A Rationalist's Argument for God 

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THE LOGIC OF GOD by Andrew Dorman (c) 2013

ABSTRACT


The concept of God is typically understood as an abstract being that is beyond the domain of logic. Such a factor alone may lead a person toward disbelief. But I will demonstrate here that this factor, inconsistent with with any God, if there is one, may be more of a negative reflection on logic than the concept being analyzed, at least according to how logic is currently understood. I contend that this limitation on logic exists because there remains unacknowledged a more fundamental principle implied by those logical principles typically regarded as most foundational: Aristotle?s laws of thought. This more fundamental principle, which I will address as a unity among oppositions, will be demonstrated to withstand a wider domain than those outlined by Aristotle, and thus more logically prior. Such a more inclusive unifying factor may include all possible worlds, including absolute ideas such as the concept of God. Thus, this principle of the unity of opposition may bring even a concept such as God into the considerations of knowledge, as will be demonstrated here.

Key words: God, logic, principle of non-contradiction, contraries, laws of thought, unity of opposition


TEXT:

The study we traditionally describe as logic was predominantly formulated by a man: Aristotle, the ancient Greek philosopher. The most fundamental of these laws is that which is known as the Principle of Non-Contradiction. Aristotle himself said about the principle's importance: "Some indeed demand that even this shall be demonstrated, but ... if there are things of which one should not demand demonstration, these persons could not say what principle they maintain to be more self-evident than the present one."[1] However, in this paper, I will offer and support a more "self-evident" principle, which would be more inclusive of what may be considered logically possible. This principle to be proposed may, in fact, expand logic's domain to even include such abstract, seemingly illogical terms as "God" into a meaningful context, for example.

The principle of non-contradiction is as follows: "Nothing can both be and not be at the same time and in the same respect." Traditionally, this principle is the most basic because even if one tried to refute it, by doing so, one would still be making a definite statement. This is so because any definite statement would necessarily rule out its contradictory ? either the statement would be definitely true, or its false. Even if somebody made a claim against the principle, that person would need to use that principle by the definite nature of her claim. Evidently, then, the principle of non-contradiction is basic to any such claim -- regardless of what the claim may be.

However, for one to accept the principle of non-contradiction as the most basic principle would, in turn, would implicitly need to accept time as part of logic's foundation. Recall, Aristotle specified: "in the same time and in the same respect." The problem here is that logic is supposed to be objective and absolute, yet time appears to be relative even within the confines of our physical world. Furthermore, time would only apply to physical worlds, as time is interrelated with space. Yet logic, in order to be purely objective, is supposed to account for _any_ or _all_ possible worlds, including any non-physical possibility, which may make no use of time.

But Aristotle's logic is only fundamental of reality as it relates to time. If there were no frame of reference as to time, there would be no chance of a contradiction. So, in such a case, the law of non-contradiction would be non-applicable -- such as there would need to be another foundational law to take its place. Moreover, Aristotle's purported other laws of thought are dependent on this one. So, nor would these qualify.

Interestingly, though, in this manner, Aristotle's laws of thought may not even apply to psychological states. This is because one's feelings, intentions, motivations, and purposes aren't necessarily related to time directly, but appear to transcend time. This is most easily realized in the notion of having 'mixed feelings,' for instance.

How ironic it is that logic is so limited -- especially when we consider that such mental states (or, in general, thoughts) are the only things we have first-hand experience of, and can truly be certain of, as well -- as in their being self-validating. For instance, a visually-non-impaired person can imagine herself as being blind from birth, but she cannot know what it would be consciously like to be blind from birth, unless she was, in fact, blind from birth. Likewise, a person could feel a love-hate relationship about a thing at the same time and the same respect, yet that feeling would still be contrary, yet true and self-validated, as long as that's the way that person actually feels.

The reason why Aristotle, when he formulated these laws, didn't factor in this seemingly transcendent aspect of ourselves may be found in his ontology.  He accepted any actuality as a combination of matter and form. Furthermore, he supposed that matter is the necessary basis for any change whatsoever. In fact, Aristotle went so far to suppose that our immaterial, active intellect (nous) takes the form of what is thought of. Motivation, on the other hand, would stem more from our desires, which he distinguished from mind -- albeit Aristotle advised we should temper these desires with our reason. Pure form existed only as God, which he described as an immaterial, unchanging unmoved mover.

However, even though Aristotle tried to create a closed system of thought in his organon, his limitation on change would prove to be burdensome to such a goal when it came time to explain how such an immaterial unmoved, unchanging mover created the cosmos -- except to say that he believed the cosmos of motion to be just as eternal as God itself. Supposedly, God would have no knowledge or participation of the cosmos except as a final cause for which the cosmos itself desired. In other words, by such an account, the cosmos of motion would have more internationality than does God. This is despite Aristotle describing God as pure mind. But, for Aristotle, pure mind just thinks on thought itself. From our perspective, this would appear as inactive, if as anything at all.

