[Note: This is a continuation of the discussion from Tuesday's post on Mathematics and Religiously-Based Explanations.]
In ancient Greece a religious controversy once broke out over the square root of two. The Pythagoreans, a Hellenic organization of thinkers who believed that all things were essentially reducible to numbers, had an irrational aversion to irrational numbers. Because they believed that numbers represented a realm of invisible mathematical entities upon which the visible world depended, the Pythagoreans insisted that there could be no genuinely irrational numbers and attempted to keep such knowledge a secret. Legend has it that Hippasus of Metapontum, a disciple of Pythagoras, was at sea when he discovered that the square root of 2 is irrational. His fellow Pythagoreans, outraged by the finding, threw him overboard.
Today, of course, we are more enlightened and rarely drown mathematicians who disagree with a theory (instead she'd just be denied tenure). But while disagreements over theories may not spark a murderous rage, they are as religiously motivated and reductionist as they were in Hippasus' day. Yet for the most part, such presuppositional beliefs remain unexamined even among Christians. Although we should know better, we too often fail to understand the guiding role that religious beliefs and other presuppositions have on theory-making.
Even when the importance of Christian-based scholarship is acknowledged it is generally for the wrong reasons. While we may not use such language to describe our intentions, we tend to take a postmodern view in which we are offering an alternative "meta-narrative" to compete among a pluralism of other viewpoints. What we fail to comprehend is that the reason it is imperative for Christians to "think Christianly" about theory-making is that is essential for adequate scholarship.
This is not to say that the only worthy scholarship is that which is produced by Christians. In his infinite wisdom, God saw fit to spread the gifts of reason and science among all of the mankind. Because he knew we Christians would be spending much of our intellectual capital debating such issues as infant baptism and church structure, he enlisted non-believers to help carry the load on such areas as physics, economics, and medicine.
As generally useful as it might be, though, common grace can only carry us so far. Whereas the Christian believes that all aspects of reality* (physical, social, biological, spatial, physical, etc.,) are dependent upon God�s sustaining power and can therefore be interdependent, the unregenerate thinker will eventually claim that one aspect is identical with or depends on another.
In the previous post we saw how this worked out in the field of mathematics. Leibnitz related all aspects of reality to the mathematical. Mill reduced not only the mathematical aspect but all pretheoretical experience to the sensory aspect. In a similar manner, Russell folded the mathematical aspect into the aspect of logic while Dewey reduced it to the biological. These examples are typical of the way that presuppositions about the way that aspects of reality relate to one another control the theory-making process.
Examine any theory from the social or natural sciences that were later discredited and you will find a common thread: they all reduce at least one aspect of reality to another and treat one aspect as primary. The problem with this, as philosopher Roy Clouser notes, is that it assigns some part of creation the role of lawgiver to creation. Because the non-theists denies a role for a self-existent creator and sustainer, they must invoke some aspect of creation to perform those essential functions.
Naturally, such attempts to treat an aspect of creation as "divine" will prove futile. But the non-theist has no other choice. Forced to explain one aspect as a reduction of another (i.e., the mind reducible solely to the physical brain) they must necessarily embrace either absurdity (e.g., eliminative materialism) or logical incoherence (e.g., how does a physical object "know" another physical object?).
But Christians--charter members of the true "reality-based community"--have the ability to set the theories aright. Unlike the reductionists, we do not deify nature and so are not forced to deny some essential aspect of the natural world. We have the freedom to produce robust and coherent theories about the natural realm because we are not forced to square circles.
*These aspects of reality are more thoroughly explored by the late Christian philosopher Herman Dooyeweerd and his theory of modal aspects. Dooyeweerd believed that God created certain laws and norms of reality that were both irreducible yet interrelated. Though the list wasn't exhaustive, he spelled out 15 "spheres of human life and experience": Spatial; Kinematic; Physical (energy + mass), Biotic (life functions); Sensitive (sense, feeling, emotion); Analytical (distinction); Formative (deliberate shaping: history, culture, technology, goals and creativity); Lingual (meaning carried by symbolic); Social (social interaction); Economic (frugal use of resources); Aesthetic (harmony, surprise, fun); Juridical (due); Ethical (self-giving love, generosity); and Pistic (vision, aspiration, commitment, creed).
