85 ideas
| 3099 | Inference is never a conscious process [Harman] |
| 3077 | Reasoning might be defined in terms of its functional role, which is to produce knowledge [Harman] |
| 3092 | If you believe that some of your beliefs are false, then at least one of your beliefs IS false [Harman] |
| 13689 | 'Theorems' are formulas provable from no premises at all [Sider] |
| 13705 | Truth tables assume truth functionality, and are just pictures of truth functions [Sider] |
| 13710 | In D we add that 'what is necessary is possible'; then tautologies are possible, and contradictions not necessary [Sider] |
| 13706 | Intuitively, deontic accessibility seems not to be reflexive, but to be serial [Sider] |
| 13711 | System B introduces iterated modalities [Sider] |
| 13708 | S5 is the strongest system, since it has the most valid formulas, because it is easy to be S5-valid [Sider] |
| 13712 | Epistemic accessibility is reflexive, and allows positive and negative introspection (KK and K¬K) [Sider] |
| 13714 | We can treat modal worlds as different times [Sider] |
| 13720 | Converse Barcan Formula: □∀αφ→∀α□φ [Sider] |
| 13718 | The Barcan Formula ∀x□Fx→□∀xFx may be a defect in modal logic [Sider] |
| 13723 | System B is needed to prove the Barcan Formula [Sider] |
| 13715 | You can employ intuitionist logic without intuitionism about mathematics [Sider] |
| 3093 | Any two states are logically linked, by being entailed by their conjunction [Harman] |
| 3098 | Deductive logic is the only logic there is [Harman] |
| 13680 | Maybe logical consequence is a primitive notion [Sider] |
| 13679 | Maybe logical consequence is more a matter of provability than of truth-preservation [Sider] |
| 13678 | The most popular account of logical consequence is the semantic or model-theoretic one [Sider] |
| 13682 | Maybe logical consequence is impossibility of the premises being true and the consequent false [Sider] |
| 13722 | A 'theorem' is an axiom, or the last line of a legitimate proof [Sider] |
| 3094 | You don't have to accept the conclusion of a valid argument [Harman] |
| 8195 | Undecidable statements result from quantifying over infinites, subjunctive conditionals, and the past tense [Dummett] |
| 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] |
| 3080 | Logical form is the part of a sentence structure which involves logical elements [Harman] |
| 13696 | When a variable is 'free' of the quantifier, the result seems incapable of truth or falsity [Sider] |
| 13700 | A 'total' function must always produce an output for a given domain [Sider] |
| 13703 | λ can treat 'is cold and hungry' as a single predicate [Sider] |
| 13687 | No assumptions in axiomatic proofs, so no conditional proof or reductio [Sider] |
| 13688 | Good axioms should be indisputable logical truths [Sider] |
| 13691 | Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step' [Sider] |
| 13690 | Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms [Sider] |
| 13685 | Natural deduction helpfully allows reasoning with assumptions [Sider] |
| 13686 | We can build proofs just from conclusions, rather than from plain formulae [Sider] |
| 13697 | Valuations in PC assign truth values to formulas relative to variable assignments [Sider] |
| 13684 | The semantical notion of a logical truth is validity, being true in all interpretations [Sider] |
| 13704 | It is hard to say which are the logical truths in modal logic, especially for iterated modal operators [Sider] |
| 13724 | In model theory, first define truth, then validity as truth in all models, and consequence as truth-preservation [Sider] |
| 13698 | In a complete logic you can avoid axiomatic proofs, by using models to show consequences [Sider] |
| 13699 | Compactness surprisingly says that no contradictions can emerge when the set goes infinite [Sider] |
| 8194 | Surely there is no exact single grain that brings a heap into existence [Dummett] |
| 13701 | A single second-order sentence validates all of arithmetic - but this can't be proved axiomatically [Sider] |
| 8190 | Intuitionists rely on the proof of mathematical statements, not their truth [Dummett] |
| 8198 | A 'Cambridge Change' is like saying 'the landscape changes as you travel east' [Dummett] |
| 8192 | I no longer think what a statement about the past says is just what can justify it [Dummett] |
| 13692 | A 'precisification' of a trivalent interpretation reduces it to a bivalent interpretation [Sider] |
| 13693 | A 'supervaluation' assigns further Ts and Fs, if they have been assigned in every precisification [Sider] |
| 13695 | Supervaluational logic is classical, except when it adds the 'Definitely' operator [Sider] |
| 13694 | We can 'sharpen' vague terms, and then define truth as true-on-all-sharpenings [Sider] |
| 13683 | A relation is a feature of multiple objects taken together [Sider] |
| 13702 | The identity of indiscernibles is necessarily true, if being a member of some set counts as a property [Sider] |
| 13721 | 'Strong' necessity in all possible worlds; 'weak' necessity in the worlds where the relevant objects exist [Sider] |
| 13707 | Maybe metaphysical accessibility is intransitive, if a world in which I am a frog is impossible [Sider] |
| 13709 | Logical truths must be necessary if anything is [Sider] |
| 13716 | 'If B hadn't shot L someone else would have' if false; 'If B didn't shoot L, someone else did' is true [Sider] |
| 13717 | Transworld identity is not a problem in de dicto sentences, which needn't identify an individual [Sider] |
| 13719 | Barcan Formula problem: there might have been a ghost, despite nothing existing which could be a ghost [Sider] |
| 3100 | You have to reaffirm all your beliefs when you make a logical inference [Harman] |
| 8199 | The existence of a universe without sentience or intelligence is an unintelligible fantasy [Dummett] |
| 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] |
| 3096 | Coherence avoids scepticism, because it doesn't rely on unprovable foundations [Harman] |
| 3095 | Induction is an attempt to increase the coherence of our explanations [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] |
| 3086 | Are there any meanings apart from in a language? [Harman] |
| 3078 | Speech acts, communication, representation and truth form a single theory [Harman] |
| 8193 | Verification is not an individual but a collective activity [Dummett] |
| 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] |
| 8189 | Truth-condition theorists must argue use can only be described by appeal to conditions of truth [Dummett] |
| 8191 | The truth-conditions theory must get agreement on a conception of truth [Dummett] |
| 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] |
| 3083 | Many predicates totally resist translation, so a universal underlying structure to languages is unlikely [Harman] |
| 8197 | Maybe past (which affects us) and future (which we can affect) are both real [Dummett] |
| 8196 | The present cannot exist alone as a mere boundary; past and future truths are rendered meaningless [Dummett] |