Knowing maths

In science, and especially in physics, concepts are defined in mathematical language. In this way we might say that knowing the maths of a theory is possible. However, are mathematical statements truths? Their claim to universality is based on the definition of concepts through axioms that are ‘such obvious concepts’ that they must be universal. However since they only describe themselves they are not in any real sense true; they do not claim to describe some universal physical existence. The role of maths is to provide abstract objects that we can use as tools in our reflections on our observations of reality. They do not of themselves provide knowledge of reality.

The use of the word ‘knowledge’, in the sense of knowing something means it must be true, makes the idea of a framework for the sources of knowledge seem over-ambitious or at least the sources in this framework don’t seem to be genuine sources. Observation and reason are not sources of ‘knowledge’ but instead should be considered as routes to better understanding which only reach ‘knowledge’ when pursued to their ultimate. Nevertheless I shall continue to refer to observation and reason as ‘the sources of knowledge’ in anticipation of applying a more appropriate meaning to the word ‘knowledge’.

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