Rational numbers == infinitely repeating sequences of digits

[untermensche]

Dodge.

But at least you admit that the terms have all been defined.

None exist before they are defined.

And of course if something is defined as one thing it means it is not some other thing defined differently.

 

[Jokodo]

Dodge.

But at least you admit that the terms have all been defined.

They, the terms you use, lack any definition.

None exist before they are defined.

If that is so, all your claims are literally meaningless as long as you refuse to define your terms. Not even wrong, content-free. Thanks for admitting.

And of course if something is defined as one thing it means it is not some other thing defined differently.

Non-sequitur.

 

[untermensche]

Pathetic.

0.33333.... does not refer to 1/3.

It does not refer to anything but itself.

1/3 is just an equation that creates 0.3333...

An equation that produces something is not referring to it.

You have a strange religion.

 

[Jokodo]

Pathetic.

0.33333.... does not refer to 1/3.

The truth value of that statement is undefined as long as you refuse to clarify what it is you wish to talk about.

It does not refer to anything but itself.

The truth value of that statement is undefined as long as you refuse to clarify what it is you wish to talk about.

1/3 is just an equation that creates 0.3333...

Hey, we're making progress: a statement that's clear enough to be determined false!

"A common fraction is a numeral which represents a rational number. That same number can also be represented as a decimal, a percent, or with a negative exponent. For example, 0.01, 1%, and 10−2 all equal the fraction 1/100. " - https://en.m.wikipedia.org/wiki/Fraction_(mathematics)

 

[untermensche]

The truth value of that statement is undefined as long as you refuse to clarify what it is you wish to talk about.

Worthless dodge. You don't want definitions.

When I tried to work towards a definition of "3" you wanted no part of it.

You started. We agreed it was a pattern.

That is as far as you would go towards defining it. I said it was a specific pattern and you changed the subject.

So all we have so far is "3" is a specific pattern.

If we can agree with this we can possibly move towards a definition.

But you really don't want a definition.

 

[Jokodo]

The truth value of that statement is undefined as long as you refuse to clarify what it is you wish to talk about.

Worthless dodge. You don't want definitions.

It's not a dodge, it's a fact.

When I tried to work towards a definition of "3" you wanted no part of it.

You started. We agreed it was a pattern.

That is as far as you would go towards defining it. I said it was a specific pattern and you changed the subject.

So all we have so far is "3" is a specific pattern.

What "3"?

If we can agree with this we can possibly move towards a definition.

You're not going to get me to agree to a claim that cannot possibly have a truth value. Again, what "3"?

But you really don't want a definition.

I've been begging you to define your terms since forever.

 

[untermensche]

What "3"?

The "3" you must be looking at to ask about.

But you really don't want a definition.

I've been begging you to define your terms since forever.

I had given you a definition of "3" many times.

"3" is a symbol that can be assigned to a value, an abstract value, imaginary value, conceptual value, within a predefined system of values.

Once assigned within a system it is nothing else.

It does not point to any other system of values.

Once you have a system of values you can also create specific abstract operations that can be carried out on those values to produce different values.

So the value 1 and and the value 3 point to nothing but themselves within a specific value system.

But if you divide 1 by 3 (shorthand 1/3) you can create a new value that also only points to itself within the system of values.

 

[Jokodo]

What "3"?
The "3" you must be looking at to ask about.

The "3" I'm looking at is a pattern of differently illuminated pixels. Of course, this cannot what you're talking about since it makes almost everything that follows false.

But you really don't want a definition.
I've been begging you to define your terms since forever.
I had given you a definition of "3" many times.

Never one that's consistent with even half of your claims.

"3" is a symbol that can be assigned to a value, an abstract value, imaginary value, conceptual value, within a predefined system of values.

I think you want to say "can be used/interpreted as a symbol", but I'll let this pass.

Once assigned within a system it is nothing else.

Which "it"? The pattern of differently illuminated pixels or the symbol created by interpreting it as a symbol? Or the value it has been assigned? Your claim is clearly false of the first, which is still a pattern of differently illuminated pixels whatever else it may be.

It does not point to any other system of values.

What's that "it" again that's clearly not the "3" I'm looking at?

Once you have a system of values you can also create specific abstract operations that can be carried out on those values to produce different values.

So the value 1 and and the value 3 point to nothing but themselves within a specific value system.

So it's the values you want to talk about? Too bad for you this makes all of your talk about final values gibberish. Also, what would it even mean for an abstract value to point even at itself?

