66 ideas
| 23326 | In the third century Stoicism died out, replaced by Platonism, with Aristotelian ethics [Frede,M] |
| 23335 | In late antiquity nearly all philosophers were monotheists [Frede,M] |
| 16137 | Earlier views of Aristotle were dominated by 'Categories' [Frede,M] |
| 23249 | The early philosophers thought that reason has its own needs and desires [Frede,M] |
| 9724 | Until the 1960s the only semantics was truth-tables [Enderton] |
| 9703 | 'dom R' indicates the 'domain' of objects having a relation [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] |
| 9710 | We write F:A→B to indicate that A maps into B (the output of F on A is in B) [Enderton] |
| 9707 | 'F(x)' is the unique value which F assumes for a value of x [Enderton] |
| 13201 | ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [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] |
| 13204 | The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton] |
| 13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [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] |
| 9702 | A 'domain' of a relation is the set of members of ordered pairs in the relation [Enderton] |
| 9701 | A 'relation' is a set of ordered pairs [Enderton] |
| 9706 | A 'function' is a relation in which each object is related to just one other object [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] |
| 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] |
| 9715 | An 'equivalence relation' is a reflexive, symmetric and transitive binary relation [Enderton] |
| 9716 | We 'partition' a set into distinct subsets, according to each relation on its objects [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] |
| 16157 | Insurance on the original ship would hardly be paid out if the plank version was wrecked! [Frede,M] |
| 9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
| 5806 | Belief is the power of metarepresentation [Dretske] |
| 5801 | A mouse hearing a piano played does not believe it, because it lacks concepts and understanding [Dretske] |
| 6445 | You have knowledge if you can rule out all the relevant alternatives to what you believe [Dretske, by DeRose] |
| 19544 | Closure says if you know P, and also know P implies Q, then you must know Q [Dretske] |
| 19545 | We needn't regret the implications of our regrets; regretting drinking too much implies the past is real [Dretske] |
| 19547 | Reasons for believing P may not transmit to its implication, Q [Dretske] |
| 19546 | Knowing by visual perception is not the same as knowing by implication [Dretske] |
| 19548 | The only way to preserve our homely truths is to abandon closure [Dretske] |
| 19549 | P may imply Q, but evidence for P doesn't imply evidence for Q, so closure fails [Dretske] |
| 19550 | We know past events by memory, but we don't know the past is real (an implication) by memory [Dretske] |
| 5802 | Representations are in the head, but their content is not, as stories don't exist in their books [Dretske] |
| 5809 | Some activities are performed better without consciousness of them [Dretske] |
| 5808 | Qualia are just the properties objects are represented as having [Dretske] |
| 5803 | In a representational theory of mind, introspection is displaced perception [Dretske] |
| 5807 | Introspection is the same as the experience one is introspecting [Dretske] |
| 5805 | Introspection does not involve looking inwards [Dretske] |
| 23333 | The idea of free will achieved universal acceptance because of Christianity [Frede,M] |
| 23337 | The Stoics needed free will, to allow human choices in a divinely providential cosmos [Frede,M] |
| 23334 | For Christians man has free will by creation in God's image (as in Genesis) [Frede,M] |
| 5804 | A representational theory of the mind is an externalist theory of the mind [Dretske] |
| 5800 | All mental facts are representation, which consists of informational functions [Dretske] |
| 23336 | There is no will for Plato or Aristotle, because actions come directly from perception of what is good [Frede,M] |
| 23313 | The Gnostic demiurge (creator) is deluded, and doesn't care about us [Frede,M] |