Causal theories don't allow for errors in justification [Dancy,J] |
2772 | Coherentism moves us towards a more social, shared view of knowledge [Dancy,J] |
2743 | What is the point of arguing against knowledge, if being right undermines your own argument? [Dancy,J] |
2751 | Probabilities can only be assessed relative to some evidence [Dancy,J] |
2757 | The argument from analogy rests on one instance alone [Dancy,J] |
2758 | You can't separate mind and behaviour, as the analogy argument attempts [Dancy,J] |
2744 | Verificationism (the 'verification principle') is an earlier form of anti-realism [Dancy,J] |
2760 | Logical positivism implies foundationalism, by dividing weak from strong verifications [Dancy,J] |
2761 | If the meanings of sentences depend on other sentences, how did we learn language? [Dancy,J] |
2763 | There is an indeterminacy in juggling apparent meanings against probable beliefs [Dancy,J] |
2762 | Charity makes native beliefs largely true, and Humanity makes them similar to ours [Dancy,J] |
7260 | If there are intuited moral facts, why should we care about them? [Dancy,J] |
7261 | Internalists say that moral intuitions are motivating; externalist say a desire is also needed [Dancy,J] |
7262 | Obviously judging an action as wrong gives us a reason not to do it [Dancy,J] |
7265 | Moral facts are not perceived facts, but perceived reasons for judgements [Dancy,J] |
18681 | The base for values has grounds, catalysts and intensifiers [Dancy,J, by Orsi] |