I'm reposting this with a number of clarifications that are of great importance regarding the distinctions between
organic logic and alternate forms of logic, and I'm going to pull portions out of it in response to QW's ongoing confusion.
It's imperative for all Christians to get the principle of identity straight, as Christ is the universal Logos! With regard to the academic rendering of the principle of identity, which must be correctly understood first,
the following is not a subjective belief, but should be objectively and abundantly self-evident to all, especially the particulars of the expanded edition of the analogy in this post, which, by the way, touches on what Boss is so eloquently arguing.
The fact of the matter is that the nuts and bolts of constructive logic hammer the points I've been making about the principle of identity home; they do not undermine it at all as QW has suggested.
To save time, I'm gong to copy and paste portions of this in answer to some of Fox's and QW's posts.
This idea that I think I have God all figured out or am being unfair to some is bogus! It's not my mind that's closed or being dogmatic.
Objective, universally apparent truths are not by definition the stuff of dogmatism! Objective assertions regarding the framework, framework, framework, framework, framework of the cognitive facts of human apprehension relative to the problem of origin, or the objectively apparent framework, framework, framework, framework, framework serving as the starting point for questions like free will, regardless of what your personal solution might be, has nothing to do with telling you what you should believe about God. Personal opinions that might pop up here or there as asides will be in red.
Fox, I know you know what follows because I know your mind on certain particulars from other posts and threads in which you have expressed your understanding of these things. If only you would stop and carefully considered this version of the post without all that personal stuff you might realize that the notion you have in your head about what I'm doing is all wrong. Put the past away and start fresh. What have you got to lose?
Constructive/Intuitionistic logic 101
Neither organic logic nor any additional/alternative forms of logic are philosophy, in and of themselves. They're tools used by scientists, philosophers, theologians, engineers, mathematicians, linguists. . . . The fundamental nature of philosophy is the indispensable business of metaphysical definition premised on the delineations of the organic principle of identity. Unlike the vast majority of system-building philosophies,
What is it? can be objectively and universally weighed, tested or falsified as it most immediately goes to conceptualization and linguistics.
As for as system-building philosophies go . . . if it's not directly based on natural law as delineated by the principle of identity and affirmed by scripture: I've got no use for it.
What you have failed to share with the others, QW, is that the identity of constructive logic is an artificial analytic tool predicated on the organic principle of identity, as any other form of logic must necessarily be, that merely precludes double negation elimination and the law of the excluded middle from its set of axioms.
Ultimately, it's a microcosmic, alternate-world model of logic within the macrocosmic real-world model of organic logic. Notwithstanding, it's a very useful tool as it provides a means of evaluating propositions in terms of direct evidence about the real world. Also, in alternate-word mathematics, especially, this model serves to amplify organic logic's power in very much the same way that various technologies amplify our senses. It also provides alternate ways of looking at the real world that may divulge new possibilities, albeit, from negative perspectives that go back to real-world positives.
The foundational law of the principle of identity, the discrete law of identity as considered separately from its elaborations, and the law of contradiction still operate. It cannot be otherwise. But instances of excluded middles or double negation eliminations cannot be generally demonstrated, only discretely demonstrated on a case by case basis.
In organic logic, the major premise of the transcendental argument (MPTA), for example, is assigned a truth value as it's inhabited by its own objectively demonstrable proof: it cannot be falsified, as any counterargument necessarily presupposes it to be true. God exists! The principle of identity, the foundation of knowledge, universally applies! For its logical proof is unassailable.
(Now, of course, GT and QW are still making
the same unremarkable point as Jake that this does not mean that this contention is ultimately true. HELLO! AFTER FOURTEEN-HUNDRED posts. . . . In alternate-world forms of logic is the MPTA necessarily true logically or axiomatically? HELLO! AFTER FOURTEEN-HUNDRED posts. . . .
NO. IT"S NOT!
It’s regarded to be unproved. I KNOW THIS.
But don't lose sight of the fact that this observation is the ultimate counterargument that still proves the MPTA to be true in the real world of organic logic.)
Note that nothing since that last personal opinion is in red. As for those who subscribe to metaphysical anti-realism, that all is an illusion, that all logic is relative, which is not true, by the way, in organic or alternate forms of logic, as we shall see, that, therefore, nothing can be said to be objective knowledge . . . you win. I surrender. We necessarily presuppose certain things: We exist, the cosmos exists and a transcendent realm of being may exist. Fine. I mean, you know,
yawn, but fine. Carry on. . . .
