Next in Wikipedia’s list of Unsolved Problems in Philosophy is the Molyneaux Problem, which asks the following:
If a man born blind, and able to distinguish by touch between a cube and a globe, were made to see, could he now tell by sight which was the cube and which the globe, before he touched them?
As the Wikipedia article itself states, this is no longer a problem for the academic field of philosophy but rather for science (arguments calling science the “natural philosophy” notwithstanding). I don’t know whether psychology has, on the whole, definitively answered this question, but it seems as though the pieces are all in place to allow a scientific and experimental investigation of the problem, leaving we pedants with time to focus on other problems.
Nextly we come to the problem that has made this post take so long to get written. I simply don’t know what to do with it. The Infinite Regression of Justification notices that, with knowledge defined as justified, true belief, we must ask after the validity of any justification, and we must justify a justification. The infinite regress here is clear, and now we must know how to deal with this.
My only personal approach is to deny binaries and absolutism. For me, a fact that is justified down the entire infinite regress would be considered “absolute knowledge.” The reality of such knowledge is up for debate, but it is not material to this discussion: most of our knowledge is not so infinitely justified, and in this view we can, I think, have a better understanding of our knowledge-base if we accept a sort of Popperian critical approach to knowledge and allow that which we know to always be, in principle, mutable. There will be those facts whose justification is so deep and, perhaps, so widely varied (such as the assurance that the floor will be under our foot when we next take a step) that our assurance of its truth is close enough to total as to be effectively immutable, but so long as we recognize that we might just indeed change our beliefs given the right new justification, we can resolve this infinite regression problem.
I’ve written about this problem as a justification for a deep analytical skepticism in the past, but that was not, I think, correct. I think instead we should not use this infinite regression as an excuse to refuse to every know anything, but rather as a justification to recognize the in-principle limitedness of our knowledge. We can then think of knowledge as a web of related facts, models, and theories that lays atop the objective world and closely resembles it, but does not match it exactly. Learning and study and experience, then, which can refine our beliefs and give us more and deeper justifications for individual truths, can bring our individual webs of knowledge into closer resemblance to absolute reality, but an actually exactly accurate map (which may or not be possible) would basically be identical to, and thus interchangeable with, absolute reality.
I know that this is less an attack on the problem of Infinite Regression and more of a loosely-tied-together rambling on related topics, but this is the closest I have to a response to this problem. It is a pain in the ass of a problem, and I think it may be at the core of the epistemological approaches strangling English-language philosophical creativity. I think the philosopher or school that can break this problem and introduce a new and vital knowledge-model will be a valuable contributor to Western thought.
To copy and paste viciously from Wikipedia,
Plato suggests, in his Theaetetus, Meno, and other dialogues, that “knowledge” may be defined as justified true belief. For over two millennia, this definition of knowledge has been reinforced and accepted by subsequent philosophers, who accepted justifiability, truth, and belief as the necessary criteria for information to earn the special designation of being “knowledge.”
In 1963, however, Edmund Gettier published an article in the periodical Analysis entitled “Is Justified True Belief Knowledge?”, offering instances of justified true belief that do not conform to the generally understood meaning of “knowledge.” Gettier’s examples hinged on instances of epistemic luck: cases where a person appears to have sound evidence for a proposition, and that proposition is in fact true, but the apparent evidence is not causally related to the proposition’s truth.
This problem provides for us a nice change of pace, in that the way I will examine this does not hinge on fuzzy categorical boundaries (although I probably could take that route and simply bitch about the category of thought-objects called “knowledge” being fuzzily defined). It seems to me as though such an attack would reduce what can be understood as a fascinating question of experience into a dry semantic debate, and the English-speaking world has been doing far too much of that this past century or so.
So the problem persists. It persists, in fact, as no shallow problem at the periphery of philosophy. It appears to be yet another one of these boundary-conditional problems, yet another one of this issues of resolution of scale; like the progress of scientific models, if we simply hone our thinking we can create a more accurate model of knowledge that derives its creative foundation from the currently accepted “justified, true belief.” But this makes the problem too easy, allowing us a apologetic “it’ll do for now”, and does not allow for the wider methodological space available to philosophy that cannot be approached under a scientific method.
