The Unknowable Thing-in-Itself: A Primer on Metaphysics

Giving Hume His Due
Before totally discarding Hume, he is given a last word:

Kant strove to save truth for science by erecting a wall between the phenomenal and noumenal realms, yet this wall, by its simple prospect, did not give synthetic knowledge any greater degree of certainty. The value in Kant’s insight lay in his determination that understanding exists first in the mind and then in experience.* Our idealization of the world is a demonstration of the elastic nature inherent in intuition for constructing its understanding—it is not proof reality is rationally and objectively reductive. Hume’s skepticism cannot be completely eradicated as a result, only faulted for failing to give a full account of the intuition that led to it.

(*Husserl would not accept Hume’s stating of the case, either. Our associations of objects, either contiguously or in a series, does not begin at an atomistic level. We intend objects out of our subjective experience, since any phenomenal experience carries a potential infinity of variations of an object and its past or present contexts. What is essential is what is eminent, and of which every object must be regarded as a horizon of possibility and not a distinct thing.)

Logic versus Intuition
“Analysis is the synthesis of the whole which it divides, and synthesis the analysis of the whole which it constructs ” ~F. H. Bradley

The chief analytical philosophers, Frege and Russell, rejected Kant’s concept of synthetic a priori knowledge, though with differing agendas as to how analytic logic related to mathematics. Frege’s scheme was to provide a logical foundation for mathematics, believing mathematical concepts like numbers had distinct Platonic reality behind our world of “copies”. Russell, more circumspect about mathematics’ reach into the real world, limited his ambition. Analytical philosophers, on the whole, were positivistic, insisting rational assertions could have the weight of empirical evidence because they could be proven true by either logical or scientific proof. Analytic a priori knowledge then, which is formally true, is (and can be made) the foundation of all knowledge. This belief notwithstanding, analytical philosophy gave rise to paradox that, far from refuting Kant, added credence to his view.

In assessing Frege’s work, Russell detected a fatal flaw, leading him to articulate a class of paradoxes that can be explained by attempting to define a container in relation to its contents: A set is something that contains numbers, yet as a defining rule to determine its contents, the set cannot be counted as part of its own contents: i.e., a set cannot be a member of itself. This paradox was latent in Cantor’s “naïve” set theory, which was devised as a way of classifying infinities. Russell’s paradox ended Frege’s hope. Axiomatic Set Theory was developed to remedy the paradox, not by solving it but by avoiding it: i.e., creating rules (axioms) where deeper intuition is allowed to trump naïve logic. However, like limits to check infinity in calculus, or renormalization to check infinity in physics, this is a workaround.*

Regardless, the larger goal of grounding mathematics in logic was eventually abandoned with the arrival of Gödel’s Incompleteness Theorem,* where it was shown that a mathematical system of any complexity generates proofs that can neither be proved nor disproved within the system. Gödel’s theorem went some ways towards vindicating Kant by showing how mathematics was more “creative” (synthetic) that logical. Tarski’s equally important Undefinability Theorem was one more nail in the coffin: It proved that arithmetical truth is not defined in arithmetic itself.

Physicist John Barrow coined The Groucho Marx Effect, as though stumbling over Russell’s paradox anew in the empirical sciences. Groucho famously said, “I wouldn’t want to belong to any club that would accept me as a member,” and Barrow has observed how this Russell-like paradox predictably pops up time and again across all disciplines devoted to scientific understanding. In his view, the more we understand a problem, the more likely we are oversimplifying it. Quoting from Wikipedia: “Conversely, the closer we get to a description of reality, the more complex and incomprehensible the description becomes.”(The next round of entries will examine the empirical sciences in detail.)

(*Another example of logical indeterminacy is Turning’s Halting Problem in computational science, where a programmed machine must decide whether to run forever or turn off after an input. This problem cannot be solved with an algorithm.)

(*Wittgenstein attempted to save the Verification Principle for analytic philosophy, though to make logic hermetic required divorcing it from the empirical world. Ironically, the Verification Principle itself cannot be proven by the Verification Principle, and so falls into the very paradox it hoped to vanquish.

Ayer, in another workaround, argued 7+5=12 is analytic if and only if by the symbolic expression of “7+5=12” you mean the symbol “12”.)

Logic versus Language
The distinction between synthetic and analytic knowledge can be put thusly: Insight becomes logical after-the-fact but not before, although Kant contends that some judgments arising from synthetic insight may remain forever synthetic.

We allow the descriptive nature of words to convince us all words are analytically self-naming as ideas. A blanket of verification readily papers over ambiguity inherent in verbal concepts. The truth in statements is not deducible from definitions alone, for words often rename other words whose core concept is never objectified. Where “bird” points to something in a posteriori experience to find empirical credence, “truth” is irreducible to analysis. Regardless, we never allow vagueness in words to impede our arguments, because apriority does not simply place ideas in our heads but it also attaches value to them.

