Find the Fallacy

Two mathematicians begin a discussion by assuming that A=B. Then they begin making changes. They add an equal term to both sides of the equation. A+A=A+B or 2A=A+B. Then they subtract an equal number from both sides. 2A -2B = A+B -2B. They look at this and agree that this all makes sense. Then they agree that this equation can be simplified by a simple operation. 2(A-B) = A+B-2B. This again simplifies to 2(A-B) = A-B. The result astounds them. Two times (A-B) equals (A-B)? Two equals one????

The answer is that the fallacy occurs only at the final step.

We get to 2(A-B) = A-B. But at this point we should recall that if you subtract something from itself you always get zero. So A-B = 0 and 2(A-B) also equals 0.

It is surely the case that 0 = 0, but thus stated the air of paradox has disappeared.

You obviously can’t get from there to the conclusion 2=1, only to the conclusion that

2(0) = 1(0).

The final step would be division by zero, which the basic rules prohibit. Precisely to avoid such paradoxes as this!

My point? Just that zero, and the rules governing its use are more exotic human conceptual inventions than one might think. The casualness with which we usually treat zero comes from familiarity, not from simplicity. This confirms the point I sought to make yesterday, that our most successful inventions are also discoveries, and vice versa.

This turns out to be, not especially Kantian, but certainly Jamesian, or well within the area of their overlap.

William James Quote

“Why do we thus so markedly select the tangible to be the real? Our motives are not far to seek. The tangible qualities are the least fluctuating. When we get them at all we get them the same. The other qualities fluctuate enormously as our relative position to the object changes. Then, most decisive still, the tactile properties are those most intimately connected with our weal or woe. A dagger hurts us only when in contact with our skin….”

Principles of Psychology, chapter 21, The Perception of Reality

What is Reality? Don't Ask

Some people regard this as the deepest of philosophical questions. Some even regard it as the heart of metaphysics. What is reality? or ... what does it mean to be?

In wrestling with this, philosophers and wanna-bes alike have produced gnomic answers. What is it to be?

To be is to be perceived. That's a good one, George.

Existence is identity. Noted, Ayn. But Prince Hamlet has an "identity" of sorts. He is a very specific fictional character. Identity, then, is not always existence.

Reality is the fulfillment of purpose, complete or incomplete. said Josiah Royce.

Being never was, and never will be, because it is completely whole in the now. Classic -- one of the fragments of Parmenides.

And so forth.

The pragmatic answer to "what is reality," though, is to un-ask the question. For any effort to give a verbal answer to the question will only amount to substituting for the word "reality" or the word "existence" some other word or collection of words. And how will that be an advance, unless there is some confusion in the first word that requires such clarification?

There is no confusion as to what is reality, except the artificial confusion caused by philosophic niggling. Why not? because reality is a primary notion. It is the turtle at the bottom of whatever tower of turtles you want to postulate. It doesn't rest on any other turtle further down so efforts to conjure one up, by "defining" reality, are themselves necessarily unreal.

If you are going to argue over what is reality you may as well argue over what is Nothing, and move thence to the classic dispute over whether it is a verb, whether nothing noths and nihil annihilates.

Beyond the question of "what is reality" there is the far more valuable question, "what is real?" What kinds of things do we acknowledge as the furniture of the world and what are their relations to one another?

Reality

Let's ask that everlasting favorite question: what is reality?

We must begin any chain of thought somewhere, and since the question itself presumes that "reality" is our goal, not our premise, we can't start there.

So let's begin with what is sometimes taken to be its antonym, "appearance."

I submit that although there is a sense in which it is right to take appearance/reality as antonyms (and I'll get back to that) there is a broader sense in which our conception of reality has to be built up out of appearances.

Reality, broadly considered, has the following four constituents:

1)Everything that has ever appeared to anyone – whether the appearing has been long-lasting or fleeting, consequential or not – a wood stove keeping you warm or purple spots before your eyes indicating illness. Everything that has ever appeared to anyone has this much reality – it really has appeared! So we start with that. This is the "cogito" part of a famous formula.

2)Also, there are potential appearances. The noise the tree makes in the uninhabited forest. Of course, somebody might have been there. Somebody might be there the next time a tree falls. We ought to have a conception of reality broad enough to include such unrealized possibilities.

3)Invisible cosmic machinery. We postulate that various things must be happening or have happened in order to make sense of that which appears to us. After all, appearances are strikingly law-like and predictable. The sun appears to rise in the east every morning. We postulate the laws of gravity and inertia that make sense of this, and this machinery too is real.

4)Those to whom things appear. Conscious minds. Us. This is the "Sum" part of the formula.

So reality, I imagine you might say, has all of those constituents. But it is often used in a narrower sense, focused especially upon (3). This is what we mean when we say, “I’m not interested in the appearances, only in the underlying realities.” Some appearances are privileged because they fit nicely with one another into a coherent whole, and with the underlying cosmic machinery we postulate. Other appearances, like the strange sights I dreamy last night, or the purple spots that swim briefly before my eyes when I suffer from a fever, don’t have that privilege, and are “merely” appearances, nothing more.

We might also consider the English language term “realty” or “real estate.” Land and the buildings permanently affixed to it are more real than other forms of property, by common consent as suggested in the language used to describe them. Why is that?