A collection of infinitely many distinct elements

[doronshadmi]

"NOR,NXOR" isn't what I'd call "exact".

What exactly are you going to replace AND with?

NOR or NXOR.

Each one of them can be used in order to represent non-locality (in addition to AND).

 

[Reality Check]

Please read very carefully http://www.internationalskeptics.com/forums/showpost.php?p=3783689&postcount=833 .

Read that and it very clearly states that TOUM.pdf is incomplete since that document does not have much of the post at test 6.

Only if you force the law of excluded middle on x, but then you get exactly what you forced, which is, locality.

Indeed locality is not non-locality, so you cannot conclude anything about non-locality by forcing locality, and you cannot conclude anything about locality by forcing non-locality.

One more time: None of terms in "(x € A) and (x ~€ A)" have any mention of locality or non-locality.

• Is € local or non-local?
• Is ~€ local or non-local?
• Is and local or non-local?
• Is x local or non-local?
• Is A local or non-local?
• Is a sub-element local or non-local?
• Is an element local or non-local?
• Is an urelement local or non-local?

If your answer is yes to any of these then you have to tell the reader of TOUM.pdf!

Otherwise I take it that you are willing for anyone who reads TOUM.pdf to consider you a crackpot because you state something that can never be true.
If you updated it to say what you actually mean then there is a chance someone would take test 6 seriously.

 

[Reality Check]

NOR or NXOR.

Each one of them can be used in order to represent non-locality (in addition to AND).

Are you now saying that the real, complete, final, will never change, can never be misinterpreted test 6 is as below?
If any of these tests is true:
"Definition" 6a: (x € A) AND (x ~€ A)
"Definition" 6b: (x € A) NOR (x ~€ A)
"Definition" 6c: (x € A) XOR (x ~€ A)
then x is non-local.

Then you need to add this to TOUM.pdf.

 

[doronshadmi]

Are you now saying that the real, complete, final, will never change, can never be misinterpreted test 6 is as below?
If any of these tests is true:
"Definition" 6a: if (x € A) AND (x ~€ A) then (x ~€ A) is non-local.
"Definition" 6b: if (x € A) NOR (x ~€ A) then (x ~€ A) is non-local.
"Definition" 6c: if (x € A) XOR (x ~€ A) then (x ~€ A) is non-local.

Then you need to add this to TOUM.pdf.

You have a typo mistake at 6c. It has to be NXOR

My framework is not a deductive-only context dependent framework, or in other words, the reader is not passive but an active participator of the framework.

By using symmetry it is easily shown that NOR, AND , NXOR are particular representations of non-locality:

NOR:
00 --> T
01 --> F
10 --> F
11 --> F

AND:
00 --> F
01 --> F
10 --> F
11 --> T

NXOR (NOR together with AND):
00 --> T
01 --> F
10 --> F
11 --> T

 

[Reality Check]

You have a typo mistake at 6c. It has to be NXOR

My framework is not a deductive-only context dependent framework, or in other words, the reader is not passive but an active participator of the framework.

By using symmetry it is easily shown that NOR, AND , NXOR are particular representations of non-locality:

NOR:
00 --> T
01 --> F
10 --> F
11 --> F

AND:
00 --> F
01 --> F
10 --> F
11 --> T

NXOR (NOR together with AND):
00 --> T
01 --> F
10 --> F
11 --> T

Then you are going to update TOUM?

 

[ddt]

No, there is no "exists" quantifier and everybody knows that. Assume that any poster can better read than you can write.

Really?

Please explain your support of jsfisher's conclusion abuot x, expressed by:

[...]

[latex]$$$ \exists (x \epsilon A) : (x \epsilon A) \wedge \neg (x \epsilon A) $$$[/latex]

You have claimed earlier there is some x and some A such that x is non-local w.r.t. A. jsfisher did nothing more than express that statement in a logical formula - and then concluded that your logic is inconsistent.

Yesterday you had another story.

Notions are developed during interaction with other notions.

You claimed you had been working for 20 years on this. One might think you'd have pinned down such a thing much earlier. There is no evidence to date in these threads that you read (and understood) a single book on logic - not even a single book on mathematics - in those 20 years.

But don't you worry, it does not hold in your case because you already know everything so you do not need any evolution.

I enjoyed a thorough education in math. That doesn't mean I know everything, and I'm still open to learning new things. You might have noticed that Apathia directed me to "Law of Forms", which was new to me.

ETA: Now think about this one:

Now how about the rest of your logic? Do you decide after all to stick with classical logic?

 

[doronshadmi]

You have claimed earlier there is some x and some A such that x is non-local w.r.t. A. jsfisher did nothing more than express that statement in a logical formula - and then concluded that your logic is inconsistent.

