115 ideas
| 15661 | Horkheimer's critical theory was interdisciplinary, and aware of its own context and function [Horkheimer, by Finlayson] |
| 19306 | It is a principle of reasoning not to clutter your mind with trivialities [Harman] |
| 3099 | Inference is never a conscious process [Harman] |
| 19304 | The rules of reasoning are not the rules of logic [Harman] |
| 19307 | If there is a great cost to avoiding inconsistency, we learn to reason our way around it [Harman] |
| 19309 | Logic has little relevance to reasoning, except when logical conclusions are immediate [Harman] |
| 6950 | You can be rational with undetected or minor inconsistencies [Harman] |
| 3077 | Reasoning might be defined in terms of its functional role, which is to produce knowledge [Harman] |
| 19303 | Implication just accumulates conclusions, but inference may also revise our views [Harman] |
| 12596 | Reasoning aims at increasing explanatory coherence [Harman] |
| 12599 | Reason conservatively: stick to your beliefs, and prefer reasoning that preserves most of them [Harman] |
| 6954 | A coherent conceptual scheme contains best explanations of most of your beliefs [Harman] |
| 3092 | If you believe that some of your beliefs are false, then at least one of your beliefs IS false [Harman] |
| 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] |
| 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] |
| 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] |
| 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] |
| 12595 | We have a theory of logic (implication and inconsistency), but not of inference or reasoning [Harman] |
| 3093 | Any two states are logically linked, by being entailed by their conjunction [Harman] |
| 3098 | Deductive logic is the only logic there is [Harman] |
| 3094 | You don't have to accept the conclusion of a valid argument [Harman] |
| 3084 | Our underlying predicates represent words in the language, not universal concepts [Harman] |
| 3080 | Logical form is the part of a sentence structure which involves logical elements [Harman] |
| 3081 | A theory of truth in a language must involve a theory of logical form [Harman] |
| 12597 | I might accept P and Q as likely, but reject P-and-Q as unlikely [Harman] |
| 9725 | 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn] |
| 12598 | Reality is the overlap of true complete theories [Harman] |
| 13730 | The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn] |
| 19305 | The Gambler's Fallacy (ten blacks, so red is due) overemphasises the early part of a sequence [Harman] |
| 19310 | High probability premises need not imply high probability conclusions [Harman] |
| 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] |
| 19308 | We strongly desire to believe what is true, even though logic does not require it [Harman] |
| 3100 | You have to reaffirm all your beliefs when you make a logical inference [Harman] |
| 3089 | Only lack of imagination makes us think that 'cats are animals' is analytic [Harman] |
| 3088 | Analyticity is postulated because we can't imagine some things being true, but we may just lack imagination [Harman] |
| 3101 | Memories are not just preserved, they are constantly reinferred [Harman] |
| 3074 | People's reasons for belief are rarely conscious [Harman] |
| 3097 | We don't distinguish between accepting, and accepting as evidence [Harman] |
| 6369 | In negative coherence theories, beliefs are prima facie justified, and don't need initial reasons [Harman, by Pollock/Cruz] |
| 19311 | In revision of belief, we need to keep track of justifications for foundations, but not for coherence [Harman] |
| 19312 | Coherence is intelligible connections, especially one element explaining another [Harman] |
| 3096 | Coherence avoids scepticism, because it doesn't rely on unprovable foundations [Harman] |
| 8800 | If you would deny a truth if you know the full evidence, then knowledge has social aspects [Harman, by Sosa] |
| 6955 | Enumerative induction is inference to the best explanation [Harman] |
| 3095 | Induction is an attempt to increase the coherence of our explanations [Harman] |
| 6952 | Induction is 'defeasible', since additional information can invalidate it [Harman] |
| 6953 | All reasoning is inductive, and deduction only concerns implication [Harman] |
| 17060 | Best Explanation is the core notion of epistemology [Harman, by Smart] |
| 12602 | There is no natural border between inner and outer [Harman] |
| 12603 | We can only describe mental attitudes in relation to the external world [Harman] |
| 8130 | Qualities of experience are just representational aspects of experience ('Representationalism') [Harman, by Burge] |
| 12601 | The way things look is a relational matter, not an intrinsic matter [Harman] |
| 3073 | We see ourselves in the world as a map [Harman] |
| 3076 | Defining dispositions is circular [Harman] |
| 3075 | Could a cloud have a headache if its particles formed into the right pattern? [Harman] |
| 6951 | Ordinary rationality is conservative, starting from where your beliefs currently are [Harman] |
| 3086 | Are there any meanings apart from in a language? [Harman] |
| 12592 | Concepts in thought have content, but not meaning, which requires communication [Harman] |
| 3078 | Speech acts, communication, representation and truth form a single theory [Harman] |
| 12590 | Take meaning to be use in calculation with concepts, rather than in communication [Harman] |
| 12593 | The use theory attaches meanings to words, not to sentences [Harman] |
| 12588 | Meaning from use of thoughts, constructed from concepts, which have a role relating to reality [Harman] |
| 12589 | Some regard conceptual role semantics as an entirely internal matter [Harman] |
| 12600 | The content of thought is relations, between mental states, things in the world, and contexts [Harman] |
| 3090 | There is only similarity in meaning, never sameness in meaning [Harman] |
| 3082 | Ambiguity is when different underlying truth-conditional structures have the same surface form [Harman] |
| 3079 | Truth in a language is explained by how the structural elements of a sentence contribute to its truth conditions [Harman] |
| 3085 | Sentences are different from propositions, since two sentences can express one proposition [Harman] |
| 3087 | The analytic/synthetic distinction is a silly division of thought into encyclopaedia and dictionary [Harman] |
| 12594 | If one proposition negates the other, which is the negative one? [Harman] |
| 12591 | Mastery of a language requires thinking, and not just communication [Harman] |
| 3083 | Many predicates totally resist translation, so a universal underlying structure to languages is unlikely [Harman] |
| 5121 | Basing ethics on flourishing makes it consequentialist, as actions are judged by contributing to it [Harman] |
| 5122 | Maybe consequentialism is a critique of ordinary morality, rather than describing it [Harman] |
| 5120 | What counts as 'flourishing' must be relative to various sets of values [Harman] |
| 5123 | Maybe there is no such thing as character, and the virtues and vices said to accompany it [Harman] |
| 5124 | If a person's two acts of timidity have different explanations, they are not one character trait [Harman] |
| 5125 | Virtue ethics might involve judgements about the virtues of actions, rather than character [Harman] |