Todos sueñan lo que son, aunque ninguno lo entiende. —Calderón de la Barca
A profoundly thought-provoking work of Nietzsche, often overlooked, is the small essay entitled On truth and lies in a nonmoral sense. This was the first truly intelligent critique of science which I read, and, in all of its brevity, one that has very rarely been matched.
I read this work at seventeen, when I was a young student in the department of philosophy. Ten years later, today, with a few years of experience in science and research, and close to graduating from the mathematics department, I read it again. What I write here may be considered a commentary on this particular work, though I should strive to provide more general observations on the nature of scientific knowledge as I understand it.
The central thesis of this work, at least as far as I can see, is that scientific theories are not representations of an objective reality, but rather the subjective (and hence ultimately arbitrary) cognitive elaboration of certain stimuli. (Here «subjective» does not refer to the individual subject, but to the human subject.) To Nietzsche, inferring objective properties from the result of any such stimulation is unwarranted:
[...] the further inference from the nerve stimulus to a cause outside of us is already a result of a false and unjustifiable application of the principle of sufficient reason.
The phrase «the stone is hard» then expresses the result of a subjective feeling and not an objective «hardness» in the rock. A word is but the formulation of a qualitas occulta underlying the infinite complexity and multiplicity of that to which the word refers:
Truths are illusions which we have forgotten are illusions; they are metaphors that have become worn out and have been drained of sensuous force, coins which have lost their embossing and are now considered as metal and no longer as coins.
Reason is understood as an inherently tautological instrument:
If I make up the definition of a mammal, and then, after inspecting a camel, declare "look, a mammal," I have indeed brought a truth to light in this way, but it is a truth of limited value.
Furthermore, inquiry through science and reason is viewed as fundamentally anthropocentric. Oblivious to the fact that in trying to describe reality «he again proceeds from the error of believing that he has these things immediately before him as mere objects», the scientist acts as the astrologers who treated stars as agents in man's service:
It is even a difficult thing for him [the inquirer] to admit to himself that the insect or the bird perceives an entirely different world from the one that man does, and that the question of which of these perceptions of the world is the more correct one is quite meaningless [...]
If we could perceive matters «as a bird, now as a worm, now as a plant, or if one of us saw a stimulus as red, another as blue, while a third even heard the same stimulus as a sound - then no one would speak of such a regularity of nature». Quite pertinently, Nietzsche cites Pascal's famous passage on a laborer who dreams each night that he's a king.
In my opinion, Nietzsche's insights are fundamentally correct. This early work of his draws strongly from Schopenhauer's conception of the world as will and representation, which I also deem fundamentally right. Such a thing as a purely objective reality, a ding an sich, is not only unknowable but unimaginable. Every species is endowed with more or less broad, but necessarily bounded faculties of representation which are specific to it. Yet, contrary to the belief that this undermines science, I would venture this itself constitutes a scientific fact. Hopefully the reader will allow me to digress a bit in order to bring forth my point.
For some reason, it is common to teach that the Newtonian revolution «overcame» mind-body dualism by exorcising the ghost from the machine and providing a more or less complete description of the physical world. This could not be further from the truth. Newtonian physics is based on the concept of force, which serves to correctly explain nature, but which has no material ground. The postulates of, say, gravitational force or electrostatic force proceed simply from observing that distant (i.e. non-contacting) objects attract, repel and generally influence each other. What distinguishes the gravitational and the electrostatic force is simply the observed properties of this otherwise arcane interaction. There is no understanding of what the word force means beyond this.[^1]
In this sense, the epithet physical is meaningless and serves a merely honorific function, just like the epithet real. To say the real truth is simply to say the truth, but with a certain emphasis; to say the physical world is simply to say the world, with a certain decoration. We have no notion of what physical means and, instead of ridding ourselves of the ghost in the machine, Newton destroyed the machine and left us with the ghost alone. [^2]
Furthermore, it is correct to claim that what we call reality is a specific representation, and, to repeat Nietzsche's words, that
[...] the further inference from the nerve stimulus to a cause outside of us is already a result of a false and unjustifiable application of the principle of sufficient reason.
We can safely say certain stimuli are processed so and so, and acquire a rather sophisticated understanding of the underpinnings of such processing (as is the case, for instance, in the visual system). But we are limited, both in our perception of a moving object as well as in our description of the visual system itself, by the specific encoding which our nervous system imposes upon the external world. A trivial corollary of this is that human understanding has limits. It is conceivable that our brains are simply ill-prepared to grasp certain properties of the world—and I suspect philosophers are correct when suggesting that mental phenomena may depend on some of these properties.
Take, for instance, the cognitive faculties of rats, a matter of thought-provoking research. Though able to learn highly intricate mazes, rats cannot learn to traverse a prime-maze, i.e. a maze with $i=1,\ldots, N$ turns which is solved by the program: $\textbf{if } i \textbf{ is prime turn right else turn left}$. This suggests three interesting things with regard to the way in which «reality» relates to our innate, limited representational faculties.
