Project Reason is a 501(c)(3) nonprofit foundation devoted to spreading scientific knowledge and secular values in society. The foundation draws on the talents of prominent and creative thinkers in a wide range of disciplines to encourage critical thinking and erode the influence of dogmatism, superstition, and bigotry in our world.
The fact that the orderly language of mathematics is capable of describing our universe, and the fact that our brains are powerful enough to invent and utilise mathematical concepts, is often considered a compelling example of why the universe must require a designer. This is one of the more tempting theological arguments, but I’d like you to consider some points against it, and show me where I may be making wrong steps.
Essentially, I think this view is an entirely hubristic one. It seems to rest on the unwarranted (and probably unacknowledged) assumption that the human intellect is a superior one, and that the mathematics it uses is intrinsically good. It seems perfectly reasonable to think, however, that despite the wonderful efficacy of mathematics, there could be intelligences far superior to our own elsewhere in the universe with even better, even more efficient systems to understand the universe. To think that ours is special and indicative of a designer appears to place human intellect on a pedestal we can’t be sure it deserves.
Also, it seems that the awe felt at the fact mathematics works is a little entangled. Rather than viewing consciousness as arising from the world and then, at some point, suddenly, mystically capable of understanding the world through mathematics, is it not more logical to imagine that a universe based on the laws this one features, if it gives rise to consciousness, would necessarily give rise to a consciousness equipped to understand its laws? We are able to understand things mathematically because we evolved to understand our environment in order to survive and reproduce more effectively in it. If we were in some other universe with other laws, we would have evolved a completely different system, maybe a much more chaotic one to suit a more chaotic environment, and we would be marvelling at the wonderful way that our devised language of physics fits reality so well.
I can’t remember who first described the image, but I think it’s similar to the caricature that a puddle one day forms in a small hole in the ground, and it thinks to itself, “My! This hole is perfectly suited to my shape! I surely can only conclude that this hole was designed with me in mind.” I don’t think there must be a special reason why maths fits - instead, it was a necessary consequence of our evolution, and we can’t draw conclusions from our aesthetic sense that mathematics is wonderful when, in fact, it could be an unnecessarily complicated system for all we know.
The fact that the orderly language of mathematics is capable of describing our universe, and the fact that our brains are powerful enough to invent and utilise mathematical concepts, is often considered a compelling example of why the universe must require a designer.
A designer is not required. The universe we live in follows rules that make it possible to exist. Perhaps there were myriad fits and starts of universes that did not fall within the parameters necessary for long-term existence. These fizzled or blasted apart. Finally the current universe came into being, and has endured, at least thus far. This is akin to the thinking, by creationists, that the earth must have been formed by God just for us, as so many of its characteristics fulfill the “Goldilocks” criteria; that is, they are neither too much, nor too little, but just right. Our distance from the sun is one of these parameters. However, it seems clear that, had the earth not been within this “Goldilocks zone,” we simply would not be here to discuss the notion.
Essentially, I think this view is an entirely hubristic one. It seems to rest on the unwarranted (and probably unacknowledged) assumption that the human intellect is a superior one,
Our intellect is certainly superior here on earth, but as you say, not necessarily the best in the universe (or the best theoretically possible).
Also, it seems that the awe felt at the fact mathematics works is a little entangled. Rather than viewing consciousness as arising from the world and then, at some point, suddenly, mystically capable of understanding the world through mathematics, is it not more logical to imagine that a universe based on the laws this one features, if it gives rise to consciousness, would necessarily give rise to a consciousness equipped to understand its laws? We are able to understand things mathematically because we evolved to understand our environment in order to survive and reproduce more effectively in it.
Other species also understand the laws of mathematics, though intuitively. A bird understands aerodynamics viscerally. A bee understands engineering geometry instinctively. However, we are the only creatures who can apply abstract symbols to these topics to communicate them. Even for us, our intuitive or instinctual understandings are far more sophisticated than our mathematical models. (Otherwise a baby would never learn to stand and walk.)
I can’t remember who first described the image, but I think it’s similar to the caricature that a puddle one day forms in a small hole in the ground, and it thinks to itself, “My! This hole is perfectly suited to my shape! I surely can only conclude that this hole was designed with me in mind.”
An analogy can also be made for language, and it’s abstractions, reading and writing. Amazingly complex. But since they arose from us, we are able to understand.
The fact that the orderly language of mathematics is capable of describing our universe, and the fact that our brains are powerful enough to invent and utilise mathematical concepts, is often considered a compelling example of why the universe must require a designer. This is one of the more tempting theological arguments, but I’d like you to consider some points against it, and show me where I may be making wrong steps.
I suppose my problem is grasping why this is a convincing argument in the first place. Isn’t the fact that our brains are powerful more of a hint that we have a designer rather than that the universe has a designer? Can you link to the argument you’re refuting?
