Rational numbers == infinitely repeating sequences of digits

[Jokodo]

Find the contradiction.

There may not be a contradiction within this one post, or even within your current position taken together (in case you have a consistent position, highly doubtful), but it stands in contradiction to what you said earlier so it is logically impossible for you to have been right "all along" and still be right.

3 in a symbol that refers to an abstract value within an abstract system of values.

You're still unclear as to what exactly you're talking about here: The digit character '3', the string "3" of length 1 consisting of only that character, or the number 3 that string refers to. I shall assume that with 3, the symbol you meant the string "3", and with the "abstract system of values" the conceptual framework of numbers.

At any rate, it is a contradiction to what you said earlier, that numbers and digits are the same thing and only refer to themselves. Here you have, in your words, a "symbol" that refers to an "abstract value". Since symbols and abstract values are different categories, something obviously refers to something other, no matter how much you wave about.

It also follows that saying the number (represented by) 0.333... (in decimal notation) "doesn't have a last digit" is as nonsensical a thing to say as talking about disyllabic animals would be*, since numbers (your "abstract values", or something close to them) don't have digit counts as an attribute (no more than animals have syllable counts), only strings do.

Within that system it is nothing else.

Which system? The conceptual scheme of numbers, or the decimal notation as a symbolic mapping from strings to numbers?

If it's the former, and it still refers to the "symbol" a.k.a. string "3", it isn't anything in that system, it's simply not part of it - no more than the word "dog" is a mammal. If it's the latter, well obviously, although "be" is a weird verb to use here ("represent" or "refer to" would be clearer) - part of what makes the decimal system useful is that it allows strings to unambiguously refer to one and only one number. This however in no way precludes that other symbols can refer to to the same abstract value in different notations - or even in the same notation, e.g. the strings "3.0", "3.0000", "3.000...", or "2.999..." - it is not a prerequisite for the system's usefulness that it be 2-way unambiguous, and indeed it isn't.

And it does not refer to any other system.

Whatever "referring to a system" is even supposed to mean. It sounds like a random collection of words from the lexicon strung together in a grammatical but meaningless sentence to me. Maybe you meant referring to a value taken from another system?



* You might actually find something like this as a hint in crossword puzzle. To a competent speaker of English, it has a slightly off flavor since it mixes linguistic and metalinguistic usage: it is talking about a thing and it's name at the same time, the way you're inadvertently doing here all the time.

 

[untermensche]

There may not be a contradiction within this one post, or even within your current position taken together (in case you have a consistent position, highly doubtful), but it stands in contradiction to what you said earlier so it is logically impossible for you to have been right "all along" and still be right.

Your claims of contradictions are nothing but admissions on your part you have not understood. I am going to move past your slow learning abilities.

3 in a symbol that refers to an abstract value within an abstract system of values.

You're still unclear as to what exactly you're talking about here: The digit character '3', the string "3" of length 1 consisting of only that character, or the number 3 that string refers to. I shall assume that with 3, the symbol you meant the string "3", and with the "abstract system of values" the conceptual framework of numbers.

It should have said "3 is a symbol" but that should have been obvious.

You not understanding when I say 3 is a symbol I mean 3 is a symbol is the kind of slow learning I'm talking about.

When you understand this part we can move on.

 

[Jokodo]

You're still unclear as to what exactly you're talking about here: The digit character '3', the string "3" of length 1 consisting of only that character, or the number 3 that string refers to. I shall assume that with 3, the symbol you meant the string "3", and with the "abstract system of values" the conceptual framework of numbers.

It should have said "3 is a symbol" but that should have been obvious.

It is obvious, and if you can read English, you will notice that I didn't harp on about the typo at all - I simply ignored it assuming that you meant "3 is a symbol".

It is pretty much the only thing that's obvious in that sentence. The other obvious thing is that you're saying, abstractly, "X is a symbol that refers to Y". Whatever X is and whatever Y is, that is the direct negation of your earlier claim that X does not refer to anything other than itself. The sentence may be true, or false, or meaningless, depending on whether X is meant to be a digit, a string, or a number, but it cannot be both true and its negation also be true.

 

[untermensche]

So we agree "3" is just a symbol. It is nothing more?

If we agree we can take another baby step forward. We need to progress in baby steps so I can see my contradiction.

 

[Jokodo]

So we agree "3" is just a symbol. It is nothing more?

In your words, it is a symbol that refers to an abstract value.
Also in your words, it doesn't refer to anything but itself.

These two statements cannot both be correct at the same time.

As an analogy, if I say "Uganda is a land-locked country on the Atlantic coast", you don't have to check the map to know that this can't be correct. Without checking the map or ever having heard of Uganda, I can tell that they can't both be right at the same time. They can be undefined if no entity by the name of "Uganda" exists, they can both be wrong if it exists and isn't a country, or if it exists as a country and borders the ocean, but not the Atlantic ocean, or one of them is false and the other one true. Or possibly, the borders could have changed so that one was true at one time, and the other at a different point in time. (As it happens, Uganda is indeed landlocked, so it's the second part that's false here.)

The statement even remains contradictory if two entities exist by the same name, and one part is true of one of them and the other of the other: "Georgia is a US state in the Caucasus region of Eurasia" is false whichever Georgia it is you meant to talk about. So maybe when you said that "3 doesn't refer to anything but itself" you meant a different "3" than when you said "3 refers to an abstract value"?

Same with your claims: I have no need to agree or disagree with this claim in order to tell it is in contradiction to your earlier claim that numbers/digits (which you use interchangeably) do not refer to anything but themselves. Any time spent trying to decipher what it is exactly you mean is wasted when it is clear from the get-go that you're contradicting yourself.

