104 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] |
9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
9634 | Set theory says that natural numbers are an actual infinity (to accommodate their powerset) [Brown,JR] |
9613 | Naïve set theory assumed that there is a set for every condition [Brown,JR] |
9615 | Nowadays conditions are only defined on existing sets [Brown,JR] |
9617 | The 'iterative' view says sets start with the empty set and build up [Brown,JR] |
9642 | A flock of birds is not a set, because a set cannot go anywhere [Brown,JR] |
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] |
3094 | You don't have to accept the conclusion of a valid argument [Harman] |
9605 | If a proposition is false, then its negation is true [Brown,JR] |
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] |
3084 | Our underlying predicates represent words in the language, not universal concepts [Harman] |
12597 | I might accept P and Q as likely, but reject P-and-Q as unlikely [Harman] |
9649 | Axioms are either self-evident, or stipulations, or fallible attempts [Brown,JR] |
9638 | Berry's Paradox finds a contradiction in the naming of huge numbers [Brown,JR] |
9604 | Mathematics is the only place where we are sure we are right [Brown,JR] |
9622 | 'There are two apples' can be expressed logically, with no mention of numbers [Brown,JR] |
9648 | π is a 'transcendental' number, because it is not the solution of an equation [Brown,JR] |
9621 | Mathematics represents the world through structurally similar models. [Brown,JR] |
9646 | There is no limit to how many ways something can be proved in mathematics [Brown,JR] |
9647 | Computers played an essential role in proving the four-colour theorem of maps [Brown,JR] |
9643 | Set theory may represent all of mathematics, without actually being mathematics [Brown,JR] |
9644 | When graphs are defined set-theoretically, that won't cover unlabelled graphs [Brown,JR] |
9625 | To see a structure in something, we must already have the idea of the structure [Brown,JR] |
9628 | Sets seem basic to mathematics, but they don't suit structuralism [Brown,JR] |
9606 | The irrationality of root-2 was achieved by intellect, not experience [Brown,JR] |
9612 | There is an infinity of mathematical objects, so they can't be physical [Brown,JR] |
9610 | Numbers are not abstracted from particulars, because each number is a particular [Brown,JR] |
9620 | Empiricists base numbers on objects, Platonists base them on properties [Brown,JR] |
9639 | Does some mathematics depend entirely on notation? [Brown,JR] |
9629 | For nomalists there are no numbers, only numerals [Brown,JR] |
9630 | The most brilliant formalist was Hilbert [Brown,JR] |
9608 | There are no constructions for many highly desirable results in mathematics [Brown,JR] |
9645 | Constructivists say p has no value, if the value depends on Goldbach's Conjecture [Brown,JR] |
9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
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] |
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] |
9611 | 'Abstract' nowadays means outside space and time, not concrete, not physical [Brown,JR] |
9609 | The older sense of 'abstract' is where 'redness' or 'group' is abstracted from particulars [Brown,JR] |
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] |
9640 | A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR] |
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] |
9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |
651 | Eurytus showed that numbers underlie things by making pictures of creatures out of pebbles [Eurytus, by Aristotle] |