|« Use passive voice to shift the blame on someone else||Just a minute, improve your rhetoric »|
Every now and then, a conversation with a friend transforms into a debate about the existence of absolute truth.
I think absolute truth exists, but not many ideas or statements can be labeled as 'absolute truth'. To be more specific, I think that absolute truth can only be applied to some mathematical concepts.
Q: What is absolute truth?
A: Absolute truth is something that is true regardless of the context (this definition is subject to change).
- For example we can say that "parallel lines never intersect", but this is only true in the context of Euclidian geometry. Even though it is a math-thing, it is not an absolute truth.
- Another example is "1+1=2", it is a bit more difficult to counter. The statement is true if '+' means "add two numbers", but it could also mean "concatenate", so the result would be "11".
- Try to prove that "1+1=2" without first defining '2' as the next integer after '1'; if you can't, then why not "1+1=3"? (for very large values of '1' :-)
As you can see, playing with math doesn't automatically make you right. The weakest link here is the fact that we use our language as a communication tool, and the language is filled with backdoors, kludges and other things that make our existence a bit difficult. Synonyms, homonimes, homophones - they add ambiguity to a world which has enough uncertainty of its own...
Sometimes we can use language to "prove" something; but the fact that a statement sounds nice in a human language, does not make it more credible. Consider the sentence "Absolute truth does not exist". Something cannot be true and false at the same time, but the problem with this sentence is that if it is true, it is false; sounds like a self-contradiction.
What's the catch? The catch is that if there is absolute truth, it does not necessarily mean that the sentence "Absolute truth does not exist" is one of those absolute truths. So, even if this nifty linguistic trick looks cool on paper, it does not make sense in the real world.
Absolute truth cannot be expressed in words
This will result in the projection of the concept upon our vocabulary, a process that implies the fact that some input information will be lost, therefore there is no guarantee that we will be able to reconstruct the original concept having read its description in words. Think of it as drawing a 3D object on a sheet of paper (you get the projection of 3D on 2D). The vocabulary can be limited, lacking words that represent certain concepts; moreover, words can make a sentence ambiguous.
Even if we use symbols, their definition can vary too (ex: '+' means "add" or "concatenate"; it means 'OR' if we're in the realm of Boolean algebra; while in the case of "Mary+John=Love" the '+' means something entirely different).
Once we accept the idea that words cannot be used to express absolute truth, the problem of "Absolute truth does not exist" is solved, and so is "1+1=2".
Q: Why is there a need for absolute truth?
A: This is a tough one, but I have to answer it, especially that I wrote that "I think absolute truth exists". My opinion is that absolute truth makes it possible for the universe to exist, being one of its intrinsic features. Without absolute truth the universe would be unpredictable, because there is no reliable way of determining whether the process that took place yesterday will happen tomorrow, following the same principles.
A chemical reaction will behave the same way if the compounds and their volumes and the circumstances are the same (note how the attempt to express it in words makes it less universal).
The value of π is always the same. I won't risk writing the numerical value, because that will only be an approximation of π, not the actual π. I won't try defining it in words because it implies defining "circle", which implies defining "point" ;-) (there is no definition for "point")
Gravity affects objects in the same way.
If you paid attention so far, at this point you could say "A-ha! gotcha!". In the case of gravity things are different if you deal with very small objects, or with very large objects; in the case of chemical reactions - the outcome depends on the context. In other words, these don't qualify as absolute truths because they are different in different circumstances.
The problem lies within our [current] inability to comprehend the entire universe. Imagine that we know everything, and that we are able to formulate a sentence that fully describes the behaviour of gravity in each possible circumstance. Ex: if (small object) then bla bla; if (medium object) then tala bla; if (large object and there is no light) then if (speed is below the speed of light) then bla bla bla; else bla2 .....
Since the sentence contains all the possible IFs, it can be perceived as absolute truth as a whole, because everything there is was taken into account.
