infinite making the finite intelligible--not so garbled version

This is an example of a rough draft rather than a polished one....it's from an email I just sent to "me bros":

Nice points about infinity, bro... I'll try to give some feedback

I agree that you can't divide one by zero. But maybe there's more than one way to ARRIVE AT the concept of infinity in mathematics. For example, they talk about nearly parallel lines that meet "at infinity," which means they keep getting closer but never touch. SECOND EXAMPLE: THINK OF THE PROGRESSION: 1/2, 1/4, 1/8, 1/16, etc. IT BECOMES zero at infinity. IN THESE TWO CASES, THERE IS No need to talk about dividing one by zero. But yes, YOU COULD OBJECT THAT these TWO counterexampleS replace one impossibility (DIVIDING ONE BY ZERO) with TWO NEW ONES: none of us is ever going to get to the infinity that lies at the end of the 1/2, 1/4, 1/8 series. Yet we can think about it: THAT'S what's amazing about math In order for mathematics to do all the stuff it's supposed to do, you have to have the concept of OBJECTS OF THOUGHT you'll never experience (THAT IS, CONCEPTS OF zero and infinity).

I ain't no mathematician, but I'm gonna stick my neck out here and make an assertion. HERE IT IS: In order to do ANY mathematics AT ALL, you must have concepts of infinity and of zero.

TAKE THE FOLLOWING ALGEBRAIC EQUATION AS AN EXAMPLE OF THE PRINCIPLE THAT I HAVE JUST MENTIONED:
(x-1)2 = 2x - 2.

THIS EQUATION Seems simple enough, But in order for it to be absolutely true, it has to be true IN ALL CASES, INCLUDING the case in which x EQUALS 1. But IF YOU LOOK AT that case, you WILL NOTE THAT THE quantity in parentheses EQUALS ZERO. THAT IS, WHEN YOU REPLACE X WITH ONE YOU GET THE FOLLOWING:

(1-1)2 = 2x -2.

THE QUANTITY IN THE PARENTHESES DOES EQUAL ZERO. SO IN ORDER FOR YOU TO GRANT THAT THE ORIGINAL EQUATION IS ABSOLUTELY TRUE, YOU HAVE TO ACKNOWLEDGE THAT IT WORKS EVEN WHEN IT (OR PART OF IT) EQUALS ZERO. AFTER ALL, If THE quantity IN PARENTHESES were any other AMOUNT THAN ZERO, then the original equation would BE FALSE IN THIS ONE INSTANCE. IT WOULD THEREFORE not be absolutely true. HENCE zero is indispensable for absolute truth.

Take the same equation and ask, WHICH ONE OF THE FOLLOWING IS true:
1. for every possible value of x
or
2. for only a limited number?

If you choose 2. as your answer, then the original equation is not absolutely true. But if you choose 1, then you are affirming that it is true for an infinite number... of numbers. Now we will never experience that infinity... yet we somehow know that truths of mathematics are applicable to them. If you ask me, that's amazing!

Drawing a conclusion: in order to affirm the truth of even the simplest equation (like the one above)... you have to be open to there being an infinite number of numbers on the number line... where you will also find zero (and in deference to Byran I'll acknowledge that this infinity points both in the positive and negative direction).

In other words, we are able to talk about the finite and make sense of it only through our openness to the infinite.

This may seem like a leap of logic but I am willing to back it up: I would say that the same is true outside of mathematics. If you talk about justice, goodness, beauty, truth... stuff like that... if you believe that our everyday talk about such things is in some sense genuine knowledge of reality... if you think that talk about these things like justice and beauty is not just a bunch of blathering about how you feel but objectively true, then you are, as Jesus said, "not far away from the Kingdom of God." That is, if these concepts (i.e., of justice, beauty, goodness, and truth) have real content rather than being a form of self-deception or mob control, then there is a God.

Does that seem like a bit of a stretch? I don't think so, but I will wait for your feedback before yammering on.

P F Strawson's Freedom and Resentment: the argument laid out

Here is a summary and comments on the essay Freedom and Resentment by PF Strawson. He makes some great points, and when he is wrong, it is in such a way as to clarify things a great deal. My non-deterministic position is much better thanks to having read this. I’ll summarize it in this post and respond in a later one. In a nutshell: PFS first argues that personal resentment that we may feel toward another for having failed to show goodwill toward us would have no problem coexisting with the conviction that determinism is true. Moral disapprobation, as an analog to resentment, is likewise capable of coexisting with deterministic convictions. In fact, it would seem nearly impossible for a normally-constituted person (i.e., a non-sociopath) to leave behind the web of moral convictions, even if that person is a determinist. In this way, by arguing that moral and determinist convictions can coexist in the same person, PFS undermines the libertarian argument ...

Daniel Dennett, disqualifying qualia, softening up the hard problem, fullness of vacuity, dysfunctional functionalism

Around track 2 of disc 9 of Intuition Pumps , Dennett offers what I would call an argument from vacuity. He argues that David Chalmers unwittingly plays a magic trick on himself and others by placing a set of issues under the one umbrella called the "hard problem of consciousness." None of these issues is really , in Dennett's opinion, a hard problem. But in naming them thus, Chalmers (says Dennett) is like a magician who seems to be playing the same card trick over and over again, but is really playing several different ones. In this analogy, expert magicians watch what they think is the same trick played over and over again. They find it unusually difficult to determine which trick he is playing because they take these performances as iterations of the same trick when each is in fact different from the one that came before. Furthermore, each of the tricks that he plays is actually an easy one, so it is precisely because they are looki...

robot/computers, awareness of causality, holism

For a purportedly cognizant machine to be aware of causality, it would seem (given how it happens with us rational animals) that being aware of its own causal interactions is a necessary condition for its being aware of how causal relations exist in nature. But to be aware of its own causal interactions, the machine would have to have a sense of its acting as a whole, as an individual, and as being acted upon at a whole. It would not suffice merely to register information from this or that outside source: there would have to be a sense of the whole acting and being acted upon. It seems that such awareness requires appropriation and that machines can't do that (at least not in the precise sense that I have discussed in this blog).

The Human Question

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