I do think there is a serious question about the nature and utility of reason, as is implied with someone's rejecting the principle of non-contradiction.
Then there’s the whole problem of religious certainty. Paul says, “I know Him whom I have believed.” And I say, “Oh yeah? And what exactly is THAT supposed to mean?”
But I don’t do it too loudly because I think I know, experientially, what he means.
The law of noncontradiction states, in the words of Aristotle, that “one cannot say of something that it is and that it is not in the same respect and at the same time”; or “It is impossible that the same thing can at the same time both belong and not belong to the same object and in the same respect” (Aristotle, Metaphysics).
By way of illustration, this law predicts that an entity cannot be and not be at the same time. (This kind of statement reminds me of the dilemma posed by Schrödinger’s cat….)
The law of non-contradiction is alleged to be neither verifiable nor falsifiable, on the ground that any proof or disproof of it must use the law itself, and thus cannot do more than beg the question.
Or to put it another way, the law of contradiction puts us in the position of cycling round and round in a system that furnishes us no way out to find a way to put our foot down on firm ground. It is a “rational” tool that in its operation hides its own “radix,” or root.
Rationality — reason, ratio, logic — implies a test of something against a more ultimate, universal criterion. Logic itself cannot provide this criterion, though it seems somehow to be in a certain sense the beneficiary and reflection of it. Otherwise, logic wouldn’t “work.”
This situation seems analogous to the situation broached by Gödel's incompleteness theorems, the first of which states that:
For any consistent formal, recursively enumerable theory that proves basic arithmetical truths, an arithmetical statement that is true, but not provable in the theory, can be constructed. That is, any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete [i.e., has universal application as an infallible tool that can give us complete, certain, truthful knowledge in all situations].In this formulation, “theory” refers to an infinite set of statements, some of which are taken as true without proof (these are called axioms), and others (called theorems) that are simply accepted as true because they are implied by the axioms [which as just noted remain in principle unproved and seemingly unprovable by means of formal science and mathematics].
There are infinitely many other statements in the theory that share Gödel’s incompleteness property of being true but not provable from the theory itself. Here again, we see a situation where we can’t “put our foot down on firm ground” as to the ultimate provenance (or providence) that ultimately governs the truth of such statements, as it manifests to human observation in the observational field of actual human observers.
So if as you say it is true that Alamo-Girl “eschews the principle of non-contradiction, so reductios wouldn’t work with her,” I definitely can see her point. Indeed, I share her conclusions: Such “reductios” only go so far, and then they simply suspend, fade away, “into thin air.”
And they will continue to be so suspended, until we finally recognize that the foundation, or root, of truth of the reality that we humans commonly experience as denizens of four-dimensional space-time, knowledge of which we so desperately seek, is not to be found within 4D space-time through any natural — or "unnatural" (e.g., magical, miraculous, symbolic, mythological, poetic, artistic, historical, or any other project that is not amenable to scientific exploration) — process.
This problem is not, it seems to me, about process in the first place. For this source transcends 4D space-time as both its creator and its ultimate organizational principle; or as Christians say, its Logos.
In short, we seek not the process, but the cause of the process.
Alamo-Girl presents her catalog of epistemological insight in hierarchical order, with the greatest truth value at the top of her well-meditated list, decreasing by degrees as one descends the list. The gamut runs from the Divine Word (Logos) to “personal imaginings.”
But we need to remember that often “personal imaginings” are also true and valid — in the degree that they are informed by principles higher in the catalog, and especially by the first.
Which is probably why you, Mad Dawg, said:
Then there’s the whole problem of religious certainty. Paul says, “I know Him whom I have believed.” And I say, “Oh yeah? And what exactly is THAT supposed to mean?”I figure you know such things “experientially” because your experience does not reduce to mere logic alone — which as just described does not declare its own ultimate source, so cannot give us “certainty” about anything since its own foundation, being undeclared, remains uncertain.But I don’t do it too loudly because I think I know, experientially, what he means.
