Deeper than primes

[doronshadmi]

Quote:So your "axiomatic framework" holds '=' as an observer, but you still haven't come up with the "concluder."

0 < x < ∞

"observer = concluder = researcher", where in this expression "=" has ∞ magnitude of existence, and "observer","concluder","researcher" have x magnitude of existence.

 

[doronshadmi]

It is clearly not based on this assumption.

Yes it is, a member of X is identical to X, otherwise there is no paradox.

 

[doronshadmi]

So you can solve the paradox by removing the tautology "( x implies not x ) implies not x".

Fine. That was the easy part.

Now rewrite the 2,300 years (at least) of mathematics you have just wiped out.

Nothing was wiped out.

By understanding cardinals 0, x or ∞ and 0 < x < ∞, Russell's paradox is not universal (it is limited to a flat framework, where a member of X is identical to X, because distinct identities share the same level of existence), and therefore not a tautology.

Flat-lend reasoning is a context-dependent framework, such that each framework has its own tautology.

This is not the case with OM, which is not a context dependent framework (totalities like "that has no predecessor" and "that has not successor" are considered), therefore OM's tautology is indeed universal.

 

[doronshadmi]

Surely, you can define something, no?

Yes, but in order to get the definitions in http://www.internationalskeptics.com/forums/showpost.php?p=6347415&postcount=11584 or http://www.internationalskeptics.com/forums/showpost.php?p=6356155&postcount=11640 you have to get out of your context-dependent box.

Surely, you can demonstrate Doronetics superiority, no?

How about, a non context-dependent framework, which deals with real complexity (including real superposition, real uncertainty, real redundancy, infinite interpolation, infinite extrapolation), which has real universal tautology (because totalities are considered), which deals with magnitudes of existence, which deals with non-locality and locality, which uses non-local numbers, which is naturally free from Russell's paradox (because it is not limited to distinct things that share the same level of existence) and the garbage can of proper classes, which enables to enter the mathematician (his/her non-personal aspect) as a valid factor of the mathematical research, which enables to deal with ethical challenges in terms of the survival and development of complex systems, etc ... etc.. ?

 

[Robin]

Nothing was wiped out.

By understanding cardinals 0, x or ? and 0 < x < ?, Russell's paradox is not universal (it is limited to a flat framework, where a member of X is identical to X, because distinct identities share the same level of existence), and therefore not a tautology.

Flat-lend reasoning is a context-dependent framework, such that each framework has its own tautology.

This is not the case with OM, which is not a context dependent framework (totalities like "that has no predecessor" and "that has not successor" are considered), therefore OM's tautology is indeed universal.

What is interesting to me about this answer is that you do not appear to understand what my objection was.

Tell me - on what basis do you think I was saying that the removal of the " ( x implies not x ) implies not x" would wipe out 2,300 years of mathematics?

 

[doronshadmi]

What is interesting to me about this answer is that you do not appear to understand what my objection was.

Tell me - on what basis do you think I was saying that the removal of the " ( x implies not x ) implies not x" would wipe out 2,300 years of mathematics?

Please show me how exactly " ( x implies not x ) implies not x" is related to what I say about this subject.

 

[Robin]

Please show me how exactly " ( x implies not x ) implies not x" is related to what I say about this subject.

If you don't understand I will explain.

But first my prior question - on what basis do you think I was saying that the removal of the " ( x implies not x ) implies not x" tautology would wipe out 2,300 years of mathematics?

 

[doronshadmi]

If you don't understand I will explain.

But first my prior question - on what basis do you think I was saying that the removal of the " ( x implies not x ) implies not x" tautology would wipe out 2,300 years of mathematics?

As I get it "( x implies not x ) implies not x" = "if (if p then ~p) then ~p" = "always false" = "contradiction"

Please show how Russell's paradox is a non context-dependent (universal) fallacy.

 

[Robin]

As I get it "( x implies not x ) implies not x" = "if (if p then ~p) then ~p" = "always false" = "contradiction"

On the contrary, "if (if p then ~p) then ~p)" is always true. That is why it is called a tautology.

