100 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] |
10676 | The Axiom of Choice is a non-logical principle of set-theory [Hossack] |
10686 | The Axiom of Choice guarantees a one-one correspondence from sets to ordinals [Hossack] |
23623 | Predicativism says only predicated sets exist [Hossack] |
23624 | The iterative conception has to appropriate Replacement, to justify the ordinals [Hossack] |
23625 | Limitation of Size justifies Replacement, but then has to appropriate Power Set [Hossack] |
10687 | Maybe we reduce sets to ordinals, rather than the other way round [Hossack] |
10677 | Extensional mereology needs two definitions and two axioms [Hossack] |
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] |
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] |
23628 | The connective 'and' can have an order-sensitive meaning, as 'and then' [Hossack] |
23627 | 'Before' and 'after' are not two relations, but one relation with two orders [Hossack] |
10671 | Plural definite descriptions pick out the largest class of things that fit the description [Hossack] |
10666 | Plural reference will refer to complex facts without postulating complex things [Hossack] |
10669 | Plural reference is just an abbreviation when properties are distributive, but not otherwise [Hossack] |
10675 | A plural comprehension principle says there are some things one of which meets some condition [Hossack] |
10673 | Plural language can discuss without inconsistency things that are not members of themselves [Hossack] |
10680 | The theory of the transfinite needs the ordinal numbers [Hossack] |
10684 | I take the real numbers to be just lengths [Hossack] |
23626 | Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack] |
10674 | A plural language gives a single comprehensive induction axiom for arithmetic [Hossack] |
10681 | In arithmetic singularists need sets as the instantiator of numeric properties [Hossack] |
10685 | Set theory is the science of infinity [Hossack] |
23621 | Numbers are properties, not sets (because numbers are magnitudes) [Hossack] |
23622 | We can only mentally construct potential infinities, but maths needs actual infinities [Hossack] |
12598 | Reality is the overlap of true complete theories [Harman] |
10668 | We are committed to a 'group' of children, if they are sitting in a circle [Hossack] |
10664 | Complex particulars are either masses, or composites, or sets [Hossack] |
10678 | The relation of composition is indispensable to the part-whole relation for individuals [Hossack] |
12887 | A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim] |
10665 | Leibniz's Law argues against atomism - water is wet, unlike water molecules [Hossack] |
10682 | The fusion of five rectangles can decompose into more than five parts that are rectangles [Hossack] |
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] |
10663 | A thought can refer to many things, but only predicate a universal and affirm a state of affairs [Hossack] |
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] |
10683 | We could ignore space, and just talk of the shape of matter [Hossack] |