So we can see here, Aristotle's account for mind is the area in which he fell short in completely developing his ideas. Namely, he doesn't explain the dynamic of how something immaterial, unchanging and inactive could create anything at all. God, even by Aristotle's own account, seems to be epiphenomenal. God may be a necessary motivation for the cosmos to move by the cosmos' love toward it, as Aristotle asserted, but one may also grow to love one's own shadow and be moved by that, as well. However, that factor would not make a shadow any more real in the world.

What his observations on actualities have missed is that our own thoughts appear to us as non-physical. That which appears to us as perceivable thoughts are content, not the thought itself. Moreover, such content is unobservable first-hand to all but the one who's having the thought. Yet even Aristotle accepted that perception does not suffice as being synonymous with thought. Perception pertains to the senses, yet a thought would be that which the perception is about. Furthermore, a thought may be completely abstract and non-sensory. In essence, then, the most evident non-physicality in existence appears to us as our own thoughts -- especially those abstractions that lay the foundation to whatever we think about in general, such as meaning itself.

The interesting thing here is that even Aristotle admitted God implies more of an abstraction than a thing-in-itself. In fact, if we consider the attributes commonly assigned to God, all-knowing, all-good, and all-powerful, then God should be described as pure, absolute intentionality -- not simply thought itself. Such attributes are the only attributes essential to any truth claim, especially when discussing truth itself: 'Knowledge' is of all things, 'goodness' relates to their value, and 'power' is the means to support or otherwise enforce such claims, non-contradictorily when applicable.

So, continuing on, the question to ask is: What would be more basic than contradiction, which would cover in its domain the non-physicality of thought, as well as possibly God itself? Well, if we examine contradictions, we notice they involve statements and, by definition, consist of propositions. Propositions, in turn, consist of terms. So what elements then make terms inconsistent, one may ask? Opposition. In fact, it's is the opposition of terms that causes inconsistencies, leading to contradiction. Thus a more fundamental principle than contradiction would involve opposition of terms: what Aristotle labeled 'contraries' -- i.e., those terms typically regarded as opposites (e.g., pleasure / pain). Such terms are of the same category, but diametrically opposed in practice.

Not surprisingly by now, though, Aristotle even incorporated time into his evaluation concerning contraries. He did so by distinguishing correlations from all other forms of contrariety by crediting only these as being interdependent. Correlations, by the way, are two-placed predicates in which one term mirrors the other, typically joined by the predicate "of." When we look at correlations, in fact, we can see what Aristotle meant by their uniqueness ? for example, "double-half": If x is "double" of y, then y is "half" of x. One _condition_ leads to the other, and vice versa. Likewise, "parent-offspring": If x is the "parent" of y, then y is the "offspring" of x. All correlations, in fact, relate to the external world, and thus, are necessarily interdependent at the same time _and_ in the same respect.

Yet, contrary to Aristotle's claim, I contend that all contraries are interdependent conceptually, at least -- that is to say, one _idea_ leads to the other and vice versa, in a timeless fashion. Aristotle seems to have misunderstood "interdependency," especially when he asserted contrary "pairs of opposition" are not _in any way_ interdependent.[2] Consider the example of day-night. If for twenty four-seven, our world only consisted of an unchanging mode of daylight, then we would not conceive of any idea of "day-time." In fact, we probably would not distinguish it as anything at all -- as there would be nothing to distinguish it from.

Essentially, all opposites, in any conceptual sense, stand as the necessary condition of the other. Contraries aren't potentially their opposites, they _are_ their opposites. This is so because each concept is linked entirely with its opposite. Opposites are only perceived as "two" when judged in relation to space-time. Only when they are associated with content do they become disjointed. A label may not refer directly to its opposite, but the concept and/or actuality would that it signifies. 

In order to put such unity into logical symbolic form, I would first suggest that any variable directly within [] or () will now signify the opposite of that variable, such as [x] standing in for the opposite of x. As such, I suggest that the formula "x and -[x] (inclusively or) [x] and -x" would properly signify the unity of opposition I am speaking of. Placed into simpler shorthand, the formula itself is comparable to the principle of excluded middle, which is "x v -x," and may likewise be used in much the same manner as the former principle, albeit its domain would be less divisive. The difference now is that the "or," in this context, is exclusively inclusive whenever the second variable is exclusively the first variable's opposite. Thus, what we now have is a principle of included middle, a unity of opposition -- a principle even more prior than non-contradiction. Meanwhile, the principle of excluded middle may stay as it is, as a lesser law.

