Deeper than primes - Continuation

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doronshadmi said:
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This is nothing but your philosophical view, which does not agree with, for example, Poincaré's philosophical view (as appears at the end of http://en.wikipedia.org/wiki/Set-theoretic_definition_of_natural_numbers#Problem):
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This made me laugh out loud; it demonstrates exactly what is wrong with Doron's grasp of mathematics.

Doron, mathematics is not a 'mix and match' game; Poincaré's view is not compatible with the Peano axioms which *you* need for *your* story.

So either you take the Poincaré route and see where you get, or you go the number route and see where you get.

It is not Lego, you know...
 
realpaladin said:
This made me laugh out loud; it demonstrates exactly what is wrong with Doron's grasp of mathematics.

Doron, mathematics is not a 'mix and match' game; Poincaré's view is not compatible with the Peano axioms which *you* need for *your* story.

So either you take the Poincaré route and see where you get, or you go the number route and see where you get.

It is not Lego, you know...
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I'm sure you realize that Doron dredged up a 4-month old post of mine to embark on this latest aside. Looks like his continued Google trek to find things he can misinterpret in support of doronetics led him to the Poincaré view of numbers as fundamental concepts.

Misinterpret he does, too. Even with numbers taken as fundamental (per Poincaré), Doron would still need to connect them to set theory. The route is the same (via the induction set), and cardinality still begins as a relative measure.
 
jsfisher said:
I'm sure you realize that Doron dredged up a 4-month old post of mine to embark on this latest aside. Looks like his continued Google trek to find things he can misinterpret in support of doronetics led him to the Poincaré view of numbers as fundamental concepts.

Misinterpret he does, too. Even with numbers taken as fundamental (per Poincaré), Doron would still need to connect them to set theory. The route is the same (via the induction set), and cardinality still begins as a relative measure.
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Ah, but at the moment we are in the realm of philosophy, or so our travel guide tells us.

And we all know philosophy knows no bounds, or rules, right? Right? Errr....
 
EDIT:

jsfisher said:
... and cardinality still begins as a relative measure.
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Where this relative measure is understood in terms of numbers by Poincaré's philosophical view, so?

As clearly seen in http://www.internationalskeptics.com/forums/showpost.php?p=10033406&postcount=3837, you simply unaware about the impact of your philosophical view on your mathematical understanding.

Moreover ( http://en.wikipedia.org/wiki/Cardinality ):
There are two approaches to cardinality – one which compares sets directly using bijections and injections, and another which uses cardinal numbers.
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In other words, what depends on what is a philosophical point of view of cardinality.

Because of your blindness to your philosophical point of view your one level reasoning (which is used as your philosophical point of view of sets (but you unaware of it)) is not sufficient enough in order deal in details with http://www.internationalskeptics.com/forums/showpost.php?p=10033329&postcount=3833.

By explaining Cantor's theorem with examples without loss of generality, set {} exists even if according to its definition (as used by Cantor's theorem) any attempt to define some A member as its member, is involved with contradiction (at the level of members of that set).

Actually, Cantor's theorem holds (there is a set, which is a member of P(A), that is not paired with any set that is a member of A (which enables to conclude that there is no bijection)) exactly because the level of being a set holds even if the level of being its member is involved with contradiction.

In other words, the existence of set's level is platonic, where the existence member's level is non-platonic.
 
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doronshadmi said:
Where this relative measure is understood in terms of numbers by Poincaré's philosophical view, so?
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And which was, of course, one of the main critiques on Poincaré's view; you need numbers first, or else you can not measure 'how relative' (my mangling of otherwise lengthy discourse) the cardinality is.

Doron, do you realize that this view holds little value in the world of mathematics and that this has been so from before you were born?
 
doronshadmi said:
In other words, the existence of set's level is platonic, where the existence member's level is non-platonic.
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Doron, you *do* realize that there is no such thing as something being 'platonic', right?

Either you hold the view of Mathematical Platonism, which is orthogonally complete or you don't (a view which can be orthogonally complete as well).

But what you are doing here is playing Lego with anything that comes before you and if it doesn't fit, you simply break it, ignore it or glue it on.

That does not make for a complete, rigorous or consistent theory or philosophy...
 
doronshadmi said:
Where this relative measure is understood in terms of numbers by Poincaré's philosophical view, so?
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That would be incorrect on two counts. First, relative measure in this context refers to the comparison of one set to another. So, just based on the meaning of words, you are wrong.

Second, set theory (let's assume ZFC so we maintain a common basis) has no ability to count members. So, just based on the axioms of ZFC, you are wrong.

(There's a third count that arises from infinite sets, but I'll just let that one sit.)
 
doronshadmi said:
Moreover ( http://en.wikipedia.org/wiki/Cardinality ):
There are two approaches to cardinality – one which compares sets directly using bijections and injections, and another which uses cardinal numbers.
Click to expand...

