Infinity times zero does not equal 0. It is indeterminant.
You need to use limits. Say the number of points in a line is x. If the length of the line is L, then the width of each point is L/x. As x goes to infinity, then L/x goes to 0. But as x goes to infinity, the length (i.e., the number of points times the width of each point) goes to x * (L/x) = L.
Remember, points and lines and infinity are all abstractions. If you think about them as if they were things you could poke with a stick, then you are going to come up with some unintuitive results. However, if you keep your definitions in order (because not all infinities are the same, not all zeros are the same, etc.) then everything should work out.
I want to suggest that when a Christian says "I have faith in God" that it means something entirely different than "I believe that God exists." In the Christian sense of the term, "faith" means something like "trust" or "commitment." One could believe that God exists (or even have proof) and still not trust (have faith) in God. James says, for example, that even demons believe that God exists - but they don't have faith.
Now, I don't know about you, but I would hope that the object of my faith (that is, the thing I am putting my trust in) has at least these two characteristics: 1) is real and 2) is something worth trusting/committing to. For example, if you had to have surgery, you'd probably want some evidence that 1) the person you are seeing is actually a surgeon and 2) that this person has a good track record with the kind of surgery that you need. Having evidence of both of these things is probably the minimum you'd require in order to take the "leap" of putting your trust in the surgeon's hands. But blindly putting your faith in the first person you meet on the street doesn't seem like it is "enough" or "all that you need." Does it?
Many theologians have defined faith in a similar way as I have described above - requiring that knowledge precedes faith. I think you are right that (for the most part) a lot of atheists have a different idea of what constitutes "evidence" than religious people. For example, I agree with most people that the main arguments for God are not sound. A lot of atheists tend to think this means there is no evidence for God while I think most religious people (well, me at least) believe that they still might offer us clues (evidence, if you will) that God exists. In other words, an unsound argument could mean either 1) one or more of the premises is false, or 2) a reasonable person need not accept all the premises as true (but it might not be unreasonable to accept them, either). A lot of atheists, in my experience, seem to view God-arguments in the first way while a lot of religious people seem to view them in the second way.
Interesting that this post was brought back to the top today, since I just finished reading an article called "The Enchantments of Mammon: Notes Toward a Theological History of Capitalism" by Eugene McCarraher. He challenges the tales of disenchantment told by people like Weber and Marx. One point he makes is that we find enchantment not so much in what we know, but in how we act. Slavoj Zizek puts it this way with regards to money:
In other words, even if we don't think the world is enchanted, we may act as if the world is enchanted. MacCarraher argues that such is the case and tries to provide a "sketch of enchantment in American economic culture." From "management theory" to corporate branding, he argues that we still accept a enchanted view of economics, in deed, if not by word.
Most people (in my experience), religious or not, fully accept (let's say) 95% of what science tells us. Many people might be ignorant of various scientific theories, laws, etc. but when it comes down to it we live in a very "pro-science" culture. I have yet to find a person who has a problem with Avogadro constant or with the laws of projectile motion or thousands of other things that we call "science." Overall, given how religious the US is and given how infatuated we all are with most things scientific and technical, I find the proposition that there is a conflict between science and religion to be ludicrous at best. The few issues in science that some religious people don't accept (while fully embracing the rest of science) are framed by a few extreme people on both sides to be the all-important issues when deciding if somebody is "pro-science" or not. I think it is time to face up to the reality that most people in the Western world have quite a healthy love affair with science. Even the creation scientists and the ID folks want the things that they believe in to be considered "scientific" to the rest of society. To put all this in a slightly different way, there's a certain irony in discussions about the conflict of science and religion that take place in a society that is immersed in a techno-scientific way of thinking. Or give an analogy ... picture two kids in a chocolate factory, gorging themselves on every single piece of chocolate that comes down the conveyor belt. When a piece of white chocolate comes past, the first kid lets it pass because he really isn't a fan of white chocolate. The second kid quickly snatches it and puts it in his mouth, but then accuses the first kid of not liking chocolate. What's more, the first kid every once in a while grabs some nougat, claiming that it is the best chocolate in the factory. The second kid, of course, recognizes that nougat isn't really chocolate and this just makes him angry since he doesn't like the idea of trying to pass off nougat as chocolate. All the while, both kids continue to stuff chocolate in their mouths, even while arguing.
Somewhat relating this to the OP, generally the media loves to only look to those extremes that I talked about above. When was the last time you saw a newspaper or magazine article about a Christian who is studying the properties of (let's say) steel? You don't, because from the point of view of a typical reporter, that story is a snooze-fest. So the way I see it is that it is not so much about whether compromise is possible or not, but rather about seeing the bigger picture or both science and religion.
As far as "scientific literacy" goes, I think part of the problem is that the term has come to mean "knowing a certain number of facts that the sciences have shown us to be true." I think scientific literacy would better be seen as knowing what role science plays in a society, knowing what scientists do, etc. That's not to say that scientific facts aren't important, but rather that one can know many scientific facts and still know very little about the complex thing we call science.
