When talking philosophy with my students or with nonphilosophers, it's really useful to see their facial expressions, so I can get a sense for when they've gotten what I'm trying to say, and when I need to keep explaining things. One of the things that makes philosophy blogging in nonphilosophical places so challenging is that I can't see the faces of my audience as I write, and I don't have as good a sense for how much explaining to do.
I may have overexplained a little bit in my latest post at Ezra Klein's blog, which responds to some really bad arguments against atheism that came up in an LA Times op-ed. Other than that, I'm quite happy with the post.
(Backstory: Lee Siegel, the author of the op-ed, is a really weird guy -- he had to leave The New Republic when it was discovered that he was dishonestly using aliases to defend himself in comments. In his time at TNR, he took some mean swipes at Ezra, so I'm not especially well-disposed towards him.)
Monday, October 15, 2007
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12 comments:
"Open any well-researched book of mathematics or the sciences, and you'll find plenty of true statements right there in front of you."
Neil,
Prove to me that this is truth without relying on faith that the particular instance of math or science is going to continue to be truth.
In the cases of math, it's easy -- mathematical facts aren't the kinds of things that change with time.
As for science, we just infer to the best explanation of the observed phenomena.
Neil,
In order to claim that mathematical facts aren't the kind of "things" that change with time, you would need to experience all time to make a definitive statement or qualify your statement to a given time period. Unless you have lived for billions of years and expect to live for billions more, you have no basis other than faith to claim that mathematical facts do not change with time.
With regard to science, "the best explanation of the observed phenomena???" You mean, a guess? Is that not faith?
Based on what you are telling me, your faith in math and science is no more logical or valid that a faith in God which is based on several unexplainable "miracles." Have you ever experienced a miracle?
Anonymous:
How do you get "guess" out of "the best explanation of the observed phenomena"? Of course science does involve coming up with explanations that might turn out to be wrong (which is what makes it different from faith, by the way), but that's not the same as simply guessing. At least, it seems like coming up with a theory that explains (1) why things fall down, (2) the rate at which things fall down, and (3) the motion of large bodies in space with respect to each other, is just a little bit more than guessing. For example, you can use it to predict how fast a shuttle needs to accelerate to leave the Earth's orbit. Guesses, generally, can't predict things, and if they do it's just mere luck.
Anyway, your reasoning suggests that science is all about guesses, and guesses are just like faith. You must have a LOT of faith to keep your computer running...
There's also something pretty fascinating about the idea that to know that something (like math) doesn't change over time, you have to first experience all time. It's fascinating because you're claiming that ALL knowledge, even knowledge of mathematics, is empirical knowledge. That's very scientistic of you.
But here's a question: even if you experienced all time, and mathematical facts changed at some point (which is not the same as people discovering new mathematical facts, which happens all the time), how would you know? Seriously. Imagine it. One day you get up, look outside, and it turns out that today 2+2=5? Huh?
Roman,
You stated, "Of course science does involve coming up with explanations that might turn out to be wrong."
Then how can you deny that you are operating on a faith that science is correct at any given time?
Furthermore, science works toward proving an external truth as it exists. It never claims to contain the truth, correct? The truth is external, and our limited knowledge forces us to work toward that truth. This is precisely where faith comes in. We must beleive that a truth exists and we have not yet achieved it in order for math or science to be valid. I'm not saying you need to believe in a little old man in heaven. I'm saying that you must believe that truth is external and math and science always fall short of attaining that truth, otherwise you are waisting your time.
With regard to math changing, we may not realize it has changed. If the fundamental principles of existence change, then mathmatical principles simply reflect the change and the external truth as it exists. Math is not truth in and of itself. It is just a barf of numbers, words and symbols which reflect the truth as it exists to the limit of your human ability. Faith is essential for us to continue to move ever closer to the truth.
Anonymous:
I think you are overlooking the predictive power of science. Whether or not one needs to believe that there is a truth "out there," so to speak, which science attempts to grasp, is questionable. Many people--including many scientists--don't think this is necessary. A pragmatist, for example, might think that "truth" involves a future agreement among all parties, which would involve something like perfect predictability. But one doesn't need to believe that this will actually be achieved, or that it is achievable, in order to strive for it. You claims, in other words, are based on a notion of truth as something "out there", which we are trying to approximate--a naive realism that not quite so many philosophers or scientists these days share. They might be wrong in that, of course, but it at least shows that it is not necessary to have faith as you describe it.
