Aristotle

“ If ultimate principles do exist not everything can be demonstrable, nor can the process of demonstration continue to infinity. A necessary consequence of either of these conclusions would be that there can be no immediate and inseparable propositions, but that everything must be mediate and separable, for that which is demonstrated is demonstrated by the interposition of one term between two others, not by the addition of one from outside. Hence, if Deduction could go on to infinity, infinite means might exist between two terms. ”

“ In saying ‘the white thing is a stick,’ I mean ‘that which has the accidental quality of whiteness is a stick,’ not that ‘the white thing’ is the subject of which ‘stick’ is the predicate. It is in fact a stick not because it is white nor from being essentially white, so that ‘this white thing’ is only accidentally a stick. ”

“ It clearly terminates in the case of predications concerning the essence of a thing, for if the essential attributes can be defined and are knowable, and if one cannot reach to the end of the infinite, predications of essential attributes must needs have some limit. To give a general turn to the statement we may express ourselves thus. It is equally possible to say with truth that ‘this white thing is walking’ and ‘that great thing is a stick,’ or again ‘the stick is great’ and ‘the man is walking,’ but there is a difference between the two pairs of expressions. ”

“ The mind cannot traverse an infinity, and as Substance, for instance, is definable, its attributes must be limited. In other words demonstration is applicable only to Essentials (καθ’ ατά) which cannot be unlimited, for that would render definition impossible. As it is possible, the attributes are limited. Hence demonstration possesses certain principles which are not themselves capable of any demonstration. That affirmative demonstration terminates at a certain point may be proved dialectically as follows. ”