I don’t really disagree with anything you’ve said, apart from possibly where you suggest that the universe might necessarily give rise to a consciousness which is equipped to understand the laws of the universe.
Mathematical equations are tautological, i.e. they hold true at every case conceivable, and thus their truth value is of no importance. 2+2=4 is always true in every conceivable situation, given the correct definitions for 2, 4, +, and =. Tautologies logically bear no cause, since they have to hold true no matter the circumstance, and any proposition, even a contradiction, implies tautologies. Therefore the argument is unsound, and actually can be used to disprove a case of gods.
The fact that the orderly language of mathematics is capable of describing our universe, and the fact that our brains are powerful enough to invent and utilise mathematical concepts, is often considered a compelling example of why the universe must require a designer.
I tend to cut to the chase rather than to chase down the wrinkles and wild, winding path of the logic behind religious apologetics. It’s incumbent upon the apologist to demonstrate the alleged connection, here, between the premise and the conclusion. I see none. This is simply a non-sequitur. Of course in the hands of a “good” religious apologist it will be a rather detailed one, but until/unless a clear connection between the premise and conclusion can be soundly argued, that’s all pure window dressing—attempting a feat of epistemic sleight of mind through linguistic legerdemain.
The real problem I see in putting the time and effort into chasing all the rabbits such an apologist will loose is that it’s all just a pep rally kind of validation exercise for those who are into the particular pep rally in question. Anyone who’s not isn’t going to be impressed, and those who are will feel intense team pride at the end.
Well that, and I just don’t care much for chasing rabbits ... I do like to eat them, however, when properly prepared.
Mathematical equations are tautological, i.e. they hold true at every case conceivable, and thus their truth value is of no importance. 2+2=4 is always true in every conceivable situation, given the correct definitions for 2, 4, +, and =. Tautologies logically bear no cause, since they have to hold true no matter the circumstance, and any proposition, even a contradiction, implies tautologies. Therefore the argument is unsound, and actually can be used to disprove a case of gods.
I think that’s right. Even gods could not do the logically impossible. Mario’s god will never be able to make 2+1=4. Not even for Mario. But something like that is what it would take to make Mario’s god believable. That’s too bad for Mario.
I don’t really disagree with anything you’ve said, apart from possibly where you suggest that the universe might necessarily give rise to a consciousness which is equipped to understand the laws of the universe.
I have a slightly different take on this argument, which I will try to summarize. While the presence of laws of nature, logic and mathematics do not require a creator, they are consistent with the existence of one. We have a universe that operated according to specific laws that has led to the evolution of conscious, intelligent life (us). That these laws functioned in such a way as to create something as complex as a human brain is consistent with a purposeful process. It didn’t just lead to chaos, but it led to order - and not just mechanical order, but living, thinking, feeling units of complex order called humans, with a moral sense and a capacity for contemplating and discovering their environment and its origins. This is similar to the process that we go about in creating our most complex machines, such as robots. We make them into an image of ourselves. To say that the universe is being created in the image of its maker is entirely consistent with the evidence. Not conclusive, by any means, but consistent.
So, to reiterate, this is not a proof of a creator, but only an observation that the evidence supports. I would say that the evidence is just as strong for a cosmic beginning that involved intelligence as one that did not.
BRUCE: ...this is not a proof of a creator, but only an observation that the evidence supports.
Ah, Bruce, far be it from me to burst people’s bubbles but I think you are reading more into this than is warranted by the facts. As you say, none of the evidence proves gods. All it leaves is a last little gap for those who want gods. And with science, we know what has happened to those, don’t we? The gaps, I mean.
So, to reiterate, this is not a proof of a creator, but only an observation that the evidence supports. I would say that the evidence is just as strong for a cosmic beginning that involved intelligence as one that did not.
Occam might not agree. And a sense of god as a personal experience is irrelevant to everyone but that person, unless that sense is exported.
Mathematical equations are tautological, i.e. they hold true at every case conceivable, and thus their truth value is of no importance. 2+2=4 is always true in every conceivable situation, given the correct definitions for 2, 4, +, and =. Tautologies logically bear no cause, since they have to hold true no matter the circumstance, and any proposition, even a contradiction, implies tautologies. Therefore the argument is unsound, and actually can be used to disprove a case of gods.
Welcome. You and Burt should be something to watch.
‘Or for those who believe they have experienced God. Science has done nothing with them. It cannot speak where it cannot observe.’
Oh, the same old flapdoodle, or in Texas vernacular, horseshit, from our compartmentalizing Christian lawyer.
Bruce, why do you ‘believe’ that your experience was your premised tautological knowledge of your God, and not simple biochemistry?
You ‘choose’ faith’ and then pretend it is equal with all other opinions and choices.
That is both stupid and nuts.
Occams razor is sharper and more intellectually honest than any God concept in human history, and the only people who deny that are the people that don’t understand the simplicity of it.
