70 ideas
| 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] |
| 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] |
| 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] |
| 13701 | A single second-order sentence validates all of arithmetic - but this can't be proved axiomatically [Sider] |
| 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] |
| 14308 | We can bring dispositions into existence, as in creating an identifier [Dennett, by Mumford] |
| 7384 | Words are fixed by being attached to similarity clusters, without mention of 'essences' [Dennett] |
| 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] |
| 7374 | Light wavelengths entering the eye are only indirectly related to object colours [Dennett] |
| 7369 | Brains are essentially anticipation machines [Dennett] |
| 7393 | We can't draw a clear line between conscious and unconscious [Dennett] |
| 7367 | Perhaps the brain doesn't 'fill in' gaps in consciousness if no one is looking. [Dennett] |
| 7394 | Conscious events can only be explained in terms of unconscious events [Dennett] |
| 7391 | We can know a lot of what it is like to be a bat, and nothing important is unknown [Dennett] |
| 7387 | "Qualia" can be replaced by complex dispositional brain states [Dennett] |
| 7376 | We can't assume that dispositions will remain normal when qualia have been inverted [Dennett] |
| 7372 | In peripheral vision we see objects without their details, so blindsight is not that special [Dennett] |
| 7373 | Blindsight subjects glean very paltry information [Dennett] |
| 7385 | People accept blurred boundaries in many things, but insist self is All or Nothing [Dennett] |
| 7383 | The psychological self is an abstraction, not a thing in the brain [Dennett] |
| 7386 | Selves are not soul-pearls, but artefacts of social processes [Dennett] |
| 7381 | We tell stories about ourselves, to protect, control and define who we are [Dennett] |
| 7382 | We spin narratives about ourselves, and the audience posits a centre of gravity for them [Dennett] |
| 7370 | The brain is controlled by shifting coalitions, guided by good purposeful habits [Dennett] |
| 7379 | If an epiphenomenon has no physical effects, it has to be undetectable [Dennett] |
| 7365 | Dualism wallows in mystery, and to accept it is to give up [Dennett] |
| 7371 | All functionalism is 'homuncular', of one grain size or another [Dennett] |
| 7366 | It is arbitrary to say which moment of brain processing is conscious [Dennett] |
| 7380 | Visual experience is composed of neural activity, which we find pleasing [Dennett] |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| 7368 | Originally there were no reasons, purposes or functions; since there were no interests, there were only causes [Dennett] |