On logic and truth

Logical reasoning requires that we assume something. After that, every conclusion is also an assumption in the chain of logical deductions. This chain of deductions does, however, proceed from either the generic to the specific or vice versa (ie, if men are mortal and Aristotle is a man, then Aristotle is mortal, or if Aristotle is a man and Aristotle is mortal, then men are mortal, respectively).

These two entrances to logical reasoning are orthogonal. None is right or wrong, although it is unsupported both to assume that men are mortal and to deduce that men are mortal just because Aristotle is mortal, respectively. However, the facts 1. that the two entrances are orthogonal, 2. that every deduction in both entrances also is an assumption, and 3. that an assumption in one is a deduction in the other means that the two form two distinct systems: nominalism and realism, or objectivity and subjectivity, respectively. These two systems do thus discuss the same matter (ie, reality) logically in two totally different ways. The difference between them is that the former discusses process, whereas the latter discusses pattern. This may not be immediately obvious, but understanding that class orthogonally corresponds to process helps to straighten out this difference.

Now, the fact that they are different means that they have different internal relations as well as relations to the reality they discuss. The former (ie, nominalism) is internally consistent but ambiguous in relation to reality, whereas the latter (ie, realism) is consistently contradictory. It means that we when we discuss reality can only choose between being ambiguous in relation to reality or being consistently contradictory. The option of being both unambiguous and non-contradictory simply does not exist. Logic can thus not reach the truth.

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