The inherent priority of the unity of opposition is that it conceptually reflects why the actuality behind Aristotle's laws is true. In fact, such unity would be at the core limit of reality itself. This is due to the linked nature of any given statement's terms to their opposites. As stated, we can conceive of two opposites such as "He is big," and "He is not big," for instance -- we can even imagine them both being true, albeit at different times and different respects. But if it was not for the linked nature of opposition, say "big" and "small," as they are linked by definition, we wouldn't be able to know either.

Furthermore, without any such linkage between terms, we would not be able to make sense of our perceptions. For instance, without contrariety, one could no longer assert "He is not big," for example, because that statement would not mean he is any smaller necessarily. One may just as well conclude that he is too skinny, or too old, or too hungry, or warm, or sinister, or walking, etc. 'Bigness' would no longer imply a size extreme. Expanded universally, knowledge itself would be impossible without such unity. What would result if there were no unity between opposites? Only non sequiturs. Thus, even the idea of a contradiction would prove impossible.

Overall, then, the unity of opposition is more prior. Whereas the principle of non-contradiction is "basic to any definitive claim," the unity of opposition is basic to any form of definition whatsoever. This is chiefly the reason why the unity of opposition should be the core principle itself, rather than the law of non-contradiction, which would be its lesser. It is just that opposition is necessarily prior to any contradiction, as demonstrated here.

Lastly, the objectivity of such laws ought to be considered. As stated earlier, whereas the principle of non-contradiction is limited to our world, the unity of opposition is inclusive of any possible world. For instance, the latter may apply to entities more perceptive than us, if any -- perhaps those mentally agile enough to _cognitively_ experience an opposition as one, at the same time and in the same respect. But, more to the point, such a unifying law may even relate to one whom may simultaneously experience the good-bad of every event, as well as every possible world eternally, as would God.


CONCLUSION:

In conclusion then, Aristotle's logic has been shown to be unsuited to report, as he intended, on possible absolute truths, but better suited for merely contingent ones. Yet logic should define objectivity purely. The thing for one to remember here is that logic endeavors to evoke the core concepts of reality itself, not merely that of our external world. Fortunately, we have proven here a more fundamental principle than that which was previously laid out for us. This principle -- the unity of opposition -- not only is more basic, its domain may even include seemingly non-physical entities such as abstract thoughts, if not God or Gods, as well. But, most importantly, it provides greater legitimacy to the laws that Aristotle himself has formulated.

Thank you.


References

1. Aristotle. (1924) _Metaphysics_ Book IV, Part 4. Translated by W. D. Ross.
2. Aristotle. (1928) _Categories,_ Pt. 10. Translated by E. M. Edghill.



Video version:

Atheists typically claim that God is illogical. Many atheists, in fact, use this claim to discredit God. But I will demonstrate here that this claim may be more of a negative reflection on logic itself, at least according to how it's commonly understood.

What we traditionally consider as logic was predominantly formulated by a man: Aristotle, the ancient Greek philosopher. The most fundamental of these laws is that which is known as the Principle of Non-Contradiction, which stated plainly is this: "Nothing can both be and not be at the same time and in the same respect."

The principle of non-contradiction is the most basic because even if one tried to refute it, by doing so, one would still be making a definite statement that would necessarily rule out its contradictory.

Evidentally, then, the principle of non-contradiction is basic to any definitive claim -- regardless of what the claim may be. Aristotle himself said about the principle's importance (from his _Metaphysics_): "Some indeed demand that even this shall be demonstrated, but ... if there are things of which one should not demand demonstration, these persons could not say what principle they maintain to be more self-evident than the present one."

Well, i would like to bring to the table a more "self-evident" principle, and I believe by the end of the video you'll agree with me on its fundamentality.

As we've seen, at present, logic accepts time as part of its foundation. Recall, this occurred when Aristotle specified in his most basic of laws: "in the same time and in the same respect." However, logic is supposed to be objective and absolute, yet time appears to be relative even within the confines of our physical world. Furthermore, time may only apply to physical worlds per se -- as time is interrelated with space.

Yet logic, in order to be purely objective, is supposed to account for ANY or ALL POSSIBLE WORLDS, including any non-physical possibility, if such is the case. Even Aristotle would've considered this basic to the study.

The reason why Aristotle, when he formulated these laws, didn't presuppose any world beyond the physical is likely because ancient Greece was, generally, a physicalist culture. At that time, for instance, our very being was considered to consist only of four humours, all of which were physical in nature -- blood, phlegm, black bile, and yellow bile. Neither was it surprising when Empedocles considered transcendent experiences such as love and hate as fluids, for instance....

So, Aristotle's logic is only fundamental in consideration of reality being related to time. Interestingly, though, in this manner, the Principle of NC doesn't even apply to human intentionality, as one's intentions, motivations, and purposes aren't necessarily related to time directly. This is best realized in the notion of having 'mixed feelings' at the same time and in the same reflect, for instance. How ironic it is that logic is so limited, though, when we consider that intentionality (or, at least, consciousness) is the only thing we not only have first-hand experience of, but the only thing we can truly be certain of, as well (as in being self-validating).

