Tuesday, January 4, 2011

Limits of Logic

Reality and the Limits of Logic
or, “This Essay Doesn't Exist”

At its core, philosophy is the search for the meaning of life, as approached from a variety of viewpoints. This search is conducted, to varying degrees, through the use of rational thought, or logic. As shall be shown through the examples of such notable thinkers as Renée Descartes, George Berkeley, and David Hume, however, the seemingly-infallible progression of logic is actually inherently flawed in its application, and therefore the conclusions it leads to are, at the very least, doubtful. This is not to advocate for the abandonment of logical thought; rather, it is simply to advise the temperance of any belief with the understanding of the basic tentative nature of all knowledge. In an ironic twist, the method used in this paper to disprove the infallibility of logic is, and must be, logical reasoning. While this may seem to contradict the aim of this paper, it will be shown that, indeed, it is evidence in favor of the concept of logic's limits.

Deductive reasoning in philosophy tends to follow a certain pattern, perhaps ultimately best outlined in its barest form in Descartes' Meditations on First Philosophy in Which the Existence of God and the Distinction between the Soul and the Body Are Demonstrated (hereafter to be referred to as Meditations), in which he applies skeptical thought to not only the conclusions that he has come to during his life, but also the bases of those conclusions. This method of deductive reasoning, informed by his basic skepticism and doubt, is a particularly effective one for the purpose of discerning reality, as it allows one to let go of one's presuppositions and forces one to prove again any beliefs, rather than bringing what one assumes to be true into one's thought process. Indeed, the title of Descartes' first Meditation is “Concerning Those Things That Can Be Called Into Doubt”. In it, he begins with an explanation for his thought experimentation, an explanation as good as any at bringing to light the merits of logic proceeding from nothing, or “re-proving”. Descartes writes that he has come to realize “how numerous were the false opinions that in [his] youth [he] had taken to be true, and thus how doubtful were all those that [he] has subsequently built upon them.” (Descartes, 69, emphasis mine) Descartes realizes that, logically, if he cannot confirm the truth of the “opinions” of his youth—which could include not only his beliefs but also what he was taught and what he reasoned—and if, inevitably, the beliefs he holds are founded upon those opinions, than it follows that he cannot confirm the truth of what he now believes to be true. This is the beginning of his logical process; he states that he “would do well to. . . pretend for a time that these opinions are wholly false and imaginary” in spite of his belief that, while doubtful, his opinions are “nevertheless highly probable.” (Descartes, 71)

Proceeding from this realization, Descartes attempts to determine how he can confirm the truth or existence of anything, as his previous method of assuming based simply on perception had proven false. Having discarded perceptions, however, Descartes does not discard his belief in God. Descartes' justification for the existence of God is his belief that all concepts are derived from perception. For example, he can hold the conception of substance because he observes he himself to exist as substance. In the case of God, however, this theory doesn't hold water, as Descartes, being a finite being, thinks he cannot conceive of an infinite being on his own, having no experience or perception to base the idea on. Therefore, in Descartes' mind, God must exist for the idea of him to do so.
While on the surface this may seem a logical idea, it is in fact one that makes a number of assumptions. Descartes asserts that his knowledge of the infinite is in fact more objective and whole than his knowledge of “darkness” as an absence of light or “rest” as a “negation of motion”. In fact, Descartes argues, he “clearly understand[s] that there is more reality in an infinite substance than there is in a finite one.” (Descartes, 79) This is, however, an assertion without any real argument. Not only can the existence of infinite substances not be proven without this being true, but it cannot be true without infinite substances existing. This circular reasoning means that, in spite of the strong foundations of his logical process, Descartes' statements about the infinite nature and inherent reality of God are arbitrary and unprovable. So too is his famous assertion “Cogito ergo sum”. While it remains one of the most well-known philosophical statements of all time, it is hardly one of the best thought-out. Descartes falls victim to a fallacy that Hume will later highlight in his writings on morality: that of the transition of “is” to “ought”. No matter how much evidence Descartes accumulates (his perceptions, his reasoning, and the idea that because he thinks it logically follows that there must be a thinker) there is no logical connection between his evidence and the actuality of existence, and therefore no way to prove the “sum” part from the “cogito”.
One alternative to Descartes' arguments, and one that follows similar logical lines, is presented in George Berkeley's A Treatise Concerning the Principals of Human Knowledge. Berkeley, realizing that all he could confirm was his perception of substances, proposed that the substances themselves did not exist independent of perception. Because perception is the only thing one can experience or know of, argues Berkeley, and since even “the very patrons of matter themselves do not pretend there is any necessary connection between [existence outside of our minds or perceptions] and our ideas,” then the possibility exists that there are no “bodies” corresponding to the ideas and perceptions we hold to reflect reality. (Berkeley, 120-121) Furthermore, even our ideas of objects are defined by perceiving them. Berkeley challenges his reader to imagine an object, which would seem to be a simple task. However, all one is doing, asserts Berkeley, is imagining an object as one would perceive it. It is impossible to imagine anything “existing unconceived or unthought of”, which would be the only method in which to prove the objects to exist independent of the mind.

