What is the significance of "A=A"?

Question

It seems too obvious to mention. Does it have any relevance to philosophy/logic?

Answer 1

Generally that statement is used to denote that someone is making an over-simplified argument.  Another way of expressing it is 'pigs is pigs'--in the context that in fact we're not talking only about 'pigs' but in fact a range of things in a category.

For example, in the USA, the government's policy in the 'war on drugs' for about four decades now has been 'drugs is drugs'.  A detailed, objective, and informed look at the problem reveals that to be an oversimplification; the problems and solutions that might work for alcoholism, nicotine, marijuana, cocaine, opiates, hallucinogens, amphetamines, prescription-drug abuse, barbituates, etc. are not all identical.  Yet our government applies one policy to all of those drugs except nicotine and alcohol.

If you call a variety of things, not all identical, by the name of their category and then insist that the category is consistent, you're making the "A=A" argument.

Answer 2

It's a common "internet speak" symbol among Star Wars fans for the Twin-Pod cloud cars of Bespin's Cloud City.  One could say, for example,

|o|  - - -  A=A

><   ->  x_x*  +  /\

(translation: The TIE Fighter shot lasers at the Twin-Pod Cloud Car, then an X-Wing Starfighter flew to the Death Star and there was a lightsaber fight)

Answer 3

It has great significance in Aristotelean philosophy; and Aristoteleans who know its meaning also know that anyone who tried to ignore the implications of "A=A" will find out exactly what it means.

TR (sry if I got the name wrong) said "that someone is making an over-simplified argument."

It is not a matter of "over-simplification." It is a matter of making an axiomatically conceptual statement.

"An axiomatic concept is the identification of a primary fact of reality, which cannot be analyzed, i.e., reduced to other facts or broken into component parts. It is implicit in all facts and in all knowledge. It is the fundamentally given and directly perceived or experienced, which requires no proof or explanation, but on which all proofs and explanations rest.

Ayn Rand

"Everything that exists has a specific nature. Each entity exists as something in particular and it has characteristics that are a part of what it is. "This leaf is red, solid, dry, rough, and flammable." "This book is white, and has 312 pages." "This coin is round, dense, smooth, and has a picture on it." In all three of these cases we are referring to an entity with a specific identity; the particular type of identity, or the trait discussed, is not important. Their identities include all of their features, not just those mentioned.

"Identity is the concept that refers to this aspect of existence; the aspect of existing as something in particular, with specific characteristics. An entity without an identity cannot exist because it would be nothing. To exist is to exist as something, and that means to exist with a particular identity."

from "Aristotle's Law of Identity"; http://www.importanceofphilosophy.com/Me...

The "A" on the left is thus the object of the preposition in the sentence which fills the formula, for example "This leaf......"

The second "A" is the prepositional phrase: "is red, solid, dry, rough, and flammable."

The most famous "A is A" is "Existence exists." You cannot argue it without contradiction. If "nothingness" preceeded "existence," "nothingness" would be what existed. It would have been an existent. If it was not the only existent, then other things would also have existed and "nothingness" would be a moot point. "Nothingness" cannot be an existent; therefore, "existence exists" is unarguable, not as an oversimplification, but as an axiomatic concept, a fact of language.

A is A works in any language because that is the way language works, just as Aristotle's Logic works in any language--even after 2500 years no one has proved his definitions of the laws of logic wrong. (They merely differ as to the number of "valid" forms there are. Aristotle said 24. Modern philosophers say 15--and that is out of 256 forms! Think of how many statements of "logic" we make every day without knowing that most of them, if analyzed, would be found to be "invalid," i.e., illogical.)

Answer 4

It has a finite purpose,

It helps one to distinguish real and ideal.

As an idea the 'A's on both sides are equal.

But as physical reality, both the 'A's are not equal. One is on the LHS and another on the RHS.

Answer 5

It is the basis of all logic. It has three forms which are the axioms of logic:

1. A is A (law of identity)

2. not-A is not A (law of excluded middle)

3. A is not not-A (law of non-contradiction).

Obviously, these laws are basically one and the same. But they apply to different kinds of statements. The law of identity applies to single terms; the law of the excluded middle applies to disjunctions; and the law of non-contradiction applies to conjunctions.

You say "it is too obvious to mention". But that obviousness is deceptive. For instance, can you name me one self-same thing (i.e., to which the formula A = A applies)?

If, as Plato summarised Heraclitus' philosophy, "all things flow" (i.e., are in flux), then there is never something to which the law of identity applies. Thus Heraclitus said: "You cannot step twice into the same rivers; for fresh waters are ever flowing in upon you." And a disciple of his is said to have said you cannot step into the same river even *once*...

Answer 6

It's the law of identity and it is foundational to logic. Everything is that which it is. There are no contradictions.

Answer 7

also known as the "reflexive property" in mathmatics, it is useful in geometry when one side is shared by more than one geometric shape.

Try taking that out of context and applying it to human traits.

Answer 8

It is its self LOGIC.

Answer 9

{A=A}, that is 2 equal parts of something, 2 equal sides of the same thing, something that wont stand the test of time...anything 2 things that is the same to one another will fall.....one of those things has to be equal but opposite to one another,....like dislike, in out, up down, left right, alive dead, ect.