From Human Action (4th Ed.), pg. 36: “It is a general fallacy to believe that the writings of Lucien Levy-Bruhl [guy who studied cognition in ancient/primitive cultures] give support to the doctrine that the logical structure of mind of primitive man was and is categorially different from that of civilized man. On the contrary, what Levy-Bruhl, on the basis of a careful scrutiny of the entire ethnological material available, reports about the mental functions of primitive man proves clearly that the fundamental logical relations and the categories of thought and action play in the intellectual activities of savages the same role they play in our own life. The content of primitive man’s thoughts differs from the content of our thoughts, but the formal and logical structure is common to both.”
And there is a bit more discussion of similar topics around there.
Also, it seems apparent to me that without logical thinking ability, primitive man could not have survived. For example, without deduction, if a man is being chased by three cheetahs in the dark and he knows he has only speared two of them, if there is now silence how does he make the decision whether to keep running or attempt to fight? Process of elimination. He needs the same representational system that lets a child solve this very simple logic puzzle: “I’m thinking of a number, either 1, 2, or 3. It’s not 1 and it’s not 2. What is it?” Our systems of logic are either innate (nature) or are built up by a process of trial and error as we develop (nurture), and probably both (nature and nurture).
To see why the latter is plausible, consider: is the logical representation system in your own mind any more sophisticated, efficient, and precise after having spent a few years studying advanced math? After having to conceptualize the notion of an infinite series of numbers adding up to a finite quantity? After learning about infinity and then “bigger infinities”? After thinking about infinite-dimensional spaces?
I certainly think so. Whereas at first your ways of conceptualizing numbers and infinities may have been very inefficient and haphazard, succeeding in math forced you to scrap and/or refine those representational systems in your own mind to accommodate new concepts without introducing any ambiguity. If you had a flaw in your logical representation structure in your mind, that flaw would manifest itself in the form of wrong answers or lack of comprehension. In order to proceed beyond that area of math (which seems impossible at the time, but eventually you do), you MUST have had to fix that flaw in your logical representational system. Maybe it’s still not perfect, but it’s now serviceable enough to handle the subject at hand. And so on, as you move up in math, or whatever field - I chose math because it’s a field of pure concepts.
Similarly, the trials and tribulations of everyday life force us to develop better and better representational systems for dealing with the logic of the real world. How much of it is inborn and how much is learned we can’t know yet, but if the idea that “something cannot be both green and not green at the same time” (and the abstraction of that idea to " ‘A and ~A’ is impossible") is not hardwired into us, it is surely learned through trial and error pretty soon. Likewise with other of the cataloged formal logical operations. As you encounter each new situation, you can say with more and more accuracy, “Aha! This must an example of this logical concept.” If reality proves consistent with your conclusion, you learn to trust that logical concept more. If reality proves you wrong, you either revise your logic or you continue to be wrong. But flawed logic doesn’t just make you a fool, at the extreme it makes you dead.