55 ideas
| 13939 | No possible evidence could decide the reality of numbers, so it is a pseudo-question [Carnap] |
| 16252 | Metaphysics uses empty words, or just produces pseudo-statements [Carnap] |
| 10676 | The Axiom of Choice is a non-logical principle of set-theory [Hossack] |
| 10686 | The Axiom of Choice guarantees a one-one correspondence from sets to ordinals [Hossack] |
| 23623 | Predicativism says only predicated sets exist [Hossack] |
| 23624 | The iterative conception has to appropriate Replacement, to justify the ordinals [Hossack] |
| 23625 | Limitation of Size justifies Replacement, but then has to appropriate Power Set [Hossack] |
| 10687 | Maybe we reduce sets to ordinals, rather than the other way round [Hossack] |
| 10677 | Extensional mereology needs two definitions and two axioms [Hossack] |
| 13342 | Carnap defined consequence by contradiction, but this is unintuitive and changes with substitution [Tarski on Carnap] |
| 13251 | Each person is free to build their own logic, just by specifying a syntax [Carnap] |
| 23628 | The connective 'and' can have an order-sensitive meaning, as 'and then' [Hossack] |
| 23627 | 'Before' and 'after' are not two relations, but one relation with two orders [Hossack] |
| 10671 | Plural definite descriptions pick out the largest class of things that fit the description [Hossack] |
| 10666 | Plural reference will refer to complex facts without postulating complex things [Hossack] |
| 10669 | Plural reference is just an abbreviation when properties are distributive, but not otherwise [Hossack] |
| 10675 | A plural comprehension principle says there are some things one of which meets some condition [Hossack] |
| 10673 | Plural language can discuss without inconsistency things that are not members of themselves [Hossack] |
| 10680 | The theory of the transfinite needs the ordinal numbers [Hossack] |
| 10684 | I take the real numbers to be just lengths [Hossack] |
| 23626 | Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack] |
| 10674 | A plural language gives a single comprehensive induction axiom for arithmetic [Hossack] |
| 10681 | In arithmetic singularists need sets as the instantiator of numeric properties [Hossack] |
| 10685 | Set theory is the science of infinity [Hossack] |
| 23621 | Numbers are properties, not sets (because numbers are magnitudes) [Hossack] |
| 23622 | We can only mentally construct potential infinities, but maths needs actual infinities [Hossack] |
| 13936 | Questions about numbers are answered by analysis, and are analytic, and hence logically true [Carnap] |
| 8748 | Logical positivists incorporated geometry into logicism, saying axioms are just definitions [Carnap, by Shapiro] |
| 8960 | Internal questions about abstractions are trivial, and external ones deeply problematic [Carnap, by Szabó] |
| 13933 | Existence questions are 'internal' (within a framework) or 'external' (concerning the whole framework) [Carnap] |
| 13934 | To be 'real' is to be an element of a system, so we cannot ask reality questions about the system itself [Carnap] |
| 13938 | A linguistic framework involves commitment to entities, so only commitment to the framework is in question [Carnap] |
| 10668 | We are committed to a 'group' of children, if they are sitting in a circle [Hossack] |
| 13935 | We only accept 'things' within a language with formation, testing and acceptance rules [Carnap] |
| 10664 | Complex particulars are either masses, or composites, or sets [Hossack] |
| 10678 | The relation of composition is indispensable to the part-whole relation for individuals [Hossack] |
| 10665 | Leibniz's Law argues against atomism - water is wet, unlike water molecules [Hossack] |
| 10682 | The fusion of five rectangles can decompose into more than five parts that are rectangles [Hossack] |
| 14305 | In the truth-functional account a burnt-up match was soluble because it never entered water [Carnap] |
| 19542 | It is nonsense that understanding does not involve knowledge; to understand, you must know [Dougherty/Rysiew] |
| 19543 | To grasp understanding, we should be more explicit about what needs to be known [Dougherty/Rysiew] |
| 19541 | Rather than knowledge, our epistemic aim may be mere true belief, or else understanding and wisdom [Dougherty/Rysiew] |
| 13932 | Empiricists tend to reject abstract entities, and to feel sympathy with nominalism [Carnap] |
| 13937 | New linguistic claims about entities are not true or false, but just expedient, fruitful or successful [Carnap] |
| 19540 | Don't confuse justified belief with justified believers [Dougherty/Rysiew] |
| 19539 | If knowledge is unanalysable, that makes justification more important [Dougherty/Rysiew] |
| 18699 | Carnap tried to define all scientific predicates in terms of primitive relations, using type theory [Carnap, by Button] |
| 13940 | All linguistic forms in science are merely judged by their efficiency as instruments [Carnap] |
| 13048 | Good explications are exact, fruitful, simple and similar to the explicandum [Carnap, by Salmon] |
| 10663 | A thought can refer to many things, but only predicate a universal and affirm a state of affairs [Hossack] |
| 12131 | All concepts can be derived from a few basics, making possible one science of everything [Carnap, by Brody] |
| 19538 | Entailment is modelled in formal semantics as set inclusion (where 'mammals' contains 'cats') [Dougherty/Rysiew] |
| 11968 | The intension of a sentence is the set of all possible worlds in which it is true [Carnap, by Kaplan] |
| 18285 | All translation loses some content (but language does not create reality) [Carnap] |
| 10683 | We could ignore space, and just talk of the shape of matter [Hossack] |