But if you divide 1 by 3 (shorthand 1/3) you can create a new value that also only points to itself within the system of values.

That doesn't follow even if I allow you to jump back between the word d-o-g, the species canis lupus familiaris, and my neighbors' terrier at will.

 

[untermensche]

The "3" I'm looking at is a pattern of differently illuminated pixels. Of course, this cannot what you're talking about since it makes almost everything that follows false.

How the pattern is generated is meaningless.

All that is required is you have a mind that can recognize it as a distinct pattern.

You clearly recognize the pattern since you can refer to the same pattern I do.

This is nothing but hand waving nonsense.

Never one that's consistent with even half of your claims.

You've shown no inconsistencies.

"3" is a symbol that can be assigned to a value, an abstract value, imaginary value, conceptual value, within a predefined system of values.

I think you want to say "can be used/interpreted as a symbol", but I'll let this pass.

No it is a symbol. It symbolizes a value within an imaginary value scheme. There is a one to one correspondence between a symbol and an imagined value. A symbol in context only has one value.

Once assigned within a system it is nothing else.

Which "it"? The pattern of differently illuminated pixels or the symbol created by interpreting it as a symbol? Or the value it has been assigned? Your claim is clearly false of the first, which is still a pattern of differently illuminated pixels whatever else it may be.

The pattern is merely what the mind recognizes. A symbol is a recognized pattern that can refer to some other thing. The symbol points to a specific value within a predefined scheme.

The "it" is the one to one correspondence between a specific symbol in context and it's value within a predefined scheme.

It does not point to any other system of values.

What's that "it" again that's clearly not the "3" I'm looking at?

If you see a "3" and know its value then you know it as is a specific value within a predefined value scheme.

You know it as nothing else.

But if you divide 1 by 3 (shorthand 1/3) you can create a new value that also only points to itself within the system of values.

That doesn't follow even if I allow you to jump back between the word d-o-g, the species canis lupus familiaris, and my neighbors' terrier at will.

Saying 1/3 is shorthand for 1 divided by 3 makes no sense to you?

 

[Jokodo]

How the pattern is generated is meaningless.

All that is required is you have a mind that can recognize it as a distinct pattern.

You clearly recognize the pattern since you can refer to the same pattern I do.

This is nothing but hand waving nonsense.



You've shown no inconsistencies.

Do I really have to dig out the post where you said "3" doesn't refer to anything but itself? Where you talking about a different than now when you say it refers to an abstract value?

"3" is a symbol that can be assigned to a value, an abstract value, imaginary value, conceptual value, within a predefined system of values.

I think you want to say "can be used/interpreted as a symbol", but I'll let this pass.

No it is a symbol. It symbolizes a value within an imaginary value scheme. There is a one to one correspondence between a symbol and an imagined value. A symbol in context only has one value.

If by "in context" you mean "as long as we interpret it that way", this is a tautology. Otherwise it's false. The string "3.0" can refer to an integer 3 (e.g., the length of an array) only we need to convert it to real to perform floating point arithmetic on it (e. g., take its mean); it can refer to an exact real value; it can be shorthand for 3.0+/-0.05 when talking imprecise measurements (in this case it's distinct from 3.00), or it can refer to theorem #0 of section #3.

Once assigned within a system it is nothing else.

Which "it"? The pattern of differently illuminated pixels or the symbol created by interpreting it as a symbol? Or the value it has been assigned? Your claim is clearly false of the first, which is still a pattern of differently illuminated pixels whatever else it may be.

The pattern is merely what the mind recognizes.

That may be so, but it doesn't make the pixels go away.

A symbol is a recognized pattern that can refer to some other thing. The symbol points to a specific value within a predefined scheme.

The "it" is the one to one correspondence between a specific symbol in context and it's value within a predefined scheme.

So, substituting your definition, we get: Once assigned within a system the one to one correspondence is nothing else. That's not a meaningful statement.

It does not point to any other system of values.

What's that "it" again that's clearly not the "3" I'm looking at?

If you see a "3" and know its value then you know it as is a specific value within a predefined value scheme.

You know it as nothing else.

But if you divide 1 by 3 (shorthand 1/3) you can create a new value that also only points to itself within the system of values.

That doesn't follow even if I allow you to jump back between the word d-o-g, the species canis lupus familiaris, and my neighbors' terrier at will.

Saying 1/3 is shorthand for 1 divided by 3 makes no sense to you?

