Can we be certain that A=A?

[Arra]

Can we be 100% certain that A=A and that 1+1=2? It seems reasonable. 2 is just a symbol for 1+1. We define 2 to be 1+1. They are the same thing, so the statement 1+1=2 is equivalent to A=A, the Law of Identity. And 'A=A' it isn't really saying anything new. We already knew A was A before we wrote down 'A=A'. This is obviously important because all deductive arguments come down to an A=A claim. But can we go so far as to say we're 100% sure that A=A? Someone I was talking to suggested that, no matter how logical or self-evident something seems, it's possible that we're making some mental error and are wrong. It seems we cannot be certain that the results of most deductive arguments are true. I'm sure everyone has occasionally made some 'logic error' in their brain, momentarily believing that a cube has 8 faces for examle. But what I'm talking about is the Law of Identity itself. Can we be certain that something must be equal to itself?

[sloth]

I do not believe that we can know anything for sure. The most universally real thing that I have found has been consciousness. To be honest, I think that having full faith that A=A is a very simplistic way of viewing everything. This is especially true when you start considering concepts such as the holographic universe paradigm, which states, basically, that nothing is as it seems at all. What we perceive of the universe might be nothing more than interference patterns. No. I do not know anything. There are a few things that I believe, but I'm not even sure what that means anymore. I do not know that the sun will come up tomorrow. I do not know that I have a body, and a brain. I may be a two dimensional concept that perceives himself as being three dimensional. I may be a seven dimensional atom. I have always wondered if just maybe... instead of there being an uncountable number of atoms that make up this universe, maybe there is only one atom, and an uncountable number of different ways to view it.

[Sornaensis]

If A is itself then it is A. Tautologies are fun.

[Artelis]

If A is itself then it is A. Tautologies are fun. You failed to note that A is really just a pointer to itself, and therefore not itself. A is only what it's called, but not the name of A. Therefore: A != A Duh.

[DuB]

If you're arguing that A's referent is not identical to A itself, I would agree, but I think you need to use different notation to indicate that this is what you mean to say. If we let 'A' refer to A's referent (so it is, in a sense, a second-order referent) and A refer to the thing itself (a first-order referent), then clearly 'A' != A. However, if we use A in both cases to refer to the thing itself rather than its referent, then it's difficult to conceive how A != A; or, for that matter, 'A' != 'A'. Edit: I think I may have technically misused the term referent... hopefully its clear enough anyway.

[Arra]

If you're arguing that A's referent is not identical to A itself, I would agree, but I think you need to use different notation to indicate that this is what you mean to say. If we let 'A' refer to A's referent (so it is, in a sense, a second-order referent) and A refer to the thing itself (a first-order referent), then clearly 'A' != A. However, if we use A in both cases to refer to the thing itself rather than its referent, then it's difficult to conceive how A != A; or, for that matter, 'A' != 'A'. I meant the latter.

[DuB]

Right; my comments were directed at Artelis. Apologies for the double post. I guess the main problem I have with considering this problem is that it's not clear what it would even mean for A != A. What follows? Formally we would write the proposition as ~(A=A). But then we could apply this to the negation itself: a negation is not a negation. Okay, so A=A. But then we could go further and say that an identity relation is not an identity relation, so ~(A=A). But then we're back to where we started. No matter what you try to do, you end up logically paralyzed in an endless loop. Let's just let A be A

[Artelis]

Right; my comments were directed at Artelis. oh god, sorry, I was making an inside joke at A Roxxor I'm on the A=A side since the idea of A being a pointer to itself is just silly, because then A still equals A (pointer = pointer, urr).

[Arra]

oh god, sorry, I was making an inside joke at A Roxxor I'm on the A=A side since the idea of A being a pointer to itself is just silly, because then A still equals A (pointer = pointer, urr). Well if one of the As is the original and the other is a pointer to the original A (A = *A) then the two variables aren't identical. I guess my point was, can we be 100% certain that A=A? I'm not talking about pointers, I could also say "is this fork itself?" or "am I me?". I mean it seems clear that something must be equal to itself, but whatever brain process decides it's clear could have been a malfunction, so we can't say we're 100% certain.

[Alric]

A does in fact equal A. We know this with 100% certainty. We also know that 1+1=2, with 100% certainty. There really isn't any doubt at all. The world we live in is very logical with solid rules that govern how the world works. Some things are always true, no matter what. Such as A=A. If A does not equal A, then you are no longer in our reality.

[stormcrow]

The map is not the territory. But the map can be extremely useful for understanding the territory. Yes A=A because it suits our purposes to do so. A=A because the users of a common language understand it to be so. Lets interchange A with "Dog". D-O-G is the signifier(the sound, words) and "dog"(the meaning, the object in the real world that D-O-G is signifying) is the signified. In this sense the word D-O-G is not an actual dog (see the first sentence.) it is just a symbol. Are you insinuating that symbols are unstable and arbitrary?

