I will say more about this in the coming days, but for now, I want to make a bold statement that modern man (mankind, womankind) is a multidimensional creature living in a multidimensional environment but more often than not operating out of but a single dimension. Western man's emphasis on the rational is just one such path.
There are actually three components to how we know. I give them below, but I want to refer to this as an example of a trinity, which I need to explain. By trinity (lower case “t”), I mean a (pale) reflection of Trinity (uppercase T, referring to orthodox Christian doctrine of the Godhead - more later).
The word trinity is useful, if we define it to imply unity in diversity. Thus my “trinities” will have three interconnected components that make the trinity incomplete (or even nonsense) if we omit even one of the components. I think a trinity as a three legged stool, if we take away one leg we no longer have a stool.
The three components to how we know are reason, intuition and experience. Western thought, especially academia is dominated by rationality, as are certain Church groupings. But many are dominated by experience. In terms of the inner healing which is my passion, it is especially negative experiences that dominate. Finally, still others are dominated by intuition. Then there are the pairings, i.e. dominated by experience and intuition, but excluding reason etc. I am claiming that in order to have balance, we need all three.
A neutral (nonthreatening) example of how the three ways of knowing are interrelated is mathematical. I teach (point set) Topology – in many ways an extension (generalization) of calculus. What I find though, is that the student's experience of calculus, often gets in the way. It is too narrow, and often leads them down the wrong path. I tell them in addition to reason, you need to re-educate your too narrow intuition.
Einstein on the other hand, had amazing intuition. He tells the story of how he discovered the theory of relativity. He tell that he was laying on a grassy bank gazing at a sunbeam through half closed eyes and wondering what it would be like to ride on a beam of light, when the theory of relativity came to him intuitively. He then went to his lavatory and proved it. Notice the relationship here. On the one hand, it was not by a series of logical steps that he arrived at his conclusion, on the other he needed the logical steps to prove his theory. Another example of intuition is the way that mathematicians (my limited experience) arrive at theorems. We so often have conjectures (intuitive ideas of what is true), which may or may not be true. We use reason and experience (discovering examples that contradict our guesses of what is true) to arrive at what can be known.
To address the title of this post, I want to say that we will not find God by reason alone. Reason alone is insufficient to find Him. We can use reason to discover things about Him (admittedly from our presuppositions), but in the end to use a dirty word in some Christian circles, if we are to find Him, then we need to experience Him. I say more on the subject of this post in the next one “I will not believe in, or accept anything that cannot be verified by one of the five senses!”
By the way here is a question with theological implications. 'Do we discover or invent mathematics?'
Subscribe to:
Post Comments (Atom)
To start with you last question. I suggests the following answer(s).
ReplyDelete(1) We discover laws.
(2) We discover or intuit analogies for these laws in other areas where, on its face, these laws seem to make no sense.
(3) In these other areas, we invent structures that are true to their foundations (they possess the same or similar properties of older, familiar objects in these areas), while enjoying new properties which exhibit a manner of lawfulness of (1).
(3') Sometimes the lawfulness is tantalizingly similar, and we discover new lawfulness by an inventive re-imagining of the laws if (1).
I showed my son how to plot solutions to a linear equation (in two variables) as points on on a sheet of paper (a coordinate plane with origin near the bottom left corner, positive x and y values ticked). I let him discover that these lay on a line. I let him convince himself that every point on that line matched a solution, and (then) that every solution mathched some point on that line. He discovered a manner of lawfulness.
But he had solutions with negative numbers, and I deliberately made the sheet of paper (mainly) first quadrant. I told him that if every solution is a point on the line, find the points for these. Seeing the lawfulness required his inventive thought; that the line (y = x - 8) in fact extended below the page as well as above -- in two directions. He needed to be inventive in the visual representation in order to discover the full extent of the lawfulness.
"...modern man (mankind, womankind) is a multidimensional creature living in a multidimensional environment but more often than not operating out of but a single dimension."
ReplyDeleteOh yes, oh yes, oh yes!
There are things that I need to say, Phil, and this might (just might) be a small part of what your creating this blog is for. If what I feel right now truly is enthusiasm (en + theos), I trust that He will keep me in check. If not (but also if so), I trust you to keep be in check!
For reasons not worth getting into here, I will call your "dimensions" aspects. We humans, and the world we live in, are multi-aspectual.
It interests me, the hubris of authors of some introductory level psychology textbooks, who give there books such titles as
Psychology: The Science of Human Behavior"
-- as if all human behavior is behavior [psychologically "qualified" behavior, but I get ahead of myself]. Chomsky studied human linguistic behavior. Marx, Smith, Keynes and Hayek studies human economic behavior. None were psychologists, or thought themselves to be doing psychology, even as some of them recognized an important psychological side (aspect) to what they were studying.
Marx wanted to account for all human behavior in historic-economic terms, just as Freud wanted to account for all human behavior in psychic terms. Ultimately, both wanted to reduce these to a physical account (today we might say a chemico-physical account), but recognized this reduction to be outside their respective expertise.
But these are only the perhaps most glaring example of what is a near-ubiquitous desire among scientists: to account for all aspects in terms of a few. The claimed justification for it is that the result will be an account that is as simple as it is universal, notwithstanding that trying to understand why the financial crises of 2009 occurred, in terms of (say) the interaction of elementary particles, is absurd. An economic account simply cannot be reduced to a physical account, even if we assume that the latter phenomena are causally determined in every detail by the latter. Once this is understood, the radical commitment to reductionism is revealed, separate from any questions of theoretical justification.