These assertions of Berkeley's would apparently refute the idea of an objective, infinite substance of any sort, and therefore the idea of God. After all, how could such a thing exist if indeed there is nothing that can be confirmed to exist outside of the mind? And yet, Berkeley takes almost as a given the existence of God, referring to the idea of bodies without minds as “God [creating] innumerable beings that are entirely useless.” (Berkeley, 121) This is consistent with his view of the functions of so-called “natural laws”, which he says are ideas with a steadiness, a predictability, such as the idea that “food nourishes, sleep refreshes, and fire warms.” (Berkeley, 123) To Berkeley, these “laws” are the product of the will of some sort of “great spirit”, or deity-like figure, a concept he gives no real justification for besides the inane argument that natural laws would require a great spirit to be consistent, and that by observing—subjectively, remember—consistency, one could determine the true laws governing and ordering nature. Like Descartes, Berkeley utilizes circular logic in his argument. The basis of his support of the existence of a “great spirit” is in his belief in “natural laws” which could not exist without a “great spirit” to create an orderly world in which the laws would function. Not only that, but he makes an intuitive leap that cannot be justified with the evidence he provides: having just finished showing that there is not necessarily any connection between perceptions and what truly exists, Berkeley turns around and claims that, through perception, the truth of “natural laws” can be discovered. Because he does not bring himself to doubt the existence of the “great spirit”, and therefore does not subject that idea to the same intellectual rigor that he has subjected other concepts to, Berkeley, too, fails to account for the influence of his personal beliefs on his logical conclusions.

There is, however, a third philosopher whose conclusions, while possibly less satisfying than those of Descartes and, to a lesser degree, Berkeley, are far more contextualized with the knowledge of his own—and his logic's—fallibility. At its heart, David Hume's basic argument about perception seems to reflect that of Berkeley. However, while Berkeley stopped at showing to be utterly ridiculous the idea that a substance could exist or be thought to exist unobserved or unperceived, Hume extends this theory to the self. “When [one's] perceptions are removed for any time,” argues Hume, “. . . so long am I insensible of myself and may truly be said not to exist.” (Hume, 127) Here is an immediate refutation of Descartes' “I think (or doubt), therefore I am.”; rather, Hume would argue, one thinks, and therefore there is thinking. Nothing further can be extrapolated. This is the purest logic exhibited so far by any of the three philosophers, for it denies the assumption of even the most basic belief in the self, whereas Descartes and Berkeley's arguments are essentially tautological, proceeding as they do from the idea that reason can reveal something deeper than perceptions, even though reasoning simply reveals definitions that have been arbitrarily assigned. Hume also allows, as the other philosophers were less overt in doing if indeed they did at all, for the possibility that his theory is incorrect or non-universal. He says that if any man believes that he has a different sense of himself from Hume's that there is the possibility that this other man “perceive[s] something simple and continued which he calls himself,” though he does assert that he is “certain there is no such principle in [him].” (Hume, 127) This idea of the slef—or lack thereof—is what informs the rest of Hume's philosophy.

Hume argues that the sense data of the current moment, being the only thing we can confirm that we have ever experienced, is the only evidence we can proceed from. From there, he continues on to claim that memory is merely another perception of our current state, similar to our emotions, and that it tells us nothing concrete about any sort of linear past or progression of causation. Instead, the use of memory is to define personality, as “memory along acquaints us with the continuance and extent of this succession of perceptions. . .the source of personal identity.” (Hume, 131) The conclusion Hume reaches in his Treatise of Human Nature is one that goes far beyond the notion of the self he was attempting to disprove: when he says that “the whole of this doctrine leads us to a conclusion. . . all the nice and subtle questions concerning personal identity can never possibly be decided and are to be regarded rather as grammatical than as philosophical differences,” he might as well be speaking of philosophical conclusions as a whole. (Hume, 131) Because the very manner in which these conclusions are reached can be called into doubt, so too can any conclusion itself.

Hume's philosophy, however, fails in two ways. First, he defines “self” in a rigid, antiquated manner, thus allowing for his disproving of its existence. His definition of the self as a constant being that exists at different points in time is too limited—essentially, he is setting himself up to be able to disprove it. Secondly, and perhaps more egregiously, Hume presents a theory that utterly lacks pragmatic justification. While there is no way to disprove his conjecture about the “self”, there is also no practical way to apply it. Therefore, despite its logical strengths, Hume's arguments are of no use in and of themselves.

Having exposed the faults in the reasoning of some of the most influential Western thinkers, I will now attempt to provide a compelling alternative, one that builds upon Hume's logical structure. Given that all we can know is our perceptions, and also that simply denying the self leads to a philosophy without application, I propose that the definition of reality be changed to refer to our current experience. That is to say, reality is not some great objective thing, nor is it even a subjective existence created by our perceptions. Reality is what we experience in each individual moment, and the self if the perspective from which we experience it. This concept both satisfies Hume's objections to the perception of a constant self and allows for the existence of something other than sense data in our experiences. Not only that, but it allows for debate and disagreement over the nature of the self and experience, as our fallible perceptions can be changed, and the self governing them can be as well.

Philosophy is the search for truth, always through some form of logical thought or another. In this search, however, many lose sight of the path they are treading, and forget that, in their quest to truly know anything, they must begin from knowing nothing. Even then, the fallible nature of our understanding prevents us from ever comprehending true objectivity, if indeed it exists at all. Hume said it perhaps best of all when, at the end of his Treatise, he wrote “Can I be sure that, in leaving all established opinions, I am following truth? And by what criterion shall I distinguish her, even if fortune should at last guide me on her footsteps?” (Hume, 132, emphasis mine)

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Limits of Logic by Philip Halim is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.