Logic is all about assumptions and deductions. We have to assume something to be able to deduce something. Deductions are then logically “true” based on their assumptions. It means that logic is sensible only if the assumptions are sensible, ie, self-evident or undeniable.
The fundamental problem with this procedure is, however, that every assumption also is a possible deduction, since the process of assumption-deduction can go either from the specific to the generic or vice versa, and that since every deduction from sensible assumptions also is sensible (per definition) there are two orthogonal (diametrically opposed) entrances to logic, and thus two orthogonal logical systems. We can, for example assume 1a. that Aristotle is human and 1b. that humans are mortal, and then deduce that Aristotle is mortal, or 1b. that Aristotle was an idiot, and then deduce that humans are idiots. In the former we deduce that Aristotle is mortal from the assumption that humans are mortal, and in the latter we deduce that humans are idiots by assuming that Aristotle was an idiot. Both these deductions are logically “true”, but the latter appears insensible.
So, what’s the problem with the latter deduction? Well, it appears to reside in that the assumption that “Aristotle was an idiot” is insensible, but it actually doesn’t. Instead, it resides in that we can deduce something about something inside a group that share some trait, ie, go from the generic to the specific, but can’t deduce something about something in a group from a single member of that group, ie, go from the specific to the generic. It is simply insensible to deduce that the swede Karl is stupid by assuming that the swede Arne is stupid (although none the less logical).
These two entrances to logic is called science (the former) and populism (the latter). Populism is thus not illogical, but just insensible.