In other words, the most universal example of non-physicality in existence are our own thoughts -- of which we experience only the content of in space-time, not the thought itself. If you don't agree with me, look at your own thoughts if you can (regardless of what you believe, or don't believe). Your experience, minus the content, would be rather undescribable.

The interesting thing here is that God, likewise, implies more of a mind than a body -- in fact, if we consider the attributes commonly assigned to God, all-knowing, all-good, and all-powerful, then God would be pure intentionality.

So, continuing on, the question to ask in regards to what is most fundamental in reality, is this: What does a contradiction consist of, then, if it, in itself, is not most basic? Well, if we examine contradictions, we notice they involve statements, and by definition, consist of propositions. Propositions, in turn, consist of terms. So what elements then make terms inconsistent, one may ask? Opposition.

Thus a more fundamental principle than contradiction would involve opposition of terms: what Aristotle labeled 'contraries' -- i.e., what's typically regarded as opposites (e.g., pleasure / pain). They're features same in kind, but diametrically opposed.

Not surprisingly, however, Aristotle even incorporated time into his evaulation of contrary terms. He did so by distinguishing correlations from all other forms of contrariety by crediting only them as being interdependent, whereas all other contraries are not. Correlations, btw, are two-placed predicates in which one is term mirrors the other, typically joined by the predicate "of.' When we look at correlations, in fact, we can see what Aristotle meant by their uniqueness -- for example, "double-half": If x is "double" of y, then y is "half" of x. Likewise, "parent-offspring": If x is the "parent" of y, then y is the "offspring" of x. All correlations, in fact, relate to the external world, and thus, are necessarily interdependent at the same time _and_ in the same respect.

Yet, all contraries are interdependent conceptually, at least -- that is to say, in a timeless fashion. Aristotle seems to have misunderstood "interdependency," especially when he said contrary "pairs of opposition" are not _in any way_ interdependent. Consider the example of day-night. If for 24-7 all we had was an unchanging mode of daylight, then we would not conceive of the idea of "daytime". In fact, we probably wouldn't distinguish it as anything at all -- as there would be nothing to distinguish it from.

Hypothetically, Aristotle may have proposed the distinction because he believed all things consist of contraries  (i.e., things may turn into their opposites). So if correlations weren't to be distinguished from other contraries conceptually, then that would imply that all of reality is relative. That idea may have been inconceivable back in Aristotle's day, but hardly is it so in this day-in-age. In fact, it appears that everything in the physical world is relative, including space-time. The only that fundamentally remains constant in reality is the opposite of constancy itself, in fact: change.

Overall, then, all opposites, in any conceptual sense, stand as the necessary condition of the other. Contraries aren't potentially their opposites, they _are_ their opposites. This is so because each concept is linked entirely with its opposite. Opposites are only perceived as "two" when judged in relation to space-time. Only when they're associated with content do they become disjointed. A label excludes its opposite, but the actuality referred to would not. 

In fact, it's the unity of opposites that reflects why the reality behind Aristotle's laws are true. Such unity would be at the core limits of reality itself. This is due to the linked nature of a given statement's terms to their opposites. As stated, we can conceive of two opposites such as "he is big," and "he is not big," for instance -- we can even imagine them both being true, albeit at different times and different respects, but if it wasn't for the linked nature of opposition, say "big" and "small," as they are linked by definition, we wouldn't be able to know either. Furthermore, without any such linkage between terms, we wouldn't be able to make sense of our perceptions. For instance, without contrariety, one could no longer assert "He's not big," for example, because that statement wouldn't mean he's any smaller necessarily. One may just as well conclude that he's too skinny, or old, or hungry, or warm, or sinister, or walking, etc. Bigness would no longer imply a size extreme.

Expanded universally, knowledge itself would be impossible without such unity. What would result if there were no unity between opposites?: only non sequiturs. Thus, even the idea of a contradiction would prove impossible. This is why the unity of opposition is more prior. Whereas the principle of non-contradiction is "basic to any definitive claim," the unity of opposition is basic to any form of opposition whatsoever.

So, essentially, the unity of opposition should be the core priniciple itself, rather than the law of non-contradiction, which would be its lesser. It's just that opposition is necessarily prior to any contradiction, as we've shown.

In conclusion, then, Aristotle's logic has been shown here to be unsuited to report, as he intended, on absolute truths, but better suited for merely contingent ones. Yet logic should define objectivity purely. The thing to remember here is that logic endeavors to evoke the core concepts of reality itself, not merely that of our external world. Fortunately, we've prohere a more fundamental principle than that which was previously laid out for us. This principle -- the unity of opposition -- not only is more basic, its domain may even include God or Gods, if need be. But, most of all, it provides greater legitimacy to the laws that Aristotle himself has

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