Sure it does. It doesn't however make it so that the operation rather than the value it produces is the only thing it refers to and it certainly doesn't make it so that that value must and not shared by other representations, or as the result of other operations.

 

[untermensche]

Do I really have to dig out the post where you said "3" doesn't refer to anything but itself? Where you talking about a different than now when you say it refers to an abstract value?

It is a symbol for a specific value withing a predefined value system.

It refers to one value. It does not refer to anything else.

It does not refer to 6/2. This is two values and an operation.

If by "in context" you mean "as long as we interpret it that way", this is a tautology.

In context means within a predefined value system.

So 3 has one value in some system. And 0.3 has a different value because it is within a different context.

The other symbols are your context.

3 has no other symbols to consider.

The string "3.0" can refer to an integer 3

The value scheme known as the "integers" is a specifically defined scheme.

3 has one place in that scheme. Adding any amount of zero's after the decimal does not change the value within that predefined scheme.

...it can be shorthand for 3.0+/-0.05 when talking imprecise measurements....

That is not a value. It is an infinite amount of values.

And it is not saying the value of 3.0 in the scheme is 3+/- 0.05.

It is saying a measurement of 3.0 in the scheme is assigned the value of 3.0 +/- 0.05.

A very different thing.

The pattern is merely what the mind recognizes.

That may be so, but it doesn't make the pixels go away.

Utterly meaningless point.

You are not experiencing pixels. You are experiencing what your brain creates from the illuminated pixels.

You can't experience a pixel. Your mind has no pixels.

But you can experience and recognize a pattern. To a mind "3" is only a recognizable pattern.

So, substituting your definition, we get: Once assigned within a system the one to one correspondence is nothing else. That's not a meaningful statement.

How is something full of meaning meaningless?

Within some scheme "3" corresponds to a specific value.

It does not refer to any other value within that scheme.

And it is not referring to any other scheme of values. It exists withing one. Period.

Saying 1/3 is shorthand for 1 divided by 3 makes no sense to you?

Sure it does. It doesn't however make it so that the operation rather than the value it produces is the only thing it refers to and it certainly doesn't make it so that that value must and not shared by other representations, or as the result of other operations.

Performing an operation on two values gives you a different value.

The different value is derived by the operation.

Being derived is very different from "referring to".

Can you give me 1/3 of a dollar in change?

 

[Jokodo]

Trying to reinvent all of ontology, semiotics, mathematics from scratch is an honorable endeavor. It's however also rather foolish.
It's like you're reinventing the wheel and haven't even gotten to the point where you realize that it, maybe, shouldn't be square.

It is a symbol for a specific value withing a predefined value system.

It refers to one value.

...which is, for what feels like the 200th time, in contradiction to the claim that it doesn't refer to anything. The two claims can both be false, or both undefined, but they cannot possibly both be right.

It does not refer to anything else.

It does not refer to 6/2. This is two values and an operation.

It may not refer to 6/2 (though it does), but the value it refers to can still be the same as the value "6/2" refers to, or produces if you prefer. You could be right about this, and your conclusion still wouldn't follow.

In context means within a predefined value system.

So 3 has one value in some system. And 0.3 has a different value because it is within a different context.

The other symbols are your context.

3 has no other symbols to consider.

The string "3.0" can refer to an integer 3

The value scheme known as the "integers" is a specifically defined scheme.

3 has one place in that scheme. Adding any amount of zero's after the decimal does not change the value within that predefined scheme.

...it can be shorthand for 3.0+/-0.05 when talking imprecise measurements....

That is not a value. It is an infinite amount of values.

It may not be a value for whatever definition of value you have in mind, but it is a potential meaning and indeed frequent meaning of the string "3.0" so whatever else this may or may not show, it shows that you're wrong to claim that "it doesn't refer to anything else".

And it is not saying the value of 3.0 in the scheme is 3+/- 0.05.

It is saying a measurement of 3.0 in the scheme is assigned the value of 3.0 +/- 0.05.

You just said that 3.0 +/- 0.05 is not a value. Now it is? I guess you were using two different definitions of value then and now?

A very different thing.

The pattern is merely what the mind recognizes.

That may be so, but it doesn't make the pixels go away.

Utterly meaningless point.

You are not experiencing pixels. You are experiencing what your brain creates from the illuminated pixels.

You can't experience a pixel. Your mind has no pixels.