The problem is that there is a great difference between knowing everything and imagining knowing everything :-) Humanity might not have enough time or intelligence to find all the IFs, to grasp all the concepts. However, our inability to understand the truth does not mean that the truth is not there.
I can say that the universe itself is the absolute truth, because everything within it is subject to its laws; i.e. the universe is the only "thing" that "knows" all the "laws". Humans have a very limited scope, and so do any alien civilizations that exist elsewhere - we can only observe a subset of the universe, but never the entire universe.
Some say that god is the absolute truth, I agree, as long as by "god" you mean "universe" ;-)
sunt deacord ca adevarul absolut, valabil in orice context e o himera...
I have too little knowledge (anyone has enough?!) about the topic (both mathematical and philosophical knowledge) to accept a certain theory that I could thouroughly, not intuitively, support. What I mean is that I tend to think that a Mathematical Structure, explaining everything, exists (hence it would be an 'absolute truth')... but I have no clear arguments,
An interesting paper is http://arxiv.org/PS_cache/arxiv/pdf/0704/0704.0646v2.pdf
which is neither too mathematical, nor too weak, i.e. it has substance.
BTW... the point can be defined. :) Primitively, a point is merely an element of a set which has some properties assigned to it. You may check any Linear Algebra book to see how Affine Spaces are defined based on Vector Spaces.
Also '1+1=2' is also true. Natural numbers have been defined (http://en.wikipedia.org/wiki/Natural_number#Formal_definitions). Or, to be short, 1+1 is always two in the monoid of natural numers with the standard binary operation addition. You might say, what if we're not speaking about natural numbers. But then the question has no basis, that is it's not anymore a valid question. It's like asking: book + pen = ?
It was pleasant reading your article. I didn't figure out how to properly insert links. Feel free to edit my comment.
The point about the theory of everything is right on, in my opinion. Imagine that the universe is a simulation, which we can temporarily pause, then "dump" the state to a file. A theory of everything would be able to go through all the data and confirm that the state is a valid one; i.e. "all the variables and their values were reviewed, and found to be consistent - therefore this is a valid snapshot".
Now, we can simplify that - no need to pause or to save a snapshot, do it on-the-fly. A theory of everything is my #1 candidate for something that qualifies as absolute truth, because it takes into account the context, which is the universe itself.
"1+1=2" is not a good candidate for absolute truth; you've specified yourself that if we are dealing with natural numbers, and that we do arithmetic addition. First of all, try to argue that "1+1=2" without first defining '2' as the successor of '1' (in terms of Peano's arithmetic). And then, how about "1+1=10" and "1+1=1"? (the first is addition in base two, the second is a logical OR) So, this one requires a context before one can evaluate whether the expression is true or not. A better candidate is "1=1", but it doesn't work in imaginary worlds which were defined as "imagine a world in which one is not equal to one" :-) or worlds in which the symbol '=' is assigned the meaning of "not equal".
The problem here, in my opinion, is that we are using language, and this applies some limitations to our freedom. As discussed in the article, language takes the "absolute" out of it, making it only "local". Dumping the languages and switching to a pure symbolical/conceptual line of thought should do the trick - adding one and one (as defined in "sum") gives two, whether you are a christian, a communist, a zombie, a squirrel, or an agnostic theocratical overlord on the other end of the universe :-) But as soon as I start putting this into words, a nitpicker's heaven is created! Define "define", define "and", etc.
Thanks for the reference to the paper on arxiv.org, I will try to understand it, the pictures look promising :-)
Switching to points; I knew I wouldn't get away with this one easily. I have no problem with treating a point as "a tuple of coordinates". But it is a bit uncool to accept Euclide's(?) definition of "the smallest trace the pencil can leave on the canvas", because this definition is highly "platform dependent". Hmmm... maybe this is worth being discussed in a separate story; sometimes a point is a dot, sometimes we mean 'coordinates', and.. that's beyond the scope of this comment.
Thank you for your time, and I'm glad you liked reading the story.
p.s. The links are ok as they are; actual A tags are prohibited, to give spammers no incentive to post comments.
And here is a nice comic.