Whatever this nothing more is supposed to mean, and whatever it is this time you mean with "3" (is it a number? a digit? a string? something else entirely?), your most recent claim may be true or false, but it's not compatible with your earlier claims.

If you have dropped some or all of the claims you've made in the first 3/4 of this discussion, please let us know which ones. Anything else is wasting both of our time.

...

I will give it a go, though: It's a length 1 character sequence, the most common use of which is to symbolically refer to a number ("abstract value" if you prefer, at any rate itself an abstract concept with its own set of rules), though it's frequently also used to refer to other things (e. g. a chapter in a book, or an item in a list,...). Can you agree with this?

 

[untermensche]

Are you now saying "3" is not a symbol?

We can move on to what it is a symbol of but first we have to agree it is a symbol and nothing else.

Do you agree "3" is a symbol?

Do you agree it is nothing but a symbol?

 

[Jokodo]

Are you now saying "3" is not a symbol?

We can move on to what it is a symbol of but first we have to agree it is a symbol and nothing else.

Do you agree "3" is a symbol?

Do you agree it is nothing but a symbol?

No need to agree or disagree in order to be able to tell that "it refers to something" and "it refers to nothing" cannot both be right.

 

[untermensche]

It is a symbol. It doesn't refer to anything without more.

But we agree "3" is only a symbol. It is nothing else?

 

[Jokodo]

It is a symbol. It doesn't refer to anything without more.

Without more of what? And how does is this supposed to undo the contradiction?

But we agree "3" is only a symbol. It is nothing else?

By "3" you mean the number, the string, the digit, or something entirely different?

 

[untermensche]

If I say "3" is a symbol don't I need to say more than that to define the symbol?

I am in search of this mysterious contradiction.

So we agree "3" is just a symbol.

It is nothing more.

Can we move on to trying to figure out what it is a symbol of?

 

[Jokodo]

If I say "3" is a symbol don't I need to say more than that to define the symbol?

I am in search of this mysterious contradiction.

There's nothing mysterious. You claimed "3" refers to an abstract value. You also claimed it doesn't refer to anything.

So we agree "3" is just a symbol.

It is nothing more.

Can we move on to trying to figure out what it is a symbol of?

You still haven't told me what IT you want to talk about.
For all I know you're trying to pull an analogue of "Georgia is a US State. Georgia is in the Caucasus. Therefore, the US HAS territories in the Caucasus". It's called equivocation, or colloquially untermensche.

I may (or not) agree once you clarify whether you are talking about the String, the number, or something else that exists in your head only.

 

[untermensche]

Are you saying "3" is only a symbol or more than a symbol?

We will get to what it might be a symbol of but we first have to agree "3" is only a symbol.

Do you agree or disagree?

I did not think this would be so hard.

 

[Jokodo]

Are you saying "3" is only a symbol or more than a symbol?

We will get to what it might be a symbol of but we first have to agree "3" is only a symbol.

Do you agree or disagree?

I did not think this would be so hard.

Do you agree Georgia is a US state? Do you agree Georgia is a former Soviet republic?

 

[Jokodo]

I've answered this multiple times. Most recently like this: "["3"] a length 1 character sequence, the most common use of which is to symbolically refer to a number ("abstract value" if you prefer, at any rate itself an abstract concept with its own set of rules), though it's frequently also used to refer to other things (e. g. a chapter in a book, or an item in a list,...). Can you agree with this?"

This assumes you want to talk about the string.
If that's not so the answer might differ, so it's your turn to define your terms!

 

[untermensche]

That is not a responce.

I am asking a simple question.

Is "3" merely a symbol or is it something more?

 

[Jokodo]

That is not a responce.

I am asking a simple question.

Is "3" merely a symbol or is it something more?

I've answered that question under the assumption that you meant to talk about the string "3". If that is not so, it's your turn to clarify. Your refusal to do so tells that whatever argument you're going to make crucially depends on equivocation.

I also have a simple question for you: Is Georgia in Eurasia?

 

[untermensche]

"3" is not a string. It is not a number. It is not a value.

On it's own.

On it's own it means nothing.

It only has meaning if you place it within a predefined scheme.

Do you agree with that?

 

[Jokodo]

"3" is not a string. It is not a number. It is not a value.

On it's own.

On it's own it means nothing.

It only has meaning if you place it within a predefined scheme.

Do you agree with that?

No.

I agree that the string "3" "means nothing" outside of a certain language in which means something. That's a universal property of labels and doesn't distinguish it one bit from the strings "dog" or "Georgia".

You haven't answered my question: Do you agree that Georgia is in Eurasia?

 

[untermensche]

A string?

It is a curvy line.

By referring to it as a string you have already placed it within a mental scheme. You have already assumed it is a part of some whole you are imagining.

It is not a part of anything or related to anything until we attach meaning to it within a scheme.

 

[Jokodo]

A string?

It is a curvy line.

By referring to it as a string you have already placed it within a mental scheme. You have already assumed it is a part of some whole you are imagining.

It is not a part of anything or related to anything until we attach meaning to it within a scheme.

The "3" you type, the "3" that appears on your screen, the "3" that is transmitted through the internet as binary code, and the "3" that appears on my screen (and some 15 stages I omitted) are all different objects, most of which are not "curvy lines". By treating them as one and the same object, you've already placed them within a mental scheme. You're dangerously getting close to a theory of sign as might have been entertained by one of Aristotle's contemporaries. Only 2500 years left to catch up before you can make a contribution to its current incarnation!

We're getting off topic, though. Is Georgia in Eurasia, yes or no?