Why Logic Fails When Describing Abstract Ideas

Quite recently on the forum, there was an excellent thread about the life and work of Ludwig Wittgenstein. Although the man himself was fascinating, this article was simply inspired by his questioning of language and logic. If you wish to read more about the man himself and the subsequent discussion, check out the thread here.

How do we know what we can’t know? Let’s think it through, step by step.

Physical Existence

We can describe everything that physically exists with language. For instance, I can describe the shirt I am currently wearing. It is a grey, crew neck, long sleeved shirt made out of cotton and polyester. It helps to insulate my body and keep me warm. My description, although perhaps not comprehensive, is enough to paint a picture in your mind of what my shirt is like.

Were I to describe my shirt further, I might go into more detail on the shade of the color, the direction of the stitching, the slight discolorations, or the exact length. In fact, I could even pull out a microscope and describe the shape of every little dust particle on my shirt.

Supposing technological limitations were not a factor, I could continue to describe my shirt for all of eternity, focusing on smaller and smaller pieces until we get to sub-atomic particles and sub-sub-atomic particles. Never once would language fail me in this instance. There will always be words to describe what I am seeing, because the shirt physically exists. We could perform the same exercise with a red shirt, a baseball, a human being, or the Grand Canyon and still be able to describe with language that which we see.

Non-Physical Existence

How about non-physical entities? Can words describe those? First, we must dissect what a non-physical entity is. If something is non-physical, it, by definition, has not been seen, heard, touched, smelled, or tasted by a human. Suppose I told you that you have a tail. You ask me if I have seen this tail, and I say no. 

‘Have you felt it?’ No. 

‘Have you heard it?’ No.

‘Have you tasted it?’ No.

‘Have you smelt it?’ Yuck, no.

‘Well, then, how do you know I have a tail, Will? Prove it!’ I can’t. I just know it.

This anecdote is a trivial illustration, yet demonstrates an important point. We cannot empirically prove that non-physical things exist. If it doesn’t physically exist, the senses cannot process it. However, this brings is us to a conundrum: if we cannot empirically prove that the non-physical exists, how can we be sure that logic exists?

We seem to think that logic exists, and it is definitely not a physical, tangible thing. Well, the answer is simple: we can’t. Can we describe what logic looks, tastes, sounds, feels, or smells like? Nope.

Non-Sensory Methods of Description

“But, AHA! William! The dictionary has a definition for logic! They’ve described what it is! Checkmate, you pretentious sot! Merriam-Webster says logic is “a proper or reasonable way of thinking about or understanding something.”

Ok, well let’s unpack this definition a bit. What is the dictionary definition of “proper?” According to the same dictionary it means, “Correct according to social or moral rules.”

What does correct mean? “True or accurate”

True? ‘Agreeing with the facts’

Fact? ‘Something that truly exists or happens’

Exist? ‘To have actual being’

Being? ‘The state of existing’

Existing? ‘To have actual being’

Being? ‘The state of… Wait a second! This looks familiar!’ Well, my friend, you’ve learned your lesson. The dictionary is nothing but a big circular argument.

“Well, we never went down the path of ‘reasonable’ in our original definition…” If you really want to, I’ll humor you, then.

Reasonable: ‘Fair and sensible’

Fair: ‘Agreeing with what is thought to be right or acceptable’

Right: ‘Morally or socially correct or acceptable’

Correct: ‘True or accur… well, by Jove, we’ve done it again.’

What does this little traipse through the dictionary prove? It proves that language is useless when trying to describe the non-physical, because it will always end up in a circular definition: a fallacy. It’s meaningless to say that logic is “proper,” because “proper’s” definition ends up in a fallacy (which is, ironically, illogical). Therefore, we still have not succeeded in describing logic.

All is lost?

What can we do now? Kill ourselves and hope for some answers in the afterlife? No. All we need to do is stop using logic.

“Stop using logic? That’s absurd! What are you, a Christian or something?”

Calm down. We need to explore other venues of understanding. I know just the guy who can help us… let me grab my Lamp of the Enlightenment and rub it a few times. Suddenly, the ghostly apparition of Blaise Pascal appears before us.

‘Why have you disturbed my rest, William? I was chilling with Pook in heaven.’

‘Pook’s dead?!’

‘Uh, never mind. What did you want to ask?’

‘We wish to know how to understand without logos, oh master.’

‘We know the truth not only through our reason but also through our heart. It is through the latter that we know first principles, and reason, which has nothing to do with it, tries in vain to refute them. The skeptics have no other object than that, and they work at it to no purpose. We know that we are not dreaming, but, however unable we may be to prove it rationally, our inability proves nothing but the weakness of our reason, and not the uncertainty of all our knowledge, as they maintain. For knowledge of first principles, like space, time, motion, number, is as solid as any derived through reason, and it is on such knowledge, coming from the heart and instinct, that reason has to depend and base all its argument…

It is just as pointless and absurd for reason to demand proof of first principles from the heart before agreeing to accept them as it would be absurd for the heart to demand an intuition of all the propositions demonstrated by reason before agreeing to accept them. Our inability must therefore serve only to humble reason, which would like to be judge of everything, but not to confute our certainty. As if reason were the only way we could learn!'(Pascal’s Pensées, 1995, 28, #110)

Blaise Pascal slowly fades back into nothingness.

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