When scientists (in the sense of theoreticians generally -- e.g. including philosophers and economists) who are not mathematicians ask themselves "what is mathematics?", they are not immune to this tendency. It has been reduced, by various thinkers, to logic, to psychology, to practical functionality, and more; though it never really is reduced in a satisfying way, and often with no more than a facile attempt.
Physicists are prone to do the same thing in their own field of expertise, and here the efforts rise to the level of a program whose results are much more elaborate and impressive even if, in the end, no more satisfying. Is a certain particle simply the reading on an instrument? If we measure its mass with two different instruments, are we measuring two different properties? Is a particle a "thing in there" -- pointing at a bubble chamber? Is a particle simply a mathematical object, satisfying a theory? Should ten billion dollars be spent on an instrument designed to detect it? Which reductionist school of thought would consider this a priority?
Now Phil, the dénouement, which I will try to keep short(er). You are interested in mathematics as a way if illustrating certain theological issues that concern you. I am speaking here of problems, and of healing, that can occur within mathematics as a discipline. This is not (or has not) been your prime focus I think, and we do not need to explore it on this blog. But I think (and hope) that you may be intrigued.
ReplyDeleteThis reductionism -- this taking some aspect of creation, and elevating to the status of lawgiver for the other aspects of creation -- also appears in mathematics, among mathematicians. I don't mean this in the sense of Hilbert believing that it is ultimately games played with marks on paper, or the sense in which many mathematicians consider their objects to be real in a kind of Platonic sense. These are serious issues, but Platonism is often more a pious notion in the back of a mathematician's mind, than something that steps in to control his or her everyday work.
[ctd]
ReplyDeleteIn all of the aspects we might plausibly list, mathematicians work primarily with two, very simple aspects: that of number, and that of space. These two are (I won't make a technical argument -- or even a nontechnical argument -- for it at this point) the most fundamental of all the aspects. You cannot have physics if there is no number and space, just as you can have no psychology without biology and physics.) So mathematical research is not entangled with (say) physics, in the way that phsyics is entangled with math. What remains as a temptation to reductionism -- at the level of practical mathematical research -- is number and space.
And the history of mathematics has seen shifts: from the arithmeticization of mathematics to its geometrizations and back again, with one side or other ascendant for recognizable historical periods. Since the invention of the calculus, this conflict has manifested itself in more sophisticated ways, as the central importance of the continuum (spatial) became manifest, and a great deal of theoretical attention was devoted to it, at a time when the ideal of arithmetization in mathematics was transcendant.
Mathematics has suffered less dramatically and obviously than other disciplines. And it might (might) be fair to say that it has suffered less grievously than others, insofar as we may wish to call anything that falls short of the glory intended for it as ungrievous. But it is the nature of many problems that the depth and significance or the problem grow as one comes to learn more of it.
Am I speaking of a Christian Mathematics? The term would be peculiar, so much so that I am uncomfortable with it. Christian Physics sounds just as odd. Christian Psychology and Christian Economics sound more plausible. What of Christian Philosophy? A philosopher, who was a Christian, once asked me, why not simply "Good Philosophy"?
There is a profoundly healing approach towards economics and psychology that identifies this kind of reductionism -- from what I said above, whether I am write or wrong, we can speak of this reductionism as a form of idolatry -- and attempts to heal it from within. The approach is common to both disciplines. The nature of the approach does not depend on the nature of the discipline -- though its purpose is to reveal and delimit the nature of the disciplines. It speaks to mathematics in the same terms as it speaks to psychology and economics, even as its effect is the unshackling of the terms of mathematics, psychology, and economics. God will be rarely mentioned in the approach, although he is at the root of it. I say, as a Christian, that he is at the root of it. It is a Christian philosophical approach which, in principle, and in its speaking of Creation (which is most of what it does), depends only on the refusal to reduce one part of Creation to another, to lord on part of Creation over another. Iin practice, it is a philosophy exercised with a heart that has been freed from this tendancy.
ReplyDeleteI have been reflecting on this approach for the past twenty years or so. It is an approach which, as an historical matter, began its development about sixty or so years ago, though it's most direct spiritual roots can be found in the century that precedes it. It is Dutch, and is still struggling to make itself known in the Anglosphere, if you will. It is a philosophical approach, but it has broken with one what has, arguably, been the one central dogma to philosophical though until that time (and even now). It rejects what it takes to be the pretended autonomy of theoretical thought.
Redemption of the sciences (and math in particular) does not involve slapping on the word of our Lord in some superficial manner. Such efforts have often led to the debasement of the disciplines in a way far more than what has been done by unbelief. In particular, with mathematics, it may seem that there is no "application of Christianity thought" to the subject other than by way of some pastiche that does not even approach the issue of what mathematics is, and what the fall has done to it. The church has done such a pastiche in many of the sciences. Seeing how the Lord can lead us to a reforming of mathematics in terms of its own inner principles can point the way to seeing what is really need in psychology and economics -- and indeed in all areas of human thought.
Having said all that, I point you to a recent talk by Danie Strauss called "The Significance of a Non-Reductionist Ontology for the Disciplines of Mathematics and Physics--An Historical and Systematic Analysis"
It addresses the problem in the context of the continuum, and may serve as a useful introduction to a Christian philosophical approach in a more general sense.
[Please accept my apologies for going into twentieth inning overtime.]
Cheers!
- Largo
Thanks Lago, interesting. I am glad that you were "en theosed" by my post. My thoughts about the question were a tad more simplistic, and mystical than yours. If the unknown answer to a research question is out there to be discovered, who put it there?
ReplyDeleteSee Steve Bishop's resources on Christian approach to Math(s).
ReplyDeleteThank you Gregory!
ReplyDelete