In other words, what depends on what is a philosophical point of view of cardinality.
Click to expand...


When you attempt to use an article as a reference to support your baseless assertion, it would probably be best if you actually read and then understood the article. Cherry-picking a sentence that you think sounds right may not be.

Had you bothered to read (and comprehend) the whole article, you would have read the section under the Cardinal Numbers heading to find how cardinality and numbers can be associated, namely equivalence relations. In other words, it starts with a relative measure.
 
EDIT:

jsfisher, relative measure is based on the notion of being paired (or not), and it can't be done unless number 2 or number 1 are used, even if they are not explicitly defined.

So the notion of numbers is used as an hidden assumption of any relations, including equivalence relations.

Philosophy exposes such hidden assumptions, exactly because it has meta view of (in this case) Mathematics.

Actually the notion of meta view is the ability to be aware of something by using at least 2 view points, where one is the meta view and the other is the view.

By using Philosophy, I show that the outer "{" and "}" is the platonic meta view of set, where what is between the outer "{" and "}" is the non-platonic view of set.
 
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doronshadmi said:
jsfisher, relative measure is based on the notion of being paired (or not), and it can't be done unless number 2 or number 1 are used, even if they are not explicitly defined.

So numbers are hidden assumptions of any relations, including equivalence relations.
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Even if this were meaningfully true, how does any of this impact the misrepresentation of Cantor's Theorem you have been butchering?
 
jsfisher said:
Even if this were meaningfully true, how does any of this impact the misrepresentation of Cantor's Theorem you have been butchering?
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In order to deal with this question, you have to deal in details with all of is written in http://www.internationalskeptics.com/forums/showpost.php?p=10034238&postcount=3847, such that the meta view of philosophy is not ignored.

By using Philosophy (as done, for example, in http://www.internationalskeptics.com/forums/showpost.php?p=10034238&postcount=3847) I show that the outer "{" and "}" is the platonic meta view of set, where what is between the outer "{" and "}" is the non-platonic view of set.

By not using Philosophy you easily misrepresent my posts.

In other words, it is about time that you actually express things in terms of this forum, which is "Religion and Philosophy" forum.

As long as you are not doing that, there is no communication between us.
 
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doronshadmi said:
In order to deal with this question, you have to deal in details with all of is written in http://www.internationalskeptics.com/forums/showpost.php?p=10034238&postcount=3847, such that the meta view of philosophy is not ignored.
Click to expand...

In "details" for a "meta" view... and the meta view of philosophy nonetheless...

doronshadmi said:
By using Philosophy (as done, for example, in http://www.internationalskeptics.com/forums/showpost.php?p=10034238&postcount=3847) I show that the outer "{" and "}" is the platonic meta view of set, where what is between the outer "{" and "}" is the non-platonic view of set.
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"Using philosophy"... I never knew that it was an exact science with algorithms one could apply to issues...

As far as I knew before I met master philosopher Doron Shadmi, a 'philosophy' starts at an atomic level (i.e. well defined building blocks) and goes from there. Too bad Doron always jumps into his philosophy somewhere in the middle...

And "platonic meta view", well since Doron, in *none* of his posts explains what 'platonic' exactly is (hint: it is a made up term by Doron), I can only guess he uses Plato to lend some credibility to his hotch-potch because he should rather call it 'Doronic meta view'...

doronshadmi said:
By not using Philosophy you easily misrepresent my posts.

In other words, it is about time that you actually express things in terms of this forum, which is "Religion and Philosophy" forum.

As long as you are not doing that, there is no communication between us.
Click to expand...

Yes, JSFisher, *use* Philosophy (with a capital P)!

Come on Doron, if you can't see that just saying 'use Philosophy' completely disqualifies any of your theories from being anywhere near scientific, all hope is lost.
 
Let's explain in more detailed way the following quote:

doronshadmi said:
As long as one does not understand that platonic existence is a discovery that does no need any meaning in order to exist (it is a tautology of existence that does not need any further interpretation or meaning), one wrongly gets this discovery only in terms of subjective invented multiple interpretations and meanings that are not the discovered tautology of existence.
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"Tautology of existence" means that existence is logically always true, whether it is discovered or not. This kind of existence is known as platonic.

This notion is notated in my posts by the outer "{" and "}".

What is between the outer "{" and "}" is not "Tautology of existence" (it is non-platonic), because one of the options is {} (there is nothing between the outer "{" and "}").

"Tautology of existence" holds whether there is nothing or there is something between the outer "{" and "}", or in other words, what is between the outer "{" and "}" is logically not a "Tautology of existence" (it is non-platonic) and therefore it is logically inaccessible to the platonic.