As for mathematics, you seem to be assuming that mathematical axioms and deductive principles (which together comprise mathematics; not a barf of numbers and symbols) are somehow dependent on empirical reality. Frankly, that seems extremely odd. That is, you are assuming that mathematical principles should be seen as reflecting some underlying reality. I have no idea how that could be possible.
If reality changed and we were not aware of it, you are suggesting, then the principles of mathematics would also change without our knowing it. There are two problems here. First, how can mathematics be a feature of mind-independent reality? That is just strange. Second, again, how could 2+2 suddenly equal 5? What would that mean? I am saying that this is not a coherent--not even an imaginable--possibility.
Roman,
I know it isn’t convenient for an atheist to admit that an external objective truth exists, but just because many scientists don’t think it is necessary to admit this doesn’t make it so. Many scientists once didn’t think it necessary to admit that the world was round. However, a commitment to an external truth proved that the world was not flat, regardless of what the scientists agreed upon. If the future agreement among all parties insisted that the world was not flat but triangular, would that make it so? That is absurd, but fun to think about and even more fun to hang your hat on if you are an atheist (wink, wink).
In order to hold to a true understanding of science and not scientism, you must admit that an objective external truth exists, and we are struggling ever closer to a better understanding of it.
With regard to math, of course math is dependent on external truth. It may offer an interesting test to try to find a way that it isn’t. However, if you find a point in which math is not dependent on external objective truth, then you have either made an error or the math formula you are using has proven to be flawed.
I think you seem to miss the point with regard to changing reality and math. My point is simply that math is not independent of reality, but strictly depends on external truth in order to make sense and be useful. If it did not conform to the external truth or reality, then it would lose its predictive power, as would science. How can a detached system predict a future reality if it is not closely linked and strictly limited by the external truth it attempts to predict? Indeed, it would lose its meaning. Again, I know this truth is inconvenient for an atheist, but it is the truth, no less. To put all faith in math or science is to miss the simple point that math and science are meaningless if they do not conform to the external truth.
My point is obviously not something like "whatever most scientists think must be right." You seemed to be suggesting earlier that you can't do science, or that you are "wasting your time" unless you believe that there is some true world out there that science is trying to grasp. My point was just that this is false: you can do science, and do it perfectly well, without this sort of faith.
Here's why: Scientific theories do two things. (1) They explain phenomena, and (2) they predict phenomena. These are connected. If a theory has no predictive power, then there is no way to verify it and it is worthless--we would have no way of knowing whether it explains anything. But now look: you can obviously try to formulate theories that have predictive power without believing that there is some true reality that you're trying to get. That kind of belief is actually completely irrelevant to scientific practice and success.
But now what you are saying is that you have to believe that there is a true world out there "in order to hold to a true understanding of science." Well, I can't argue with that. Obviously God has explicitly told you what the "true understanding" of science is, and I can't compete with that. But since your "true understanding" of science is completely irrelevant to scientific practice, efficacy, etc, it really doesn't matter all that much. But keep in mind that you are using this "true understanding" of science as a premise in an argument meant to establish that this is the true understanding of science. That's not likely to convince someone who has studied rudimentary logic.
Also, I can't see why doubting--or just not caring about--whether an objective world exists might be particularly convenient for atheists. Plenty of atheists do and have believed that an objective world exists--they just don't think that objective world contains a God. (And of course theists can doubt that an objective world exists--George Berkeley is a classic historical example.)
As for math, again you're not really offering any argument. Here's just one point: Take any mathematical formula that has been formally proven. What's interesting, is that it is really impossible to imagine what it could even mean for that formula to be false: mathematical formulae are just not the sorts of things that could, once proven, still turn out to be false, because they are proven deductively and not inductively. That's how math differs from science. But now take any theory about the external world, and it is perfectly possible that that theory might be false. Mathematics gives us necessary claims, and empirical knowledge gives us contingent ones. So math can't possibly be based on empirical knowledge (which is why you wouldn't need to experience all of time in order to get true mathematical claims, and experiencing all of time wouldn't help anyway).