As for the rest of you,
read on. . . .
In constructive logic the MPTA (in spite of the fact that it is logically true, academically, under the terms of
classical logic) cannot be assigned a truth value in terms of ultimacy because the substance of its Object does not assert any direct material evidence, only inferential evidence, namely, the cosmological order, and the inferentially apparent synchronization of our minds with the cosmological order's properties and mechanisms (more on this vital distinction below).
In other words, we've all been talking about the MPTA in terms of ultimacy, on the terms of constructive logic, all along, most of you unawares.
Instead, the MPTA would be assigned an unknown truth value, as it's not inhabited by a proof of direct evidence. It would be regarded as being valid, though not in the same sense as in organic logic, until it was disproved by direct evidence or by deducing a contradiction, and since
no contradiction can be deduced about it, it remains something that is unproven or unfalsifiable in constructive logic. This is merely the same thing as saying that currently transcendental propositions are not subject to scientific falsification.
That's nothing new!
In other words, the MPTA cannot be falsified in either of the respective worlds of logic, but for different reasons.
As I said before, because the principle of identity, which is the basis of the MPTA, is organic,
one can never escape it or opt out of it. In fact, even in doing constructive logic, one is never actually not aware of the law of the excluded middle or double negation elimination.
We simply enter into a world of logic where those aspects of organic logic are not presupposed to be axioms. That
's all.
An analogy that assumes God's existence in terms of ultimacy for the sake of illustration:
From this side of heaven, under the rules of organic logic, God exists! That is, He exists . . . logically. The truth value or logical validity of the MPTA is objectively and independently affirmed by any counterargument.
But under the rules of constructive logic/mathematics, God might or might not exist. The proposition is unprovable, but only because constructive logic requires direct evidence, i.e., the inferential evidence of established theory in science, which, by the way, is still a tricky business as certain "established theories" are arguably premised on metaphysical naturalism.
(This demonstrates why QW's thinking that science precedes philosophy is foolishness. With all due respect, it’s his notion that's “philosophical bullshit.”)
Any proposition can be considered within the world of constructive logic, but not all propositions can be assigned a truth value. Constructive logic cannot consider inferential, empirical evidence about something metaphysical . . . unless constructive logic is being applied by someone who is "standing" in the metaphysical realm of being. Theoretically, an observer beyond this mortal coil could safely assert that God exists under the rules of both organic and constructive logic, as he would be in the realm of direct evidence, not partially or wholly stuck in the inferentially evidential realm of being asserting a logical "truth" of pure reason based on the existence of the cosmological order.
And those of us who believe our being is in Christ Jesus, just like Boss is talking about, can and do assign a truth value to God's existence on the terms of constructive logic as persons who believe they are standing in the metaphysical realm of being, though still tied to this mortal coil via our physical bodies, with direct evidence and a testimony to go with it. We just can't make others experience that evidence directly and, therefore, cannot assert the rules of constructive logic in any universally objective or scientific way. Others have to open up their minds and say yes to God in order to experience this reality directly.
Can I get a witness, brothers and sisters?
In short, QW has never really been alluding to anything that constitutes a game changer as far as the principle of identity is concerned. He's simply making the very same rather unremarkable observation that all of us
with an IQ above that of a gnat have made all along: the existence of God, beyond the rules of logic and evidence of the organic principle of identity, is not demonstrable/provable in terms of ultimacy, as those proofs for God's existence are based on inferential evidence, not direct evidence, in spite of the fact that the cosmological order
does constitute direct evidence for God’s existence under the terms of organic logic.
As for the vitally important distinction: the organic laws of logic (comprehensively, the principle of identity) evince two distinct levels of being.
One of them is a scientifically falsifiable: the laws of human apprehension/thought are intrinsically organic, universally hard-wired, at the very least, in our brains by nature. Most scientists and philosophers hold this to be true with plenty of scientific evidence. This is not merely intuitively true. Hence, in constructive logic this would be assigned a truth value.
The other is a theological proposition: the laws of human apprehension/thought are ultimately grounded in God. God is the universal Principle of Identity on Whom the rational forms and logical categories of human consciousness (RFLCHC) are contingent. Ultimately, this is the reason for the apparent synchronization of the RFLCHC with the rest of the cosmological order. This proposition, of course, would only be assigned a valid, might or might not be true value in constructive logic until disproved by direct evidence or by deducing a contradiction.