On the subject of being able to know a "truth"

[Kyriakos]

I was reading through my own excellent thread on truth being something one can know or not, and recalled a very interesting part of the exchanges there:

The spanning set of true statements should be finite.

If the spanning set of true statements in finite you can create a finite spanning set of false statements.

They appear in the fourth page of the thread1

I find this to be a very interesting (part) of the topic, which was idealism, epistemology, human knowledge, axiom-based calculation and so on.

Indeed i cannot readily give a definitive answer as to which of the two posters are closer to being correct in their aphorisms there. Warpus claimed that the entire progression of 'correct statements' has to be finite in a human system of thought, while Zelig argued that if this is true it should follow that the entire multitude of false statements in the same set has to be finite as well. The immediate context in the thread was whether false statements are vastly more in number than correct ones, and if so whether any of them (or both) are infinite in number.

*

You can post your own view on this I think that both correct and false statements may be 'practically infinite' from a human point of view, but finite from an ideal other (hypothetical) point of view. Furthermore i think that going from correct statement in human throught to the next one, is likely less than a line progression, and more like a move in a labyrinth which has many different progressions one can follow to a next level, and then a next level which is partly formed by the previous path followed in the level before. So in that sense the 'correct statements' themselves are not indivisible bits in a ladder you climb to a next level, but again are able to influence further levels and tie into other statements which alter the whole system of thought.

 

[Gori the Grey]

The sky is blue.
My previous statement is correct.
My previous statement is correct.
My previous statement is correct.
My previous statement is correct . . .

As long as there is language, there will be an infinite set of true statements.

 

[Borachio]

Yes. But each statement takes a finite length of time to state, or appreciate, or whatever.

So, unless the Universe is of infinite duration, there can only be a finite number of statements, true or not.

And besides, we've yet to determine if the set of statements can include duplicates. Strictly speaking the elements of any set should be unique, otherwise it's called a bag, iirc.

 

[Gori the Grey]

Each of these statements is unique; they each refer to a different thing in the universe.

As to the infinite duration of the universe, good point. My claim further depends on there being speaking beings within that universe (maybe sonnet writers!), so the infinity I argue for is a hypothetical one rather than a real one.

 

[Borachio]

Each of these statements is unique; they each refer to a different thing in the universe.

True. I can't argue with that. They do look remarkably similar though.

 

[Old Hippy]

The sky is blue.
My previous statement is correct.
My previous statement is correct.
My previous statement is correct.
My previous statement is correct . . .

As long as there is language, there will be an infinite set of true statements.

I'm just looking out the window
its black with occasional shiny white bits...

 

[Gori the Grey]

Change original sentence, then, to "isn't blue." Each subsequent sentence remains a true claim about something else (the accuracy of a sentence), and those statements are in theory infinite.

Yes, Borachio, they look superficially like the same statement, but because the referent is different in each case (of this infinite regress), they are different truth claims.

My only point is that the self-referentiality of language makes for the possibility of an infinite number of things (other sentences) about which truth claims can be made.

 

[Kaitzilla]

Heh.

How about:
"My computer isn't 100 meters away from me."
"My computer isn't 101 meters away from me."
"My computer isn't 102 meters away from me."
etc. etc.

Seems like there are infinite true statements to me.

 

[warpus]

The sky is blue.
My previous statement is correct.
My previous statement is correct.
My previous statement is correct.
My previous statement is correct . . .

As long as there is language, there will be an infinite set of true statements.

If you normalize the set and remove duplicates, it will again be finite.

Heh.

How about:
"My computer isn't 100 meters away from me."
"My computer isn't 101 meters away from me."
"My computer isn't 102 meters away from me."
etc. etc.

Seems like there are infinite true statements to me.

.. ...

I think I'm wrong.

 

[Borachio]

It's neat, isn't it? If you can get a mapping from true statements to the natural numbers then clearly the set of true statements must be infinite.

And countably so, at that. QED.

 

[Kyriakos]

^But (as you already noted ) even such sets of statements are appearing as a theorised object, cause you won't be able to include them in a set which is not utilising the notion of infinity so as to function as infinite. By which i mean: x+ x/2 + x/4 + x/8 + ... will tend to equal 2x after the set reached infinity, but it won't reach it outside of the set notion. (cause infinity is not something we experience; it is a notion). You won't make all of those statements in a finite time (finite universe or other). I think we should therefore exclude all those statements which can be bounded in an infinite progression without much fuss, such as the examples given already in the thread

(in a way it could be paralleled to seeking progressions without worrying about the theorised infinity of decimals between any two set points in that progression).

 

[Gori the Grey]

I think we should therefore exclude all those statements which can be bounded in an infinite progression without much fuss

What is "without fuss"?

This is a sentence. The previous sentence had “sentence” as it’s final word. In the sentence before this one, the word “final” is used as a synonym for “last.” The previous sentence began with the word “in,” but there it was capitalized, whereas in this sentence it is not. The sentence before this one raises the question as to whether an uncapitalized word is the same thing as a capitalized word: whether “In” is the same thing as “in” (in speech, perhaps; in writing clearly not). By raising the question of whether “In” is the same thing as “in,” the previous sentence is creating a fuss over a matter about which we generally don’t think at all. The previous sentence had the word “fuss” in it. Unlike the previous sentence, the sentence two back is without “fuss.”