Plus there is the fact that so much of human experience, personal and social, is extra-rational, anti-rational, and even irrational by the standards of native "common sense," and also by the standards of mathematics and logic — which are “incomplete” because what we know of these domains is confined to what we can confirm about them from direct experience in the spatio-temporal order to which we are physically accustomed.
And for all human observers, such direct knowledge must remain incomplete, partial for the simple reason that — as Alamo-Girl has pointed out — each human observer travels on a "worldline." This means that human observers do not and cannot see the world immediately "entire" from a common point of view.
This means the best we can get is a partial perspective of the "all that there is."
We are hampered in this exploration by the “modern” habit of thought that seems to preclude any possible understanding of the physical world as a world that was divinely created, and is as such an image or reflection of the divine will which brought it into existence — a will that is purposive, tending from the beginning to a final end of all things, keyed to such concerns as truth, beauty, goodness, and justice — matters that are wholly inaccessible to the techniques of modern day science, or even logic.…
It is precisely here that intelligent human beings must make the transit from “value” (i.e., a function of measurement) to “meaning” (a function of truth).
As marvelous as the achievements of organized science are, science is constitutionally incapable of addressing problems of “meaning.”
But “meaning” is what thoughtful human beings actively seek….
Many people aware of such problems understand themselves to be living in the tension between two orders of being: the natural (physical) and the spiritual (soul).
The former fits well into the description given by Newton that is now regarded as the “classical description” of the physical universe. It is with relativity theory, and quantum mechanics, that we begin to appreciate that the “classical description” does not cover all cases that have come to the attention of human beings, and with good reason: Not all such cases are reducible to, or even reconcilable to, scientific technique as it is presently constituted (e.g., methodological or metaphysical naturalism).
Further, Newtonian mechanics seems exceptionally difficult to reconcile with the idea of human liberty. Some people seem to think that this alone is sufficient reason to doubt the very existence of human liberty.
Other people say that to doubt the existence of human liberty is to be ignorant, and perhaps willfully so, of the actual empirical record of the human past and present (and presumably, future) in which free human acts have transformed persons and societies, which acts collectively constitute the historical record of humanity from the earliest extant sources to our own day.
We Christians hold that reason and free will are the natural endowment of man because it was God’s purpose to make man both reasonable and free. Strangely, it appears that if we give short shrift to the former, to reason — limited tool that it is, for the foregoing reasons — then eventually we have to pay for this with a corresponding diminution of human freedom. The “divine economy” in action here….
Anyhoot, I began this reflection with a desire to show how the complementarity principle associated with the Copenhagen School of quantum mechanics is a better formulation by which to address the contents of human experience in its connection to reality in general than the non-contradiction principle. After three pages, I still haven’t gotten there, and it seems timely to just sign off for now. But before I do, let me just state that the complementarity principle refers to two seemingly mutually exclusive entities that are both necessary for the complete description of the system which they together comprise. This is a situation where the non-contradiction principle does not and cannot apply in principle.
But for now, I’ll just close. Anyone up for a discussion about the complementarity principle can just speak up, or not as the case may be.
In any case, I hope you, dear Mad Dawg, have found something “fun” about this strange little contribution to the discussion.
You do some pretty profound thinking and I mean that as a sincere compliment.
Rationality — reason, ratio, logic — implies a test of something against a more ultimate, universal criterion. Logic itself cannot provide this criterion, though it seems somehow to be in a certain sense the beneficiary and reflection of it. Otherwise, logic wouldn’t “work.”
He maketh me to lie down in green pastures: he leadeth me beside the still waters. He restoreth my soul: he leadeth me in the paths of righteousness for his name's sake.
Yea, though I walk through the valley of the shadow of death, I will fear no evil: for thou [art] with me; thy rod and thy staff they comfort me.
Thou preparest a table before me in the presence of mine enemies: thou anointest my head with oil; my cup runneth over. Surely goodness and mercy shall follow me all the days of my life: and I will dwell in the house of the LORD for ever. - Psalms 23
Or not.
;-)