mathematics

russell’s paradox is paradoxical – but not in that way overview Russell’s paradox is held as an example of why set-theoretic sets cannot not contain themselves – the paradox depends upon a set, which is the result of a specifically crafted predicate, containing itself, in violation of respective predicate constraints. #todo plainly describe Russell’s paradox However fun and engaging russell’s paradox is – by the time the specifically crafted predicate enters the scene (of russell’s example), a more fundamental paradox (of a set containing itself) has already occurred....

what are we studying when we are doing mathematics? map and territory Consider map and territory 1 2: Science interprets territory, formally, to compose representational maps Engineering composes (or shapes) territory, by applying map to circumstances, through action Mathematics, central to science and engineering, formalises cartography and navigation of map and territory, and more: mathematics charts the form and characteristics 3 of the nexus 4 between map and territory – fundamentals of constraint, structure and behaviour 5, of interpretation, representation, and cognition 6 alignment Consider that:...