113 ideas
| 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] |
| 19306 | It is a principle of reasoning not to clutter your mind with trivialities [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] |
| 9123 | Someone standing in a doorway seems to be both in and not-in the room [Priest,G, by Sorensen] |
| 8720 | A logic is 'relevant' if premise and conclusion are connected, and 'paraconsistent' allows contradictions [Priest,G, by Friend] |
| 9672 | Free logic is one of the few first-order non-classical logics [Priest,G] |
| 9697 | X1 x X2 x X3... x Xn indicates the 'cartesian product' of those sets [Priest,G] |
| 9685 | <a,b&62; is a set whose members occur in the order shown [Priest,G] |
| 9675 | a ∈ X says a is an object in set X; a ∉ X says a is not in X [Priest,G] |
| 9674 | {x; A(x)} is a set of objects satisfying the condition A(x) [Priest,G] |
| 9673 | {a1, a2, ...an} indicates that a set comprising just those objects [Priest,G] |
| 9677 | Φ indicates the empty set, which has no members [Priest,G] |
| 9676 | {a} is the 'singleton' set of a (not the object a itself) [Priest,G] |
| 9679 | X⊂Y means set X is a 'proper subset' of set Y [Priest,G] |
| 9678 | X⊆Y means set X is a 'subset' of set Y [Priest,G] |
| 9681 | X = Y means the set X equals the set Y [Priest,G] |
| 9683 | X ∩ Y indicates the 'intersection' of sets X and Y, the objects which are in both sets [Priest,G] |
| 9682 | X∪Y indicates the 'union' of all the things in sets X and Y [Priest,G] |
| 9684 | Y - X is the 'relative complement' of X with respect to Y; the things in Y that are not in X [Priest,G] |
| 9694 | The 'relative complement' is things in the second set not in the first [Priest,G] |
| 9693 | The 'intersection' of two sets is a set of the things that are in both sets [Priest,G] |
| 9692 | The 'union' of two sets is a set containing all the things in either of the sets [Priest,G] |
| 9698 | The 'induction clause' says complex formulas retain the properties of their basic formulas [Priest,G] |
| 9695 | An 'ordered pair' (or ordered n-tuple) is a set with its members in a particular order [Priest,G] |
| 9696 | A 'cartesian product' of sets is the set of all the n-tuples with one member in each of the sets [Priest,G] |
| 9686 | A 'set' is a collection of objects [Priest,G] |
| 9689 | The 'empty set' or 'null set' has no members [Priest,G] |
| 9690 | A set is a 'subset' of another set if all of its members are in that set [Priest,G] |
| 9691 | A 'proper subset' is smaller than the containing set [Priest,G] |
| 9688 | A 'singleton' is a set with only one member [Priest,G] |
| 9687 | A 'member' of a set is one of the objects in the set [Priest,G] |
| 9680 | The empty set Φ is a subset of every set (including itself) [Priest,G] |
| 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] |
| 13373 | Typically, paradoxes are dealt with by dividing them into two groups, but the division is wrong [Priest,G] |
| 13368 | The 'least indefinable ordinal' is defined by that very phrase [Priest,G] |
| 13370 | 'x is a natural number definable in less than 19 words' leads to contradiction [Priest,G] |
| 13369 | By diagonalization we can define a real number that isn't in the definable set of reals [Priest,G] |
| 13366 | The least ordinal greater than the set of all ordinals is both one of them and not one of them [Priest,G] |
| 13367 | The next set up in the hierarchy of sets seems to be both a member and not a member of it [Priest,G] |
| 13371 | If you know that a sentence is not one of the known sentences, you know its truth [Priest,G] |
| 13372 | There are Liar Pairs, and Liar Chains, which fit the same pattern as the basic Liar [Priest,G] |
| 12598 | Reality is the overlap of true complete theories [Harman] |
| 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] |
| 19542 | It is nonsense that understanding does not involve knowledge; to understand, you must know [Dougherty/Rysiew] |
| 19543 | To grasp understanding, we should be more explicit about what needs to be known [Dougherty/Rysiew] |
| 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] |
| 19541 | Rather than knowledge, our epistemic aim may be mere true belief, or else understanding and wisdom [Dougherty/Rysiew] |
| 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] |
| 19540 | Don't confuse justified belief with justified believers [Dougherty/Rysiew] |
| 19539 | If knowledge is unanalysable, that makes justification more important [Dougherty/Rysiew] |
| 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] |
| 19538 | Entailment is modelled in formal semantics as set inclusion (where 'mammals' contains 'cats') [Dougherty/Rysiew] |
| 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] |