80 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] |
| 13706 | Intuitively, deontic accessibility seems not to be reflexive, but to be serial [Sider] |
| 13710 | In D we add that 'what is necessary is possible'; then tautologies are possible, and contradictions not necessary [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] |
| 13678 | The most popular account of logical consequence is the semantic or model-theoretic one [Sider] |
| 13679 | Maybe logical consequence is more a matter of provability than of truth-preservation [Sider] |
| 13682 | Maybe logical consequence is impossibility of the premises being true and the consequent false [Sider] |
| 13680 | Maybe logical consequence is a primitive notion [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] |
| 13688 | Good axioms should be indisputable logical truths [Sider] |
| 13687 | No assumptions in axiomatic proofs, so no conditional proof or reductio [Sider] |
| 13690 | Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms [Sider] |
| 13691 | Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step' [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] |
| 13695 | Supervaluational logic is classical, except when it adds the 'Definitely' operator [Sider] |
| 13693 | A 'supervaluation' assigns further Ts and Fs, if they have been assigned in every precisification [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] |
| 20043 | Evolutionary explanations look to the past or the group, not to the individual [Stout,R] |
| 20058 | Not all explanation is causal. We don't explain a painting's beauty, or the irrationality of root-2, that way [Stout,R] |
| 4001 | The meaning of a word contains all its possible uses as well as its actual ones [Nagel] |
| 20035 | Philosophy of action studies the nature of agency, and of deliberate actions [Stout,R] |
| 20084 | Agency is causal processes that are sensitive to justification [Stout,R] |
| 20061 | Mental states and actions need to be separate, if one is to cause the other [Stout,R] |
| 20079 | Are actions bodily movements, or a sequence of intention-movement-result? [Stout,R] |
| 20080 | If one action leads to another, does it cause it, or is it part of it? [Stout,R] |
| 20059 | I do actions, but not events, so actions are not events [Stout,R] |
| 20081 | Bicycle riding is not just bodily movement - you also have to be on the bicycle [Stout,R] |
| 20044 | The rationalistic approach says actions are intentional when subject to justification [Stout,R] |
| 20039 | The causal theory says that actions are intentional when intention (or belief-desire) causes the act [Stout,R] |
| 20047 | Deciding what to do usually involves consulting the world, not our own minds [Stout,R] |
| 20065 | Should we study intentions in their own right, or only as part of intentional action? [Stout,R] |
| 20067 | You can have incompatible desires, but your intentions really ought to be consistent [Stout,R] |
| 20078 | The normativity of intentions would be obvious if they were internal promises [Stout,R] |
| 20036 | Intentional agency is seen in internal precursors of action, and in external reasons for the act [Stout,R] |
| 20066 | Speech needs sustained intentions, but not prior intentions [Stout,R] |
| 20073 | Bratman has to treat shared intentions as interrelated individual intentions [Stout,R] |
| 20069 | A request to pass the salt shares an intention that the request be passed on [Stout,R] |
| 20070 | An individual cannot express the intention that a group do something like moving a piano [Stout,R] |
| 20071 | An intention is a goal to which behaviour is adapted, for an individual or for a group [Stout,R] |
| 20038 | If the action of walking is just an act of will, then movement of the legs seems irrelevant [Stout,R] |
| 20050 | Most philosophers see causation as by an event or state in the agent, rather than the whole agent [Stout,R] |
| 20052 | If you don't mention an agent, you aren't talking about action [Stout,R] |
| 20077 | If you can judge one act as best, then do another, this supports an inward-looking view of agency [Stout,R] |
| 20049 | Maybe your emotions arise from you motivations, rather than being their cause [Stout,R] |
| 20046 | For an ascetic a powerful desire for something is a reason not to implement it [Stout,R] |
| 20060 | Beliefs, desires and intentions are not events, so can't figure in causal relations [Stout,R] |
| 20055 | A standard view says that the explanation of an action is showing its rational justification [Stout,R] |
| 20056 | In order to be causal, an agent's reasons must be internalised as psychological states [Stout,R] |
| 20053 | An action is only yours if you produce it, rather than some state or event within you [Stout,R] |
| 20048 | There may be a justification relative to a person's view, and yet no absolute justification [Stout,R] |
| 20068 | Describing a death as a side-effect rather than a goal may just be good public relations [Stout,R] |
| 20083 | Aristotelian causation involves potentiality inputs into processes (rather than a pair of events) [Stout,R] |