Mathematics is based on axioms – which by nature are not provable. They are merely a starting premise that we can build on to reach mathematical conclusions. As Richard Feynman put it, “all we ask of an axiom is that it does not lead to contradictory consequences.”
For instance, we define parallel lines as lines in a plane that do not intersect. That is essentially a definition we all agree on. But it is not actually provable. You either accept that definition and follow the logic, or you don’t.
If you don’t accept that definition, we’re just not talking about the same thing. The value of establishing axioms is that we can build on them, and reach all sorts of mathematical conclusions.
Axioms are not limited to mathematics. For instance, a common axiom is materialism – the view that nothing exists except matter.
From a philosophical stand point, its easy to see why this view is based on an assumption (as is idealism, spiritualism, etc). The best way to demonstrate this is to consider the famous “Brain in a Vat” thought experiment.
This philosophical thought experiment asks you to consider a scientist keeping you alive by holding your brain a jar, and hooking it up to a sophisticated computer capable of providing electrical impulses that perfectly simulate your reality.
Authenticity of Realty
If true, there would be no rational way ever prove the authenticity of this scenario since the entirety of your observational tools are in question.
In a material sense, we are all in fact a brain in a vat. Our brains are fully enclosed within our skulls in total darkness. They do not “see”, “hear’ or “feel”, they merely receive electrical signals and use these to represent our reality. Our entire observational capabilities are tied to the signals are brains receive.
But like any good axiom, there is no contradiction with materialism. From a material perspective, this is not only sensible, understanding this is incredibly useful. Every conclusion based from the natural sciences begins with this axiom.
Varying Degrees of Certainty
Yet there is an underlying implication in recognizing this as an axiom, rather than a universal truth. Though we may willingly cast aside the possibility that we’re in a jar in some lab, what we cannot cast aside is that there is no verifiable way to have absolute knowledge about whether this is true or not. More importantly, there is no method accessible to us to be absolutely certain that anything is true.
That isn’t to say we don’t have varying degrees of certainty with respect to the material world. Of course we do. We can reasonably be more certain that day will follow night than pigs will fly.
All natural sciences are based on these varying levels of certainty. But we can never be absolutely certain, because no matter how improbable, our reality could conceivably be one grand illusion, and there is no way to disprove this.
The Unknowable Truth
“Truth” is a complicated subject. In many senses, we know the “truth” about many things because any required axioms are implied, such as with materialism.
“Absolute truth”, best defined as whatever might be valid no matter what the context, is different. Absolute truth doesn’t require any assumptions.
So when we ask questions like how we got here, what’s the meaning of life, and is the entirety of reality purely physical – the answers are unknowable. We have no way to verify what is absolute truth.
Many people have difficulty coming to terms with the notion that absolute truth is technically unknowable. Many will claim to be in possession of such truth, conveniently overlooking the irony of their own cognitive biases steering them toward such views.
We don’t need to have absolute certainty about anything. The world works on varying degrees of certainty. Even our best laid scientific theories are open to revision.
Uncertainty is far from problematic. You can be fairly certain you’ll live through the night, but you don’t ultimately ever know. That doesn’t consume you with fear, and you go on with your life.
The Wisdom of Humility
Understanding the difference between varying degrees of certainty and absolute certainty is a matter of wisdom. This view is not new. Over 2000 years ago Socrates said, “The only true wisdom is in knowing you know nothing.”
Remember, all claims to genuine knowledge are based on the axiom that we are capable of knowing or determining our reality. This is an incredibly practical axiom, but it is unprovable. Thus, we really have no way or knowing anything at all.