Roman,
You stated, “Obviously God has explicitly told you what the ‘true understanding’ of science is, and I can't compete with that. But since your ‘true understanding’ of science is completely irrelevant to scientific practice, efficacy, etc, it really doesn't matter all that much. But keep in mind that you are using this ‘true understanding’ of science as a premise in an argument meant to establish that this is the true understanding of science.”
I have not done this. On the contrary, I am using pure reason to explain that math and science are meaningless in and of themselves, and to put all your faith in them is no more reasonable that putting your faith in anything else. Math and Science only find meaning in their reflection to the objective external truth. This is such a fundamental premise that I find it hard to comprehend how you can attempt to argue against it.
An external reality exists, and if math or science does not reflect this external reality or attempt to better understand it, then math and science would lack any meaning. The predictive power of math and science stems directly from the fact that math and science reflect the truth as it exists.
In order for you to prove that math is indeed truth in and of itself, math would need to have meaning without application. The only reason math has meaning is that it can be applied to the world.
Furthermore, the entire premise of the scientific method is to take a hypothesis and turn it into a theory. While it may prove to be a reliable theory, it never attains the level of a “truth,” because it can always be refined or proven wrong.
More importantly, the idea that truth is simply a future agreement among all parties fundamentally conflicts with reason. Here is an example:
A village in India is one mile down river of two different factories, one which tans leather and another which creates pharmaceuticals. Both are discharging a by-product into the river, and a chemical reaction is occurring in the river which causes severe illness in the lower village. Just below the village, two tributaries further dilute the chemical, making it harmless to other villages down stream. The red-cross comes in and tests the water and discovers the caustic chemical, notifies the authorities and the illnesses stop.
In this instance, the future agreement among all parties works. All parties agree that it was the chemical resulting from the two factories that was causing the illness. The truth has been discovered and can be linked to the future agreement theory.
However, what if the source of the illness is never discovered? What if the red-cross doesn’t have testing equipment which detects the caustic chemical, and the village is ravaged by illness. Eventually, the remaining members of the village move down to the lower village where people are not getting sick. Here, the external truth was never discovered and the future agreement theory breaks down.
Now imagine that a scientist develops a process to detect a chemical which doesn’t exist. What is the purpose? How can the process ever be proven if it cannot be applied? It may work in theory, but it is simply that, a theory.
Lastly, you stated, “Take any mathematical formula that has been formally proven. What's interesting, is that it is really impossible to imagine what it could even mean for that formula to be false: mathematical formulae are just not the sorts of things that could, once proven, still turn out to be false, because they are proven deductively and not inductively. “
This is the same statement you made before. Regardless of whether math is deductive or inductive, it is limited by the human minds who have created them. We only know our relatively small area of the universe and really don’t know definitively that this math works in all corners of the universe. We have never been there. Furthermore, we don’t know how physical existence changes, much like the village moving south and combining with the citizens of the lower village. Once the tributary water has entered the stream, the fundamental truth which existed up stream, while still truth in that context, is inapplicable or different in the lower village. So, math here in our little corner of the universe at this point in time seems to reflect the truth as we see it. However, in 50 billion years at the other end of the galaxy in the middle of black hole, 2+2 may in fact equal 5. We simply don’t know.
To put all your faith in math and science actually defies reason, as reason assures us that math and science are limited by our own ability to understand the external reality. So, faith is required, whether you trust gnomes, fairies, Jesus Christ or Math and Science.
Totally unrelated, but whoa:
http://chronicle.com/news/article/3335/brian-leiter-blogger-king-of-philosophy-and-law-to-move-from-texas-to-chicago
he had to leave The New Republic when it was discovered that he was dishonestly using aliases to defend himself in comments.
That is a lie! You are a slandering fraud!
Lie Siegel is the best writer of the 20th and 21st centuries combined, and he would never, NEVER do such a thing!
beware of the darkeness. the time of error awaits us.
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