By understanding the logical difference between platonic and non-platonic levels of existence, one easily understands that actual infinity is at the platonic level (notated by the outer "{" and "}"), which is logically inaccessible by any amount of members exactly because their existence is logically restricted only to the non-platonic level (members may exist, or not).

If one understand this post, he\she can easily understand http://www.internationalskeptics.com/forums/showpost.php?p=10034959&postcount=3854.
 
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doronshadmi said:
Let's explain in more detailed way the following quote:




"Tautology of existence" means that existence is logically always true, whether it is discovered or not. This kind of existence is known as platonic.

This notion is notated in my posts by the outer "{" and "}".

What is between the outer "{" and "}" is not "Tautology of existence" (it is non-platonic), because one of the options is {} (there is nothing between the outer "{" and "}").

"Tautology of existence" holds whether there is nothing or there is something between the outer "{" and "}", or in other words, what is between the outer "{" and "}" is logically not a "Tautology of existence" (it is non-platonic) and therefore it is logically inaccessible to the platonic.

By understanding the logical difference between platonic and non-platonic levels of existence, one easily understands that actual infinity is at the platonic level (notated by the outer "{" and "}"), which is logically inaccessible by any amount of members exactly because their existence is logically restricted only to the non-platonic level (members may exist, or not).

If one understand this post, he\she can easily understand http://www.internationalskeptics.com/forums/showpost.php?p=10034959&postcount=3854.
Click to expand...

Besides the fact that when brackets are *always* necessary, they are never necessary (i.e. it is common practice to just leave them out), none of this word-salad defines anything atomically and rigorously.

Also, it is presented as assertions, not rules/clauses built upon axioms.

I stand with the Doron Shadmi's errors in my signature that he first needs to give a list of axioms in his philosophy, then the clauses and then, and only then, can he build upon it.

As it stands it is of less worth than a 12-year old's essay on 'What I did this summer' (i.e. 'And then... and then... and then... ').
 
There are persons that are unable to understand that Philosophy can be used in order to understand better the axiomatic method.

http://www.internationalskeptics.com/forums/showpost.php?p=10032027&postcount=3819,

http://www.internationalskeptics.com/forums/showpost.php?p=10034959&postcount=3854

or

http://www.internationalskeptics.com/forums/showpost.php?p=10035060&postcount=3856

are simply beyond their scope, exactly because they have no ability to use notations in order to express philosophical notions like platonic or non-platonic existence (and how these philosophical notions are used by mathematical axioms).

Moreover, if some stuff is given to them they will not check it by themselves, instead they will look for other persons and pick only the arguments that fits to their fixed view about the stuff (and it is a fixed view exactly because they do not bother to do the following: To check the stuff by themselves, and only then to express their detailed arguments about the given stuff).

<SNIP>
Edited by LashL: 
Edited for civility.
 
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doronshadmi said:
There are persons that are unable to understand that Philosophy can be used in order to understand better the axiomatic method.
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I previously remarked about a tendency to get things ass-backwards. Prophecy fulfilled.
 
jsfisher said:
I previously remarked about a tendency to get things ass-backwards. Prophecy fulfilled.
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1. Generally, "reverse engineering" can be useful, so getting things backwards can be a good idea, I suggest you to try it from time to time in order to develop your mind to get things form different directions.

2. Your "ass-backwards" argument is simply your way to avoid http://www.internationalskeptics.com/forums/showpost.php?p=10034959&postcount=3854.

3. Why am I not surprised?
 
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doronshadmi said:
In order to deal with this question, you have to deal in details with all of is written in http://www.internationalskeptics.com/forums/showpost.php?p=10034238&postcount=3847, such that the meta view of philosophy is not ignored.

By using Philosophy (as done, for example, in http://www.internationalskeptics.com/forums/showpost.php?p=10034238&postcount=3847) I show that the outer "{" and "}" is the platonic meta view of set, where what is between the outer "{" and "}" is the non-platonic view of set.

By not using Philosophy you easily misrepresent my posts.

In other words, it is about time that you actually express things in terms of this forum, which is "Religion and Philosophy" forum.

As long as you are not doing that, there is no communication between us.
Click to expand...


Funny that you mention the location of this topic. Wasn't it moved from the math and science area when you weren't able to "express things in the terms of [that] forum"?
 
doronshadmi said:
1. Generally, "reverse engineering" can be useful, so getting things backwards can be a good idea, I suggest you to try it from time to time in order to develop your mind to get things form different directions.
Click to expand...

If you equate an ass-backwards approach to reverse engineering (with or without scary quotes), then you are confessing to yet another conceptual crevasse.

2. Your "ass-backwards" argument is simply your way to avoid http://www.internationalskeptics.com/forums/showpost.php?p=10034959&postcount=3854.
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You posts get discounted, not avoided.


Be all this as it may, though, what does this have to do with your misconstrued ideas about Cantor's Theorem?
 