In the first sense, we must criticize those philosophical directions that consider this a prescriptive problem. It is a dishonesty to try to sculpt a definition of what one can or should call “knowledge.” I think it safe to say that even philosophers who approach this problem in that vein will try to bind the scope of their definition into some resemblance of that which is called “knowledge” in ordinary conversation, otherwise the word simply becomes a vacuous word-symbol, and the resolution of this problem can stem clearly and effectively from that definition. Since any legitimate approach will attempt to bind itself to that meaning of the word which is used in daily conversation, it is most honest to simply drop the prescriptive attack and just attempt to describe what knowledge is, and not what it ought to be.
The problem so revised, we are immediately and rather gracelessly confronted with perhaps one of the most inelegant and undying problems in thought: subjectivity. “Knowledge” to me is not necessarily “knowledge” to you, and you and I can both believe ourselves to know facts which are mutually contradictory. How is this resolved? The answer to that question, I would say, is “functionally.” More specifically, in our experience of the world, knowledge is not a static entity, not a simple aggregate of information with some positively correlating operator against the real world, but it is a body of function-serving tissue. The function which knowledge serves is to provide us with a framework for realizing and operating in the world around us.
Gettier’s Problem, then, resolves itself thusly: knowledge is not “justified, true belief” as much as it is that particular reflection of the world held within the individual psyche that re-projects itself back out onto the world, shaping the way the world presents itself to the experiencing agent. With this, we can begin to break down the boundaries of the epistemological and phenomenological questions and resolve them into a single, experienced moment of understanding where knowledge and world meet at the locus of the experiencing agent. In this sense, any belief or understanding which is sufficiently compatible with the objective world as to not cause a cognitive dissonance can be considered knowledge. This allows us to respect and distance ourselves from the individually solipsistic worlds of our neighbors while continuing to exist inside our own solipsisms, while still preserving the integrity of the intersubjective and objective spaces.
With this reconceptualization of knowledge and, more specifically, the relationship between knowledge and the experiencing/knowing agent, we resolve Gettier’s Problem by cutting off the source from which it would have spawned: prescriptive definition.
There is a paradox in metamathetics that asks the thinker to conceive of “the smallest number not describable in fewer than eleven words.” The paradox arises when the thinker notes that that description itself is ten words long, and thus any number to which it refers is, indeed, describable in fewer than eleven words.
This particular paradox is shown to be a false paradox when it’s pointed out that the number doesn’t necessarily have to exist. That is, any number which it describes would be paradoxical, but if that number doesn’t exist, there is no paradox.
Thinking along these lines, however, engenders thoughts about the whole problem of paradoxes of expressibility. Medieval theologians (such as Cusanus) endorsed the notion of God as a being so great, so Maximum, that complete comprehension of Him is impossible, that we cannot possibly understand God. Similar ideas have been expressed by others (the Taoist notion that “The Tao which can be spoken is not the eternal Tao” comes to mind), but the essential notion is that one is contemplating the uncontemplatable or expressing the inexpressible.
Many observers have pointed out paradox here. This has been taken in a variety of directions, from rationalists using it as justification for a reductio the denies God, to dialetheists using these kinds of problems as justification for a worldview wherein some contradictions hold. But these vectors rely on the notion that this is a true paradox—a notion which does not, I think, hold water.
Let us take the most easily discussable instantiation of this: a concept that is inexpressible. Lao-Tzu wrote that “The Tao which can be spoken is not the eternal Tao.” This line has been translated in ways that are less paradoxical, but this is one of the most famous, and a version with which most Taoists are familiar.
The problem, as has been pointed out, is that this seems to imply that anything said about the Tao is false. If anything said about the Tao is not true, we’ve entered a sort of Liar’s Paradox, where that statement (as well as any of the other text relating to the Tao) is also not true, and therefore of zero epistemic value to us.
The failure, here, is in a confusion of accuracy with entirety. That is, the Tao is, according to Lao-Tzu, something whose fundamental nature, whose entire quality, is beyond articulation or expression. We cannot contain it in words. But that does not mean we cannot contain parts of it in words, or that it does not have some describable qualities.
Such is the case with the Tao. It is impossible to express it directly and entirely. But it is so infinite that it does include certain expressible traits, and thus we are not perjuring ourselves when we claim that the Tao cannot be spoken.
