78 ideas
9136 | The paradox of analysis says that any conceptual analysis must be either trivial or false [Sorensen] |
9131 | Two long understandable sentences can have an unintelligible conjunction [Sorensen] |
13252 | Some truths have true negations [Beall/Restall] |
13247 | A truthmaker is an object which entails a sentence [Beall/Restall] |
9139 | If nothing exists, no truthmakers could make 'Nothing exists' true [Sorensen] |
9140 | Which toothbrush is the truthmaker for 'buy one, get one free'? [Sorensen] |
13249 | (∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically [Beall/Restall] |
13243 | Excluded middle must be true for some situation, not for all situations [Beall/Restall] |
13242 | It's 'relevantly' valid if all those situations make it true [Beall/Restall] |
13245 | Relevant consequence says invalidity is the conclusion not being 'in' the premises [Beall/Restall] |
13246 | Relevant logic does not abandon classical logic [Beall/Restall] |
13254 | A doesn't imply A - that would be circular [Beall/Restall] |
13255 | Relevant logic may reject transitivity [Beall/Restall] |
13250 | Free logic terms aren't existential; classical is non-empty, with referring names [Beall/Restall] |
18395 | Sets are mereological sums of the singletons of their members [Lewis, by Armstrong] |
15496 | We can build set theory on singletons: classes are then fusions of subclasses, membership is the singleton [Lewis] |
15500 | Classes divide into subclasses in many ways, but into members in only one way [Lewis] |
15499 | A subclass of a subclass is itself a subclass; a member of a member is not in general a member [Lewis] |
15498 | We can accept the null set, but there is no null class of anything [Lewis] |
15502 | There are four main reasons for asserting that there is an empty set [Lewis] |
15503 | We needn't accept this speck of nothingness, this black hole in the fabric of Reality! [Lewis] |
15497 | We can replace the membership relation with the member-singleton relation (plus mereology) [Lewis] |
15506 | If we don't understand the singleton, then we don't understand classes [Lewis] |
15511 | If singleton membership is external, why is an object a member of one rather than another? [Lewis] |
15513 | Maybe singletons have a structure, of a thing and a lasso? [Lewis] |
15507 | Set theory has some unofficial axioms, generalisations about how to understand it [Lewis] |
10191 | Set theory reduces to a mereological theory with singletons as the only atoms [Lewis, by MacBride] |
15508 | If singletons are where their members are, then so are all sets [Lewis] |
15514 | A huge part of Reality is only accepted as existing if you have accepted set theory [Lewis] |
15523 | Set theory isn't innocent; it generates infinities from a single thing; but mathematics needs it [Lewis] |
13235 | Logic studies consequence; logical truths are consequences of everything, or nothing [Beall/Restall] |
13238 | Syllogisms are only logic when they use variables, and not concrete terms [Beall/Restall] |
13234 | The view of logic as knowing a body of truths looks out-of-date [Beall/Restall] |
13232 | Logic studies arguments, not formal languages; this involves interpretations [Beall/Restall] |
13241 | The model theory of classical predicate logic is mathematics [Beall/Restall] |
13253 | There are several different consequence relations [Beall/Restall] |
13240 | A sentence follows from others if they always model it [Beall/Restall] |
9119 | No attempt to deny bivalence has ever been accepted [Sorensen] |
9135 | We now see that generalizations use variables rather than abstract entities [Sorensen] |
15525 | Plural quantification lacks a complete axiom system [Lewis] |
15518 | I like plural quantification, but am not convinced of its connection with second-order logic [Lewis] |
13236 | Logical truth is much more important if mathematics rests on it, as logicism claims [Beall/Restall] |
9125 | Denying problems, or being romantically defeated by them, won't make them go away [Sorensen] |
9137 | Banning self-reference would outlaw 'This very sentence is in English' [Sorensen] |
13237 | Preface Paradox affirms and denies the conjunction of propositions in the book [Beall/Restall] |
15524 | Zermelo's model of arithmetic is distinctive because it rests on a primitive of set theory [Lewis] |
15517 | Giving up classes means giving up successful mathematics because of dubious philosophy [Lewis] |
15515 | To be a structuralist, you quantify over relations [Lewis] |
15520 | Existence doesn't come in degrees; once asserted, it can't then be qualified [Lewis] |
15504 | Atomless gunk is an individual whose parts all have further proper parts [Lewis] |
15501 | We have no idea of a third sort of thing, that isn't an individual, a class, or their mixture [Lewis] |
9116 | Vague words have hidden boundaries [Sorensen] |
15516 | A property is any class of possibilia [Lewis] |
9132 | An offer of 'free coffee or juice' could slowly shift from exclusive 'or' to inclusive 'or' [Sorensen] |
14748 | The many are many and the one is one, so they can't be identical [Lewis] |
6129 | Lewis affirms 'composition as identity' - that an object is no more than its parts [Lewis, by Merricks] |
15512 | In mereology no two things consist of the same atoms [Lewis] |
15519 | Trout-turkeys exist, despite lacking cohesion, natural joints and united causal power [Lewis] |
15521 | Given cats, a fusion of cats adds nothing further to reality [Lewis] |
15522 | The one has different truths from the many; it is one rather than many, one rather than six [Lewis] |
10566 | Lewis prefers giving up singletons to giving up sums [Lewis, by Fine,K] |
14244 | Lewis only uses fusions to create unities, but fusions notoriously flatten our distinctions [Oliver/Smiley on Lewis] |
10660 | A commitment to cat-fusions is not a further commitment; it is them and they are it [Lewis] |
13244 | Relevant necessity is always true for some situation (not all situations) [Beall/Restall] |
9128 | It is propositional attitudes which can be a priori, not the propositions themselves [Sorensen] |
9130 | Attributing apriority to a proposition is attributing a cognitive ability to someone [Sorensen] |
15509 | Some say qualities are parts of things - as repeatable universals, or as particulars [Lewis] |
9118 | The colour bands of the spectrum arise from our biology; they do not exist in the physics [Sorensen] |
9124 | We are unable to perceive a nose (on the back of a mask) as concave [Sorensen] |
9126 | Bayesians build near-certainty from lots of reasonably probable beliefs [Sorensen] |
9121 | Illusions are not a reason for skepticism, but a source of interesting scientific information [Sorensen] |
13239 | Judgement is always predicating a property of a subject [Beall/Restall] |
9134 | The negation of a meaningful sentence must itself be meaningful [Sorensen] |
13248 | We can rest truth-conditions on situations, rather than on possible worlds [Beall/Restall] |
13233 | Propositions commit to content, and not to any way of spelling it out [Beall/Restall] |
9133 | Propositions are what settle problems of ambiguity in sentences [Sorensen] |
9129 | I can buy any litre of water, but not every litre of water [Sorensen] |
9122 | God cannot experience unwanted pain, so God cannot understand human beings [Sorensen] |