127 ideas
18835 | Logic doesn't have a metaphysical basis, but nor can logic give rise to the metaphysics [Rumfitt] |
19306 | It is a principle of reasoning not to clutter your mind with trivialities [Harman] |
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] |
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] |
18819 | The idea that there are unrecognised truths is basic to our concept of truth [Rumfitt] |
18826 | 'True at a possibility' means necessarily true if what is said had obtained [Rumfitt] |
18803 | Semantics for propositions: 1) validity preserves truth 2) non-contradition 3) bivalence 4) truth tables [Rumfitt] |
12204 | The logic of metaphysical necessity is S5 [Rumfitt] |
18814 | 'Absolute necessity' would have to rest on S5 [Rumfitt] |
18798 | It is the second-order part of intuitionistic logic which actually negates some classical theorems [Rumfitt] |
18799 | Intuitionists can accept Double Negation Elimination for decidable propositions [Rumfitt] |
18830 | Most set theorists doubt bivalence for the Continuum Hypothesis, but still use classical logic [Rumfitt] |
18843 | The iterated conception of set requires continual increase in axiom strength [Rumfitt] |
18836 | A set may well not consist of its members; the empty set, for example, is a problem [Rumfitt] |
18837 | A set can be determinate, because of its concept, and still have vague membership [Rumfitt] |
18845 | If the totality of sets is not well-defined, there must be doubt about the Power Set Axiom [Rumfitt] |
3093 | Any two states are logically linked, by being entailed by their conjunction [Harman] |
11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
18815 | Logic is higher-order laws which can expand the range of any sort of deduction [Rumfitt] |
12595 | We have a theory of logic (implication and inconsistency), but not of inference or reasoning [Harman] |
9390 | Logic guides thinking, but it isn't a substitute for it [Rumfitt] |
3098 | Deductive logic is the only logic there is [Harman] |
18804 | The case for classical logic rests on its rules, much more than on the Principle of Bivalence [Rumfitt] |
18805 | Classical logic rules cannot be proved, but various lines of attack can be repelled [Rumfitt] |
18827 | If truth-tables specify the connectives, classical logic must rely on Bivalence [Rumfitt] |
12195 | Soundness in argument varies with context, and may be achieved very informally indeed [Rumfitt] |
12199 | There is a modal element in consequence, in assessing reasoning from suppositions [Rumfitt] |
12201 | We reject deductions by bad consequence, so logical consequence can't be deduction [Rumfitt] |
18813 | Logical consequence is a relation that can extended into further statements [Rumfitt] |
18808 | Normal deduction presupposes the Cut Law [Rumfitt] |
3094 | You don't have to accept the conclusion of a valid argument [Harman] |
18840 | When faced with vague statements, Bivalence is not a compelling principle [Rumfitt] |
12194 | Contradictions include 'This is red and not coloured', as well as the formal 'B and not-B' [Rumfitt] |
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] |
11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
18802 | In specifying a logical constant, use of that constant is quite unavoidable [Rumfitt] |
12597 | I might accept P and Q as likely, but reject P-and-Q as unlikely [Harman] |
12198 | Geometrical axioms in logic are nowadays replaced by inference rules (which imply the logical truths) [Rumfitt] |
18800 | Introduction rules give deduction conditions, and Elimination says what can be deduced [Rumfitt] |
18809 | Logical truths are just the assumption-free by-products of logical rules [Rumfitt] |
18807 | Monotonicity means there is a guarantee, rather than mere inductive support [Rumfitt] |
18842 | Maybe an ordinal is a property of isomorphic well-ordered sets, and not itself a set [Rumfitt] |
17462 | A single object must not be counted twice, which needs knowledge of distinctness (negative identity) [Rumfitt] |
18834 | Infinitesimals do not stand in a determinate order relation to zero [Rumfitt] |
18846 | Cantor and Dedekind aimed to give analysis a foundation in set theory (rather than geometry) [Rumfitt] |
17461 | Some 'how many?' answers are not predications of a concept, like 'how many gallons?' [Rumfitt] |
12598 | Reality is the overlap of true complete theories [Harman] |
9389 | Vague membership of sets is possible if the set is defined by its concept, not its members [Rumfitt] |
18839 | An object that is not clearly red or orange can still be red-or-orange, which sweeps up problem cases [Rumfitt] |
18838 | The extension of a colour is decided by a concept's place in a network of contraries [Rumfitt] |
14532 | A distinctive type of necessity is found in logical consequence [Rumfitt, by Hale/Hoffmann,A] |
18816 | Metaphysical modalities respect the actual identities of things [Rumfitt] |
12193 | Logical necessity is when 'necessarily A' implies 'not-A is contradictory' [Rumfitt] |
12200 | A logically necessary statement need not be a priori, as it could be unknowable [Rumfitt] |
18825 | S5 is the logic of logical necessity [Rumfitt] |
12202 | Narrow non-modal logical necessity may be metaphysical, but real logical necessity is not [Rumfitt] |
18828 | If two possibilities can't share a determiner, they are incompatible [Rumfitt] |
18824 | Since possibilities are properties of the world, calling 'red' the determination of a determinable seems right [Rumfitt] |
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] |
12203 | If a world is a fully determinate way things could have been, can anyone consider such a thing? [Rumfitt] |
18821 | Possibilities are like possible worlds, but not fully determinate or complete [Rumfitt] |
18831 | Medieval logicians said understanding A also involved understanding not-A [Rumfitt] |
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] |
18820 | In English 'evidence' is a mass term, qualified by 'little' and 'more' [Rumfitt] |
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] |
20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
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] |
18817 | We understand conditionals, but disagree over their truth-conditions [Rumfitt] |
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] |
18829 | The truth grounds for 'not A' are the possibilities incompatible with truth grounds for A [Rumfitt] |
11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |
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] |