A Missing Foundation to Reason?

Post by dcleve

This is an extension of my earlier discussion on the Munchausen Trilemma, and the difficulty of justifying any belief. Here, I offer a discussion on the same theme, with a look at classical reasoning, and whether, or why, we can or should trust its validity.

A key starting point in my discussion is informed by the thinking about mathematics, and Euclidean Geometry in particular, over the last several centuries. For most of the history of thought, mathematics and geometry were treated as undeniable - they were just the way things were. Several centuries ago, however, mathematicians discovered they could make different postulates, and derive completely different math systems. This brought the "necessity" of our math into question, but whether this was substantive or just a peculiar aberration was not settled. UNTIL -- non-Euclidean math ended up being what fit our best model of physics.

This changed decisively how math is perceived. It is no longer considered undeniable, or a logical necessity. Instead, math is treated as an almost arbitrary formalism, which may or may not correspond with how the world seems to work.

Less widely recognized is that logic is also a system of formalisms, and is plausibly likewise subject to arbitrary alternatives.

This becomes clearer, when one realizes that set theory is a branch of mathematics, AND that set theory is a key feature of formal logic.

I suggest that the traditional view of logic as the “laws of thought,” “the rules of right reasoning,” or “the principles of valid argumentation” https://www.britannica.com/topic/philosophy-of-logic is incorrect. And that instead, one could postulate an almost infinite number of variant logics. This is a hypothesis that people have explored, and they HAVE come up with multitudes of self-consistent logic types, which would produce different truth outcomes from each other if applied to a problem.

I further suggest that we humans seem to have an inborn basic reasoning skill: https://www.scientificamerican.com/article/babies-think-logically-before-they-can-talk/ http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.335.7003&rep=rep1&type=pdf

This basic reasoning is mostly effective, but has some major shortcomings: https://www.edge.org/conversation/daniel_kahneman-the-marvels-and-the-flaws-of-intuitive-thinking-edge-master-class-2011

When we use our inborn basic reasoning to critique itself, and then correct the discovered shortcomings, I think we basically end up with formal Aristotelian logic. What my suggestion holds, then is that reasoning is radically contingent, and the reasoning we have ended up with, was the result of evolutionary tuning for effectiveness. This would make reasoning, and the rules by which we think -- an empirical discovery, justified solely by its Darwinian success. This pragmatic/ success oriented, Darwinian justification for science and empiricism has generally been taken as DIFFERENT from the justification for accepting reasoning. The thinking I advance here, is that they are both solely pragmatically justified.

The problem I discuss, and possible answers to that problem, are closely related to an interesting essay by one of the more philosophically insightful physicists, Lee Smolin. https://arxiv.org/pdf/1506.03733.pdf Smolin's focus is on rejecting any variant of platonic idealism, or any reality to Popper's world 3. Smolin accepts my premise with respect to math, and by identifying logic as a subset of math, he agrees with the thrust of my discussion. He treats logic and math to be underlying features of physics, which could have been otherwise. How logic and math are created by physical substance, he does not know -- this would become a further project for physics to explore. I offer Smolin's essay, not as something I endorse, but as an indication that this is a subject, and question, which our exploration of the relation between physics and math/logic is forcing upon us.

My second image is a book cover for a book I have not read, but which illustrates the potentials for alternate logics. A portion of the abstract highlights the potential for alternate logics:

Science tells us what is true; that is science's prerogative. But the universe has beauty and goodness as well as truth. How reconcile and unify? The pancalistic answer is that the good and the true is so because it is beautiful. The final court of appeal is aesthetic. Nothing can be true without being beautiful, nor anything that is in any high sense good. The ascription of beauty, a reasoned, criticised, thought-out ascription of æsthetic quality, is the final form of our thought about nature, man, the world, the all.

I know of at least one field that is a valid subject of study, and falls outside empiricism or reasoning, and that is aesthetics. That one can use aesthetics as a truth reference, and source of logic, which would be orthogonal to science, is a consequence of these observations. That someone tried to do this in a major philosophical work -- is unsurprising to me, but may be a surprise to some of the other posters here.

B&B orig: 6/12/19