73 ideas
| 5196 | Philosophy is a department of logic [Ayer] |
| 5189 | Philosophers should abandon speculation, as philosophy is wholly critical [Ayer] |
| 7919 | Humeans rejected the a priori synthetic, and so rejected even Kantian metaphysics [Ayer, by Macdonald,C] |
| 5195 | Critics say analysis can only show the parts, and not their distinctive configuration [Ayer] |
| 5179 | Philosophy deals with the questions that scientists do not wish to handle [Ayer] |
| 4749 | We cannot analyse the concept of 'truth', because it is simply a mark that a sentence is asserted [Ayer] |
| 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] |
| 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] |
| 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] |
| 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] |
| 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] |
| 5202 | Maths and logic are true universally because they are analytic or tautological [Ayer] |
| 6523 | Positivists regard ontology as either meaningless or stipulated [Ayer, by Robinson,H] |
| 9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
| 5183 | Only tautologies can be certain; other propositions can only be probable [Ayer] |
| 6525 | Logical positivists could never give the sense-data equivalent of 'there is a table next door' [Robinson,H on Ayer] |
| 5170 | Material things are constructions from actual and possible occurrences of sense-contents [Ayer] |
| 5198 | We could verify 'a thing can't be in two places at once' by destroying one of the things [Ierubino on Ayer] |
| 2619 | Whether geometry can be applied to reality is an empirical question outside of geometry [Ayer] |
| 5197 | By changing definitions we could make 'a thing can't be in two places at once' a contradiction [Ayer] |
| 5204 | To say that a proposition is true a priori is to say that it is a tautology [Ayer] |
| 6524 | Positivists prefer sense-data to objects, because the vocabulary covers both illusions and perceptions [Ayer, by Robinson,H] |
| 5193 | Causal and representative theories of perception are wrong as they refer to unobservables [Ayer] |
| 5200 | The main claim of rationalism is that thought is an independent source of knowledge [Ayer] |
| 4729 | Empiricism lacked a decent account of the a priori, until Ayer said it was entirely analytic [O'Grady on Ayer] |
| 5180 | All propositions (especially 'metaphysics') must begin with the senses [Ayer] |
| 5169 | My empiricism logically distinguishes analytic and synthetic propositions, and metaphysical verbiage [Ayer] |
| 5185 | It is further sense-experience which informs us of the mistakes that arise out of sense-experience [Ayer] |
| 5199 | Empiricism, it is said, cannot account for our knowledge of necessary truths [Ayer] |
| 5190 | The induction problem is to prove generalisations about the future based on the past [Ayer] |
| 5191 | We can't use the uniformity of nature to prove induction, as that would be circular [Ayer] |
| 5177 | Other minds are 'metaphysical' objects, because I can never observe their experiences [Ayer] |
| 5178 | A conscious object is by definition one that behaves in a certain way, so behaviour proves consciousness [Ayer] |
| 5172 | If the self is meaningful, it must be constructed from sense-experiences [Ayer] |
| 5173 | Two experiences belong to one self if their contents belong with one body [Ayer] |
| 5176 | Empiricists can define personal identity as bodily identity, which consists of sense-contents [Ayer] |
| 5171 | The supposed 'gulf' between mind and matter is based on the senseless concept of 'substances' [Ayer] |
| 5181 | A sentence is factually significant to someone if they know how to verify its proposition [Ayer] |
| 5184 | Factual propositions imply (in conjunction with a few other premises) possible experiences [Ayer] |
| 5186 | Tautologies and empirical hypotheses form the entire class of significant propositions [Ayer] |
| 5205 | Moral intuition is worthless if there is no criterion to decide between intuitions [Ayer] |
| 23725 | Ayer defends the emotivist version of expressivism [Ayer, by Smith,M] |
| 5206 | To say an act is wrong makes no further statement about it, but merely expresses disapproval [Ayer] |
| 9111 | God is not wise, but more-than-wise; God is not good, but more-than-good [William of Ockham] |
| 5208 | A person with non-empirical attributes is unintelligible. [Ayer] |
| 5187 | When we ascribe an attribute to a thing, we covertly assert that it exists [Ayer] |
| 9112 | We could never form a concept of God's wisdom if we couldn't abstract it from creatures [William of Ockham] |
| 5207 | If theism is non-sensical, then so is atheism. [Ayer] |
| 5209 | The 'truths' expressed by theists are not literally significant [Ayer] |