A=A

Discussion of the nature of Ultimate Reality and the path to Enlightenment.
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N0X23
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A=A

Post by N0X23 »

Would any one know the Mathematical term for A=A?

jimhaz
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Re: A=A

Post by jimhaz »

(infinity/1)=(infinity/1/1)
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DHodges
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Re: A=A

Post by DHodges »

Quote:Quote:<hr>Would any one know the Mathematical term for A=A?<hr>
It's known as the <a href="http://www.geniebusters.org/915/04e_ex01C.html" target="top">Law of Identity</a>
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Diebert van Rhijn
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Re: A=A

Post by Diebert van Rhijn »

Although origins of this 'law' are murky looking at DHodge's link, I think the so-called "Aristotle's Law of Identity" is a logical and also metaphysical construct that demonstrates a fundamental principle, like an axiom, where reasoning as a whole appears to be based on.

Aristotle said it thus, in his Metaphysics: "It is impossible for the same thing to belong and not belong simultaneously to the same thing in the same respect" This would be the most secure of all principles because "it is impossible to be in error about it".

This then at some points reflects in mathematics. A real mathematical equivalence of this law would be pointless since mathematics as a whole is derived from the application of logic. Mathematics cannot be used to describe the law in a some mathematical form, it would only expand on it, not really equal it.

But the closest thing in modern mathematics would be the description of the equivalence relation. See also: <a href="http://www.absoluteastronomy.com/encycl ... quivalence relation defined</a> or in general perhaps the <a href="http://www.absoluteastronomy.com/encycl ... definition of mathematical equality</a>.

Something else that popped up when going through some writings from Aristotle that might be related to 'grasping' A=A. What is your opinion about:Quote:Quote:<hr>
Thus it is clear that we must get to know the primary premisses by induction; for the method by which even sense-perception implants the universal is inductive. Now of the thinking states by which we grasp truth, some are unfailingly true, others admit of error-opinion, for instance, and calculation, whereas scientific knowing and intuition are always true: further, no other kind of thought except intuition is more accurate than scientific knowledge, whereas primary premisses are more knowable than demonstrations, and all scientific knowledge is discursive. From these considerations it follows that there will be no scientific knowledge of the primary premisses, and since except intuition nothing can be truer than scientific knowledge, it will be intuition that apprehends the primary premisses-a result which also follows from the fact that demonstration cannot be the originative source of demonstration, nor, consequently, scientific knowledge of scientific knowledge.If, therefore, it is the only other kind of true thinking except scientific knowing, intuition will be the originative source of scientific knowledge. And the originative source of science grasps the original basic premiss, while science as a whole is similarly related as originative source to the whole body of fact.

From the end of <a href="http://classics.mit.edu/Aristotle/poste ... >Posterior A</a><hr>
N0X23
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Re: A=A

Post by N0X23 »

I found that the equation A=A is called a Reflexive Property of Equality, or a Reflexive Identity.

It’s simply a proof, a demonstration of a truth, a foundation that can be used to be built upon.

I think that Quinn uses that equation as an effective rebut against todays popular postmodernist declaration, that the Truth can not be known, nor does truth ultimately exist.

Also I think it pertains to Consciousness and Reality. Reality or Truth, is Consciousness interacting with itself.

Jimhaz: Infinity is an incriminate of time, which Consciousness is beyond.

I do not understand your explanation.



Thank you for all the input.
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David Quinn
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Re: A=A

Post by David Quinn »

I'd be wary of trying to slot a profound principle like A=A into an academic or mathematic category. Even though there is some overlap between the way Aristotle and I use A=A, I tend to use much more deeply. For me, A=A goes to the root of all logic, perception, and existence. It's not just an arid axiom that is only applicable within the realm of formal academic logic.
Sapius
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Re: A=A

Post by Sapius »

I don't find 'A=A' more profound than having breakfast. Considering it "profound" is a personal thing, which I'm not against. Basically I find it to be the simple basis of conscious thinking since one cannot even begin to reason if he does not have the ability to recognize and differentiate between the "I" and the not "I's" and name them, which comes naturally at this stage of evolution, no big deal.
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Dan Rowden
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Re: A=A

Post by Dan Rowden »

Ok, so comprehending the basis of consciousness isn't a big deal. So, what would constitute a profound insight for you, Sapius?


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Sapius
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Re: A=A

Post by Sapius »

Dan, please note that I speak to you here knowing fairly well your level of understanding, which is different, but not necessarily "higher".

Should there be some-one-thing more "profound" then another once you recognize the Reality of Existence, Totality!? Show me one "thing" that could exist on its own to claim a "higher" status than another. If claims of 'profound insight' need legs of a conscious mind to stand upon, I'm sure you know that consciousness is no more permanent than a soap bubble.

It's all well and fine when one talks about such comparisons when trying to guide others to something one thinks is good for them too, but it is because that person actually finds satisfaction in wanting others to experience what he thinks is an ultimate experience. And THAT satisfaction IS mental happiness, which David denies simply because it consists the word 'happy'.

I'm sure you are aware that most of my comments are directed towards David to help him iron out any creases in his understanding. Personally, if somebody recognizes the Truth about existence, it makes me unimaginably Happy, and at the same time, if one doesn't, it Really does not matter. With David, it is not the same, he does get annoyed at ignorance, which shouldn't be the case if he actually has come to realize the Truth about Totality and Existence, and the equal importance of All That There Is, since no one thing could exist without another. Recognizing this eliminates all frustrations of everything that one thinks should not exist and keeps fighting against it.

One cannot realize the Truth about ignorance if it were not there in the first place, so, personally, I have nothing against ignorance either, nor do I have any intense love for Truths that set you free, for neither could survive or have any meaning without another.

Now, a straight answer to your question would be; In my personal opinion, if there is any thing that could be considered "profound", then it could surely be nothing more than just the pure Experience of existence, no matter what that is, for nothing could exist without that "I". Recognizing that this "I" does not inherently exist, is also a logical conclusion by the very same "I". In other words, "I" exists, therefore everything IS, but at the core of it, this too is just another simple logical conclusion, nothing more.




Naturyl
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Re: A=A

Post by Naturyl »

Here are some thoughts I offered on another forum:

For me, one helpful interpretation is "Awareness = Awareness," consistent with the implications of monism, as discussed here:

<a href="http://factbased.proboards37.com/index. ... 3568559</a>

For me, this is only one of several useful and interesting ways of looking at the equation.

A=A is a favorite of QRS advocates. Although I disagree with them in some ways, I think that they are onto something with the so-called "Law of Identity." Although it is easily dismissed as a pseudo-profound tautology, I think that we would be hasty to agree with such dismissals without understanding what is really being said in A=A. IMO, there is a lot more to this deceptively simple equation than meets the eye.
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