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The major problem with that is that Mathematics is the one discipline in which we can, without a shadow of a doubt, prove something is true. Everything else just works until something proves it wrong.

I did read it, I was just too tired to really respond.

If you're going to look at it that way, everything is an abstract that cannot be proven. It's just an extension of the incontrovertable philosophical argument "You cannot prove to me you exist".

However, there is a problem with at least one of your points. The number three, contrary to your statement, is not ficticious. Three represents real objects. It is only negative numbers that are actual abstracts (and anything coming from them, like the square root of minus one, and so on), as they were created to allow more complex sums to be solved. To stand for debt, and so forth.

And as for the "different systems" idea - in religion, a system cannot be proved wrong, for each denies the truth of the other. In mathematics, if a system does not work and another does, the first will be discredited. In the end, almost all mathematics could be achieved with simple addition, subtraction, multiplication and division. Everything else, however (calculus and so on and so forth), is there to make it easier. If you wanted to find the gradient of y = 32/4x^2, for example, would you rather differentiate or draw the graph? Both are viable options, but one is much easier than the other.

"Nothing exists"? I'm afraid that just isn't so. Within mathematics, the concept of zero exists, without it we could do nothing but the simplest calculations (just look at Roman numerals and imagine trying anything harder than twenty times twenty - even that's not so good), but zero itself does not. How could it? It is the embodiment of nothing, an ephemeral ghost which states, "I represent the nonexistence of anything." It does not exist.

So, really, it comes down to this: mathematics is a tool we use to interact quickly and easily with the world. Hence, it is infinitely more real than the faeries, and not an abstract.

You are right that we do not prove 1 + 1 = 2. But, that is because it proves itself. We have no say over the outcome. It equals two, because it says it equals two. This is what is known as something being SELF-evident. It's proof is based on itself, not what we contribute. Simply because we do not contribute to the outcome, does not mean it doesn't exist. And if you were to go around saying that there is no proof that 1 + 1 = 2, then I think people might think of you as mad.

Math is in no way like a religion. I think you should maybe look up the word "religion". Religions are collectives of people who share similar beliefs about the SUPERnatural laws of the universe. Math is not supernatural, it is just plain natural. Supernatural laws exist above natural laws. A supernatural law can defy the fact that 1 + 1 = 2. Math also, does not involve any form of worship. Math is therefore, not like a religion.

I assume you wrote this to persuade people to be more tolerate of religions. The problem with religions is that they are usually just a compilation of premature ideas, that people decided to stick to in order to gain an empowerment over others. According to Greek religion, lightning was a reaction to Zeus being pissed off. According to Egyptian religion, the sun was a god on a chariot who rode across the sky and brought light with him. It appears that these people just looked at something they didn't understand, and without the tools to figure them out, they eventually decided to just say that a god was doing it. We now know how the sun and lightning work, because we have the tools, and we've also learned from the past that it is not wise to immediately assume that a god is doing something that we do not understand.

Religions also seem to constantly change according to what can be proven in life, so that people can rationalize and hold on to their beliefs that over the years they have become dependant on. This gives further reason for a person to question a religion and to assume that a person who sticks to this religion is simply being immature and stubborn.

Simply having knowledge of history and religions can give a person a lot of reason to reject certain religions. Christianity for example. Christianity is a relgion based on the teachings of Jesus Christ. Jesus Christ, however, stated many times in different ways that he was againts organized religion. Many of his teachings are not even implemented in the Christian religion. So if a person were to truely take into consideration the teachings of Jesus Christ, they may have to reject what the Christian religion teaches. Also, if you study up on how religions came to be, you may realize that some of them were just lies compiled to gain control over civilizations.

So the next time you meet someone who is against your religion, don't immediately assume that they are close-minded to your religion. The fact may be that they know more about your religion than you do.

Math is at least somewhat like a religion in that it takes premises and builds facts off of them, unlike science which takes facts and builds premises off of them.
One fundamental difference between religion and math, however, is that math doesn't claim to be truth, nor does it claim to give reasons or information about the workings of the real world, either natural or supernatural. It also gives no commandments or morals, no instructions on anything. In fact, on its own, math doesn't tell you much at all, whereas religion tries to tell you everything.
Everything that math "tells" you is actually a claim of science, based on the fundamental scientific postulate that the natural world can be modelled mathematically on all levels.
The only likeness between religion and mathematics, as far as I can tell, is that both make unprovable postulates. This, however, is inherent in all reasoning; all reasoning relies on the laws of inference, which themselves cannot be proved as to do so would require them to be true. This makes science a religion, this makes philosophy a religion, this makes basically reasoning systems into religions.
So while mathematics can be said to be like religion, it is not like religion in a significantly different manner or to a significantly greater extent than any other type of reason.

Some things I'd like to clear up:
Firstly, 1+1=2 is not always something that just pops out of the definitions of 1, 2, and +.
For example, if you're defining N in terms of multiplication and addition, then it is a tautology in that 2 is defined as 1+1. If you're using the Peano axioms, or some version of the Peano axioms, however, 2 is defined as the successor of 1 and while taking the successor of something in this system is equivalent to adding 1, it is not an axiom or a definition, so should not be treated as such. Similarly, in typographical number theory as formulated in Godel, Escher, Bach, it's a seven line proof. The fact that 1*1=1 takes 14 lines. While this is significantly shorter than most proofs, this is still non-trivial.

Secondly, please stop arguing about the existence or non-existence of three. Until someone gives a definition for existence in this context (i.e. physical manifestation v. conceptual possibility v. resulting from axioms), the question of the existence of an abstract is meaningless. Three has no physical manifestation in itself (in that you don't get physical 3s anywhere, just things shaped like "3" and groups of objects whose size can be modelled by the concept "3"), but it can be conceived, and it can result from axioms. Thus, depending on what definition for "existence" you're working with, 3 either does or does not exist. Arguing about something without giving definitions makes you sound like philosophers, and I don't mean that in a good way.

Ah, but can two people not come to the same conclusion regarding the validity of a mathematical statement? Are you saying that math is in fact subjective? Are you saying that math is a product of the human mind, rather than an object that exists, if not independently from humans, at least independent from any individual human? Is my math different from yours? Is there someone for whom 1+1 might not be 2, because his personal math states that it is not?
Did math not exist before humanity? If so, what of the universe before humanity? When there is no math, is the universe still regular? Can the universe operate under scientific laws when there is no math in which those scientific laws can be formulated?

Science may be tangible in that its data is received through the senses rather than through the imagination and the intellect, but it is not more objective than mathematics; in fact, it is markedly less so, given relativity and quantum mechanics. A rock may fall in a certain manner to one viewer who is stationary relative to the earth, but to one for whom the earth is moving, the rock falls in a different manner; it may fall with a certain speed to a viewer who measures velocity, but one who measures position will see a range of speeds with which the rock falls. This does not sound like objectivity to me, when the data gathered depends on the viewer.

So you're saying that math is a cultural phenomenon but not science? You are in fact certain of this? I don't see how this could be true, as you can trace the proof of every mathematical theorem, and every proof can be made rigorous. Just because the mathematical teaching style is Western does not make mathematics a Western phenomenon.

I suppose you're ignoring the fact that while the Greeks and the Chinese had no mathematical interaction at their intellectual heights, they still managed to come up with the same "system," at least as far as the laws of inference are concerned. I suppose you're ignoring every single reinvention of the wheel that mathematics has gone through, every point where a lone soul, cut off from Western academia, has managed to teach himself mathematics. No, I don't think mathematics is a cultural thing at all.

Furthermore, it is fully possible to observe something different about the physical world than your neighbor. Most of the time we call this delusion; some call it enlightenment. I don't think that it is gauranteed that two people of different cultural backgrounds would come to the same conclusion about scientific fact.



Do we know that math is a product of the human mind? Are we absolutely certain that math has no objective existence? Plato thought it existed separately from humans. St. Augustine thought it existed separately from humans. I think it does too, if by exist means not that it has a physical manifestation but that it can be potentially determined by any sentient being regardless of who that sentient being is.



So, what mathematics are you using? Note that by math, I do not mean a set of axioms attached to a set, I mean the laws of inference coupled with the notion that non-contradictory axioms can define a system. Do you use a different set of inference laws? If so, I would much like to know what they are, and what conclusions you get that I cannot in my math.



But did the Earth orbit the sun with mathematical regularity? And if so, does this regularity not demonstrate that there must be some sort of formulation of regularity?

As for the science thing, I was just pointing out that scientific observation does depend on the state of the observer, if not the identity, while math does not, and thus is inherently more objective.

But the same thing could be said about science, so it can't be said to be more objective in this sense. I personally would think that, being empirical and thus more primitive, science would stem from such a time of united human culture, moreso than math.



Perhaps this is true; as far as I know, you are correct in that the foundations are always from outside. My point, however, concerned not the foundations but other parts of mathematics, such as that soldier in a Russian prison (I've actually forgotten his name at this point) who forgot almost everything he knew about Euclidean geometry and ended up creating projective geometry instead, completely independently of others who came up with projective geometry. This suggests that at least at higher levels, mathematics is not subjective; the foundations could be questioned, but not moreso than science, in my opinion.



And how do you know that we can't accept solipsism? Sure, you can say that accepting solipsism is accepting defeat for science, but accepting subjectivity is then the defeat of mathematics, and yet you seem to have no problem with it. To tell the truth, I am fairly close to accepting solipsism myself, as all philosophy, including science, appears to be "turtles all the way down."
You can't talk about science without first postulating an objective physical world, but you can't talk about math without postulating an objective mathematical one. Otherwise the entire idea of proof is meaningless and mathematics falls apart.



I don't see how this is different from solipsism. At all. We have no proof, scientific or otherwise, that anything exists physically. The only thing we have is your fear of solipsism, which, while well-intentioned, cannot on its own hold up to logical scrutiny.



What's the difference? I am actually asking that quite seriously; unless I'm mistaken, the only definition of mathematics which in fact encompasses all of mathematics is "logic applied to sets of axioms."



I am afraid I must resort to a rather solipsistic answer to this, which you will not like but I do believe you must consider: just as I have no proof that mathematics "existed," for whatever that may mean, before intelligent life, you have no proof that the physical world existed before us. While this notion may seem fairly ridiculous, and perhaps even obscene, to you, I do wish you would consider it.
Nevertheless, if we assume that the physical world did exist before us, I still hold that any regularity in these physical laws signifies the existence of a concept of mathematics, if not in reality than at least in potentia; which, since mathematics is not time dependent (unless you wish to argue that with me), signifies that it existed even then.
I do not think that there is a physical law that is devoid of mathematics unless we turn to some version of Aristotle's "everything to its natural place," which cannot respectably called a scientific law as it makes no predictions and is vague enough to be almost meaningless.



Okay then. That is true; I have no proof of the notion that state would not affect mathematical perception; and yet you have no proof that it does. Thus, as you are the one arguing that math is subjective, it is up to you to show that math has this state-dependence; I do not have to show that it does not, because even if it does, that merely shows that it is at most as subjective as science, not moreso.



And yet I do not see support for your arguments either. What I see you doing is making a claim of possibility regarding the origins of mathematics and clinging to a rejection of solipsism that I believe cannot be justified. Saying that "if we accept solipsism then the conversation ends" doesn't really hold up, any more than saying "if God doesn't exist then theology is pointless." I am perfectly willing to accept solipsism in the exact same way I am willing to accept atheism. I do not believe in rigorous scientific proof any more than I believe in rigorous religious proof; I am not even sure that I accept the concept of truth in a non-mathematical sense.
Perhaps your definitions of math, science, and religion are so different from mine that our views are irreconcilable; the fact that I felt the need to demand a definition indicates that it in fact did have dispute, despite what you believed. Perhaps I am wrong; I have not seen anything to demonstrate such to my satisfaction.

And, personally, I find this discussion to be plenty fruitful; while I admit that part of this stems from my contrarian nature, I do believe that debating the philosophical foundations of science and math is a worthwhile endeavor in itself. After all, debating the role of secular causality versus the role of theistic causality led to the secularization of science.
Misunderstanding of science's foundations gives ammunition to proponents of teaching Intelligent Design; they say that science teaches truth and thus should be banned because its truth goes against theirs. Thus, by having this discussion, we are in fact clearing up any misconceptions that either of us may have regarding this issue of truth, objectivity, and scientific inquiry.
Furthermore, I do believe that we are, if not in the best manner, discussing the basis for your initial post; I am maintaining that math is no more a religion than science, and you are maintaining that science is inherently more objective than math; is this issue not the concern of your post?