The Axiom Of Identity *Challenged*

What is the basis for reason? And mathematics?

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Hobbes' Choice
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Re: The Axiom Of Identity *Challenged*

Post by Hobbes' Choice »

Moyo wrote:Why not build the whole system of relations on the same basis that this "=" is. It seems that if we can do this we avoid arbitrariness and acheive consistency.
The whole system of cartesian products and orderd pairs are an unnecesary frameworkthen and we can build mathematics without the suspect (because it doesnt involve computation) theory of sets.

It seems though that when you say a thing is itself you use two refferes 1. thing and 2. itself and are implicitly implying a colloqial version of (a,a).

This may be a limitation inherent to consciousness such as the failure to define "objective reality", and just as we may never have a definition for objective reality we may never be able to define equality.
There is no problem with equality, as long as you keep it where it belongs; conceptual. 1=1 is a statement of perfection, needing no other reference. The trouble starts when you want to apply this analytic truth to the world of experience, in which there is no ambiguous example of 1=1.
So whatever crazy conclusion you think you might have reached about the existence of "GOD" (whatever that is), we all know that god only exists as a concept in your own mind, and not the world of experience.
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Moyo
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Re: The Axiom Of Identity *Challenged*

Post by Moyo »

Hobbes' Choice wrote:
Moyo wrote:Why not build the whole system of relations on the same basis that this "=" is. It seems that if we can do this we avoid arbitrariness and acheive consistency.
The whole system of cartesian products and orderd pairs are an unnecesary frameworkthen and we can build mathematics without the suspect (because it doesnt involve computation) theory of sets.

It seems though that when you say a thing is itself you use two refferes 1. thing and 2. itself and are implicitly implying a colloqial version of (a,a).

This may be a limitation inherent to consciousness such as the failure to define "objective reality", and just as we may never have a definition for objective reality we may never be able to define equality.
There is no problem with equality, as long as you keep it where it belongs; conceptual. 1=1 is a statement of perfection, needing no other reference. The trouble starts when you want to apply this analytic truth to the world of experience, in which there is no ambiguous example of 1=1.
So whatever crazy conclusion you think you might have reached about the existence of "GOD" (whatever that is), we all know that god only exists as a concept in your own mind, and not the world of experience.
In order for statements to exist , they must have parts....enter the infinite regress.
Wyman
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Re: The Axiom Of Identity *Challenged*

Post by Wyman »

Moyo wrote:
Wyman wrote:The answer is that symbols cannot be referred to within a system as symbols, but only as elements of the formal system. Thus, saying that "(a,a) means that the first 'a' is before the second 'a' " is a meta-statement, outside the system.
You do realise that your point is really just a point on how we choose to represent mathematical statements? If the Greeks we still around (they used simple "English" to write down mathematical statements) , then they would have represented (a,a) as "the first "a" is before the second "a""
Which is because formal languages and their interpretations were not understood until the twentieth century thanks to Hilbert, Tarski, Godell and others who built upon, e.g. Bolyai and Lobachevsky's 'discovery' of non-Euclidean geometry.

You are confusing mathematical statements with meta-mathematical statements, just like the Greeks. You are arguing against adopting the identity axiom; but you are acting as if your objections are based upon considerations within the formal system.

To be fair, you need to weigh the system (by 'system' I mean number theory based on the axioms of logic and set theory) with the axiom and then without the axiom. I think you will see that your objections are heavily outweighed by the alternative - i.e. you can't do mathematics without it.
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Moyo
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Re: The Axiom Of Identity *Challenged*

Post by Moyo »

Wyman wrote:
Moyo wrote:
Wyman wrote:The answer is that symbols cannot be referred to within a system as symbols, but only as elements of the formal system. Thus, saying that "(a,a) means that the first 'a' is before the second 'a' " is a meta-statement, outside the system.
You do realise that your point is really just a point on how we choose to represent mathematical statements? If the Greeks we still around (they used simple "English" to write down mathematical statements) , then they would have represented (a,a) as "the first "a" is before the second "a""
Which is because formal languages and their interpretations were not understood until the twentieth century thanks to Hilbert, Tarski, Godell and others who built upon, e.g. Bolyai and Lobachevsky's 'discovery' of non-Euclidean geometry.