[Sornaensis]

Yeah, we need basic, constant truths like A = A in order for any system of logic or reasoning to work and be effective at all. Though technically A = A yields a falsehood if A is NaN duh :V

[kidjordan]

In the world of pure logic A=A is 100% true. However, the realm of pure logic does not apply to reality. I'm an empiricist and so logical truths may approximate reality closely, however, they are not the real thing. You can't prove A=A false using logic because A=A is the foundation of logic! DUH! HOWEVER, no two things are exactly alike in reality so you can disprove it empirically.

[Sornaensis]

You can't prove A=A false using logic because A=A is the foundation of logic! DUH! HOWEVER, no two things are exactly alike in reality so you can disprove it empirically. You mean I am not identical to me? What is this, I don't even...

[stormcrow]

You mean I am not identical to me? What is this, I don't even... You are not two things.

[Sornaensis]

A = A isn't a comparison of two different things.

[MindGames]

If A equals A in the sense that you are comparing one thing with itself, then A=A always holds true, even in physical reality. Don't confuse logic with pointers or anything of the like, because if you were to compare two different apects of the same thing, then you would have to signify that you were doing so in the initial equation by using different notations. The same applies in all low-level (more exact operations on memory) programming languages. You cannot compare a memory address (pointer) to the actual object in memory since they are clearly two completely diffrent objects and are treated as such by using different notation for the pointer and the object itself. Futhermore I believe such discussion is rather pointless, because A=A is only a textual representation of the relationship between two objects. What is important is that one thing is inherently equal to itself. If anything, that should be the subject in question.

[Alric]

A=A is a comparison of two identical objects. You are identical to yourself. They are the one and same object. The squiggly equal signs means approximately. The normal equal signs mean identical. So when you use the = sign you are talking about identical objects. Which works fine in math, because 1 is identical to all other 1's. Find one example, where 1 doesn't equal itself. It is impossible.

[Alric]

1=1/2+1/2=7/7=sin^2+cos^2=log10=5*5/25=(1/x)*(x/1)=1 It isn't a pointless question. Math is based on many things that look different, but are actually identical. There is nothing self evident about it, but it is still true. To answer your question though, no. It isn't always obvious, but it is always true. A=A.

[MindGames]

@Dianeva, I interpreted A=A to be a sort of equation. But even when you interpret in the literal sense, one thing is always going to equal itself. 1=1/2+1/2=7/7=sin^2+cos^2=log10=5*5/25=(1/x)*(x/1)=1 It isn't a pointless question. Math is based on many things that look different, but are actually identical. There is nothing self evident about it, but it is still true. To answer your question though, no. It isn't always obvious, but it is always true. A=A. The question is rather uninteresting, in my opinion. While it is true that there are multiple representations for the same thing, no matter how abstractly you represent it, one thing is always going to be equal to itself.

[Photolysis]

Can we be 100% certain that A=A As DuB states, logic breaks down if this isn't the case, and you get stuck in an infinite loop of negation. From a practical viewpoint an object's definition is based on its properties. If an object isn't based on this then definitions cease to have any meaning. If we only have a single item, at any given time it can only have one set of properties and therefore it must be equal to itself.

[Philosopher8659]

A = A, which is the same as a thing is not different from itself, which is the same as relation to self is inadmissible. Which is the same as do unto others as you would have them do unto you, etc, etc. As Aristotle pointed out, all logic resolves to only one of two possible states, "is" and "is not" which is the same as "same" and "different" which is a simple binary state. If you are not certain of the first principle of logic, of reason, of physical fact, it is because your ability to reason simply is not what it should be. If any of your other environmental acquisition systems were just as confused, your body would simply die. Logic does not break down, minds do. Every possible error in logic resolves back to a simple binary mistake by a logician. And, since it is a first principle, how is it that one can even get out of grade school and not know it to the core? How can people like Einstein be worshipped as great minds? How can you not know which geometry is more correct, Euclidean or Non-Euclidean? The evolution of the mind of man will be commensurate with principles of logic that are "hard wired" into that mind. One can repeat A = A but not know when or when it is not violated--and they will insist on its violation to satisfy their own desires. When it is part of a functional mind, then and only then does one know, and is certain of it. The rationality of any human being is directly related to their behavior being commensurate with the first principle of logic. (I said that. In case you missed it, this is another expression of A = A.)

[sloth]

I really am not impressed with the argument that A=A is imperative to logic. I don't even know for sure that A exists.

[DuB]

Whether or not A "exists" is irrelevant. A could stand, say, for unicorns or Sasquatch or whatever. We reason about nonexistent entities all the time. But we still have to assume that a unicorn is a unicorn in order to do so.

[sloth]

If that is the case what makes the unicorn a unicorn? I don't believe I HAVE to assume anything. Assumptions make an ass out of ump and tions.