"But Christians--charter members of the true "reality-based community"--have the ability to set the theories aright. Unlike the reductionists, we do not deify nature and so are not forced to deny some essential aspect of the natural world. We have the freedom to produce robust and coherent theories about the natural realm because we are not forced to square circles. "
If this was some statement heard at the comedy hour it might have actually made some remote semblance of sense...the only reason christian cultists even believe they are "free" to produce "robust" and coherent" "theories" is because,like you Joe,they dont have the slightest idea of what a robust coherent theory actually IS. No christian has ever produced a working theory to explain any part of their bable than can even be tested in any way imaginable...which is one of the base component of making any theory "robust" and "coherent"...the ability to actually TEST it and subject it to falsification...christians dont have to fit squares into circles because they just invoke the unprovable biblical poof magic to pretend that squares are circles and vice versa whenever it strikes their fancy to do so. There is more intelligence in the ravings of the dumbest Pythagorean att he tail end of a binge drinking session than can be found in all the collected works of christian cultist philosophers far and wide.
I have to confess, I still fail to see the point. It sounds like the argument is that a Christian philosophy will have a different view on what math means. But the reason I don’t the point of a “Christian mathematics” is that the rules of math are the same, no matter your religion or philosophy. Regardless of personal beliefs, if you sit down and work the problem correctly, you’ll get the same answer. It may mean something different to you, or illustrate some understanding of God for you, but the answer will be the same as that calculated by a non-Christian.
Perhaps the whole point of the post has gone completely over my head, but I still fail to see the possibility of a distinctly Christian math or science, any more than Hindu, Muslim, or Confucian math and science.
"This is not to say that the only worthy scholarship is that which is produced by Christians. In his infinite wisdom, God saw fit to spread the gifts of reason and science among all of the mankind. Because he knew we Christians would be spending much of our intellectual capital debating such issues as infant baptism and church structure, he enlisted non-believers to help carry the load on such areas as physics, economics, and medicine."
This is a good point. Christians, as God's new, true humanity, should be in the business of creating and discovering. That fact that others have to take up the slack is proof of how far we've jumped off the boat.
This applies to the arts, and culture in general as well.
"Christians, as God's new, true humanity... "
wow...if thats the the absolutely dumbest thing i ve ever read in my whole life its right up there in the top 5. lol
OK what the hell is the point here? I'm not getting this entire thread
I don't get that scientists have to, as you say, "explain one aspect as a reduction of another." No doubt many have, but if doing so results in an inaccurate description of a natural phenomenon then it ultimately can be disproven (or conversely, can't be reproduced) via the scientific method. If you can't prove it or disprove it, you simply have to acknowledge it as currently not explainable or understood. Which is probably not any different than saying "God did it," because even if he did you can't say anything scientifically useful about it. Science only explains what science can explain. The rest resides in the realm of the ineffable.
It's like we used to say in economics class: "Economics doesn't explain all decision making, only rational decision making."
For the record, I believe in God. I just don't believe in Christian science. It's science or it isn't science.
Frankly, I think you've just formed a supposition about what "unregenerate" thinkers "must" do that serves a Christian conceit that doesn't square with reality.
I think it comes down to metaphysics. If the Christian God exists, then a worldview based on Christianity is right, and others are wrong in part or in whole. For the practice of science (or ____, fill in the blank), metaphysical underpinnings may not matter and adherents to various systems may come up with the same theories and answers. But in other areas, maybe not. I'm thinking ethics would be a big area of divergence.
As Joe said, "In his infinite wisdom, God saw fit to spread the gifts of reason and science among all of mankind." Some people hold beliefs their metaphysics can't justify. Heck, most of us do. But God put the world together in such a way that reason and science work for everyone, even when we reject him and make up other systems to explain his creation.
Perhaps a useful analogy might be stumbling upon a huge jigsaw puzzle someone laid out on the kitchen table. You spend an hour or two putting some pieces together. Some one else does the same. Every day you swing by you notice more and more pieces put together but you don't have enough to clearly see what the whole thing will look like.
Now some in the house may speculate that whoever put this big puzzle on the table is telling us something and when we work it all out it will make sense. Others might say it's just some pretty picture or maybe not even that.
If the puzzle is ever finished we may be able to prove or disprove one of the 'puzzle-views'. Likewise a 'puzzle-view' might actually help someone to do the hard work of finding pieces that fit together. But at the end of the day the proof is in the doing. If Joe manages to put a lot of the puzzle together because his 'puzzle-view' guides him that's great. But if Joe just annoys us every day with his ranting about the secret puzzle message and how puzzle workers must be guided by the distinctly Christian 'puzzle-view' then he is just engaging in intellectual masturbation...which is the most annoying and unfun type.
"But Christians--charter members of the true "reality-based community"--have the ability to set the theories aright."
This is funny stuff. If Captain Kirk had said this to Nomad, the poor machinf would have blown its circuits much more quickly.
"Forced to explain one aspect as a reduction of another (i.e., the mind reducible solely to the physical brain) they must necessarily embrace either absurdity (e.g., eliminative materialism) or logical incoherence (e.g., how does a physical object "know" another physical object?)."
