What does logic reveal about reality?

This is about a loop in our universe (that includes us), and which I’ve long been fascinated by.

To quote from another post I wrote, The introspective cosmos:

We are each an organism with a brain that creates something we call consciousness that allows us to reflect on ourselves, individually. And the Universe created, via an extraordinary convoluted process, the ability to reflect on itself, its origins and its possible meaning.

This insight is also reflected in Eugene Wigner’s 2 miracles: the miracle that the Universe can be comprehended and the miracle that we have the ability to comprehend it to the degree that we do. Or as Einstein so famously said:

The most incomprehensible thing about the Universe is that it’s comprehensible.

As Wigner explicitly stated and Einstein implicitly believed, the medium for that comprehension is mathematics. This loop, that I alluded to in my opening, is also implicit in Roger Penrose’s 3 worlds.

The question in the title was one I found on Quora. Most of the questions that Quora’s algorithms address to me are either too silly, or too specialist and esoteric for my capabilities to respond.

In this case, after reading the other answers, I thought they had largely missed the mark, and perhaps the point. The authors may draw the same conclusion about my answer.

I found that my answer went in a subtly different direction to what I intended, but resulted in a mini-epiphany. There is a limit to what we can know because there will always be a limit to the mathematics we know, which thus far determines what we know of the cosmos.

My answer to What does logic reveal about reality?


Fundamentally, it reveals that there are limits to what we can know.

Epistemology is the ‘theory of knowledge’ (dictionary definition) - effectively, the study of what we can know. Whereas ontology is defined as ‘the nature of being’, which, in effect, is what we call reality.

Since the Enlightenment, it’s become increasingly apparent that it’s our knowledge of mathematics that determines the limits of what we can know, both at the cosmological and the infinitesimal scale. But mathematics itself has epistemological limits according to Godel’s Incompleteness Theorem.

In effect, Godel proved that, in any axiom based mathematical system, there will be mathematical truths that we can’t prove. In practice, this means that there will always be mathematical truths that lie beyond what we currently know. In this context, ‘what we currently know’ is transient. So even though we may, and will, know more in the future, it will never be complete.

The point is that we use logic to reveal these mathematical truths and so the corollary to Godel’s theorem is that there will always be a limit to what that logic can reveal, no matter how much it has revealed already. Basically, we extend our knowledge by extending our axiomatic system. To give an example: by employing the new axiom, √-1 = i, we uncovered a whole new realm of mathematics.

Some centuries later, we then used that particular mathematics (called complex algebra) to describe a newly discovered phenomena called quantum mechanics (QM). In fact, without that knowledge (revealed by pure logic) quantum mechanics would never have been developed into a consistent and highly successful theory. And arguably, QM is ‘the evanescent substrate on which we all exist’ [or reality] to quote Clifford A Pickover.

And this is the loop: QM is the substrate of the Universe, which created humans which discovered an abstract mathematics, which not only describes, but prescribes the rules for QM.