Deeper than primes - Continuation

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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.
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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.
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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.
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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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