103 ideas
| 3099 | Inference is never a conscious process [Harman] |
| 19304 | The rules of reasoning are not the rules of logic [Harman] |
| 19306 | It is a principle of reasoning not to clutter your mind with trivialities [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] |
| 10482 | The logic of ZF is classical first-order predicate logic with identity [Boolos] |
| 10492 | A few axioms of set theory 'force themselves on us', but most of them don't [Boolos] |
| 18192 | Do the Replacement Axioms exceed the iterative conception of sets? [Boolos, by Maddy] |
| 7785 | The use of plurals doesn't commit us to sets; there do not exist individuals and collections [Boolos] |
| 10485 | Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos] |
| 10484 | The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos] |
| 13547 | Limitation of Size is weak (Fs only collect is something the same size does) or strong (fewer Fs than objects) [Boolos, by Potter] |
| 10699 | Does a bowl of Cheerios contain all its sets and subsets? [Boolos] |
| 3093 | Any two states are logically linked, by being entailed by their conjunction [Harman] |
| 12595 | We have a theory of logic (implication and inconsistency), but not of inference or reasoning [Harman] |
| 3098 | Deductive logic is the only logic there is [Harman] |
| 14249 | Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley] |
| 10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
| 10225 | Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro] |
| 10736 | Boolos showed how plural quantifiers can interpret monadic second-order logic [Boolos, by Linnebo] |
| 10780 | Any sentence of monadic second-order logic can be translated into plural first-order logic [Boolos, by Linnebo] |
| 3094 | You don't have to accept the conclusion of a valid argument [Harman] |
| 10829 | A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos] |
| 10697 | Identity is clearly a logical concept, and greatly enhances predicate calculus [Boolos] |
| 3080 | Logical form is the part of a sentence structure which involves logical elements [Harman] |
| 3084 | Our underlying predicates represent words in the language, not universal concepts [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] |
| 10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
| 13671 | Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology [Boolos, by Shapiro] |
| 10267 | We should understand second-order existential quantifiers as plural quantifiers [Boolos, by Shapiro] |
| 10698 | Plural forms have no more ontological commitment than to first-order objects [Boolos] |
| 7806 | Boolos invented plural quantification [Boolos, by Benardete,JA] |
| 10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos] |
| 13841 | Why should compactness be definitive of logic? [Boolos, by Hacking] |
| 10491 | Infinite natural numbers is as obvious as infinite sentences in English [Boolos] |
| 10483 | Mathematics and science do not require very high orders of infinity [Boolos] |
| 10833 | Many concepts can only be expressed by second-order logic [Boolos] |
| 10490 | Mathematics isn't surprising, given that we experience many objects as abstract [Boolos] |
| 12598 | Reality is the overlap of true complete theories [Harman] |
| 10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
| 10488 | It is lunacy to think we only see ink-marks, and not word-types [Boolos] |
| 10487 | I am a fan of abstract objects, and confident of their existence [Boolos] |
| 10489 | We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos] |
| 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] |
| 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] |
| 8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos] |
| 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] |
| 1868 | The world was made as much for animals as for man [Celsus] |
| 1867 | Christians presented Jesus as a new kind of logos to oppose that of the philosophers [Celsus] |