"We shall not cease from exploration
And the end of all our exploring
Will be to arrive where we started
And know the place for the first time."
T.S. Eliot
Four Quartets: Little Gidding: V
Showing posts with label logic. Show all posts
Showing posts with label logic. Show all posts

Saturday, October 2, 2010

Can't Handle the Truth

Disclaimer

This post deals with a fine detail about truth, which I feel has significant implications for the theory of values that I am assembling here. Some may find it massively redundant.

Preamble

Playing a card game with some friends the other say, I brought up the example of the Experience Machine thought experiment. It was well received, and the votes added up thus: 2 would absolutely not plug into the machine under any circumstances (including myself), 2 were unsure, and 1 would definitely do it. The interesting thing about one of the two that were unsure was that she would given specific conditioner about incorporating real people into the scenario with you. We have termed this "multiplayer." It seems that asking people what minimum conditions would have to be met in order to plug in is actually a fascinating way to explore what a person values.

This lead me to question why I value truth so strongly. Is it reasonable? My intro to philosophy textbook states that "the philosopher's faith is that Truth is good and worth pursuing for its own sake." That's one heck of an assumption. It is, of course, a useful assumption if you're a philosopher, because without it, what are you doing? But that is little solace, because a priest assumes the existence of god to justify their lines of thought too.

In my various searches for a basis for values, I have actually had to overturn most of what I based by identity on. I'm dismantling, but hoping for reconstitution through rigorous application of - and deduction from - the most certain axioms: the a priori. Kant tried the very same thing, but I don't think that he dug nearly deep enough, and I find many of his axioms to be unsatisfying. Nietzsche refuted (many times) many of Kant's assumptions. The existentialists tried to find a solution, but ultimately deferred the question. They all also toss around this concept of "truth" as if it were an assumption as mentioned above.

I can't seem to find anything online written on the ontology of truth. There is quite a lot on theories of truth (which do touch on my question), but I'm looking at it from a more fundamental level. What is the ontology of truth, and to what degree should we pursue it? Is it worth sacrificing happiness as in not entering the Experience Machine?

Definition Derivation

It is reasonable to say that existence must true. But which is prior? Truth must exist, and existence (material or ideal) must be true. But that is contradictory, as something cannot precede its' own ground.

The negative of existence is nothingness. Both are true. However there cannot be an untruth in an objective reality (material or ideal). Untruth does not correspond to either existence or nothingness, as both are true, and the objective world is thus always true. Untruths can only be expressed through language as lies, and are thus only part of the mind and language. Art does not constitute untruth because a work of art is a true thing in itself, even if it "uses lies to be the truth." And even lies have an element of truth to them, as it is true that they do not express the truth.

Truth is inescapable. So where is it? We can only look at it through other things, never directly. It's always in the corner of your eye, but you can't see it directly. Truth seems to function linguistically as a way of asserting that something exists or not. It is a function of the mind to compare our understanding (an idea image) to the external reality (original image).

It is a function in the mathematical sense f(x), where we compare x to the array of reality (existence and nothingness), and return a true if x is a subset of the array, and return false if it does not. I suppose it would return a partial truth if some of the elements of x correspond to the reality array. I will call this truth-as-operation or the Truth Function. It also falls under the correspondence theory of truth.

Truth-as-Operation
f(x): iff image(x) ⊆ [[being]  [nothingness]] = true;
The Truth Function is deeply troubling to me as opposed to truth as a fundamental ontological category. Truth does not exist independently, it is merely a property of ideas. If truth were a fundamental ontological category, it could be used as a part of the basis of an a priori value theory. It cannot be used as a justification of valuing reality, because it relies on a valuing of the reality-image. It is yet another evaluative tool that requires a ground. To value truth requires valuing reality for its' own sake, unless supported by some other morality hereto unknown to me. To say that you value reality because it is true is a tautology, or even possibly absurd. You're really saying "I value what is real because I have this way of comparing my ideas to it." It's like saying that you like the Mona Lisa because you can buy a print and compare it to the original in the Louvre.

That's not to say that this operation isn't extremely useful. The usefulness of our senses - and in fact our very survival - is dependant on the Truth Function (or so we are led to believe). This is debatable on skeptical grounds, but that is a conversation that I do not have space for here.

It's quite amazing how many terms are truth-as-operations. Words such as "because," "therefore" or anything else dealing with justification including causality are all the Truth Function. All of rationalism relies on it. What is our justification for justifying something? Remarkably, we can actually ask this question because truth is not an ontological category, but a function, and can chain: f(f(x)) AKA (f o f)(x).

The expression f(f) of course does not return anything as the function does not exist independently of of an analytical subject, so truth-in-itself does not exist, which is counterintuitive to our way of thinking. We cannot justify justification unless applied to a subject.