A similar chain of reasoning holds when articulating apparently paradoxical qualities attached to other objects. If we say that God is too great to be conceived of, or more directly if we define God as that which is too great to conceived of, we arise into apparent paradox by pointing out that, in thinking of “an object to be great to be conceived,” we are conceiving of God, and thus are entering paradox. But that misjudges what is happening when we conceive of something beyond conception. When we conceive of an object beyond conception, we’re instantiating a placeholder object and giving, by fiat, the quality of inconceivability. Obviously, this object will be paradoxical, because the only quality it has is its inconceivability, and thus in conceiving of it with that quality, we are conceiving of it in entirety—this stands in violation of that quality, and thus we get paradox. But God, when defined this way, is understood to be MORE than just an unconceivable object; God is Creator or the Absolute Being or whatever else you want to add to God’s totality. But one of God’s qualities is that It is beyond full conception or understanding.
Paradoxes of these sort also resolve when we remember that expression (and even, if you construct it so, conception) is a process of representation. That is, an uttered phrase points to an actual state of affairs or an actual entity; the phrase itself is separate from the actual entity. The words are as a finger, pointing to the moon. We see paradox in these articulations when we confuse the finger for the moon.
I was in the bookstore today looking at the shelves containing my soul, my heart, my dearest love, pure thought expressed under heading “Philosophy” sandwiched (perhaps ironically, perhaps fittingly) between “New Age” and “Christianity” when I realized that the results of thought are no longer useful, entertaining, illuminating, enlightening, true. I realized that now the question is modes of thought of ways of thinking of manners of discover of means to access the truth from our own power.
I thought that Hume had it right–and that article I read—we now know reason to be objectively empty; reason is built from axiomatic assumption yanked from the proverbial ass: FUCK “self-evident truth.” It just doesn’t exist (right, non-Euclidean geometry?). And I’ve known for a while now that continuing to move through the point-A to point-B machinery of logic wouldn’t serve my holistic purposes anymore and now we have to examine slices of reality of different shapes, for different purposes, from different angles and we have to–if we wish to understand deeper and appreciate more and sense greater—unhook ourselves from the bonds of reason and step into a more continuous flow that moves with a great big “bite me” in the face of discrete typographical formalisms.
Not to say that those formalisms don’t have value: they do. They’re gorgeous, they’re wonderful, they’re powerful, but they aren’t the whole damned story, are they? Of course not. Nothing is the whole story. There is no whole story. The whole story is the slice of the story at every moment from every angle summed up into this instantaneous, momentary experience of subjectivity exploded outward into concrete absolutism.
And I realized that to revolutionize thought, to think in new ways, that was the way to access step three or four or n where n is the current stage of philosophia plus one. So here I am taking a leaf out of the postmodern novel and not restricting my motions of abstraction into the logical, the reasonable, the discrete and typographical and just letting go into a flow of thought, the mind-stream as it were or psychosis or whatever you wanna call it, it’s my real.
So we flow meaninglessly perfect from this moment unto the next with fingers hammering out apparent nonsense into the digital world for your consumption if you so choose. But this nonsense, see, it makes sense to me. Or if not sense, at least it begets a manner of understanding, it communicates an idea past that which pure logic in the Aristotelian sense could deliver.
If we want to move forward we have to realize that the logical field has been holistically captured; all that’s left are the internal details. But there’s more to be thought outside the domain to logic and this is where it is, in interpretable, objectively vapid thought-vomit that stews in its own inanity and glorifies itself with its own ironic inconoclasm, shattering meta-levels all the way into the annoyingly transfinite and wishing it hadn’t missed the lecture on induction across the infinite myriad of infinities.
Think with me, my friends, and glorify in your own absolute relevance being achieved through a following through with the patterned scale of your own intellectualism. My “meaning,” my intention should no longer be the source of your understanding of my words or my understanding of your words. Let the postmodernists have their way and we, the philosophers who don’t produce our work under the title of “literature,” shall be freed even from ourselves and that, my friends, that is thought’s next level, next moment, next pirouette into the skies of the absolutely unlimited theory.
If we reject the dual thesis, we deny, by definition, a reality of separation. Whether we do this as monists who positively assert that reality is One or we do it as more literal non-dualists and simply deny that separation is a definitive and absolute quality of Being, we are moving ourselves into a mode of reasoning whose articulation requires reason prior to separation.
But a word is a symbol whose meaning is some separated thing, quality, or action. While understanding this in a hard-and-fast manner is a mistake—a word more realistically means a sort of nebulous cloud of ideas—there is still, by necessity, a separation inherent in the act of articulation. When we cast ideas or trains of thought into language, we are imposing the semantic structure on reality; many non-dualist schools of thought spend considerable effort trying to bring the student away from linguistic thinking.