But you still have not answered the question - why do you think I said that removing this tautology would wipe out 2,300 years of mathematics?

If you don't know, then just say so.

 

[The Man]

In both cases you have used cardinality that is not used as a successor of any cardinality.

So you just can’t give the results asked?

Are you going to tell us that in flat-land μ is not a successor of any cardinality?

As your flat-land is just another invention of your fiat-land, you’ll have to tell us about it.

You still do not get that by your ridicules reasoning "-" and "+" are distinct operations only if μ = 0 (the cardinality that is not used as a successor of any cardinality).

You still do not get that the "ridicules reasoning" is still just and entirely yours.

Since this is not the case (μ can be also any cardinal > 0), your example does not hold water.

So you just can’t give the results asked?

You are still using distinct AND non-distinct operations, which is a contradiction.

You are still simply trying to ascribe some ridiculous aspect of your own failed reasoning onto others.

Flat-land is indeed an "interesting" framework, isn't it The Man?

Nope, it is just another invention of your fiat-land.

Since when you are using ∞ as a unique number?

Since when are you just making baseless assumptions? Oh wait, you’ve always done that.

If you mean ∞ + 5, then since ∞ does not have a successor then this expresssion is invalid.

I mean what I wrote and simply adding some underlining does not change the question.


So you just can’t give the results asked?

Also 0 - 5 is an invalid expresssion if 0 is a cardinal.

One expression was ∞- 5 another was 5 - 0 and no one restricted them to being cardinal numbers.

So you just can’t give the results asked?


You do understand that subtraction is not commutative, don’t you?

Since Non-locality is different than Locality, there is no contradiction.

Since exclusion specifically excludes, well, inclusion, there is.

But in your case "+","-" operations (σ-0 is excluded) are distinct AND non-distincet, which is a contradiction.

Nope, you’re the only one trying (and very poorly mind you) to make that “case” just so you can ascribe it to someone else.

Again stop trying to simply ascribe aspects of your own failed reasoning to others.

 

[doronshadmi]

On the contrary, "if (if p then ~p) then ~p)" is always true. That is why it is called a tautology.

But you still have not answered the question - why do you think I said that removing this tautology would wipe out 2,300 years of mathematics?

If you don't know, then just say so.

Let us see:

"p implies q" means that if p is true, then q must also be true.

in your case q=~p.

So (if p is true, then ~p must also be true) = ~p

So if ~p is true, then ~p must also be true, which is indeed a tautology of identity (A = A).

Am i right?

 

[doronshadmi]

So you just can’t give the results asked?

Your question is irrelevant because we are talking on the following case:

Let us do it without the claim about contradiction.


σ is an infinite cardinal.

μ is a cardinal.

σ > μ

In the case of μ=0: κ=σ, σ – 0 = σ + 0 = σ, which is trivial, because 0 is not a successor of any cardinality.

But we are talking about the case where μ > 0.

In that case κ=σ, σ – 0 = σ + 0 = σ, but then "-","+" operations are non-distinct, because we get the same result even if σ > μ AND μ > 0.

You do understand that subtraction is not commutative, don’t you?

You do understand that it is irrelevant if we deal with cardinality (only absolute values) ?

Since exclusion specifically excludes, well, inclusion , ...

Only in the case of Locality.

 

[Robin]

Let us see:

"p implies q" means that if p is true, then q must also be true.

in your case q=~p.

So (if p is true, then ~p must also be true) = ~p

So if ~p is true, then ~p must also be true, which is indeed a tautology of identity (A = A).

Am i right?

The fact that it is tautology is a well established and rather basic fact about mathematics.

The question I asked was : "why do you think I said that removing this tautology would wipe out 2,300 years of mathematics?"

If you don't know, then simply say so. If you do know, tell me.

Is there any reason that you have to be this evasive?

 

[doronshadmi]

The fact that it is tautology is a well established and rather basic fact about mathematics.

