About mathematics:-

There are various views about what mathematics ‘is’ or ‘ought to be’.

Some view mathematics, and – more broadly – logic, as a human or social construct, and hence is perhaps appropriately viewed from some ‘philosophical’ or ‘pragmatic’ perspective. The more credible of these views are noted either under the ‘SCIENCES’ tab or under this one. (I welcome suggestions for more to consider.)

Others give primacy to ‘Logic’, for which see the ‘mathematical logic’ tab under ‘LOGICS’.

A key concern is the status of ‘Applied Maths’. From a more pragmatic perspective, this is justified in the same way as anything else, such as science, according to the relevant culture.

This approach seems reasonable when applied in a context in which the consequences seem reasonable (e.g. see here). But less reasonable without such a favourable track record.

Another view, implict in much usage of the term ‘mathematization‘ , is that mathematics only needs to deal with interpretations or ‘views’ of reality ‘at face value’.   The correspondence between some possible reality and an interpretation of it is either regarded as a ‘scientific’ question, or simply taken for granted.

Yet mathematical logic has much to say on the nature of possible correspondence, and an alternative view is that any ‘given’ view out to be subject to logical analysis. Category Theory is the mathematical subject that reflects one, credible, view of what is appropriate. But not all applied maths, statistics, probability theory or science takes the same view, allowing additional ‘pragmas’. The appropriate application of mathematics is thus an open question.

 

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