Firstly, rats seem to possess some sense of numerosity directed by what is technically termed the approximate number system (ANS), which adheres to Weber's law. This is a fancy way of saying that rats discriminate different quantities based on their ratio, not their absolute difference. But despite these interesting faculties, this experiment suggests that rats have no innate notion of prime number.
Secondly, this is another of many results contradicting behaviorist theory. Not only do rats lack the capacity to figure out a prime number maze on their own, but they cannot be taught to solve it. Though rats are capable of rule-based learning, prime numbers seem to simply lie «beyond» the limits of their cognitive abilities.
Lastly, a prime-maze is a computational problem and thus its solution can be interpreted as a program. This allows us to express, at least heuristically, that the rat's brain-hardware is incapable of implementing it.
Another interesting study suggests that apparently geometric, abstract learning in rats is in fact more concrete than it may seem. The researchers successfully trained rats to find a submerged platform in a pool using the length of the walls (e.g., "the platform is in the middle of the long wall"). Then the researchers changed the color of the walls—an obviously non-geometric property—only to find that the rats' ability to find the platform was gone. This finding suggests that the rats never acquired an abstract understanding of length, separate from all sensory context, but rather formed a concrete and integrated representation of the problem such as «platform-at-long-black-wall».
However, the fact that the rat, the worm and the mosquito all live, so to speak, in different worlds, is neither a scientific problem nor a problem for science. Science is objective, but not in the sense of describing the world as-is (la cosa-en-sí, como leeríamos en Schopenhauer): as I have tried to suggest, the Schopenhauerian thesis that the world is representation is correct. Recall that Nietzsche claims science is subjective not in terms of the individual, but of the human condition, i.e. it is subjective in contrast to whatever science another cognitively capable species could hypothetically produce. Science is objective when understood within the human domain, and in the traditional sense of basing itself upon impartial analysis of the facts[^3]. That these facts are not purely given but rather elaborated by our representational faculties poses no problem, since these faculties are shared and these facts appear more or less the same to everyone.[^4]
There is another sense in which Nietzsche's view is incomplete. His critique is based solely on the reception of a stimuli and its consequent elaboration. However, the problem becomes even harder when we consider that we also carry within us «aprioristic» faculties and, I dare to say, representations. In On archetypes I discussed an example given by Campbell in The Masks of God: Primitive Mythology:
Chicks with their eggshells still adhering to their tails dart for cover when a hawk flies overhead, but not when the bird is a gull or duck, heron or pigeon. Furthermore, if the wooden model of a hawk is drawn over their coop on a wire, they react as though it were alive—unless it be drawn backward, when there is no response.
Here we have an extremely precise image—never seen before, yet recognized with reference not merely to its form but to its from in motion, and linked, furthermore, to an immediate, unplanned, unlearned, and even unintended system of appropriate action: flight, to cover. (...) Furthermore, even if all the hawks in the world were to vanish, their image would still sleep in the soul of the chick—never to be roused, however, unless by some accidente of art ($\ldots$). With that the obsolete reaction of the flight to cover would recur; and, unless we knew about the earlier danger of hawks to chicks, we should find the sudden eruption difficult to explain. 'Whence', we may ask, 'this abrupt seizure by an image to which there is no counterpart in the chicken's world? ($\ldots$)'.
What I mean is that not only do we not perceive the world as is—not only are expressions such as «the world as is» fundamentally meaningless—but we bring to the world archetypal, instinctual representations which are somehow embedded in our neurobiology. No living creature comes into the world in the form of a tabula rasa. To abuse the brain-computer analogy, like most computer hardware, the brain comes with an embedded set of instructions and programs which predetermine the manner in which external stimuli will be processed.
With regard to Nietzsche's claim that reason is tautological and self-referencing, I believe it is only partially correct. It is certainly true that formal disciplines are completely tautological, which is, by the way, an uncontroversial statement (see for instance Russell's work Human knowledge). Furthermore, formal structures are typically used as extremely simple and abstract models of real systems. But however tautological the deductions derived from a model may be, the truths they uncover about the represented system are less trivial than Nietzsche lets on. Take, for instance, the famous example of the seven bridges of Königsberg, which inspired Euler to found graph theory.
Interestingly, formal disciplines take us back to the matter of innate representations. It is generally accepted that some foundational concepts of logic and mathematics lack any clear definition. The paradigmatic example is the notion of set. Ever since Russell's paradox showed the contradictions contained in naive set theory, axiomatic set theories were developed to overcome such paradoxes without arriving at a clear, universally accepted definition of the notion. One is tempted to infer from this that, though mathematics operates by necessity in tautological fashion, some of its foundational concepts correspond to categories of thought which are embedded in our cognitive faculties, however much we struggle to define them. It is certainly the case that our biological endowment includes categories such as «number», «set», etc. This «innatist» view—for lack of a better term—may be supported by certain interpretations of Gödel's incompleteness theorems, which prove the existence of true but unprovable statements in any sufficiently complex formal system. Even within formal systems, something quite beyond the grasp of formal computation is involved in their semantics.