Empty versus Meaningful Tautology
Not being able to define words does not undercut their value, for the very act of naming is to make (or attempt to make) something that is synthetically true analytically true: We do not doubt the existence of things once we have named them, for the name becomes the proof.

This alludes to the self-contradictory category of knowledge Kant referred to as analytic a posteriori,* where self-naming terms, being self-referential by definition, are unconnected to experience. However, the term “cool,” where used as slang, is universally understood to mean “good.” We can talk about how cool means good without ever applying either term to anything in the real world. We need only refer to other words like “excellent,” “neat,” or “desirable” to possess command of its usage. This raises the paradoxical prospect where self-modifying words circle one another in endless conversations, and where an unnamed and unexamined value is attached to an undefined concept: i.e., cool means good means [?]. It is this unnamed [?] that propels the activity of renaming forward in pursuit of truth and understanding, which is to say there is no empirical object called “truth,” just as there is no empirical object called “necessary connection.” These notions are synthetic a priori. Thus, when we define something as “good” and mean “excellent,” value [?] gives us permission to interchange and invent terms without providing disambiguated proof of the underwriting quality in the terms.

Here we deal with tautology, which can only be made meaningful synthetically since analytic logic can only make a tautology empty as a self-naming activity that posits no value.* Example: Where analytic logic demands “2 + 2 = 4” is a tautology empty of all but logic in its renaming of one concept in another, to say “Love is everything” is a renaming universally understood as not being empty.* In the second instance, we say such verbal expressions have “the ring of truth” to them, not because the truth is logically deduced from its supposition, but because the truth is deduced from simple reflection.

(*Stephen Palmquist has made this category a particular study.)

(*Frege points out that analytic propositions can nevertheless impart useful information, such as where we discover “the Morning Star” and “the Evening Star” are the same thing. The “value” here is inferred from the propositions and is not a quality of the propositions themselves. When we say logic is “empty of value,” this is to stay true to the task logic sets for itself, which is quantitative in Nature.

Transcendentally, one may say numbers, symbols, and even the structure of logic possess inherent value: i.e., aesthetic and ontological value.

Contrary to Hume’s assertion that numbers were derived from experience, Frege believed numbers had distinct Platonic reality. Were we to remove objects as things to count, undifferentiated experience could not give us any number as a picture. Regardless, “3” would still have meaning because, as an idea in itself, it does not rely on space or spatial objects. Numbers, therefore, must be a priori and separate from experience. In the Kantian view, numbers are differentiated as rational concepts through the temporal sensibility of secession: reason orders or ranks them by this understanding.)

(*The positive value in the Noumenon will be discussed at length later.)

A Whole Greater Than The Sum Of Its Parts
Addressing the larger metaphysical question, a whole is greater than the sum of its parts in a way that is impossible to quantify, which makes it directly unknowable as a quantity.* Yet this is not the end of understanding but the beginning of an understanding that has little to do with quantity and everything to do with quality. Where Russell saw his paradox, like the enigma of infinity, as indicating something defective about an underlying premise, we can set “defect” aside and, in a fashion, find value in Frege’s allusion to higher order. Here we may define a set, not as something that is quantitatively outside its contents as an idea, but as a qualitative ideal (Value) that unifies. Where one set of questions leave off in the mind, another commences in what can best be described as differently-abled faculties.*

Kant himself believed in God, yet saw our mind’s epistemological framework for understanding reality as lending no evidence* to any argument for God’s Existence. It could not be argued God had infinite spatial or temporal dimensionality since space and time could not apply to anything other than our received world of experience. Consequently, God could not be the natural completion of a series, as in a first cause or a most perfect creation.* Kant accepts God as an inconceivable idea, yet rejects the idea we can supply God with experiential attributes. To the unintended effect of humility, and in anticipating Kierkegaard, Kant believed God could have no foundation in science or philosophy since these inquiries are limited to questions of phenomenology. However, for Kant, where knowledge in this world stops*—and because knowledge in this world stops, there is room for faith.

Schopenhauer, who did not believe in God, nevertheless believed in the noumenon; and by simple deduction refuted Kant’s contention that things as they exist in themselves are completely unknowable by demonstration of a will that, like reason, is not itself reductive of phenomena. Hegel, who rejected the noumenon outright, finds Kant’s reasoning self-defeating where he asserts that though understanding creates Nature, it cannot connect to things as they exist in themselves. Where, then, does understanding of Nature arise? Like Descartes, Hegel does not see this feat as being achievable by limited human experience alone. Something outside (objective reality) must connect directly to something inside (the mind); and are not these things the same thing? Indeed, as a Cosmic Mind is required for a Cosmos, can we not call this Cosmic Mind God?