I left it out because I saw it as a separate argument (one which I didn't have an objection to). And I didn't say his argument was incomplete, I said it was wrong. Showing that any particular thing isn't IC, doesn't invalidate the concept of IC (in the same way that showing any particular argument is unsound doesn't invalidate the concept of sound arguments).
The first sentence here may be true, but not because of the second and third sentences. The only thing the second and third sentences point to is that Behe incorrectly identified some structures as IC. They say nothing about the concept of IC and whether it has any validity.
The idea that there is some pure, ideal thing called "science" (i.e., "science itself" or "science proper") that can be separated from scientific institutions is wrong. The most plausible accounts (IMO) of demarcation rely on communities of experts (i.e., scientific institutions) to decide what is or is not "good science." And if you are going to characterize science as rigorously logical - as a normative enterprise - then you could stand to read a little Feyerabend. He argues that even the best candidates for "scientific norms" have been broken while scientists were practicing "good science."
Incidentally, I just finished reading a book by Peter Rollins, How (Not) to Speak of God, that argues that religious orthodoxy shouldn't be thought of as "right belief" but rather as "believing right" (that is, "believing in the right way").
Let's say we have a random number generator that produces uniformly random real numbers between 0 and 1. The probability that the generator produces the number 0.560301 next is 0. At the same time, the probability that the generator produces the number 5 next is also 0. However, the former is possible while the latter is impossible. So we can't interpret "probability of 0" to mean "impossible."
Using a frequentist approach to probability, we are talking about the limit of the number occurring over a large number of trials. So a probability of 0 could mean either:
lim x->inf 1/x
lim x->inf 0/x
Both of these will result in a probability of 0 but former still allows a possibility of the number being produced by the generator while the latter means it is impossible for the number to be produced by the generator.
PoL, I tend to agree with Angukuk. The church-goers that I know (for the most part, theologically conservative to moderate) tend to read popularized theology. My pastor reads both "academic" theology and popularizations. A lot of popularizations are geared towards how to apply theology to one's life. A lot of churches I've been to have libraries that have a variety of theology books.
And, for the record, Left Behind is fiction and I've met very few Christians who read it for anything but that (but that may say more about the Christians I know than about Christians in general - I tend to hang out with an amillenialist crowd).
About the different definitions of technology ... I wasn't implying they can be separated. I don't think technological objects can be separated from the other 3, for that matter, either. I'm just saying that there has been quite a lot written about the meanings of technology and I was curious what you meant by your two. Technology as volition is related to a lot of concepts - will, power, desire, freedom, etc. It can be seen in terms of motive - do we develop technology to help others, to master nature, to free ourselves, to increase our wealth, etc.?
My question about who "we" is stems from the fact that "we" already do have access to the "black box" of technological products - if by "we" you mean the people who design the products. I was just trying to get you to clarify a little what you meant.
My comments about the car were not merely about "complexity." I would say the same thing about "simple" tools, like a hammer, also. All technologies simultaneously open up some possibilities and close other possibilities in our very use of them. The "complexity" of the automobile culture does make this perhaps a little more apparent, but the "complexity" is not what I'm talking about.
Also, I said nothing about being "passive." I also was not advocating any sort of "precautionary principle." I also wasn't talking about sitting around waiting until all the relevant info comes in. I was talking about making an active choice to either develop or not develop certain technologies.
Also, keep in mind that very few "technology critics" are advocating "passivity." There seems to be an irrational prejudice against technology critics, on this and many other points, but thankfully Don Ihde has helped explain the task of technology critics here.
PoL, can you say a little bit more about your two meanings of "technology?" I would, following Mitcham, want to think of technology in 4 different ways - technology as object, technology as knowledge, technology as activity, and technology as volition. It sounds like your "technology as product" is like Mitcham's technology as object and your technology (as such) is a mix between his technology as knowledge and activity.
I'd also like to hear more about who "we" is. Individuals? Society? For example, when you talk about power over power, who are you talking about? Are individuals supposed to have power over power? If so, that seems like an impossible task.
Also, you argue that technological development increases power increase freedom, but you also write:
I don't know about you but "having no choice in the matter" seems to me to be an instance of technological development leading to less freedom. All I'm saying here is that technological development leads to both more freedom and less freedom - it opens up possibilities and it closes possibilities. A car, for example, is often seen as a symbol of freedom - freedom to travel where one wants, freedom not to be tied down to one place, etc. But I and many others have very little freedom as to whether we can own a car or not - we absolutely have to have one. As much as I'd like to not burn fuel, not waste my money on tune-ups and oil changes, etc., I can't really give it up because then I wouldn't be able to get to my place of employment or to the grocery store or any number of places I need to get to. The car both increases and decreases my freedom in different ways. I have very little doubt that the goals of the transhumanists would do the same thing - both increase and decrease my freedom.
I don't like your child in the river analogy for that reason. I agree with you that once a technology is developed you can't really go back and pretend it wasn't, but a child in the middle of a river can, of course, decide to go back. We can't go back, but we can choose right now where we want to go. That is the freedom we have at this moment.
I also think your understanding of Christianity is a bit naive or narrow, but that is for another thread.