I do not understand your answer.

1) Do you support (or not) jsfisher's conclusion, in this case?

2) What is w.r.t?

3) Why do you claim that jsfisher's conclusion is not based on the use of Existential quantification?

I enjoyed a thorough education in math.

It does not help very much here, isn't it?

You are unable to think beyond the context dependent framework.

Instead of be aware about this fact, you say that there is nothing beyond the context dependent framework, which is a reaction of a fanatic person (religious or not, it does not matter).

 

[ddt]

if (x € A) is true then (x ~€ A) is false.

Only if you force the law of excluded middle on x, but then you get exactly what you forced, which is, locality.

Nothing is "forced". The law of excluded middle follows from the basic rules of logic. Thus far, you haven't shown anything that changes those basic rules, and locality is just a property of elements in your universe that is defined on top of and in terms of the underlying logic.

But here you're confusing two logic laws, viz. the "law of excluded middle" and the "law of contradiction". They are similar but subtly different.

Reality Check's statement is a rephrasing of the law of contradiction. That says that a proposition Y and its negation ~Y cannot both be true at the same time. In a formula:
~ (Y and ~Y)
Every logicist agrees with that, and you can derive the law simply from the natural deduction rules.

The law of excluded middle, on the other hand, says that a proposition Y and its negation ~Y cannot both be false at the same time. In a formula:
Y or ~Y
Classical logicists agree with that; intuitionistic logicists do not agree with it, i.e., they argue that that statement is not provable.

You might argue that the two are the same, and you can apply De Morgan to get from one to the other. But in fact, if you apply De Morgan on the law of contradiction, you get
~Y or ~~Y
and now you see the essential extra step needed to get to the law of excluded middle: getting away with the double negation. And that's what an intuitionist objects to.

Let's take as example proposition Y = "there are 99 consecutive 9's in the decimal expansion of pi" (that was a favourite of Brouwer's). According to an intuitionist, a proof of Y should consist of a constructive way to show there are 99 nines, e.g. by showing where those 99 nines appear. However, when I prove that ~Y leads to contradiction and thus infer ~~Y and thus Y, I haven't shown where those 99 nines are, and therefore I haven't proved Y; I have shown ~Y to be false but I haven't (yet) shown Y to be true - its truth is still unknown.

 

[ddt]

1) Do you support (or not) jsfisher's conclusion, in this case?

Yes. But the conclusion is based on the combination of your definition and other statements you made. Nobody claimed there was an existential quantification in your definition.

2) What is w.r.t?

with respect to.

3) Why do you claim that jsfisher's conclusion is not based on the use of Existential quantification?

See at (1) above.

I enjoyed a thorough education in math.

It does not help very much here, isn't it?

It helps me very much to spot crackpots and loonies.

You are unable to think beyond the context dependent framework.

Instead of be aware about this fact, you say that there is nothing beyond the context dependent framework, which is a reaction of any fanatic person (religious or not, it does not matter).

The phrase "context dependent framework" is your invention - or you scavenged it from some other area. Google for it together with "mathematics", and you'll only find references to your posts.

So the above are empty statements, devoid of meaning.

 

[doronshadmi]

Nothing is "forced". The law of excluded middle follows from the basic rules of logic. Thus far, you haven't shown anything that changes those basic rules, and locality is just a property of elements in your universe that is defined on top of and in terms of the underlying logic.

But here you're confusing two logic laws, viz. the "law of excluded middle" and the "law of contradiction". They are similar but subtly different.

No.

"if (x € A) is true then (x ~€ A) is false." is forcing xor on x (in that case x property cannot be but local (EDIT: I forgot to add 's to x, so the right one is: "in that case x's property cannot be but local").

 

[Reality Check]

No.

"if (x € A) is true then (x ~€ A) is false." is forcing xor on x (in that case x property cannot be but local).

No.

It is using your own definition of ~€: ~€ is the negation of €.

 

[ddt]

No.

"if (x € A) is true then (x ~€ A) is false." is forcing xor on x (in that case x property cannot be but local).

Nobody "forces" logical connectives on anything. Logical connectives are there to construct logical formulae. And in particular, it's not "forcing" it on x, as the quoted formula says something about x € A and its negation. And x is not a property but an element. From TOUM, just before definition 6:

x and A are placeholders of an element.

 

[Reality Check]

"w.r.t" = "with respect to"
This is needed since your "defintions" are written as tests of x with respect to a specific A.

 

[doronshadmi]

Yes. But the conclusion is based on the combination of your definition and other statements you made. Nobody claimed there was an existential quantification in your definition.