If then, as is said, “The Tao which can be spoken is not the eternal Tao,” and any articulation is of its nature incorrect, why should the philosopher—as thinker, teacher, shaman, or guru—bother, then, to speak? The answer, I think, lies in the capacity of the mind to abstract.
Immediately and selfishly, the articulating process allows us to see how close we can get. It’s a way of testing our own skill in a game of man-versus-reality, to see what we can, in our cleverness, capture about a non-dual structure in a dualistic system. It allows a game of thinking that hones the skill of articulation like no other, especially if the thinker can hold in mind the pre-linguistic structure of reality during the moment of articulation.
More usefully, however, if the philosopher views a non-dual framework as a way of seeing reality that can improve the lives of others, that philosopher may attempt to articulate the inarticulable in order to help paint a rough picture of the path of thought that should be taken for the student to reach that same understanding.
This seems like an inherently elitist undertaking, and I suppose that in a very real sense it is. The supposition that the speaker has achieved some kind of “secret knowledge” that he or she is attempting to impart upon the listener is without question presumptuous. But if the speaker speaks in recognition of the validity of an infinite array of paths, and speaks with humility in the knowledge that the path which he or she speaks may not be the path for the listener, then I think that the presumption is dissipated, and that the speaker then speaks as a person offering advice to a friend.
Words, then, can become a tool that we can use to shape an idea in the mind of another; we can use them to sculpt a form and to help develop a position that, when the other person reaches out and grasps it, allows the assumption of the positionless position, and steps the person through the gateless gate.
We do not believe ourselves to be speaking truth, because we understand that speaking truth is not something that is done. We believe ourselves to be a finger pointing towards the moon, and we try to remind ourselves and the person to whom we’re talking to not confuse the finger for the moon.
It has been held that a statement and its negation cannot both be simultaneously true. It has been held that it is impossible to think unlogical thoughts. It has been held, in the extreme, that the universe must be logical and all truth resides in logical principles.
This is unlikely, at best.
To begin, the argument that a statement and its negation cannot both be simultaneously true is usually held as self-evident. It is held to be a basic tenet of logic, and we believe this to be true of the entire universe because we cannot usually make this happen in our own heads. So it is held to be true, in effect, because we cannot imagine how it could be otherwise. Logical itself, however, recognizes that the incredibility of an assertion is not enough reason to deny that assertion. In argument, if we claim that statement P must be true because we cannot conceive of how the negation of P would be true, we have entered into a fallacy known as the “Incredulity Fallacy.”
One of the basic rules of logic itself stems from this sort of incredulity.
Yes, to simultaneously hold an assertion and its opposite to be true defies rationale. But that does not mean it necessarily defines truth. Logic is a series of rules of reasoning and the results of these operations on simple sentences. But any total claim on the truth by logic stems either from logic itself or from a simple axiomatic declaration.
The value that logic has is that it is conveyable. With logic, we can easily and broadly transmit the path that we took to go from axiom or datum A to a conclusion. With logic, we can show this path to another person and they can see it and, because we have agreed upon these rules, they can see that the path follows the rules.
But in most games, there are actions that can be taken that are against the rules. Sometimes, in a sufficiently sophisticated game, we can embed games inside games, and follow the rules of the outer games in our breaking of the rules of the inner games.
Our incapacity to understand and transmit via clear rule paths non-logical thoughts and non-logical truth does not preclude non-logical states of being. The fact that nobody can paint and put on a wall a colorless green unicorn does not mean that such a beast is unimaginable. The fact that it is difficult to simultaneously hold an assertion and its negation to be true does not mean that an assertion and its negation cannot both be true. Very few people have the capacity to think and visualize four-dimensional space. Yet four-dimensional space is still very real. Most of us have trouble conceiving of and understanding imaginary and complex numbers, but they are still functional beasts that do not defy logic.
In the game of logic, it is impossible for a statement and its negation both to be simultaneously true. But this does not mean that this is so in the game of reality.
After a two-week hiatus, I present to you the second installment in my series of papers on the relationship between our knowledge and the truth.