You are confusing mathematical statements with meta-mathematical statements, just like the Greeks. You are arguing against adopting the identity axiom; but you are acting as if your objections are based upon considerations within the formal system.

To be fair, you need to weigh the system (by 'system' I mean number theory based on the axioms of logic and set theory) with the axiom and then without the axiom. I think you will see that your objections are heavily outweighed by the alternative - i.e. you can't do mathematics without it.
If formal statements have parts then they are susceptible to the infinite regress...if they do not have parts then they are devoid of information.
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Moyo
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Re: The Axiom Of Identity *Challenged*

Post by Moyo »

THERE WERE OTHER PERMUTATIONS THAT HAD you LOOKING MORE INTELLIGENT
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Arising_uk
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Re: The Axiom Of Identity *Challenged*

Post by Arising_uk »

Still waiting to hear how all this is an ontological argument for a 'God'?
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Moyo
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Re: The Axiom Of Identity *Challenged*

Post by Moyo »

Existence is a miracle.
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Re: The Axiom Of Identity *Challenged*

Post by Moyo »

The only permutation where you win is when you find a suitable identity element (axiom).
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Hobbes' Choice
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Re: The Axiom Of Identity *Challenged*

Post by Hobbes' Choice »

Moyo wrote:
Hobbes' Choice wrote:
Moyo wrote:Why not build the whole system of relations on the same basis that this "=" is. It seems that if we can do this we avoid arbitrariness and acheive consistency.
The whole system of cartesian products and orderd pairs are an unnecesary frameworkthen and we can build mathematics without the suspect (because it doesnt involve computation) theory of sets.

It seems though that when you say a thing is itself you use two refferes 1. thing and 2. itself and are implicitly implying a colloqial version of (a,a).

This may be a limitation inherent to consciousness such as the failure to define "objective reality", and just as we may never have a definition for objective reality we may never be able to define equality.
There is no problem with equality, as long as you keep it where it belongs; conceptual. 1=1 is a statement of perfection, needing no other reference. The trouble starts when you want to apply this analytic truth to the world of experience, in which there is no ambiguous example of 1=1.
So whatever crazy conclusion you think you might have reached about the existence of "GOD" (whatever that is), we all know that god only exists as a concept in your own mind, and not the world of experience.
In order for statements to exist , they must have parts....enter the infinite regress.
You are talking bollocks!
Statement!
Green rocking horse shit smells better than hens teeth.
Therefore rocking horse shit and hen's teeth exist.
QED you are a moron.
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Arising_uk
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Re: The Axiom Of Identity *Challenged*

Post by Arising_uk »

Moyo wrote:Existence is a miracle.
Which one?

Why should miracles necessarily have agency?

Sorry to be slow but how does this relate to your issue with the set equality/identity relation?
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Moyo
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Re: The Axiom Of Identity *Challenged*

Post by Moyo »

Hobbes' Choice wrote:
You are talking bollocks!
Statement!
Green rocking horse shit smells better than hens teeth.
Therefore rocking horse shit and hen's teeth exist.
QED you are a moron.
The existance \of a statement does not imply its truthfulness.
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Moyo
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Re: The Axiom Of Identity *Challenged*

Post by Moyo »

Arising_uk wrote:
Moyo wrote:Existence is a miracle.
Which one?

Why should miracles necessarily have agency?

Sorry to be slow but how does this relate to your issue with the set equality/identity relation?
Because everything is a concept
Scott Mayers
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Re: The Axiom Of Identity *Challenged*

Post by Scott Mayers »

Moyo wrote:YOUR minds ARE SIMPLE, YOU JUST DONT GET IT. IS THIS THE BEST you CAN DO silence?