If that is so, it doesn't matter. They're their whether or not I "experience" them, for whatever definition of "experience", and for whatever reason you thought it worthwhile to bring this up in the first place.

But you can experience and recognize a pattern. To a mind "3" is only a recognizable pattern.

So, substituting your definition, we get: Once assigned within a system the one to one correspondence is nothing else. That's not a meaningful statement.

How is something full of meaning meaningless?

Within some scheme "3" corresponds to a specific value.

It does not refer to any other value within that scheme.

And it is not referring to any other scheme of values. It exists withing one. Period.

Saying 1/3 is shorthand for 1 divided by 3 makes no sense to you?

Sure it does. It doesn't however make it so that the operation rather than the value it produces is the only thing it refers to and it certainly doesn't make it so that that value must and not shared by other representations, or as the result of other operations.

Performing an operation on two values gives you a different value.

The different value is derived by the operation.

Being derived is very different from "referring to".

Hey, maybe we should try a different approach. Let's replace all references to "3" with references to "dog", and all references to "abstract value" or "number" with "animal". It's a simple sanity check for the things you claim about labels and their referents. If your claims don't make sense for the one were we can directly assess them, your theory of ontology and/or semiotics must be broken. We can tell that much even without pinpointing where it is broken.

So I understand you're claiming 3 refers to a specific abstract value and nothing else within a scheme, 1 is a different abstract value in that scheme, and operation involving those two values doesn't refer at all, and its product is necessarily something distinct from the value of any other pattern within the scheme, and an operation using values x and y is distinct from an operation using values z and w (therefore, 1/3 and 5/15 are distinct entities). Is that a fair paraphrase? If not, where did I go wrong?

So let's translate this: "dog" refers to an animal species and nothing else within the scheme of the English language, "comodo dragon" refers to a different species, and "buffalo" and "rattlesnake" are yet other species. Each operation involving any two of these species is a separate entity, neither identical to any other like operation, nor co-referent with any other symbol within the scheme. Take for example, the operation: "determine the latest common ancestor of X and Y, and project its living descendants". It follows that "the extant descendants of the latest common ancestor of buffalo and comodo dragons" and "the extant descendants of the latest common ancestor of dogs and rattlesnakes" have to express two different sets, neither of which can be co-referent with the term "amniotes".

Since this is obvious nonsense, there must be a bug somewhere in your logic. If you won't take my hints as to where to find it, go ahead and waste your time finding it yourself.

 

[untermensche]

Trying to reinvent all of ontology, semiotics, mathematics from scratch is an honorable endeavor.

Then maybe one ay you will do it.

I am trying to discover what things are.

You are not all that interested.

...which is, for what feels like the 200th time, in contradiction to the claim that it doesn't refer to anything. The two claims can both be false, or both undefined, but they cannot possibly both be right.

What is being said is it represents a specific value within a predefined value system and nothing else.

If you took it to mean something else that is miscommunication not contradiction.

It may not refer to 6/2 (though it does), but the value it refers to can still be the same as the value "6/2" refers to, or produces if you prefer. You could be right about this, and your conclusion still wouldn't follow.

The value it refers to is the value produced by performing the operation.

You have the value 6 and the value 2 and you have a predefined operation which when performed produces another value.

An equation and it's product are two different things.

What you should say is 6/2 results in 3. But 3 does not result in 6/2. 3 on it's own results in nothing but 3.

You just arbitrarily say they are the same thing because one results in the other.

You think your arbitrary conclusions are necessary conclusions.

And you're not interested in understanding they are arbitrary conclusions not necessary conclusions.

You just said that 3.0 +/- 0.05 is not a value. Now it is? I guess you were using two different definitions of value then and now?

You are right about this. It is not a value. It is an arbitrarily assigned range of values.

That may be so, but it doesn't make the pixels go away.

Utterly meaningless point.

You are not experiencing pixels. You are experiencing what your brain creates from the illuminated pixels.

You can't experience a pixel. Your mind has no pixels.

If that is so, it doesn't matter. They're their whether or not I "experience" them, for whatever definition of "experience", and for whatever reason you thought it worthwhile to bring this up in the first place.

This has got to be the worst line of argument I have seen in a long time.

All we can talk about is what we experience about these symbols.

You have knowledge there are pixels but no experience of a pixel.

The reason we can talk about "3" is because we can experience something that is recognizable to us. How it becomes something recognizable is totally meaningless.