I agree with Hegel and Descartes, although, with Schopenhauer and Kant I preserve the concept of a non-concept: i.e., a Noumenon. The point (siding with Schopenhauer) is to lend value, in addition to a kind of non-intellectual understanding, to that which is not itself strictly reasonable. Hegel rejected the idea there could be any part of reality that was hidden from our thinking, but value, again, is its own thing. The conceivable and the Inconceivable rub against each other as a question of wonder and not reason.

(*Lord Alfred Whitehead, who set out with Bertrand Russell in Principia Mathematica to ground mathematics in logic, abandoned the project upon concluding, after Einstein’s revolution in physics, that “things” are more notion than reality. Logic could not build on quicksand, though there must be, in a Platonic sense, something immutable and timeless “out there” by which our view of reality remains cohesive and consistent. What was demonstrable in this world was change or process, not things.

The germ of this philosophy is Hegelian, where the whole is inscribed in its parts, and part-thinking, though invaluable to applied science, is more thing-like than notion-like. Change is the barrier between things and notions, where one must jump from particulars to universals by metaphysics and not science, if one hopes to form a “big picture.”)

(*Does understanding the molecular composition of paper and pencil, or the physics of friction where one meets the other, really explain poetry?)

(*As pure empirical demonstration, I agree with Kant, but I will later argue reasonable arguments for God’s Existence can be made by novel applications of reason, where what reason cannot uncover is reason enough to allow for the possibility of God.)

(*Though disallowing for rational attempts at reduction to God from phenomenological concepts, Kant allowed, in theory, that God could nevertheless inform and perhaps influence our experience: He could not be a causal agent, but could be extra-causal.)

(*For Leibniz’s, to get to reality in its simplest indivisible forms [i.e. monads], we reach the end of rationality, because there is nothing left to halve, and therefore no further “cause” to extract from halving. In other words, causation can have no completion and remain rational—one has simply reached the end of explanation in arriving at a last object. Even if we accept that science can explain everything, there is a point where one either has to be satisfied with the last brick wall as an explanation, or look elsewhere for meaning.)

Beyond Kantianism
Pure Kantianism is itself a form of rational reductivism. However, his greatest contribution to philosophy, in my estimation, lies in the rationally cogent way he defined what cannot be talked about, and how it must differ significantly and profoundly from our world of sensibility. Because it exists beyond the imagination in this way, the noumenon invigorates the imagination all the more to value it.

The German Idealists (namely, Hegel, Fichte, and Schelling) rejected Kant’s idea of a noumenal realm, and with it its capacity to underwrite an empirical view of reality. They preserved Kant’s idea that our ideas are innate and shape experience, so therefore asserted rationalism over empiricism. From Fichte’s idea we freely create the world through our ideas to Hegel’s view ideas shape the world through us, ideas are, by the judgment of Idealists, the fundamental substance of reality. However, as these ideas are restricted to the phenomenal realm, how are they judged to “progress” or “evolve,” as evolve they do? And in relation to what?

Schopenhauer sought to ground Kant’s idealism in a world shortly to be revolutionized by science, yet what Kant and he could not anticipate was how the essential empirical ideas of their day (those of Newton) were not so much to be built upon in the future as displaced. Later Popper and others in the philosophy of science maintained the transcendental distinction introduced by Kant (knowledge originates in the mind), yet rejected his noumenon for different reasons than had the Idealists.

Bryan Magee is the beginning of my journey with Kant and Schopenhauer, and he pointed out the impossibility of explaining reality via realism (with or without a transcendental distinction), and how a noumenon, far from being fanciful invention, accounts for unanswerable questions that science and the philosophy of science have no interest in addressing. As far as what science is interested in, John Horgan, in The End of Science, has taken the skeptical view that theoretical science, having reached a period of diminishing empirical returns, is likely nearing an end to explanation.

I believe in the noumenon as postulated by Kant and improved by Schopenhauer. With Schopenhauer, I reject Kant’s assertion the noumenal realm is operationally unknowable. Yet against Schopenhauer—and as demonstrated by his divided mind on the subject—I believe all reality has purpose and value, and that purpose and value, originating with the noumenon, is synonymous with God or something very much like God. With the Idealists, I believe our ideas do not simply inform the nature of physical world but also reveal something ontological about their own nature. Whether through scientific inquiry, or artistic creation, these ideas endeavor to complete the Noumenal Ideal as a project in terrestrial memory; and as indestructible matter/energy can only be conversed as it changes states, so too no idea discovered in eternity is lost to eternity.

Let us now turn to science.