There is truth. Truth exists. There is a truth to this existence, this universe. We might lack the language or the pictorial tools or the right theory and models, but there is truth.
What is this truth? what is truth?
Things exist, we exist, there is a speed of light, the square root of two is irrational, the halting problem is undecidable, there are abstract and real relations between abstract and real things.
The truth is a something that, yes, has a correspondence to the facts. That is not the end of it though (despite the pragmatic claims of some!). The truth has a correspondence to the facts because it is true! The facts HAVE to line up against a truth. The truth exists outside of specific events or objects. A number has an existence, if even only as an idea, and it has relations to other things. And the description of that number and those relations ARE truth. A computer program has its truth whether you run the program or not. If you were to run it it would halt or not halt, that potential is in the computer program from the beginning, it doesn’t arise from it’s execution.
On Proof and not Proof but Use
We can prove these truths and many more. We can prove through English words or through mathematical symbolism or computer programs. Our proofs, put into these formats, can and are often wrong and set to be revised over and over until there are no holes. No matter how fragile a proof and the act of providing proof the truth is still not diminished. It is still there, whether we know it or not and whether we can account for it or not. And the truth begs proof. It begs to be known in its fullness and to be trusted as truth to build up to other truths.
Proof isn’t always possible – in fact we’ve learned from issues in computability and incompleteness – that complete provability of all truth is impossible. This beautiful truth itself further ensures that the truth will always beckon us and will never be extinguished through an endless assault. There is always more to learn.
The unprovable truths we can still know and use. We can use them without knowing they are true. We do this all the time, all day long. How many of us know the truth of how physics works? or how are computers do what they do? and does that prevent their use – the implementation of that truth towards more truth?
Why defend truth? Why publish an essay exalting truth and championing the search for truth? Does the truth need such a defense?
Being creatures with intelligence – that is, senses and a nervous system capable of advanced pattern recognition – our ultimate survival depends on figuring out what’s true and what isn’t. If too many vessels (people!) for the gene code chase falsehoods the gene code isn’t likely to survive too many generations. Life, and existence itself, depends on the conflict between entropy and shape, chaos and order, stillness and motion, signal and noise. The truth is the abstract idea that arises from this conflict and life is the real, tangible thing born from that truth. We learn truths – which processing of this thing into that thing that keep us alive, we live to learn these things. In a completely entropic existence there is nothing. Without motion there is nothing. In total chaos there is nothing. It is the slightest change towards shape, order and signal that we find the seeds of truth and the whole truth itself. The shaping of entropy is the truth. Life is embodiment of truth forming.
So I can’t avoid defending the truth. I’m defending life. My life. In defending it, I’m living it. And you, in whatever ways you live, are defending the truth and your relation to other things. If I’m alive I must seek and promote truth. While death isn’t false, chasing falsehood leads to death or rather non existence. Could there ever be truth to a statement like “I live falsely” or “I sought the false.” There’s nothing to seek. Falsehood is easy, it’s everywhere. It’s everything that isn’t the truth. To seek it is to exert no effort (to never grow) and to never gain – falsity has no value. Living means growing, growing requires effort, only the truth, learning of the truth demands effort.
How do we best express and ask about truth?
There’s a great deal of literature on the unreasonable effectiveness of mathematics to describe the world. There’s also a great deal of literature, and growing by the day, suggesting that mathematics isn’t the language of the way the universe works. Both views I find to be rather limited. Mathematics and doing math is about certain rigor in describing things and their relations. It’s about forming and reforming ways to observe and question ideas, objectives, motion, features…. It’s about drawing a complete picture and all the reasons it should and shouldn’t be so. Being this way, this wonderful thing we call mathematics, there is no way mathematics couldn’t be effective at truth expression. Ok, for those that want to nit pick, I put “computation” in with mathematics. Describing (writing) computer programs and talking about their features and functions and observing their behavior is doing math, it is mathematics.
Art has very similar qualities. Art doesn’t reduce beyond what should be reduced. It is the thing itself. It asks questions by shifting perspectives and patterns. It produces struggle. Math and art are extremely hard to separate when done to their fullest. Both completely ask the question and refuse to leave it at that. Both have aspects of immediate impression but also have a very subtle slow reveal. Both require both the artist and the audience, the mathematician and the student – there is a tangible, necessary part of the truth that comes directly from the interaction between the parties, not simply the artifacts or results themselves.
Other ways of expressing and thinking are valuable and interesting. That is, biology and sociology and political science, and so on….. these are all extremely practical implementations or executions of sub aspects of the truth and truth expression. They are NOT the most fundamental nor the most fruitful overall. Practiced poorly and they lead to falsehoods or at best mild distractions from the truth. Practiced well and they very much improve the mathematics and art we do.
What does any of this get us? What value is there in this essay?
This I cannot claim anything more about than what I have above. For example, I don’t know how to specifically tell someone that the truth of square root of 2 is irrational has x,y,z value to them. It certainly led to a fruitful exploration and exposition of a great deal of logic and mathematical thinking that led to computation and and and. But that doesn’t even come close to explaining value or what talking about its value today, in this essay, matters.
My only claim would be that truth matters and if there is any truth in this essay then this essay matters. How that matter comes to fruition I don’t know. That it comes to any more fruition than my pounding out this essay after synthesizing many a conversation and many books on the subject and writing some computer programs and doing math is probably just a very nice consequence.
The truth’s purpose is itself, that it is true.