Functionally this requires some adjustment in language and thought. To say that "it is true that I think therefore I am" is a tautology because a self-evident statement is an expression of direct reality, and contains collapsed truth in its' self-evidency. Evidence is truth-as-operation, so the requirement is already met within the statement itself. Things that we know with certainty (a priori) do not need to be run through the Truth Function for this reason.


Rationality Bias

This entire endeavour of trying to find justification for values assumes that one should find values that are rational. Schrödinger Imperative demands that we resolve this crisis, so that is not called into question. But need it being found on a rational basis? Why do I value certainty in values? How do you justify rationality over irrationality? The Truth Function is a tool that I can use here, but should I? How do I evaluate if a Truth Function is worth using? I may need to accept it for reasons of coherence.

Outline:

  1. "Truth" is an evaluative tool
    • Compares an idea to reality
      • Truth is a property of ideas
    • Is not a fundamental ontological category
    • Being and nothingness are independent of truth
      • Truth is dependant on ideas and existence and nothingness as it is a function
      • Truth is not a candidate for a ground for values
      • One can only value reality, not truth
    • Self-evident statements contain truth already

Saturday, September 11, 2010

The Defining Game


Okay, veering away from the value thinger for a moment, I'm frustrated with the author of Zen and the Art of Motorcycle Maintenance. I'm not done reading it yet, but the author is arguing quite strongly that not all things can be defined, and they can only be grasped through some mystic immediate knowledge. I wholly disagree.

Truth is useful because it represents a glimpse of reality. Truths are tiny pinhole windows of understanding along a long wall in a dark room. The hope is that we will eventually poke enough holes in the wall to see clearly. Some disagree with this, and I'll get to Gödel and Quine in an upcoming post (I tend to have a few rough drafts on the go at a time.) I disagree as well, in the sense that we as human being could ever know everything. There are limits to our perceptions, and there is an enormous amount of information being generated every moment. Something that Pirsig points out (well, Poincaré points it out) is that there are an infinite number of hypotheses that correlate to empirical evidence. So any idea that create from a posteriori knowledge contains the possibility to being only interpretive and equally valid to another interpretation.

Portrait of a skeptic
Sadly, as a skeptic I also have to hold that only those things which are self-evident are can be considered true as the rest could be an elaborate hoax. I cannot know the validity of my perceptions or authority figures with the same certainty as the knowledge that a triangle has three sides. I would guess that each interpretation is probably at best 99% accurate, showing overlap in being able to explain some phenomena, but also being wrong to some small degree. I would assert that there is a solid reality, but that we cannot know all of it... at least not nearly yet.

Pirsig goes on to try to justify the mystic mode of "knowledge" by getting people to try to define "quality" and showing that they can't do it in a simple sentence even though we all know what we are talking about. I think the problem is with his definition of definitions. It's really nice to have something spelled out on paper, in black and white, but as an artist myself I can tell you that the syntax of that language is limited (as are all languages.) Perhaps oral/written languages are as ill-equipped to handle "quality" as music is to handle shopping lists. Behind each idea, each interpretation of bit of the world as you see it is a tiny collapsed point of an idea. Let's call this the virtual idea. To clarify, I'm not talking about Pure Idea, just the bit of a particular idea that you then express.

Wittgenstein has this great solution in his book Philosophical Investigations. He says that we learn words through "language games," such that given enough examples of something we can eventually refine our understanding of the word (as a symbol) of the virtual idea. I think Pirsig should have considered this possibility. It makes things much more difficult to write down, but can be the only way to express something (especially as language only works for shared experience.) Perhaps we need to extend our definition of valid definitions to include things known (ie: virtual ideas) that are shared understanding, but cannot be expressed in a given language.

I must admit then that formal logic may be missing something as it is bound by its syntax. Granted I would suspect then that anything proven with rigour via self-evident statements  should be true, but that you can only find a subset of all truths deducible from self-evident statements.

Outline:
  1. Ideas exist as hypotheses to help us understand reality
    • They may be refined
    • An infinite number of hypothesis exist that can explain any phenomena as long as they are deficient even in the slightest way
  2. Words are symbols (placeholders) for ideas
    • We use them to communicate
    • We can only communicate shared experience
      • Language-games define things by showing
        • Language games do not rely on strict syntax
        • There are some things that traditional definitions cannot express
          • We need to extend our concept of "definition" to include things that do not express well in the common language
  3. All languages are only able to express a subset of all things that you would like to express
    • Music cannot tell you to buy milk, but verbal language can't express some ideas that music can
  4. Formal logic is a type of language, and thus can only express a subset of truths