Science, providing for us as it does a method with which we can predict and manipulate the world around us, offers a solid and concrete argument for its own possession of the truth. But we must be wary of science, in this regard, for it plays to one of our most basic intellectual drives: rationality. We seek, natively, to make sense of the world. Wittgenstein said that it is impossible to have an illogical thought, and many have contested that envisioning a “colorless green unicorn” is impossible because of the nonsense and paradox inherent in the phrase. It is, however, my contention that the position that the rational inquiry generated by science is somehow superior in its accessibility to the truth stems from an untestable chauvinism and prejudice of the mind.
Science has always been concerned with the testing and honing of its instruments and technology in order to find more accurate results, or to be surer of the accuracy of the results already received. But the sciences—indeed, most fields of inquiry—have been historically lax in testing the source of all these tools and instruments: the thinking apparatus of the scientist (or human in general). The field of study which does concern itself with this apparatus, psychology, is not even yet fully emerged and formed as a science in the Kuhnian sense, and as such science cannot yet claim to be examining its primary tool for inquiry.
This “truth” that comes out of science is marked by rationale, reason, and logical explanation. But if, as some have suggested, our minds are only capable of logical thinking (whether we actively understand the logical path taken or otherwise), it would be necessary for science to reflect that logicality, irrespective of logicality present in that which science tests.
To structure the attack slightly differently, consider this: rationalists and atheists often criticize religious justifications for the existence of God because of the circular reasoning that presents itself in some of the arguments, i.e., “God exists; I know this because the Bible says so; I can trust the Bible because it is the word of God.” However, the assumption that posits the truth of rationality (of the a priori “pure logic” sort and the a posteriori sort of which science is a major part) is equally circular: we know that the world is rational because reason matches up with our perceived perception of the world; reason and rationality stem from the mind; our access to our perception of the world is filtered through our minds; that apparatus which performs the act of reason is the same which filters and understands the world. In both circularly reasoned cases, we have the source of “truth” claiming itself to be true. The case of the human mind is even more devilishly circular, though, because as we turn to examine it for veracity and accuracy, we must examine it through the lens of our own minds, generating a device whose total accuracy and relation the real world is essentially untestable, because we need to use the device in question to test its own accuracy.
What we then find ourselves with is a situation in which we have no reference point. That is, we have no “objective” truth against which to compare our notions of truth to determine how accurate they are. We use notions like “explanation” and “prediction” to attempt to approximate a reference point so as to judge the accuracy of a scientific theory, but what that essentially amounts to is not a measure of the correlation between theory and phenomenon, but rather a measure of the correlation between theory and the prejudiced interpretation of phenomenon.
On a quick aside, it should be noted that it is, despite the loud claims of rationalists, entirely possible to entice the mind to escape rational limitations. Many Eastern religious and pseudo-religious practices aim towards exactly such a goal, and there is ample anecdotal evidence to suggest that many entheogenic practices lead relatively quickly to a temporary escape from the rational. People who have experienced such states oftentimes report intellectual and sensory abandonment of such basic presuppositions as causality and dichotomy. While this is not the place for the discussion of such matters, the fact that such experiences are possible and even relatively common among certain sectors of society is important to note when we discuss the relationship between the mind and the world and science’s role in that relationship.
Returning to the role science plays in attempting to illuminate for us some degree of truth, it has been argued that science portrays the truth of phenomena, and that its relationship to the truth of a noumenal realm is unknowable and, in the end, irrelevant. However, phenomena being understood as events as they appear to an observer, we have a very real problem once we have established the inability of an individual to judge the accuracy of their own mind: the observer can’t even be sure if the phenomenon in question is appearing a certain way. While this seems a bit ridiculous at first, we must recognize that scientific analysis of phenomena happens, by necessity, after the phenomena in question have occurred, with the scientist operating by memory and recordings. Even non-skeptics will agree that human memory is extremely fallible, and often flawed. Memory and recordings both are subject to that undetectable super-imposition of a rational prejudice discussed earlier. This moves the data used for scientific analysis into the same realm as our entire “truth” notion: those data now must exist in a truth-space without reference point. It is not that the data are not accurate, but rather that they are of unknown and unknowable accuracy.
At this point, clearly, all knowledge, not just science, is suspect. With our inability to accurately gauge the accuracy of our own minds, we cannot with any degree of precision ever know the accuracy of any data, analysis, or thought we encounter. So where does that leave science, the monolith of rational pursuits of truth? My claim: in the same world as other untestable truth pursuits.