You regularly toss off nonsense like this as if it has been proven. You have never managed to actually pin down any absurdities or logical incoherence that must needs arise from atheism and/or materialism. Even that terribly long-winded fellow from the Caribbean who used to plague this blog couldn't do it. You either have to misrepresent the atheist with non sequiturs or feign ignorance to even give the appearance of pulling it off.
What the heck do you mean by "how does a physical object "know" another physical object?"? Are you saying physical beings cannot perceive other objects?
Which is precisely while naturalistic evolution fails as a theory. It is neither testable (organisms adapting to their environment proves only adaptability, not evolution) nor is it falsifiable.
This is an interesting thread. It almost compels me to convert back to Christianity. I can't shake this nagging suspicion, however, that it isn't just a bunch of propaganda with no basis in reality.
if Joe just annoys us every day with his ranting about the secret puzzle message and how puzzle workers must be guided by the distinctly Christian 'puzzle-view' then he is just engaging in intellectual masturbation...
Yes, that's it. That's the sort of behavior that caused me to want to disassociate myself from Christianity and evangelist types. Do you think that's an accurate description of Joe Carter's post? I mean, you could be write. I can't make it heads or tails of it, frankly.
The search for a Unified World View (the work of theologians and philosophers) has been going on longer than the search the equivalent for the material universe.
And the results are much more pleasant than how some enjoy spending their private moments.
Collin
http://evangelicalperspective.blogspot.com/
All that over irrational numbers... just imagine what his compatriots would have done to him if they had been working on determining the square root of -1.
Gary and Boontoon,
Let me explain this post for you. Joe's just blowing off a little steam-it's hard being a K Street lobbyist for God....
Joe,
You have several valid data points: Leibniz, Russell, Mill, and Dewey. These are all good examples of mathematical folk who loved to ride their favorite hobbyhorse, or who, as you put it, tried to reductionize math to just one special aspect.
And of course, you are right to point out the tendency of mathematical orthodoxy to react against radically new ideas in the spirit of the Pythagoreans.
But your observations don't support your theory, which is that a specifically Christian perspective is needed to correct the other warped perspectives that might be driving math or science. You just announce your conclusion without explaining how it actually happens or how it has happened in the past.
And I would disagree with one of your premises, which is that math (and science) has been hobbled by a blind adherence to materialistic metaphysics. I am familiar with the history of math and the work of contemporary mathematicians, and I do not see what you are claiming. For every mathematician with a hobbyhorse, there a dozen other mathematicians who are happy to write journal articles poking holes in a reductionist perspective.
A real paradigm shift can be a hard sell among established mathematicians, but not because of atheism or Christianity or some other religious beliefs (like those of the Pythagoreans).
It's a hard sell because people are often reluctant to abandon what they have been familiar with for their whole careers, and mathematicians are just people after all. I would say contemporary mathematicians are, as a group, quite open to off-the-wall ideas and theories, because they tend to be the most interesting and exciting.
Do you have any examples of Christian metaphysics actually doing battle with a freakish materialistic math theory, and proving its superiority? Since that seems to be your thesis, you ought to have several, but I would be very curious to hear about even one.
I would say the weakest part of your reasoning is the following statement:
Whereas the Christian believes that all aspects of reality* (physical, social, biological, spatial, physical, etc.,) are dependent upon God's sustaining power and can therefore be interdependent, the unregenerate thinker will eventually claim that one aspect is identical with or depends on another.
I'll take the expression "unregenerate thinker" as at least partly tongue-in-cheek. The real problem here is that you are asserting that such thinkers are bound to "eventually" think in a certain way. This is pure malarkey, even if you were to slice it thin and put a nice garnish on it.
Thank you for taking an interest in math and mathematicians. The history of math is a very interesting thread in the history of culture and civilization in general.
One of my favorite equations is e^("pi" x i) + 1 = 0, which is known as Euler's identity. Do you have any favorite equations?
Cheers,
Matthew
Bahhh, I think this is less about Joe working off some steam and more about him slacking off a bit. I'd be a bit more careful if I were him. In one or two more election cycles the right wing pundit industry is poised for some serious downsizing.
Boonton,
Maybe Joe is slacking off a bit, maybe not.
What I see is Joe declining to sit on his butt and be complacent about his worldview, and deciding to sally forth against rivals that he respects in an effort to test the mettle of his metaphysics.
If the results are a little uneven, that should not be held against Joe. Rather, it is proof that he is stretching and trying new things, and I salute that.