THIS IS A PROOF THAT THERE IS A GOD

I'd like to see someone take me on and win....pathetic you all are...
Personally, I missed this in June when I was preoccupied at some point. However, now that I see this, I do not see how this relates to "GOD" unless you simply define this as some entity of causation. Also, even your logic on this may miss something about the origins of interpreting reality. See Models vs Reality (particular post I am discussing a related concern)

That is, you might believe that your idea of "GOD" encompasses the idea of a first cause, but actually even if you were correct, your 'first cause' is what would have to encompass "GOD" only. But whatever such a first possible cause could also encompass many different ideas with exception even to any "GOD" as it is unnecessary. Your likely interpretation of "GOD" also incorporates it being an emotional value of "goodness" to which the word "god" was derived. The fact is, in your interpretation even if this entity could be such raises the question of evil. If God (= good) originated all reality, then it too must have created its contradiction of evil existing. I'm guessing that if you think that God did not originate evil that it somehow came from 'elsewhere' to which this brings back the idea of a necessary existence of BOTH good and evil, meaning that at least two things are necessary in such an origin.

See that linked discussion above to which I argue the significance of both a one and a zero (or other related pairs) that are needed to begin any sincere search for truth.

By the way, in extending the interest of the post I link above, '=' is a type of derivative likely as a form of representing two sideways ones ('11') indicating the nature of either equivalence or cancellation, as in a double negation to imply a return to the same meaning.

Assume X. Then -X is the denial and =X returns it to being X in meaning. Thus (X and -X) while contradictory in the same reality become (X OR -X) of one.
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Hobbes' Choice
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Re: The Axiom Of Identity *Challenged*

Post by Hobbes' Choice »

Moyo wrote:
Hobbes' Choice wrote:
You are talking bollocks!
Statement!
Green rocking horse shit smells better than hens teeth.
Therefore rocking horse shit and hen's teeth exist.
QED you are a moron.
The existance \of a statement does not imply its truthfulness.
And that my friend is exactly why you are talking rubbish.
You totally missed the irony.
QED you are definitely a moron, now, even in your own terms. :roll:
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Moyo
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Re: The Axiom Of Identity *Challenged*

Post by Moyo »

Scott Mayers wrote:
Moyo wrote:YOUR minds ARE SIMPLE, YOU JUST DONT GET IT. IS THIS THE BEST you CAN DO silence?

THIS IS A PROOF THAT THERE IS A GOD

I'd like to see someone take me on and win....pathetic you all are...
Personally, I missed this in June when I was preoccupied at some point. However, now that I see this, I do not see how this relates to "GOD" unless you simply define this as some entity of causation. Also, even your logic on this may miss something about the origins of interpreting reality. See Models vs Reality (particular post I am discussing a related concern)

That is, you might believe that your idea of "GOD" encompasses the idea of a first cause, but actually even if you were correct, your 'first cause' is what would have to encompass "GOD" only. But whatever such a first possible cause could also encompass many different ideas with exception even to any "GOD" as it is unnecessary. Your likely interpretation of "GOD" also incorporates it being an emotional value of "goodness" to which the word "god" was derived. The fact is, in your interpretation even if this entity could be such raises the question of evil. If God (= good) originated all reality, then it too must have created its contradiction of evil existing. I'm guessing that if you think that God did not originate evil that it somehow came from 'elsewhere' to which this brings back the idea of a necessary existence of BOTH good and evil, meaning that at least two things are necessary in such an origin.

See that linked discussion above to which I argue the significance of both a one and a zero (or other related pairs) that are needed to begin any sincere search for truth.

By the way, in extending the interest of the post I link above, '=' is a type of derivative likely as a form of representing two sideways ones ('11') indicating the nature of either equivalence or cancellation, as in a double negation to imply a return to the same meaning.

Assume X. Then -X is the denial and =X returns it to being X in meaning. Thus (X and -X) while contradictory in the same reality become (X OR -X) of one.
I said nothing about causes , whether first or not.

My 2 prong attack was this.

The element that gives identity to the elements in the universe is illogical.
In any attempt to express it involves making a concept with parts. Once there are parts ..there results an infinite regress.
ALL concepts have parts. If not they would contain no information.

If you say it is not a concept, How did you conceive of the underlined part if it was what it says it is. Proof reducto absurdum that it cannot be other than a concept.

Attack 2;

Everything is a concept.
If you can tell me one thing that is not a concept i will concede...with one rule only ...you mustnt conceive of it first.

Since the thing that make things in the universe have identity is bust we have to look elsewhere..it has to be a miracle...

since the only things that exist are minds, and our minds of their own can have no identity, we have to look to a miracle , and a miracle is a concept so it has to emanate from a mind.

Scott Mayers You are nothing on me...lol
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