If we roughly separate modes of thought into the rational, the intuitive, and the epiphanic, we can also roughly attach certain pursuits of truth to each category. Science would be a rational pursuit of truth, “common sense” could be considered an intuitive pursuit of truth, and religion could be considered an epiphanic pursuit of truth. In all three domains we see the exact same limitations that were considered in the discussion of science: the mechanism that we use to pursue truth has itself unknowable accuracy, leaving the pursuit in the domain of the unknowably accurate. This means that the truths originating from these various sources of knowledge have qualitatively identical claims on our acceptance of those truths as, indeed, true. That qualitatively identical value is, roughly, “indeterminable.”
Now, it should be clearly understood that I am not (nor could I possibly) argue that science or any other form of truth-seeking does not give us truth. What I claim is that we can’t know if it gives us truth. That is, the modes we use of logic and reasoning may be in perfect accordance with the modes of operation of the objective universe, but our lack of access to the objective universe—and our lack of access to an objective understanding of our own subjective mechanisms—means that we cannot possibly ever know with any degree of certainty how accurate our perceptions and thoughts are. From this examination we can state not that science does not give us truth, but rather that science gives us only unknown truth.
This is the first in a series of essays on the nature of truth and our relationship to it. Enjoy, dear readers.
A definition of science being something often discussed and hotly argued, I shall not attempt one here. Instead, a quick list of the functions of science shall be given. First, it seems clear that science purposes to approach some sort of understanding of the world. A weaker version of this thesis is that science gives us a framework within which we can operate and that we use as a filter for our interfacing with the world. Second, science allows us to make predictions about a future state based on initial conditions and the rules which we generate through the pursuit of science. Third, science allows us to manipulate the world around us and shape it as we so choose.
There is a fourth function of science, as well, that deserves mention. Science can also be a purpose unto itself. There are those for whom the scientific method of inquiry is simply a joy to behold in and of itself, and for its own sake. There are those for whom scientific inquiry is of itself a beautiful process. Indeed, I think it can be safely said that most people devoted to science are at least partially enraptured with the pursuit for that very reason. This reason, however, is more concerned with science as an aesthetic exercise than it is with science as a knowledge-oriented exercise, and it is knowledge with which I wish to deal.
It is clear how the third pursuit of science—manipulation—stems from the second pursuit—prediction. It is our ability to predict natural phenomena based on rules and initial conditions that allows us to generate those initial conditions necessary to create a desired effect.
It is further clear that science’s ability to make accurate predictions stems directly from the fact that it provides a framework within which to understand the world around us. That is, without a framework of understanding we could not possibly have a reference point from which we could being making informed guesses about the future. There can be no “informed” without “information.”
So it seems that the primary pursuit of science is to provide us with some sort of articulable understanding of phenomena that can then be used for other, secondary aims. At this point, we must ask ourselves about the nature of the phenomena that science understands and the nature of that understanding.
The phenomena that science examines are exactly that—phenomena. They are events in the world of perception, including that portion of the world whose perception is only open to us due to the advancements of science (phenomena at tiny scales, great distances, or in domains such as extremely low-frequency electromagnetic radiation serve as examples). To fall back to the Kantian dualism, it is impossible for science to investigate the “noumenal” realm, as it were. Despite the fact that science allows us to observe events that would be otherwise outside of our domain of experience, we only have phenomenal access to those events, and we cannot through science access any sort of “deeper” truth, penetrating past phenomena into noumena. Indeed, because science deals precisely with the world as we interact with it, science lacks the possibility of even determining if there exists a deeper, noumenal world.
An immediate reaction to this is to question the value of any understanding that comes from science. We must ask ourselves whether or not, given this inability of science to discern “true” nature (or even to discern whether or not there is a true nature to discern), science is inherently impotent. Stated lofty goals of “objective” understanding and a quest for “truth about the natural world” are left by the wayside, bringing the scientific pursuit back down to a trifling subject with limited and restricted power of understanding, just like any other human endeavor.
But this need not be the limiting amputation it at first appears to be. The phenomenal world is defined as the world to which we have access. Putting aside unshareable and untestable (to an outside observer) mystical and religious experiences, it is impossible for us to gain experiential access to any world beyond the phenomenal. As such, from our subjective position, it is not incorrect to act as though the phenomenal world is the only world that exists. While a “noumenal” world may in fact underlie the world which we experience, since we cannot access or interact with it, it is safe to operate as though it did not exist, much the same way the existence or non-existence of Mars is not something which most of us must take into consideration in our day-to-day activities.
