Simplisically, following Wittgenstein's principle that 'meaning is usage', words are not to be taken as representational of 'things in themselves' but are 'nodes of significance' within communicative behavior whose utility is evaluated by successful goal attainment. Meanings cannot be divorced from the contexts in which they are used and they in turn are agents in the construction of those transient states we call 'reality'. Lakoff goes further than this by arguing that all language is embedded in bodily behaviors such as 'entering', 'leaving', falling etc...hence the human concepts of 'inside', 'outside' etc. Thus 'words' are 'metaphors' for our bodily relationsips with what we call 'the world'.
As far as 'set theory' is concerned and its foundation for classical logic, this is related to the human behavior we call 'measurement' the first level of which
is 'the nominal' or 'naming'. The disadvantage of this is that 'things' are then deemed to have 'independent properties' which cement their set membership, when in fact set membership can be contextually dynamic as far as behavior is concerned. Non binary logics such as 'fuzzy logic' have been subsequently developed as a result.
You will find, by the way, by reading my posting history that I take the view 'existence' is always relative, and never absolute. What 'exists' is often 'agreed' by most humans because of their common physiology and needs, but where needs differ arguments about 'absolute existence' are futile.