Good,

So there is nothing to do with jsfisher's argument and definition 6.

If you disagree than show how jsfisher's argument is relevant to definition 6.

 

[doronshadmi]

Nobody "forces" logical connectives on anything. Logical connectives are there to construct logical formulae. And in particular, it's not "forcing" it on x, as the quoted formula says something about x € A and its negation. And x is not a property but an element. From TOUM, just before definition 6:

x is an element that has some proprty.

If x (an element that has some proprty) is both belong to A and does not belong to A, then x is non-local (it has non-local property).

A is not spesific because it can be urelemnt or a set, but it does not chage the fact that x has non-local property if x (an element that has some proprty) is both belong to A and does not belong to A.

The law of contradiction has nothing to do here.

Look again at this:

c) Since x is not A, it is not identical to any particular x\A relation, and we cannot assume that x is identical to (x € A).

Huh?

This Huh means that you do not get the simple notion that x is not the same as (x € A).

d) In that case "There exits (x € A) such that (x € A) AND ~(x € A)" has nothing to do with definition 6.

No, there is no "exists" quantifier and everybody knows that. Assume that any poster can better read than you can write.

In this part you think that I claim that jsfisher's argument is some version of my argument. But I say exactly the opposite, which is: By using jsfisher's argument you cannot conclude anything about definition 6.

 

[PixyMisa]

You have a typo mistake at 6c. It has to be NXOR

Indeed, that's what you said. But - why?

My framework is not a deductive-only context dependent framework

Oh, believe me, we noticed.

or in other words, the reader is not passive but an active participator of the framework.

You mean you're making it up as you go along?

By using symmetry it is easily shown that NOR, AND , NXOR are particular representations of non-locality

If it is easily shown, then by all means, show it.

 

[ddt]

Yes. But the conclusion is based on the combination of your definition and other statements you made. Nobody claimed there was an existential quantification in your definition.

Good,

So there is nothing to do with jsfisher's argument and definition 6.

If you disagree than show how jsfisher's argument is relevant to definition 6.

Sigh. Deep sigh. Do you read posts? Do you understand them?

Let's get back to definition 6:

Definition 6: If x € A and x ₡ A, then x is non-local [w.r.t. A, ddt].

The "if" part is always false, whatever x and A you look at. That's the law of contradiction, of which you said this morning that it holds in your logic. So, the logical conclusion is that not a single x is non-local.

However, you also claimed in previous posts there were non-local x's. Let's call one such x: x0, and the corresponding A: A0. So, x0 is non-local w.r.t. A0. According to your definition, this can only be the case if
x0 € A0 and x0 ₡ A0
holds - that's the "only if" part that's implied in your wording because you called it a definition. Let's define the proposition Y as
Y := x0 € A0
then the above says that the formula
Y and ~Y
holds. So from that, jsfisher inferred that in your logic

[latex]$$\exists Y: Y \wedge ~Y$$[/latex]

and that's where the existential quantifier comes from.

 

[PixyMisa]

x is an element that has some proprty.

If x (an element that has some proprty) is both belong to A and does not belong to A, then x is non-local (it has non-local property).

That's a contradiction.

A is not spesific because it can be urelemnt or a set, but it does not chage the fact that x has non-local property if x (an element that has some proprty) is both belong to A and does not belong to A.

That's a contradiction.

The law of contradiction has nothing to do here.

The "law of contradiction" would seem to live a busy life with you around, Doron. The law of non-contradiction, on the other hand, appears to have been quite excluded from consideration.

 

[ddt]

or in other words, the reader is not passive but an active participator of the framework.

You mean you're making it up as you go along?

Sounds like it, doesn't it? My younger brother did that when he was 10. He grew out of it.

By using symmetry it is easily shown that NOR, AND , NXOR are particular representations of non-locality

If it is easily shown, then by all means, show it.

909 posts and counting...

 

[ddt]

x is an element that has some proprty.

(bolding mine). Notice the difference in verb? "has" vs. "is"? You earlier said that "x is a property". Employ some rigour.

If x (an element that has some proprty) is both belong to A and does not belong to A, then x is non-local (it has non-local property) then you have a logical contradiction.

Fixed it for you.

A is not spesific because it can be urelemnt or a set, but it does not chage the fact that x has non-local property if x (an element that has some proprty) is both belong to A and does not belong to A.

A doesn't interest me at this point.

The law of contradiction has nothing to do here.

Yes it has, as you're stubbornly repeating over and over again a formula which is logically false as a consequence of the law of contradiction. Whenever "x belongs to A" is true, "x belongs not to A" must be false.