69 ideas
| 19693 | There is practical wisdom (for action), and theoretical wisdom (for deep understanding) [Aristotle, by Whitcomb] |
| 1575 | For Aristotle logos is essentially the ability to talk rationally about questions of value [Roochnik on Aristotle] |
| 1589 | Aristotle is the supreme optimist about the ability of logos to explain nature [Roochnik on Aristotle] |
| 8200 | Aristotelian definitions aim to give the essential properties of the thing defined [Aristotle, by Quine] |
| 4385 | Aristotelian definition involves first stating the genus, then the differentia of the thing [Aristotle, by Urmson] |
| 18951 | For scientific purposes there is a precise concept of 'true-in-L', using set theory [Putnam] |
| 18953 | Modern notation frees us from Aristotle's restriction of only using two class-names in premises [Putnam] |
| 18949 | The universal syllogism is now expressed as the transitivity of subclasses [Putnam] |
| 9724 | Until the 1960s the only semantics was truth-tables [Enderton] |
| 18952 | '⊃' ('if...then') is used with the definition 'Px ⊃ Qx' is short for '¬(Px & ¬Qx)' [Putnam] |
| 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] |
| 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] |
| 18958 | In type theory, 'x ∈ y' is well defined only if x and y are of the appropriate type [Putnam] |
| 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] |
| 13282 | Aristotle relativises the notion of wholeness to different measures [Aristotle, by Koslicki] |
| 9722 | Inference not from content, but from the fact that it was said, is 'conversational implicature' [Enderton] |
| 18954 | Before the late 19th century logic was trivialised by not dealing with relations [Putnam] |
| 18956 | Asserting first-order validity implicitly involves second-order reference to classes [Putnam] |
| 9718 | Validity is either semantic (what preserves truth), or proof-theoretic (following procedures) [Enderton] |
| 18962 | Unfashionably, I think logic has an empirical foundation [Putnam] |
| 4730 | For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady] |
| 18961 | We can identify functions with certain sets - or identify sets with certain functions [Putnam] |
| 18955 | Having a valid form doesn't ensure truth, as it may be meaningless [Putnam] |
| 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] |
| 18959 | Sets larger than the continuum should be studied in an 'if-then' spirit [Putnam] |
| 18957 | Nominalism only makes sense if it is materialist [Putnam] |
| 18950 | Physics is full of non-physical entities, such as space-vectors [Putnam] |
| 13276 | The unmoved mover and the soul show Aristotelian form as the ultimate mereological atom [Aristotle, by Koslicki] |
| 13277 | The 'form' is the recipe for building wholes of a particular kind [Aristotle, by Koslicki] |
| 9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
| 5991 | For Aristotle, knowledge is of causes, and is theoretical, practical or productive [Aristotle, by Code] |
| 11239 | The notion of a priori truth is absent in Aristotle [Aristotle, by Politis] |
| 23312 | Aristotle is a rationalist, but reason is slowly acquired through perception and experience [Aristotle, by Frede,M] |
| 16111 | Aristotle wants to fit common intuitions, and therefore uses language as a guide [Aristotle, by Gill,ML] |
| 18960 | Most predictions are uninteresting, and are only sought in order to confirm a theory [Putnam] |
| 16971 | Plato says sciences are unified around Forms; Aristotle says they're unified around substance [Aristotle, by Moravcsik] |
| 11243 | Aristotelian explanations are facts, while modern explanations depend on human conceptions [Aristotle, by Politis] |
| 3320 | Aristotle's standard analysis of species and genus involves specifying things in terms of something more general [Aristotle, by Benardete,JA] |
| 12000 | Aristotle regularly says that essential properties explain other significant properties [Aristotle, by Kung] |
| 23300 | Aristotle and the Stoics denied rationality to animals, while Platonists affirmed it [Aristotle, by Sorabji] |
| 11240 | The notion of analytic truth is absent in Aristotle [Aristotle, by Politis] |
| 6559 | Aristotle never actually says that man is a rational animal [Aristotle, by Fogelin] |
| 11150 | It is the mark of an educated mind to be able to entertain an idea without accepting it [Aristotle] |
| 3037 | Aristotle said the educated were superior to the uneducated as the living are to the dead [Aristotle, by Diog. Laertius] |
| 8660 | There are potential infinities (never running out), but actual infinity is incoherent [Aristotle, by Friend] |
| 12058 | Aristotle's matter can become any other kind of matter [Aristotle, by Wiggins] |
| 22729 | The concepts of gods arose from observing the soul, and the cosmos [Aristotle, by Sext.Empiricus] |