74 ideas
| 9724 | Until the 1960s the only semantics was truth-tables [Enderton] |
| 9707 | 'F(x)' is the unique value which F assumes for a value of x [Enderton] |
| 9705 | 'fld R' indicates the 'field' of all objects in the relation [Enderton] |
| 9704 | 'ran R' indicates the 'range' of objects being related to [Enderton] |
| 9703 | 'dom R' indicates the 'domain' of objects having a relation [Enderton] |
| 9710 | We write F:A→B to indicate that A maps into B (the output of F on A is in B) [Enderton] |
| 13201 | ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton] |
| 13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton] |
| 13204 | The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton] |
| 9699 | The 'powerset' of a set is all the subsets of a given set [Enderton] |
| 9700 | Two sets are 'disjoint' iff their intersection is empty [Enderton] |
| 9712 | A relation is 'symmetric' on a set if every ordered pair has the relation in both directions [Enderton] |
| 9713 | A relation is 'transitive' if it can be carried over from two ordered pairs to a third [Enderton] |
| 9701 | A 'relation' is a set of ordered pairs [Enderton] |
| 9702 | A 'domain' of a relation is the set of members of ordered pairs in the relation [Enderton] |
| 9708 | A function 'maps A into B' if the relating things are set A, and the things related to are all in B [Enderton] |
| 9709 | A function 'maps A onto B' if the relating things are set A, and the things related to are set B [Enderton] |
| 9711 | A relation is 'reflexive' on a set if every member bears the relation to itself [Enderton] |
| 9706 | A 'function' is a relation in which each object is related to just one other object [Enderton] |
| 9714 | A relation satisfies 'trichotomy' if all pairs are either relations, or contain identical objects [Enderton] |
| 9717 | A set is 'dominated' by another if a one-to-one function maps the first set into a subset of the second [Enderton] |
| 13200 | Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton] |
| 13199 | The empty set may look pointless, but many sets can be constructed from it [Enderton] |
| 13203 | The singleton is defined using the pairing axiom (as {x,x}) [Enderton] |
| 9716 | We 'partition' a set into distinct subsets, according to each relation on its objects [Enderton] |
| 9715 | An 'equivalence relation' is a reflexive, symmetric and transitive binary relation [Enderton] |
| 13202 | Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton] |
| 13205 | We can only define functions if Choice tells us which items are involved [Enderton] |
| 9722 | Inference not from content, but from the fact that it was said, is 'conversational implicature' [Enderton] |
| 9718 | Validity is either semantic (what preserves truth), or proof-theoretic (following procedures) [Enderton] |
| 9721 | A logical truth or tautology is a logical consequence of the empty set [Enderton] |
| 9994 | A truth assignment to the components of a wff 'satisfy' it if the wff is then True [Enderton] |
| 9719 | A proof theory is 'sound' if its valid inferences entail semantic validity [Enderton] |
| 9720 | A proof theory is 'complete' if semantically valid inferences entail proof-theoretic validity [Enderton] |
| 9995 | Proof in finite subsets is sufficient for proof in an infinite set [Enderton] |
| 9996 | Expressions are 'decidable' if inclusion in them (or not) can be proved [Enderton] |
| 9997 | For a reasonable language, the set of valid wff's can always be enumerated [Enderton] |
| 9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
| 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] |
| 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] |
| 20046 | For an ascetic a powerful desire for something is a reason not to implement it [Stout,R] |
| 20049 | Maybe your emotions arise from you motivations, rather than being their cause [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] |
| 22595 | Liberty is the triumph of the individual, over both despotic government and enslaving majorities [Constant] |
| 22597 | Minority rights are everyone's rights, because we all have turns in the minority [Constant] |
| 20083 | Aristotelian causation involves potentiality inputs into processes (rather than a pair of events) [Stout,R] |