70 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] |
| 18137 | Impredicative definitions are wrong, because they change the set that is being defined? [Bostock] |
| 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] |
| 18122 | Classical interdefinitions of logical constants and quantifiers is impossible in intuitionism [Bostock] |
| 18114 | There is no single agreed structure for set theory [Bostock] |
| 18107 | A 'proper class' cannot be a member of anything [Bostock] |
| 18115 | We could add axioms to make sets either as small or as large as possible [Bostock] |
| 18139 | The Axiom of Choice relies on reference to sets that we are unable to describe [Bostock] |
| 18105 | Replacement enforces a 'limitation of size' test for the existence of sets [Bostock] |
| 18109 | The completeness of first-order logic implies its compactness [Bostock] |
| 18108 | First-order logic is not decidable: there is no test of whether any formula is valid [Bostock] |
| 9119 | No attempt to deny bivalence has ever been accepted [Sorensen] |
| 9135 | We now see that generalizations use variables rather than abstract entities [Sorensen] |
| 18123 | Substitutional quantification is just standard if all objects in the domain have a name [Bostock] |
| 18120 | The Deduction Theorem is what licenses a system of natural deduction [Bostock] |
| 9125 | Denying problems, or being romantically defeated by them, won't make them go away [Sorensen] |
| 18125 | Berry's Paradox considers the meaning of 'The least number not named by this name' [Bostock] |
| 9137 | Banning self-reference would outlaw 'This very sentence is in English' [Sorensen] |
| 18100 | ω + 1 is a new ordinal, but its cardinality is unchanged [Bostock] |
| 18101 | Each addition changes the ordinality but not the cardinality, prior to aleph-1 [Bostock] |
| 18102 | A cardinal is the earliest ordinal that has that number of predecessors [Bostock] |
| 18106 | Aleph-1 is the first ordinal that exceeds aleph-0 [Bostock] |
| 18095 | Instead of by cuts or series convergence, real numbers could be defined by axioms [Bostock] |
| 18099 | The number of reals is the number of subsets of the natural numbers [Bostock] |
| 18093 | For Eudoxus cuts in rationals are unique, but not every cut makes a real number [Bostock] |
| 18110 | Infinitesimals are not actually contradictory, because they can be non-standard real numbers [Bostock] |
| 18156 | Modern axioms of geometry do not need the real numbers [Bostock] |
| 18097 | The Peano Axioms describe a unique structure [Bostock] |
| 18149 | There are many criteria for the identity of numbers [Bostock] |
| 18148 | Hume's Principle is a definition with existential claims, and won't explain numbers [Bostock] |
| 18145 | Many things will satisfy Hume's Principle, so there are many interpretations of it [Bostock] |
| 18143 | Frege makes numbers sets to solve the Caesar problem, but maybe Caesar is a set! [Bostock] |
| 18116 | Numbers can't be positions, if nothing decides what position a given number has [Bostock] |
| 18117 | Structuralism falsely assumes relations to other numbers are numbers' only properties [Bostock] |
| 18141 | Nominalism about mathematics is either reductionist, or fictionalist [Bostock] |
| 18157 | Nominalism as based on application of numbers is no good, because there are too many applications [Bostock] |
| 18150 | Actual measurement could never require the precision of the real numbers [Bostock] |
| 18158 | Ordinals are mainly used adjectively, as in 'the first', 'the second'... [Bostock] |
| 18127 | Simple type theory has 'levels', but ramified type theory has 'orders' [Bostock] |
| 18144 | Neo-logicists agree that HP introduces number, but also claim that it suffices for the job [Bostock] |
| 18147 | Neo-logicists meet the Caesar problem by saying Hume's Principle is unique to number [Bostock] |
| 18111 | Treating numbers as objects doesn't seem like logic, since arithmetic fixes their totality [Bostock] |
| 18129 | Many crucial logicist definitions are in fact impredicative [Bostock] |
| 18146 | If Hume's Principle is the whole story, that implies structuralism [Bostock] |
| 18159 | Higher cardinalities in sets are just fairy stories [Bostock] |
| 18155 | A fairy tale may give predictions, but only a true theory can give explanations [Bostock] |
| 18140 | The best version of conceptualism is predicativism [Bostock] |
| 18138 | Conceptualism fails to grasp mathematical properties, infinity, and objective truth values [Bostock] |
| 18133 | The usual definitions of identity and of natural numbers are impredicative [Bostock] |
| 18131 | If abstracta only exist if they are expressible, there can only be denumerably many of them [Bostock] |
| 18134 | Predicativism makes theories of huge cardinals impossible [Bostock] |
| 18135 | If mathematics rests on science, predicativism may be the best approach [Bostock] |
| 18136 | If we can only think of what we can describe, predicativism may be implied [Bostock] |
| 18132 | The predicativity restriction makes a difference with the real numbers [Bostock] |
| 9116 | Vague words have hidden boundaries [Sorensen] |
| 9132 | An offer of 'free coffee or juice' could slowly shift from exclusive 'or' to inclusive 'or' [Sorensen] |
| 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] |
| 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] |
| 9134 | The negation of a meaningful sentence must itself be meaningful [Sorensen] |
| 9133 | Propositions are what settle problems of ambiguity in sentences [Sorensen] |
| 18121 | In logic a proposition means the same when it is and when it is not asserted [Bostock] |
| 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] |
| 5974 | People report seeing through rocks, or over the horizon, or impossibly small works [Plutarch] |