As such, science can give us understanding about our world, the world in which we live. It cannot tell us about the foreign worlds to which we do not have access, but that capability is not demanded from it. Nor is it relevant to our operation inside the phenomenal world. Since we do not have to operate with consideration of the noumenal world, science can seek to give us a picture of the entire world with which we interact, and thus of our entire world.
I have already stated that science gives a framework with which we may understand the phenomena that present themselves to us. But perhaps more intriguingly, science allows us to perceive new phenomena and even to create ones that could not have existed beforehand. It is intuitively understood that science comes from the world, or rather that the world generates science. That is, the phenomena present themselves as facts and we coalesce those facts into scientific theories. But science also goes to the world, changing and manipulating existing phenomena and creating entirely new ones—television is a phenomenon impossible without scientific knowledge. In this respect we see that science as a field is not simply the extraction of information and principles from the phenomenal world, but also the injection of phenomena into the information and principles at hand.
In a very real sense, science as an exploratory field is in dialectic repartee with the phenomenal world around us. As the world shapes science, so science shapes the world.
Science itself understands the capacity for such intermingling of causation. The Heisenberg Uncertainty Principle rests on the observation that as we observe and understand certain phenomena, we must affect the objects of those phenomena and thus create change and new truths in our accessible world.
This state of dialogue between science and phenomena leads us to a question of finality. If the reader will pardon the trite expression, where does it all end? Will it ever be possible for science to fully understand all phenomena with which we can possibly come into contact? It would have to seem as though the answer would be “no.” Even if science gets a complete hold over all phenomena that could have occurred before the development of science (although we’re blurring the line between the phenomenal and noumenal here), science itself can continue to create new phenomena that puzzle the researchers involved. If the phenomenal universe operates on a finite set of principles, it is entirely possible to accept the idea that we could master all the fundamental principles, but when we observe a new phenomenon, we would still have to tease out which principles were involved in the phenomenon and how exactly they manifested.
Another roadblock to total scientific knowledge will be human activity. Even if science progresses so that it understands the basic, fundamental principles driving all phenomena, the collective ambiguity that is human nature will serve as a monstrous obstacle to total understanding of everything. The placement of the individual scientist or a collection of scientists within the fabric of society will limit the objectivity of the inquiry into human nature, and the understanding of people by people will always have very real epistemological concerns, centered around Wittgensteinian concerns about the limitations of an inherently subjective perspective.
Despite these blocks in the understanding that science can deliver, science is still providing us with a very real understanding of the world within which we operate. As such, it is fair to state that science provides us with some form of “truth” about the world. It is a truth that does not expand to all possible domains, but that does not change the fact that it is true. A triangle’s internal angles do not have to sum to one hundred and eighty degrees in any possible space, but that does not render false the assertion that a triangle in Euclidean space does have that property. In the same vein, while science may tell us nothing about any noumenal world, it does give us truth about the phenomenal world, which is by definition the domain with which science is concerned.
I am no physicist, and I don’t read physics journals. But through the swamps of academic literature, vague abstracts and summaries often reach the common man. In recent days, I’ve noticed an upswing in the amount of discussion going on in regards to models of gravity that differ from the currently accepted Einstein-Hilbert action of general relativity. From different actions that are still relativistic to completely different models of gravity that break away entirely from Einstein’s famous curved-space model.
The interest, here, lies in the fact that general relativity has been having some problems of late. Relativity and quantum mechanics both explain their respective domains extremely well—relativity usually handling the very, very large in space and quantum usually handling the very, very small. But for some time it’s been known that when the two theories intersect, problems arise. The classic example of a problem domain is the deep mechanics of black holes, where physicists must deal with systems that are very, very massive and very, very tiny.
General relativity has also led to other problems, from the Universe beginning as a singularity (which is mathematically undefinable) to the whole Dark Energy/Dark Matter problem.
In short, while general relativity brought us deeper insight into the mechanisms of gravity than any other model before it, it opened questions that have stood open for decades, defying any attempt to solve within the relativistic model.
Thomas Kuhn, the man who wrote The Structure of Scientific Revolutions, the seminal work on the growth and development of the sciences, said that when a scientific model begins defying attempts to solve certain problems, the field moves into a state of extra-ordinary science, wherein scientists begin to get more creative and daring when proposing solutions to existing problems. In science, it is usually held that theories should be minimally modified to solve new problems. That is, if a model must be modified in order to solve a new problem, the modification which least changes the model is ideal. During a period of extra-ordinary science, however, scientists will escape that rule and begin seeing what happens when drastic, radical changes are made.
