On the limits of logical reasoning

Logical reasoning (ie, deduction) starts from assumptions (ie, premises), which can be either concern classes or objects. The principle is that it starts from two premises, whereof one is a specific statement, like ‘Aristotle is a man’, and the other is a generic statement, like ‘men are mortal’, and the deduction is a specific statement, like ‘Aristotle is mortal’. However, ‘man’ and ‘mortal’ can also be switched between deduction and assumption into that “Aristotle is mortal”, in which case the deduction instead is that ‘Aristotle is a man’. In both cases the generic premise acts as a catalyst to arrive to the deduction. The premises can, however, also be switched into the two specific statements that ‘Aristotle is a man’ and ‘Aristotle is mortal’, in which case the deduction is the generic statement that ‘men are mortal’.

These possibilities means that it is possible to deduce every assumption from different premises, meaning that assumption actually equals deduction. Now, the problem with this fact is that it means that deduction (in itself) is both circular and ambiguous between assumption and deduction. Each of these properties is problematical but not inconsistent in themselves, but together they are inconsistent. A process that is circular both along and across can never reach an unambiguous end point. Together they thus mean that logical reasoning can never reach an unambiguous end point.