22 ideas
6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
12797 | If plural variables have 'some values', then non-count variables have 'some value' [Laycock] |
12794 | Plurals are semantical but not ontological [Laycock] |
6304 | Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik] |
17694 | Some non-count nouns can be used for counting, as in 'several wines' or 'fewer cheeses' [Laycock] |
17695 | Some apparent non-count words can take plural forms, such as 'snows' or 'waters' [Laycock] |
6300 | Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik] |
6303 | Sets are positions in patterns [Resnik] |
6302 | Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik] |
6295 | There are too many mathematical objects for them all to be mental or physical [Resnik] |
6296 | Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik] |
6301 | Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik] |
16062 | A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow] |
16061 | If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow] |
12792 | The category of stuff does not suit reference [Laycock] |
12799 | Descriptions of stuff are neither singular aggregates nor plural collections [Laycock] |
12818 | We shouldn't think some water retains its identity when it is mixed with air [Laycock] |
16060 | Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow] |
16064 | The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow] |
12795 | Parts must be of the same very general type as the wholes [Laycock] |
17696 | 'Humility is a virtue' has an abstract noun, but 'water is a liquid' has a generic concrete noun [Laycock] |
12791 | It is said that proper reference is our intellectual link with the world [Laycock] |