I’ve mentioned this before, but I’m becoming convinced that logic cannot prove anything. Or, perhaps, I should say it cannot prove anything material.
if A equals B, and B equals C, then A must equal C.
Categorically, this is true. The problem with this statement (and all logical derivatives) comes not from its definition, but from its application.
Specifically: we can’t apply it.
What is A? What is B? What is C? How do we “prove” they are equal?
The moment you attempt to apply this to the physical world, it breaks down. To prove A is equal to B, we must be capable of fully defining A and B.
Philosophers and scientists have been searching for as long as history itself for an answer to what makes a thing, a thing; what is reality? Every time we think we’ve discovered the fabric of reality, we not only discover we were wrong, but that it’s much weirder than we anticipated.
Newtonian physics ruled until Einstein came around and showed us space itself could warp, and with it time itself. Just as we got used to that idea, we discovered Quantum physics, from which we’ve realized that particles move like waves until you observe them, and only then they’re particles.
We really have no clue what reality even is. Nobody knows how or why particles travel like waves. We just know they do, and that it’s very weird.
Plato claimed there were perfect ideas set apart in a higher plane of existence 1. In that claim, he supposed there was a perfect representation of a table, by which all tables measured up. A thing was a table by the degree to which is approached this perfect ideal. All things that could be have their perfect definition somewhere in that unreachable plane. It is there that logic can prove all things 2.
Of course, no one has ever agreed on what a perfect table is or really, on what a perfect anything is at all 3. All our definitions of existence, and thus equality, are categories we’ve made up. The reason table A and B are equal is only because we’ve assigned them both the table category. It’s arbitrary; the moment you dive into specifics, definitions diverge and exceptions abound.
Logic depends on definitions. We must know A to prove it is equal to B. But we don’t and we can’t.
There can be made an argument that a definition can be sufficient without being exhaustive. If we define a table as a flat, horizontal surface held up by four legs, and apply that definition to A, B, and C, then the logical proof has worked.
They’re not wrong, but this often becomes a trap.
All we’ve really proven is that we can apply categories and our categories can be consistent to some degree 4. But tables can have five legs, or six, or more, and some have none, but are suspended or attached to walls. There are any number of exceptions that force the logical proof into ever narrowing definitions.
And more importantly, the therefore becomes a lie unless it too becomes as narrow as our definitions.
This leads us down the path to self delusion and sophistry. We say A equals B because they are both tables, but then draw conclusions as though they were actually equal in reality. This confusion between our definitions of what things are and what they actually are persists in just about every aspect of our lives.
This can become particularly pernicious when we apply our definitions to each other. We see someone exhibit behavior that’s consistent with our personal definition of a category. We thus apply the category, assume absolute equality, and use it to generate the therefore.
Everything John does is evil. We know this because he is evil. We know he’s evil because he does evil things.
The sophistry is easy to see. Clearly, John can do both good and evil things, just as all humans can. Yet I swear this logic is the backbone of most political discourse.
None of this is to say that logic is not a useful and powerful tool; nor do I suggest that it can’t provide understanding and insight. In fact, I would argue the opposite. Because it is such a powerful tool, it, like any powerful tool, is subject to abuse. But it can also lead to incredible discover and insight when used properly. The whole field of mathematics, for instance.
My point is we often think we are proving something true when, in fact, we are applying categories to reality with a breathtaking number of assumptions and then drawing conclusions from our ignorance.
I’m strongly paraphrasing here. ↩
And, incidentally, the idea that logic is something separate from us, a thing that can be used by us, but it not part of us. ↩
Except, perhaps, mathematical shapes. But then, those too are categorical ideas not seen in nature. Ironically, everyone can probably imagine a perfect circle, and even agree on its definition, but we can’t prove or demonstrate that we’re imagining a perfect circle, nor has one ever been observed. How could it when space itself is warped? ↩
This is arguably not only useful, but essential to our very intelligence. An inconsistent application of categories could easily be interpreted as a form of insanity. ↩