Philosophers and mathematicians may have tools for reducing infinities into non-infinities. Language just keeps creating more language.

Yes, without infinite time, no infinity of utterances will actually get themselves uttered. My only point is that languages are infinity-producing machines. There is no limit except time to the number of (irreducibly) new things you can make with them.

 

[Kyriakos]

^However language also allows for many types of 'infinities'. Eg infinity in a group with less iteration, or in a group with very obvious iteration, notionally can become very distinct. Eg 1+1+1+1+1+1+... is also an infinite progression, but it is a bit dull next to a somewhat less obvious (and axiomatically caused to become more poignant) infinite progression of "all prime numbers".

Another variation of the above: you can reply to an infinite number of questions of the type "which is the Xth number in the decimal numbering system?" immediately. Eg the 5th is 5, the 123th is 123 and so on. But it is of obvious nature in this system and viewed in this way, so it can be deemed as merely evident and thus not something leading to new correct views, or rather needing to be revisited for them. (which ties to the quotes in the OP ).

 

[Gori the Grey]

That's why I gave you a set that was not simply numerical in its progression. Unless you rule out truth claims aboutsensentences, the set will be self propagating. And if you do, I won't know how to play your game because the interdiction will be itself a sentence about sentences.

 

[Kyriakos]

^Even if the focus is on a progression tied to language itself (eg the sentences you posted or similar), it would be a different progression than a set and automatically produced one, cause you have to actually keep track of the sentences there so as to continue with a new one (and also have to use knowledge clearly from outside the progression itself given you increase the main terms with each new sentence so it is more like a group for including known terms in language examination rather than having the scope of leading to a new development in knowledge). Unlike with the previous examples of "this is a statement", "the above is a statement" etc, or analogous ones, your sentence progression example is more dependent on particular parameters (your own choice of focus for each new sentence), so is part of a different system.
Think of a computer dealing easily with the 'this is a statement' etc sequences, but not easily at all (if at all) with the more feeding from overall language other progression.

Also should be highlighted again that regardless of the difference in infinite sets in your 2 (or 3) examples, they appear to not be themselves leading to a progress of knowledge even within the boundaries of their set (and the OP is about a progression of statements which are correct in a given system, eg human logic, and are finite or not while still being leading to some progress in that system)

 

[Timsup2nothin]

The sky is blue.
My previous statement is correct.
My previous statement is correct.
My previous statement is correct.
My previous statement is correct . . .

As long as there is language, there will be an infinite set of true statements.

This brings up the interesting 'wave of falsehood'.

As pointed out, the opening statement is only correct part of the time. If you are a thousand iterations into the sequence when the sky changes to 'black with shiny white bits' you have to stop producing true statements from this paradigm, at least temporarily...maybe.

But the inclusion of the word 'previous' already implies some sort of temporality, so does the 'incorrectness' travel instantly through the chain of statements? Or can we carry on, based on the assertion that the statement being 'judged' as correct was in fact correct when it was made? If so, that would mean we can continue making our series of statements even if the opening statement is not currently true. However if you do that there is a requirement that the statements cannot be taken as a set that contains any sort of 'instantaneous' truth at all.

 

[Gori the Grey]

@kyr, as to genuine addition to knowledge base:

Whole academic disciplines are effectively statements about statements: grammar, rhetoric, philology, literary criticism, large chunks of philosophy. Unless you regard all of these as contributing no nontrivial knowledge, you're going to have to allow statements about statements. And once you do that, you have a theoretical infinity of truth claims.

 

[Kyriakos]

@kyr, as to genuine addition to knowledge base:

Whole academic disciplines are effectively statements about statements: grammar, rhetoric, philology, literary criticism, large chunks of philosophy. Unless you regard all of these as contributing no nontrivial knowledge, you're going to have to allow statements about statements. And once you do that, you have a theoretical infinity of truth claims.

There are always degrees of trivial examination, though. I mean you would know what is too trivial for the examiner, and avoid writing it in a university essay on something

As for knowledge being tied to statement progressions: there are on the one hand the axioms which are a set basis for math progressions/examinations, and on the other hand the limiting nature of language in regards to carrying actual 'meaning'. I use english here, but the communication is only working in part, cause i always have different substratae of meaning in mind than you or any other poster, on account of most of the terms used.

That said... a progression which is deliberately devised as a game, and not with the end to expand some knowledge within a set, is surely of different kind than one used for progressing knowledge in a set. I think the OP is bounded on the later.

 

[Terxpahseyton]

Heh.

How about:
"My computer isn't 100 meters away from me."
"My computer isn't 101 meters away from me."
"My computer isn't 102 meters away from me."
etc. etc.

Seems like there are infinite true statements to me.

I would content that this doesn't count as true statements in the sense that they do not actually show truth as such but just the truth of a lack of truth.

Parlor trickery!

 

[Gori the Grey]

I'm arguing the position that the set of true statements is infinite.

In refutation, I get told my infinities are dull infinities, trivial infinities, infinities you'd know better than to put on a university exam.

Fine, the set of things that you would regard as truths is finite!

Well played, sir.