"Which is precisely while naturalistic evolution fails as a theory. It is neither testable (organisms adapting to their environment proves only adaptability, not evolution) nor is it falsifiable."
boy,you could have saved yourself the trouble of composing an entire useless response by just admiting that you dont know Jack Sh!t about biology. Evolution is the result of organism's adaptation to their environement and then passing this ability to adapt to their offsprings. Evolution is the change of alleles in a given population over time and that change is can and HAS been mapped. evolution is constantly being tested in biology labs even as we speak and so far,it has survived no scratched that...OBLITERATED any and all attempt to falsify it by the very people who actually endorse it as a working theory. now go to be and well discuss this further when you grow up.
I've appreciated Joe's comments because they raise a point that Christians have too long overlooked. Clouser's main point - and I would STRONGLY recommend that you read all of THE MYTH OF RELIGIOUS NEUTRALITY to see the fullness of Clouser's case - is that the God of Scripture is the One who has made everything and on whom EVERYTHING DEPENDS. Therefore, could there be anything or any aspect of creation which is somehow NOT dependent on God? Add to that the radical character of sin and you have a prima facie case that all human activities (including theory-making and -using) are dependent on God and on His redemptive work. Is there a distinctively Christian mathematics? In one sense, I've yet to see it but that does not necessarily invalidate Clouser's claims. Remember common grace? It is quite possible that God has most lavishly bestowed His common grace on the numerical and physical aspects of creation - so Christian faith or lack of it would make the least difference in math and the sciences, but it could make SOME differences. For evidence of this latter claim, read the sections of Clouser's book where he gives specific examples. In one sense, all Clouser is doing is saying, from a Biblical starting point, what a number of philosophers of science have said for the past 40 years - that science is NOT pre-suppositionless.
George P.
Extending the puzzle analogy a bit, one can see how even incorrect worldviews can still motivate useful insights. The Pythagoreans were wrong to grant numbers such mystical power, yet they did make insightful contributions. A personw ho thinks the puzzle is a picture of a puppy may do a good job finding pieces that do fit together even if the picture is not a puppy.
Clouser's main point - and I would STRONGLY recommend that you read all of THE MYTH OF RELIGIOUS NEUTRALITY to see the fullness of Clouser's case - is that the God of Scripture is the One who has made everything and on whom EVERYTHING DEPENDS.
OK so despite all this intellectual huffing and puffying we basically get secular mathematics with a "because God wanted it that way" added to the end of every theorem?
I'm still not getting the point.
Joe,
If you are in town Tuesday, maybe you can walk down to Lafayette Park and mingle with the people that will be expressing their first amendment rights.
The error of reductionism is a favorite topic of mine. But I think that you are mistaken in thinking that Christians are somehow less vulnerable to these sorts of theories. Just off the top of my head, Berkeley (an Anglican Bishop) was an idealist who tried to reduce the physical world to sense impressions and Decarte was another sort of idealist who tried to reduce the physical world to geometry.
It is interesting to speculate about the sources of this intellectual disease, but I don't think you have made a very strong case that it has anything to do with Christianity.
Ooops. I was going to look up the correct spelling of Descartes but then I forgot and pressed the post button.
In one sense, all Clouser is doing is saying, from a Biblical starting point, what a number of philosophers of science have said for the past 40 years - that science is NOT pre-suppositionless.
Then what are its pre-suppositions?
Examine any theory from the social or natural sciences that were later discredited and you will find a common thread: they all reduce at least one aspect of reality to another and treat one aspect as primary. The problem with this, as philosopher Roy Clouser notes, is that it assigns some part of creation the role of lawgiver to creation. Because the non-theists denies a role for a self-existent creator and sustainer, they must invoke some aspect of creation to perform those essential functions.
Indeed it is true that science is often concerned with deducing the caues of some effect. It's a leap, though, to say that science is about identifying anything as the 'prime cause'. You can do a good job putting together a lot of jigsaw pieces by concentrating on finding pieces that fit and ignoring any ideas of what the larger puzzle looks like. In fact, often getting caught up in the larger picture, even if your 'pre-supposition' is correct, will end up getting in your way of making progress.
I think what drives many evangelical types crazy here is not that science has hidden pre-suppositions but rather that it is suppositionless and they just cannot believe anyone could honestly take such a stance. Ohh there are presuppositions but they aren't 'interesting' to the critic here. Presuppositions like the universe operates by regular rules which can be detected through observation and analysis are not what is being complained about here. What's being complained about is a lack of presuppositions such as assuming the pieces fit into some overriding story arc either explicitly theist (such as human evolution has the creation of humanity as its end goal) or atheist (human evolution is an accident therefore life can have no real meaning).
"Then what are its pre-suppositions?"
Darn good question, Boonton. If only someone would answer it. I think that since science does not presuppose the existence of a god, some religious folks consider that the same as presupposing no god. This is the same sort of faulty reasoning that leads to accusations of public schools "teaching the religion of secular humanism" because they take no position on the existence of God.