If the unsolved problems are then solved by one of these drastic, radical changes to the model, we enter a period of paradigm shift, where over roughly the span of a generation (usually), the new model is adopted and then fleshed out, changing the space of the scientific discussion inside the relevant field permanently.
It appears as though we may have begun entering into gravity’s newest period of extra-ordinary science. With radical new theories of the gravitational mechanism sprouting up, the academic community as a whole will begin to be more accepting of radical changes to the model. As the academic community becomes more accepting, more scientists will be daring enough to consider radical changes. And, eventually, one model may click.
We grew up with Einstein’s general relativity as the model of that basic force which keeps us attached to the earth. In most cases, so did our parents and grandparents. But our children might not. Our children may know that gravity is the result of some emergent property of entropy or they might know that the Big Bang is part of an infinite gravitational cycle. They might know this, because science might know this. But we know that general relativity is right, don’t we? Science knows that general relativity is right, doesn’t it? It makes one question what it means to “know” something, doesn’t it?
I begin with mathematics.
The study of the vastness of numbers has led to powerfully interesting results. If we begin by examining the Naturals—the counting numbers 1, 2, 3, etc—we can quickly and easily see that there exist an infinite number of these objects. If we next examine the Reals—those numbers existing on a continuum, containing all natural numbers, all numbers expressible as a fraction, and all numbers NOT expressible as a fraction, such as pi—we also see, relatively intuitively, that there are an infinite number of THESE objects. But a famous result shows that there are more Reals than there are Naturals, with the magnitude of the Naturals referred to as a “countable” infinity and the magnitude of the Reals called an “uncountable” infinity.
This, at first, seems strange. How can one infinity be larger than another? This result was first proven by Georg Cantor. A famous demonstration known today as the Cantor Diagonalization Argument proves this in so elegant a fashion as to be essentially uncontestable. For today, let us simply accept the truth of this separation between values of infinity. I shall allow the curious reader to investigate this independently.
We next move on to language.
Language is built around sentences expressing ideas. Those sentences are built of words. At any given moment, a language has a finite number of words. Language morphs and changes and evolves over time, adding a degree of complexity to the expressive power of a language, but I am concerned right now with language as it stands in any given instant.
When we build sentences, we combine these finite words into sentences. A given sentence is finite in length, but there is no theoretical limit to the length of an individual sentence. I’ve read sentences in books that span pages, and with embedded clauses it is trivial to demonstrate that a sentence can be of any length.
But it is clear that, however many words are in a sentence, that number must be a Natural number. That is to say, to claim a sentence has 7.6 words doesn’t mean anything. For a sentence to follow the structural rules of grammar, that sentence cannot have a fractional number of words. More to the point—and even less arguably—a sentence cannot feasibly have an irrational number (a number only expressible as a non-repeating, non-terminating decimal) of words.
What this tells us, in essence, is that there are a countable number of sentences. Not that the sentences can actually be counted by a human being, but that the infinity of sentence variation is the same size as the number of Natural numbers—a countable infinity.
A book or a paper or an argument, something built of sentences and used to convey ideas, is also necessarily finite in length. Once again, there is no theoretical limit to the number of sentences in a book, but whatever number of sentences are placed in a book, that number will be finite. So the number of feasible books or papers or arguments is countably infinite.
The point of this, then, is this: at any given moment, the number of ideas expressible in a language is countably infinite.
I find this to be quite interesting. If the number of ideas expressible through language is countable, what if the number of ideas which exist is uncountable? It seems to me as though this uncountability of the idea-space is likely true, since it is fair to call all possible numbers an idea, and so long as we accept the Reals we’ve immediately granted a number of ideas minimally equal to the number of Reals.
This means, in short, that there are ideas that language cannot possible express. As a matter of fact, there are an infinitely large number of ideas that cannot possibly be expressed in a language at a given moment.
So where are those other ideas? Well, perhaps some are expressible in non-linguistic media. Music, images, movements, and the like. Perhaps some are simply inexpressible. This is something to ponder, something to consider. It is important, I think, because it suggests the untruth of the often-believed idea that we can only think that which we can linguistically express.
I’d be interested to know where this takes the reader.