60 ideas
9123 | Someone standing in a doorway seems to be both in and not-in the room [Priest,G, by Sorensen] |
8720 | A logic is 'relevant' if premise and conclusion are connected, and 'paraconsistent' allows contradictions [Priest,G, by Friend] |
9672 | Free logic is one of the few first-order non-classical logics [Priest,G] |
9697 | X1 x X2 x X3... x Xn indicates the 'cartesian product' of those sets [Priest,G] |
9685 | <a,b&62; is a set whose members occur in the order shown [Priest,G] |
9674 | {x; A(x)} is a set of objects satisfying the condition A(x) [Priest,G] |
9673 | {a1, a2, ...an} indicates that a set comprising just those objects [Priest,G] |
9675 | a ∈ X says a is an object in set X; a ∉ X says a is not in X [Priest,G] |
9677 | Φ indicates the empty set, which has no members [Priest,G] |
9676 | {a} is the 'singleton' set of a (not the object a itself) [Priest,G] |
9678 | X⊆Y means set X is a 'subset' of set Y [Priest,G] |
9679 | X⊂Y means set X is a 'proper subset' of set Y [Priest,G] |
9681 | X = Y means the set X equals the set Y [Priest,G] |
9683 | X ∩ Y indicates the 'intersection' of sets X and Y, the objects which are in both sets [Priest,G] |
9684 | Y - X is the 'relative complement' of X with respect to Y; the things in Y that are not in X [Priest,G] |
9682 | X∪Y indicates the 'union' of all the things in sets X and Y [Priest,G] |
9692 | The 'union' of two sets is a set containing all the things in either of the sets [Priest,G] |
9693 | The 'intersection' of two sets is a set of the things that are in both sets [Priest,G] |
9694 | The 'relative complement' is things in the second set not in the first [Priest,G] |
9698 | The 'induction clause' says complex formulas retain the properties of their basic formulas [Priest,G] |
9696 | A 'cartesian product' of sets is the set of all the n-tuples with one member in each of the sets [Priest,G] |
9686 | A 'set' is a collection of objects [Priest,G] |
9687 | A 'member' of a set is one of the objects in the set [Priest,G] |
9695 | An 'ordered pair' (or ordered n-tuple) is a set with its members in a particular order [Priest,G] |
9688 | A 'singleton' is a set with only one member [Priest,G] |
9689 | The 'empty set' or 'null set' has no members [Priest,G] |
9690 | A set is a 'subset' of another set if all of its members are in that set [Priest,G] |
9691 | A 'proper subset' is smaller than the containing set [Priest,G] |
9680 | The empty set Φ is a subset of every set (including itself) [Priest,G] |
13373 | Typically, paradoxes are dealt with by dividing them into two groups, but the division is wrong [Priest,G] |
13368 | The 'least indefinable ordinal' is defined by that very phrase [Priest,G] |
13370 | 'x is a natural number definable in less than 19 words' leads to contradiction [Priest,G] |
13369 | By diagonalization we can define a real number that isn't in the definable set of reals [Priest,G] |
13366 | The least ordinal greater than the set of all ordinals is both one of them and not one of them [Priest,G] |
13367 | The next set up in the hierarchy of sets seems to be both a member and not a member of it [Priest,G] |
13372 | There are Liar Pairs, and Liar Chains, which fit the same pattern as the basic Liar [Priest,G] |
13371 | If you know that a sentence is not one of the known sentences, you know its truth [Priest,G] |
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] |
3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
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] |