With regard to non-formal disciplines, we must understand Nietzsche's description of the fraught taxonomist, who defines a mammal and then declares every new mammal he finds to be a discovery, with precision. To contradict it, it is not sufficient to claim that scientists do not posit aprioristic definitions and then search for instances of them. Nietzsche's point is more subtle, since he suggests that the nature of language renders any definition a lie—in a nonmoral sense, as the title of the work suggests. In other words, to Nietzsche it is fundamentally impossible not to act as the fraught taxonomist: whenever we speak, let alone postulate a definition, we are necessarily weaving a metaphor or a myth. And it is unjustified to then claim such metaphor corresponds to this or that objective instance.
I must admit that I do not find this point to be so convincing. To describe language as a lie, to claim that speaking the truth is nothing but uttering the correct metaphor, is somewhat simplistic. Nietzsche commits a common error among philosophers in treating language like an abstract faculty, when in fact it should be viewed as a faculty not different in kind from the visual or the auditory systems. Nietzsche's claim that language is a lie is not different from the claim that, when seeing a moving object, we don't perceive a pure object but some impure elaboration of it.
I don't mean to say that language does not have distinct and particular properties, but rather that the kind of relationship upon which Nietzsche bases his critique of language is not different from that of other human faculties. We should care about the fact that every word is a lie, in Nietzsche's sense, just as much as we should care about the fact that every visual perception is an illusion. Of course it is, but insofar as this «illusion» is the only reality we know, we must reckon that treating it as merely illusory is contradictory. Borges' short story Funes el memorioso is an interesting mental experiment on the practical impossibility of a mind that does not base itself on «Nietzschean lies».
Of course, one must understand that Nietzsche was arguing against a less flexible conception of science than the one we have today. Primitive science—say in the form of a Francis Bacon or a Darwin—understood the senses as more or less trustworthy recipients of an objective reality. The intellect's task was merely to explain it. Now, the very faculties upon which our representation of reality is based are understood as constitutive parts of that reality, just as much as the tree or the rock. In other words, our representational faculties are now part of what requires an explanation. The circularity here is not only unavoidable but unsolvable. The commonplace that neuroscience is «the brain looking at itself» is true, and whatever we can learn about ourselves is limited by that which we are trying to learn about.
Here, the brain-computer analogy comes in handy. As far as I can see, this heuristic makes sense only if we set conscious processes and cognitive faculties to play the role of the interface provided by the kernel, unconscious processes to play the role of the kernel, and the hardware playing the role of the brain. Whoever is familiar with operating systems appreciates how profoundly different these three spheres are, and how little information a level provides to its more abstract successor. Since brains are tremendously more complex than any computer system, this should readily suggest how unfathomable the gulf between our cognitive faculties and the underlying brain processes must be.
In fact, we have concrete examples of how remote from each other interface, kernel and hardware are in our own species. Visual experience, for instance, though complex, does not begin to approximate the complexity of its underlying neurobiology. Both the unconscious computations involved as well as its biological substrate are incomprehensibly more complex than the experience itself. What is more, the visual system itself is incapable of introspection: one cannot «see» how the visual system works, and we can only expect that the same applies to all cognitive faculties. Interfaces are the product of Darwinian evolution, and I cannot imagine an environment in which natural selection pushes not only for the emergence of a particular faculty but also for its self-referential transparency. It is therefore conceivable that many aspects of our own nature are ultimately unfathomable to us.
I have little else to say on the matter. I should reiterate how profound I believe Nietzsche's insights to be on this matter, regardless of finding myself at odds with a few of them. With some fortune, I hope to have shown why I believe we have no clear notion of physical, that we have rid ourselves not of the ghost in the machine but rather of the machine itself, that science supports the claim that, in Schopenhauer's terms, the world is our representation, and that this does not pose a problem to scientific objectivity.
I should wish to end this entry recalling the verses that Calderón de la Barca, whom Schopenhauer read in Spanish, wrote on this matter:
¿Qué es la vida? Un frenesí.
¿Qué es la vida? Una ilusión,
una sombra, una ficción,
y el mayor bien es pequeño:
que toda la vida es sueño,
y los sueños, sueños son.
[^1] In How to make our ideas clear, Peirce uses the concept of force as a paradigmatic example of an idea which is to be understood only through the effects which it produces. His discussion is highly stimulating and worth reading.
[^2] This interpretation of Newtonian physics is put forward in a summarized, but in my view still convincing fashion, in Chomsky's short work What kind of creatures are we?
[^3] A post-modern critique of science may object to this impartiality. I do not take such objections too seriously, since they typically rest on a complete misunderstanding of what scientific objectivity means. But this is not the place to discuss this.
[^4] I do not think it is controversial to claim that our representational faculties are shared and that facts appear more or less the same to everyone. Cultural and psychological predispositions may influence the way we interpret the facts, but not their appearance. When I see a painting of Christ I see a Jew from Nazareth who lived a virtuous life two thousand years ago; a fellow Christian sees the son of God. But no one can deny our sensory experience is, mutatis mutandis, the same.