The starting point is a pattern we can both recognize. The starting point is something in the mind not something in the world. If the pattern is not recognized by the mind it is not a pattern. It is meaningless light and dark pixels.

Hey, maybe we should try a different approach. Let's replace all references to "3" with references to "dog", and all references to "abstract value" or "number" with "animal". It's a simple sanity check for the things you claim about labels and their referents. If your claims don't make sense for the one were we can directly assess them, your theory of ontology and/or semiotics must be broken. We can tell that much even without pinpointing where it is broken.

Animal is recognition of a pre-existing thing.

Value only becomes something when a value scheme is defined.

That you make this point shows you to be completely lost.

 

[Jokodo]

Animal is recognition of a pre-existing thing.

Value only becomes something when a value scheme is defined.

That you make this point shows you to be completely lost.

If your calculator yields a demonstrably wrong result for 3+5, why should we trust it to yield a usable result for log(29576)? A logic that fails the easy cases deserves to get dumped. Your claim that the result of an operation cannot in principle be equivalent to the referent of a plain label fails simple sanity check.

Also, "species" aren't "pre-existing things" any more than numbers.

 

[untermensche]

You are waving your arms and dancing around.

Like I said you have no interest in understanding what things are.

These things (animals) we arrange into groups depending on arbitrary features exist before we begin our arranging scheme.

The idea of "value" referred to with a symbol does not exist until humans invent it and define it.

 

[Jokodo]

You are waving your arms and dancing around.

Like I said you have no interest in understanding what things are.

These things (animals) we arrange into groups depending on arbitrary features exist before we begin our arranging scheme.

The idea of "value" referred to with a symbol does not exist until humans invent it and define it.

The idea of a species as an abstract common denominator of individual animals no more does than the idea of a number as an abstract value shared by three logs and three pebbles. If your logic works, it's going to work for both.

 

[untermensche]

You are waving your arms and dancing around.

Like I said you have no interest in understanding what things are.

These things (animals) we arrange into groups depending on arbitrary features exist before we begin our arranging scheme.

The idea of "value" referred to with a symbol does not exist until humans invent it and define it.

The idea of a species as an abstract common denominator of individual animals no more does than the idea of a number as an abstract value shared by three logs and three pebbles. If your logic works, it's going to work for both.

"3" does not come from having rocks.

There were major civilizations that didn't have "3".

"3" is a mental construct. Entirely a mental construct.

But the animals are not mental constructions.

 

[Jokodo]

You are waving your arms and dancing around.

Like I said you have no interest in understanding what things are.

These things (animals) we arrange into groups depending on arbitrary features exist before we begin our arranging scheme.

The idea of "value" referred to with a symbol does not exist until humans invent it and define it.

The idea of a species as an abstract common denominator of individual animals no more does than the idea of a number as an abstract value shared by three logs and three pebbles. If your logic works, it's going to work for both.

"3" does not come from having rocks.

There were major civilizations that didn't have "3".

"3" is a mental construct. Entirely a mental construct.

But the animals are not mental constructions.

species are. With which you admit your logic doesn't work for either. Thread closed. You can probably delete your account too since this seems to be your main hobby-horse.

 

[untermensche]

"3" does not come from having rocks.

There were major civilizations that didn't have "3".

"3" is a mental construct. Entirely a mental construct.

But the animals are not mental constructions.

species are. With which you admit your logic doesn't work for either. Thread closed. You can probably delete your account too since this seems to be your main hobby-horse.

Species are categories based on pre-existing entities.

Value is not a pre-existng entity.

It is an imaginary entity.

 

[Jokodo]

"3" does not come from having rocks.

There were major civilizations that didn't have "3".

"3" is a mental construct. Entirely a mental construct.

But the animals are not mental constructions.

species are. With which you admit your logic doesn't work for either. Thread closed. You can probably delete your account too since this seems to be your main hobby-horse.

Species are categories based on pre-existing entities.

Value is not a pre-existng entity.

It is an imaginary entity.

It doesn't even matter whether species are more real than numbers (they aren't, but that's besides the point). The claims you're making aren't about numbers, they're about referential schemes and the relationships between labels and referents they entail. It either is or isn't true that a reference scheme necessitates a strict 1:1 mapping. It either is or isn't true that an operation involving the referents of Labels A and B cannot in principle have the Referent of label C as its output. If you want to argue These are true for numerals and false for cladistics, you gotta be a bit more explicit than "but their domains are different!"

Thread closed