Showing posts with label Mathematics. Show all posts
Showing posts with label Mathematics. Show all posts

Monday, August 24, 2015

6 Arguments For the Existence of the Non-Physical

I often hear materialists suggest that there is "no proof" for the existence of anything immaterial. Leaving aside the fact that the smaller material things get the less "material" they actually seem, is there no other way to evidence the non-physical?

We can begin by trying to define what actually constitutes physicality.  By and large, what we mean when we say that something is physical is that it exists a) in time and space or b) in a mind. To discover the immaterial, therefore, is simply a matter of demonstrating the existence of that which is nether a nor b.  To explore this I am drawing from the work of my favorite theological philosopher, Edward Feser in his superb book, The Last Superstition. Here are some examples:


  1. The "one over many" argument.  While there may be very many examples of triangles such as scalene, obtuse and isosceles and many shades of blue such as cobalt, turquoise and ultramarine, "triangularity" and "blueness" are not reducible to any particular triangle or blue thing.  Indeed, even if there were no physical examples of any triangle or anything blue, they would still be truths that could come to be exemplified in the future.  They also can, and many times are, exemplified even when no human mind is aware of them.  Hence, triangularity, blueness and many other "universals" are neither material nor dependent on a human mind for their existence.
  2. The argument from abstract objects.  Geometry deals with perfect lines, angles, circles, etc and discovers objective facts about them.  As the facts are objective, we haven't invented them and they could not be altered (like material things).  Clearly then, they do not depend of our minds. Also, no physical objects have the perfection that geometrical ones do so clearly they do not depend on the material world.
  3. The argument from mathematics.  Like other universals, math is necessary and unchangeable - exactly the opposite of material things.  2+7=9 was true before there was a physical universe or any mind to apprehend it and would be true even after both were long gone. Another interesting twist with this one is though there is an infinite series of numbers, there is only a finite amount of physical things and mental events.  Therefore, the series of numbers can't be equated with the physical or the mental.  Take 10 minutes to listen to mathematician David Berlinski discussing this here.  
  4. The argument from the nature of propositions. A proposition like "Kurt Cobain is a member of the 27 Club" would remain true even if the entire world and all the minds in it suddenly went out of existence.  Interestingly, even if no mind or material world had ever existed, the proposition "there is neither a material world nor any human mind" would still be true - proving that it is neither material nor mental.
  5. The argument from science.  Science is the business of discovering objective mind-independent facts (though that often is not really the case).  As such, to accept the results of science is to accept the notion that there are such things as mind-independent universals.  Here's an interesting video of MIT physicist Gerald Schroeder discussing the implications of the laws of nature as universals.   
  6. The argument from words and concepts.  How is it that I understand what you mean when you say "puppy?" Clearly, there is a universal understanding of a word that is shared over and above our various utterances of it.  If one were to argue that there is no standard conception of what various words mean then we would run into some serious problems, such as the fact that it would render all communication impossible since we would never be truly using the same words - even, perhaps, when speaking to ourselves!  Would it be possible to suggest that I think about my own Pythagorean theorem and you think about yours (which is different from mine)? Obviously not.  Rather, we are sharing one universal notion.  One that is neither physical nor mental.

Granted, all of this is a tad heady and it should be acknowledged that there is a good deal of philosophical back and forth about this approach - which I think doesn't at all defeat the premise.  I strongly suggest picking up The Last Superstition and giving it a careful read.  Each chapter builds on the previous in a deep but accessible presentation that lays out what I consider to be as air tight a case as can be made for something.

Wednesday, July 23, 2014

Can Anything Be Proven?

I was taken to task recently for presenting what I have to say in too much of an authoritative tone.  It was suggested that I not attempt to offer my thoughts on various theological questions as "proofs" inasmuch as they may not be provable and that suggesting otherwise could compromise my credibility (assuming I have any to begin with) on these topics.  In hunting around for people who really do have the proper credentials to address this question I came across this video from another of my favorite theological philosophers William Lane Craig.  Here's what he had to say about the need/concept of proof:




I think his point is well taken.  There is no need to demonstrate an argument with mathematical precision for it to be valid and powerful.  In truth, the more you even push mathematical truths the more difficult it becomes to actually prove them.  From what I understand, though it seems pretty obvious, there isn't any actual proof for the premise that 1+1=2 inasmuch as it's based on axioms which are definitionally unprovable.  Pushing things even further, it's also not possible to prove that what we perceive with our brains is reliable and accurate - effectively calling into question (from an absolute proof perspective) all that we understand and believe - literally.

Therefore, inasmuch as we need to live and function in this world, we need to decide to be ok with our lack of proof.  When we cross the street, it's considered a reasonable precaution to look left, right and left again. No one attempts to produce a formal, mathematical demonstration before taking on the risks of the crossing. We also need not concern ourselves with wonder over whether or not the people who we believe to be our parents truly are or if the sun will rise tomorrow morning.  All that's needed is a coherent argument in its favor.

My general approach to God and Torah is the same - it's not a matter of scientific proof.  A better analogy would be that of a jury hearing the evidence from a civil trial.  No one in the jury was there.  They're doing their best, based on the cognitive skills they have and the evidence that's presented to reach the correct conclusion.  Post deliberation, a decision must be made.  I believe the the preponderance of evidence rests with the position of the classical theist - others do not.  Neither of us has (ultimate) proof but each of us must act based on the conclusions we draw and those actions have significant ramifications for us - both as individuals and societally.

"Just because an idea is true doesn't mean it can be proved.  And just because an idea can be proved doesn't mean it's true."

- Jonah Lehrer