@joe-shmo saidI don't think it's too dependent on what the language is. A language consists of a finite vocabulary (with rules for making new words) and a grammar. So you just need a scheme for generating sentences. The inputs are just the vocabulary and the grammatical rules. The machine just generates strings of words which fulfill those rules. Provided the idea is expressible in English (even if it needs a new word or two) then it will be generated.
@DeepThought
But language isn't static. From what I can tell it also doesn't seem like it could be a bounded body of knowledge itself? So how are we inputting an infinite data set into you hypothetical computer?
@DeepThought
I'm trying to follow along. You feel that everything that can be known is finite and somehow bounded by language ( or rather the rules of language )?
What do you feel about the total information of the universe... finite, or infinite? And when is say universe, I'm not talking about what is currently observable. I'm talking about everything it could be, or imagined to be.
It seems like your saying everything we could imagine it to be is finite, and given by the set of information in the algorithm you propose. If so, how do you compare the set of everything we can imagine, and the total information of the universe. Are they one and the same set, or will certain things remain forever unknowable?
More simply, do you believe we will ever get to the bottom of it, or is it turtles on turtles the whole way down?
@joe-shmo saidThe amount of information in the universe is bounded, at least the observable part. The reason for that is that the largest amount of information that can be contained in a space with surface area A is proportional to A. So, there is a finite amount of stuff to know.
@DeepThought
I'm trying to follow along. You feel that everything that can be known is finite and somehow bounded by language ( or rather the rules of language )?
What do you feel about the total information of the universe... finite, or infinite? And when is say universe, I'm not talking about what is currently observable. I'm talking about everything it could be, ...[text shortened]... do you believe we will ever get to the bottom of it, or is it turtles on turtles the whole way down?
However, that is not really what you are asking. Yes, language is limited in that sense, but not because it is a natural language - a formal language suffers the same difficulties. There are a finite number of sentences. Those sentences must be used to describe nature and so our description of the world is limited by the fact that we must use language to know anything.
Just to forestall a possible objection, infinite sentences are no use as one never gets to their end so one cannot know what their meaning is.
@deepthought saidHow is something like the following become excluded from your argument?
The amount of information in the universe is bounded, at least the observable part. The reason for that is that the largest amount of information that can be contained in a space with surface area A is proportional to A. So, there is a finite amount of stuff to know.
However, that is not really what you are asking. Yes, language is limited in that sense, but not bec ...[text shortened]... finite sentences are no use as one never gets to their end so one cannot know what their meaning is.
The set of real numbers contains infinite information, and is contained within the universe.
For instance an infinite amount of sentences could be formulated like:
"In the Cartesian plane, the distance between ( x1,y1) and ( x2,y2) is given by Z"
Clearly this is a collection of infinitely many sentences that each carry distinct information.
@joe-shmo saidTry writing down the precise solution to x^2 = 2 as a decimal.
How is something like the following become excluded from your argument?
The set of real numbers contains infinite information, and is contained within the universe.
For instance an infinite amount of sentences could be formulated like:
"In the Cartesian plane, the distance between ( x1,y1) and ( x2,y2) is given by Z"
Clearly this is a collection of infinitely many sentences that each carry distinct information.
I do not agree that an axiom schema is an infinite number of axioms, it is a rule which can generate any particular instance, but you can only write it down in abstract. So while your Pythagorean formula applies to all pairs of points on the plane, it does not tell you the distance between any two particular points without the additional information given by their coordinates. It does not represent an infinite amount of information.
@DeepThought
Try writing the precise decimal representation of 1/3, it really not much different in the sense we are talking about, they both require an infinite amount of information to be described in that manner.
Anyway I'm not sure what you were getting at. We were talking about finite language, sentences, etc... as the basis for your argument. You seem to have no problem with rules like mine generating sentences in the context that language, words, etc... are finite. But if a number is a word then language is not finite. There will always be at least another word ( actually infinitely many words ) to add into the data set of the algorithm you intend to use.