23 ideas
18951 | For scientific purposes there is a precise concept of 'true-in-L', using set theory [Putnam] |
18953 | Modern notation frees us from Aristotle's restriction of only using two class-names in premises [Putnam] |
18949 | The universal syllogism is now expressed as the transitivity of subclasses [Putnam] |
18952 | '⊃' ('if...then') is used with the definition 'Px ⊃ Qx' is short for '¬(Px & ¬Qx)' [Putnam] |
18958 | In type theory, 'x ∈ y' is well defined only if x and y are of the appropriate type [Putnam] |
18954 | Before the late 19th century logic was trivialised by not dealing with relations [Putnam] |
18956 | Asserting first-order validity implicitly involves second-order reference to classes [Putnam] |
18962 | Unfashionably, I think logic has an empirical foundation [Putnam] |
10061 | The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave] |
10065 | Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave] |
18961 | We can identify functions with certain sets - or identify sets with certain functions [Putnam] |
18955 | Having a valid form doesn't ensure truth, as it may be meaningless [Putnam] |
10049 | Logical truths may contain non-logical notions, as in 'all men are men' [Musgrave] |
10050 | A statement is logically true if it comes out true in all interpretations in all (non-empty) domains [Musgrave] |
18959 | Sets larger than the continuum should be studied in an 'if-then' spirit [Putnam] |
10058 | No two numbers having the same successor relies on the Axiom of Infinity [Musgrave] |
10062 | Formalism seems to exclude all creative, growing mathematics [Musgrave] |
10063 | Formalism is a bulwark of logical positivism [Musgrave] |
18957 | Nominalism only makes sense if it is materialist [Putnam] |
18950 | Physics is full of non-physical entities, such as space-vectors [Putnam] |
18960 | Most predictions are uninteresting, and are only sought in order to confirm a theory [Putnam] |
10060 | Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave] |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |