G'night! :)

dbhalling? You're khalling's husband, I assume?

Perhaps I did get a bit confused about the distinction between an absolute and a constant. Perhaps you could clarify that distinction for me?

But anyway, I would say that reason alone cannot allow a man to discover reality. Rather, man must rely on experimentation and observation to determine what is true. Logical reasoning is an indispensable part of that process, to be sure, but it is not enough by itself.

And yes, a logical error in math does indeed demonstrate that a person has made an error. In that you are correct. However, a logical PARADOX is not the same thing as an error.

Maybe Zeno’s Paradox was a bad example. What do you think about these other paradoxes?

John Searle's Chinese Room
Hilbert's Infinite Hotel
Einstein's Twin Paradox
Schrodinger's Cat

Also, what is your opinion regarding Quantum Mechanics?

"The evil that is in the world always comes of ignorance,"

I disagree. Some revel in evil.

Didn't Ayn Rand say that reason was man's only absolute? How can there be any other absolutes if reason is the only one? Oh well, I guess we can just dismiss that as another one of her many logical contradictions.

Anyway, while it's certainly true that there are many absolutes, there are also many paradoxes. Regarding the issue of Communism, I do agree that history has proven it to be an unworkable theory based on many false assumptions (Ludwig von Mises points out in his book "Socialism" that Communists and Socialists have many very basic misconceptions about economics). But we should not allow the fact that Communism and Socialism are destructive to interfere with our logical reasoning ability, nor should we let that fact drive us to make foolish conclusions regarding mathematical calculations or the existence of paradoxes. Whenever you try to label any particular thing as an absolute, you must necessarily base your claim on several assumptions, and as such run the risk of closing yourself off to potential new knowledge. ;)

For example, you claimed that the Earth's gravity is an absolute. It is not. Although gravity itself is absolute, the local gravitational force on Earth actually fluctuates in spacial terms by about 0.7% over the Earth's surface because the mass of the Earth is not uniform. It also changes over time, but does so very, very slowly due to plate tectonics. The total mass of the Earth is also slowly but constantly increasing due to the gradual accumulation of space dust and occasional meteorites striking the Earth. If you were to simply proclaim that the Earth's size and gravity are absolutes and never change, you would close yourself off to all this knowledge.

The speed of light in a vacuum does certainly appear to be a constant, though that absolute relies on the assumption that our current scientific theories are true.
http://math.ucr.edu/home/baez/physics/Re...

Mathematically speaking, there are many paradoxes which undermine the idea that everything is always exact and precise. If you would like, you can familiarize yourself with some of the more famous mathematical paradoxes by watching the following video:

Zeno's Paradox - Numberphile:
http://www.youtube.com/watch?v=u7Z9UnWOJ...

After you're done with that, you may want to explore a few other YouTube videos about mathematical paradoxes. It'll make you reconsider Ayn Rand's claim that there are no contradictions (such a claim requires mathematical proof, which Ayn Rand never provided, indicating that she was probably an even worse mathematician than she was a philosopher).

Also, if you're going to insist that A must always be equal to A (a mathematical equation otherwise known as the Reflexive Property of Equality), there's a book you ought to read called "The God Problem: How a Godless Cosmos Creates," by Howard Bloom:
http://www.amazon.com/The-God-Problem-Go...

Review of "The God Problem":
http://www.kurzweilai.net/book-review-th...

And one other thing I must point out is that even if we accept the Reflexive Property of Equality (A = A) as completely true, that does not automatically exclude the possibility that A could also potentially be equal to B. The reason I say this is because A and B are both empty variables with no specific value until given one (this is basic algebra here). You can make them unequal by assigning them different values from each other, but they are not unequal inherently; they CAN be made equivalent if one desires them to be so. Watch, I'll give them equivalent values now:

A = (-2) + 2
B = 1 + (-1)

In the above problems, both of the equations add up to zero. Therefore, they are equal. A = B, at least for these given equations. Of course you can assemble other equations where they are not equal, but asserting as an absolute that it's totally impossible for A to ever equal B under any circumstance would be mathematically incorrect.

Another book you should read (I know, I'm recommending a lot of books) is "A Mathematician's Lament," by Paul Lockhart. Here's a short excerpt:
---
Mathematical objects, even if initially inspired by some aspect of reality (e.g., a pile of rocks, the disc of of the moon), are still nothing more than figments of our imagination.

Not only that, but they are created by us and are endowed by us with certain characteristics; that is, they are what we ask them to be. Not that we don't build things in real life, but we are always constrained and hampered by the nature of reality itself. There are things I might want that I simply can't have because of the way atoms and gravity work. But in Mathematical Reality, because it is an imaginary place, I actually can have pretty much whatever I want. If you tell me, for instance, that 1 + 1 = 2 and there's nothing I can do about it, I could simply dream up a new kind of number, one that when you add it to itself disappears: 1 + 1 = 0. Maybe this '0' and '1' aren't collection sizes anymore, and maybe this "adding" isn't pushing collections together, but I still get a "number system" of a sort. Sure, there will be consequences (such as all even numbers being equal to zero), but so be it

In particular, we are free to embellish or "improve" our imaginary structures if we see fit. For example, over the centuries it gradually dawned on mathematicians that this collection, 1, 2, 3, et cetera, is in some ways quite inadequate. There is actually a rather unpleasant asymmetry to this system, in that I can always add rocks but I can't take them away. "You can't take three from two" is an obvious maxim of the real world, but we mathematicians do not like being told what we can and cannot do. So we throw in some new numbers in order to make the system prettier. Specifically, after expanding our notation of collection sizes to include zero (the size of the empty collection), we can then define numbers like '-3' to be "that which when added to three makes zero." And similarly for the other negative numbers. Notice the philosophy here – a number is what a number does!
---
"A Mathematician's Lament," by Paul Lockhart

http://en.wikipedia.org/wiki/A_Mathemati...
http://www.amazon.com/Mathematicians-Lam...

The 25 page essay which was the precursor to the book (PDF format):
http://mysite.science.uottawa.ca/mnewman...

That particular quote is actually one of the reasons why I maintain my position that Ayn Rand was a great author but a sub-par philosopher. ;)

Although there are certainly some issues where one side is absolutely right and the other side is absolutely wrong (I personally view the issue of LGBT rights in this way), there are also other issues where both sides have a portion of truth, and where clarity can only be achieved by viewing things from multiple perspectives.

In his book "Rich Brother Rich Sister," Robert Kiyosaki says that he must frequently remind himself that God gave him a right foot and a left foot, not a right foot and a wrong foot, and that there are often many different ways to solve any particular problem.

http://www.amazon.com/Rich-Brother-Siste...

A metaphor I like to use is this: hold up your index finger at arm's length, and close one eye. Now open that eye and close your other one. Notice how your finger appears to change position? That's because your eyes are offset from each other. Your position changes your perspective. But if you open both eyes, and look through both of them together, you get something that you never could have obtained by looking through only one eye or the other; you attain the ability to perceive depth. Only then, when you use both of your eyes in unison, are you able to perceive the true position of your finger in three-dimensional space.

And some issues have more than two sides. Some issues may have twenty sides, or more, as seems to be the case with the overlapping fields of economics, politics, and social sciences. In situations such as these, one would be remiss to make an attempt at declaring what is good and what is not without fully considering all possible angles. This is one of the reason's why I've been enjoying Ludwig von Mises so much; he has the clear, cool, levelheadedness to calmly dismantle socialism from a scientific point of view rather than a moral one, while also acknowledging that other social issues, such as environmentalism, cannot rightly be called irrational, and can still have a potential justification, albeit a non-economic one.

"The evil that is in the world always comes of ignorance, and good intentions may do as much harm as malevolence, if they lack understanding. On the whole men are more good than bad; that, however, isn’t the real point. But they are more or less ignorant, and it is this that we call vice or virtue; the most incorrigible vice being that of an ignorance which fancies it knows everything and therefore claims for itself the right to kill. There can be no true goodness, nor true love, without the utmost clear-sightedness..."
~ From Albert Camus’s "The Plague" -- http://en.wikipedia.org/wiki/The_Plague

Aristotle hasn't said anything in a long time.

"For example, between anorexia and obesity, which is good and which is bad?"

Insufficient data for a meaningful answer.

Sorry, I learned to escape that trap a long time ago.

Everything can be reduced to a binary answer. If not, you haven't reduced it enough.

I'd be more than happy to oblige that request. ;)

Let us begin.

There are times when black or white reasoning is in fact fallacious. There are certainly situations where it can be applicable, to be sure, but there are also situations where it is not.

For example, between anorexia and obesity, which is good and which is bad? The obvious answer is that they're both bad, and that the good lies in the middle, or the median between two extremes.

As Aristotle says, the ideal lies at the mean between the extremes of excess and dificency.

http://www.plosin.com/work/AristotleMean...
http://en.wikipedia.org/wiki/Golden_mean...