53 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] |
| 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] |
| 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] |
| 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] |
| 6346 | The main epistemological theories are foundationalist, coherence, probabilistic and reliabilist [Pollock/Cruz] |
| 6351 | Most people now agree that our reasoning proceeds defeasibly, rather than deductively [Pollock/Cruz] |
| 6374 | To believe maximum truths, believe everything; to have infallible beliefs, believe nothing [Pollock/Cruz] |
| 6355 | Direct realism says justification is partly a function of pure perceptual states, not of beliefs [Pollock/Cruz] |
| 6359 | Phenomenalism offered conclusive perceptual knowledge, but conclusive reasons no longer seem essential [Pollock/Cruz] |
| 6366 | Perception causes beliefs in us, without inference or justification [Pollock/Cruz] |
| 6362 | Sense evidence is not beliefs, because they are about objective properties, not about appearances [Pollock/Cruz] |
| 6371 | Bayesian epistemology is Bayes' Theorem plus the 'simple rule' (believe P if it is probable) [Pollock/Cruz] |
| 6373 | Internalism says if anything external varies, the justifiability of the belief does not vary [Pollock/Cruz] |
| 6353 | People rarely have any basic beliefs, and never enough for good foundations [Pollock/Cruz] |
| 6361 | Foundationalism requires self-justification, not incorrigibility [Pollock/Cruz] |
| 6357 | Reason cannot be an ultimate foundation, because rational justification requires prior beliefs [Pollock/Cruz] |
| 6363 | Foundationalism is wrong, because either all beliefs are prima facie justified, or none are [Pollock/Cruz] |
| 6365 | Negative coherence theories do not require reasons, so have no regress problem [Pollock/Cruz] |
| 6354 | Coherence theories fail, because they can't accommodate perception as the basis of knowledge [Pollock/Cruz] |
| 6367 | Coherence theories isolate justification from the world [Pollock/Cruz] |
| 6370 | Externalism comes as 'probabilism' (probability of truth) and 'reliabilism' (probability of good cognitive process) [Pollock/Cruz] |
| 6358 | One belief may cause another, without being the basis for the second belief [Pollock/Cruz] |
| 6364 | We can't start our beliefs from scratch, because we wouldn't know where to start [Pollock/Cruz] |
| 6352 | Enumerative induction gives a universal judgement, while statistical induction gives a proportion [Pollock/Cruz] |
| 6372 | Since every tautology has a probability of 1, should we believe all tautologies? [Pollock/Cruz] |
| 6360 | Scientific confirmation is best viewed as inference to the best explanation [Pollock/Cruz] |
| 23224 | That all matter thinks is absurd, and would make each part of our bodies a distinct self-consciousness [Bentley] |