Little 10 Toes said:
Funny that you mention the location of this topic. Wasn't it moved from the math and science area when you weren't able to "express things in the terms of [that] forum"?
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After some mathematical revolutions like non-Euclidean Geometry and specially after what happened to Hibert's program because of Godel's incompleteness theorems, the majority of mathematicians tried to separate Philosophy from Mathematical development.

I disagree with this attitude, exactly because the usefulness of mata-view during mathematical work (as shown, for example, in Godel's incompleteness theorems) is actually derived from the linkage between Philosophy and Mathematics.
 
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doronshadmi said:
I disagree with this attitude, exactly because the usefulness of mata-view during mathematical work (as shown, for example, in Godel's incompleteness theorems) is actually derived from the linkage between Philosophy and Mathematics.
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That's a Munchhausen if I ever saw one; the usefulness of meta-view is derived from the linkage.

How about; the meta-view is not very useful, and if it is, then where is the proof, and therefore nobody cares about the linkage?
 
The beauty of the linkage between Philosophy and Mathematics is shown by the second incompleteness theorem of Godel, as follows:

Given mathematical formalism, it can't be consistent (avoid contradictions at its foundations) AND complete (enables to prove its all true expressions within its own framework (within formalism)) or in other words, Formalism can't prove its own consistency, where such beautiful result defiantly involves Philosophy AND Mathematics, where an expression like "Philosophy AND Mathematics" is true only if no one of the considered frameworks (Philosophy OR Mathematics) is omitted.
 
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doronshadmi said:
The beauty of the linkage between Philosophy and Mathematics is shown by the second incompleteness theorem of Godel, as follows:

Given mathematical formalism, it can't be consistent (avoid contradictions at its foundations) AND complete (enables to prove its all true expressions within its own framework (within formalism)) or in other words, Formalism can't prove its own consistency, where such beautiful result defiantly involves Philosophy AND Mathematics, where an expression like "Philosophy AND Mathematics" is true only if no one of the considered frameworks (Philosophy OR Mathematics) is omitted.
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This is just a logic quote. Care to define *where* the philosophy part is and *where* the mathematics part.

And again, nothing is *shown*, it is asserted. Show me why it can't be consistent AND complete.
You can't, because Godel couldn't in the end.

I read 'Godel, Escher, Bach' over 20 years ago when I was studying at the faculty of Mathematics and Computer Sciences.

Personally, I always thought Godel to be both overrated and useless.
 
doronshadmi said:
I find http://dspace.lu.lv/dspace/bitstream/handle/7/1405/Podnieks_Neglected_Formalism.pdf?sequence=1 interesting.
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I don't. I'd rather make my own mind up and demonstrate my abilities than strut like a peacock with other people's work.

So Doron, I think you simply are unable to demonstrate anything and have now resorted to strawmanning us with other people's works?

At best you demonstrate that none of what you dish up here is original and that all of it is simply derivative work; old-hat.

How about Organic Mathematics? How about that roadmap to unity? How about the two islands?

Do you want me to declare it all 'failed effort'?
 
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To those who do not distinguish between the philosophical meta-framework and the mathematical framework as used by Godel's Second Incompleteness Theorem, here they are:

Here is the (non-technical) mathematical part ( http://en.wikipedia.org/wiki/Gödel's_incompleteness_theorems#Second_incompleteness_theorem ):
For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, if T includes a statement of its own consistency then T is inconsistent.
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EDIT:

Here is the philosophical part:

By using the mathematical results, it is generally concluded that mathematical formalism (Formalist approach of Mathematics) can't prove its own consistency without exception, and therefore it is an incomplete framework.

Actually Godel (he was a Platonist) wished to prove that Formalism can't fully capture the objectivity of the platonic level of existence.
 
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doronshadmi said:
To those who do not distinguish between the philosophical meta-framework and the mathematical framework as used by Godel's Second Incompleteness Theorem, here they are:

Here is the (non-theatrical) mathematical part ( http://en.wikipedia.org/wiki/Gödel's_incompleteness_theorems#Second_incompleteness_theorem ):



Here is the philosophical part:

By using the mathematical results, it is generally concluded that mathematical formalism can't prove its own consistency, and therefore it is an incomplete framework.
Click to expand...

Besides being derivative, old-hat and generally *wrong*, the question arises, by whom?
 
jsfisher said:
... would now embrace formalism.
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Wrong, I embrace Philosophy AND Mathematics, by using the linkage between platonic and non-platonic levels of existence, as the foundation of Mathematics.
 
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doronshadmi said:
Wrong, I embrace Philosophy AND Mathematics, by using the linkage between platonic and non-platonic levels of existence, as the foundation of formalism.
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No you don't. You claim that you are, but fail to back it up.

All we get is derivative work from a snippet-service that anyone can use.
 
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