131 ideas
3099 | Inference is never a conscious process [Harman] |
19304 | The rules of reasoning are not the rules of logic [Harman] |
17892 | For clear questions posed by reason, reason can also find clear answers [Gödel] |
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] |
10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
21752 | Prior to Gödel we thought truth in mathematics consisted in provability [Gödel, by Quine] |
17751 | Gödel proved the completeness of first order predicate logic in 1930 [Gödel, by Walicki] |
8679 | We perceive the objects of set theory, just as we perceive with our senses [Gödel] |
17835 | Gödel show that the incompleteness of set theory was a necessity [Gödel, by Hallett,M] |
9942 | Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam] |
21716 | In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B] |
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] |
9188 | Gödel proved that first-order logic is complete, and second-order logic incomplete [Gödel, by Dummett] |
10035 | Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel] |
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] |
10042 | Reference to a totality need not refer to a conjunction of all its elements [Gödel] |
10620 | Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel] |
17886 | The limitations of axiomatisation were revealed by the incompleteness theorems [Gödel, by Koellner] |
10071 | Second Incompleteness: nice theories can't prove their own consistency [Gödel, by Smith,P] |
19123 | If soundness can't be proved internally, 'reflection principles' can be added to assert soundness [Gödel, by Halbach/Leigh] |
17883 | Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner] |
10621 | Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P on Gödel] |
17888 | The undecidable sentence can be decided at a 'higher' level in the system [Gödel] |
10038 | A logical system needs a syntactical survey of all possible expressions [Gödel] |
18062 | Set-theory paradoxes are no worse than sense deception in physics [Gödel] |
10132 | There can be no single consistent theory from which all mathematical truths can be derived [Gödel, by George/Velleman] |
10046 | The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel] |
10868 | The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg] |
13517 | If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD] |
17885 | Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable [Gödel, by Koellner] |
10614 | The real reason for Incompleteness in arithmetic is inability to define truth in a language [Gödel] |
3198 | Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey] |
10072 | First Incompleteness: arithmetic must always be incomplete [Gödel, by Smith,P] |
9590 | Arithmetical truth cannot be fully and formally derived from axioms and inference rules [Gödel, by Nagel/Newman] |
11069 | Gödel's Second says that semantic consequence outruns provability [Gödel, by Hanna] |
10118 | First Incompleteness: a decent consistent system is syntactically incomplete [Gödel, by George/Velleman] |
10122 | Second Incompleteness: a decent consistent system can't prove its own consistency [Gödel, by George/Velleman] |
10611 | There is a sentence which a theory can show is true iff it is unprovable [Gödel, by Smith,P] |
10867 | 'This system can't prove this statement' makes it unprovable either way [Gödel, by Clegg] |
10039 | Some arithmetical problems require assumptions which transcend arithmetic [Gödel] |
10043 | Mathematical objects are as essential as physical objects are for perception [Gödel] |
10271 | Basic mathematics is related to abstract elements of our empirical ideas [Gödel] |
10045 | Impredicative definitions are admitted into ordinary mathematics [Gödel] |
8747 | Realists are happy with impredicative definitions, which describe entities in terms of other existing entities [Gödel, by Shapiro] |
12598 | Reality is the overlap of true complete theories [Harman] |
4938 | Prior to language, concepts are universals created by self-mapping of brain activity [Edelman/Tononi] |
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] |
4934 | Cultures have a common core of colour naming, based on three axes of colour pairs [Edelman/Tononi] |
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] |
4924 | A conscious human being rapidly reunifies its mind after any damage to the brain [Edelman/Tononi] |
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] |
4932 | A conscious state endures for about 100 milliseconds, known as the 'specious present' [Edelman/Tononi] |
4931 | Consciousness is a process (of neural interactions), not a location, thing, property, connectivity, or activity [Edelman/Tononi] |
4923 | The three essentials of conscious experience are privateness, unity and informativeness [Edelman/Tononi] |
4941 | Consciousness can create new axioms, but computers can't do that [Edelman/Tononi] |
4930 | Consciousness arises from high speed interactions between clusters of neurons [Edelman/Tononi] |
4929 | Dreams and imagery show the brain can generate awareness and meaning without input [Edelman/Tononi] |
4940 | Physicists see information as a measure of order, but for biologists it is symbolic exchange between animals [Edelman/Tononi] |
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] |
4935 | The sensation of red is a point in neural space created by dimensions of neuronal activity [Edelman/Tononi] |
4936 | The self is founded on bodily awareness centred in the brain stem [Edelman/Tononi] |
3073 | We see ourselves in the world as a map [Harman] |
4939 | A sense of self begins either internally, or externally through language and society [Edelman/Tononi] |
4925 | Brains can initiate free actions before the person is aware of their own decision [Edelman/Tononi] |
3076 | Defining dispositions is circular [Harman] |
3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
3075 | Could a cloud have a headache if its particles formed into the right pattern? [Harman] |
4933 | Consciousness is a process, not a thing, as it maintains unity as its composition changes [Edelman/Tononi] |
6951 | Ordinary rationality is conservative, starting from where your beliefs currently are [Harman] |
4928 | Brain complexity balances segregation and integration, like a good team of specialists [Edelman/Tononi] |
4927 | Information-processing views of the brain assume the existence of 'information', and dubious brain codes [Edelman/Tononi] |
3086 | Are there any meanings apart from in a language? [Harman] |
4922 | Consciousness involves interaction with persons and the world, as well as brain functions [Edelman/Tononi] |
5793 | Concepts and generalisations result from brain 'global mapping' by 'reentry' [Edelman/Tononi, by Searle] |
4926 | Concepts arise when the brain maps its own activities [Edelman/Tononi] |
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] |
4937 | Systems that generate a sense of value are basic to the primitive brain [Edelman/Tononi] |
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] |