The question I asked was : "why do you think I said that removing this tautology would wipe out 2,300 years of mathematics?"

If you don't know, then simply say so. If you do know, tell me.

Is there any reason that you have to be this evasive?

I'll ask again: Is the considered tautology is about self identity?

If I am not in the right direction, then please explain your disagreement with me.

 

[Robin]

I'll ask again: Is the considered tautology is about self identity?

Which I will take as meaning that you don't know what I meant when I said that.

If I am not in the right direction, then please explain your disagreement with me.

The point is this. You dismissed my objection rather casually and confidently.

But it transpires you did not even understand the objection.

What does that tell me about your approach to mathematics?

 

[doronshadmi]

What does that tell me about your approach to mathematics?

First you have to show that you understand 0 < x < ∞, which is my approach to mathematics.

So please show that you understand it.

What is 0 < x < ∞?

Also your reply was to this post ( http://www.internationalskeptics.com/forums/showpost.php?p=6355413&postcount=11638 ), which deals with superposition of ids, or more generally, about Distinction.

This time please clearly explain to what part of http://www.internationalskeptics.com/forums/showpost.php?p=6355413&postcount=11638 your objection is related, and why you disagree with this part?

I'll be glad to learn from you.

 

[Robin]

First you have to show that you understand 0 < x < ∞, which is my approach to mathematics.

That is a concept within your mathematics. It is not your approach to mathematics. That is different.

When faced with an objection, you did not take the time to understand it. You simply dismissed it and tried to fob me off with some wibble.

So please show that you understand it.

Symbols - by themselves - are meaningless. What - for example, doe the underlined infinity sign stand for?

If this is some concept of your own then show me your definitions, theorems, proofs etc and I will see what I can make of them. But let's get the basic stuff out of the way first.

This time please clearly explain to what part of http://www.internationalskeptics.com/forums/showpost.php...ostcount=11638 your objection is related, and why you disagree with this part?

I would have done so in the first place had you simply asked this.

First of all - QM? What does that have to do with the case? This is mathematics.

Be that as it may. You said that the Russell Paradox was not a paradox if:

"The barber shaves AND does not shave himself"​

So, in other words it is not a paradox if "not Sxx and Sxx" is not a contradiction.

But if that is not a contradiction then "( x implies not x) implies not x" is not a tautology.

And if RAA is not a tautology then clearly indirect proof is not an inference method.

Do I really have to explain the implication of that?

I don't need to tell you that proofs are fundamental to mathematics - coming well before such niceties as you are proposing.

No proofs, no mathematics.

 

[epix]

Let us see:

"p implies q" means that if p is true, then q must also be true.

It doesn't go like that, coz 'p' and 'q' are usually reserved for premises. That syntax makes the implication a logical connective, and it's the truth table that decides what is True or what is False.

 

[Little 10 Toes]

Good luck on getting solid definitions there Robin. It's taken a while just for me to get a definition for local/non-local, words typically not associated with math, let alone domain, which doronshadmi can't really define.

Let me show you:

Please define your usage of the word domain.

The researched.

The researched what?

Domain is "that is researched".

What is researched?
Define researched.

A measurable realm.

What is "a measurable realm"?

A realm where the measured and the measurer are interacted.

So after several times of you having to clarify what your previous answer is, we're at the point where your definition of a domain is "A realm where the measured and the measurer are interacted". Clear as mud.

Define "interacted".

There were more silly messages of doron's but he still hasn't defined "interacted". BTW: any tool that is used (like a weight scale) is an agent of the measurer.

 

[Robin]

It doesn't go like that, coz 'p' and 'q' are usually reserved for premises. That syntax makes the implication a logical connective, and it's the truth table that decides what is True or what is False.

[qimg]http://www.abstractmath.org/MM/MMConditional_files/image001.gif[/qimg]

Yes. So the contradiction p and not p will always be false in the truth table and the tautology "(not p implies p) implies p" will always have true in the truth table.

If he is setting up a mathematics where p and not p is always or sometimes true then he obviously has to reinvent it from scratch.