ontology, Meta Intelligence

“Fog Everywhere” Continued

Consider mathematics and the aspect of fog. Nietzsche argued that the world is not knowable to us as a whole. This includes trying to express it with numbers. A recent example is Max Tegmark’s assertion that the universe is not something explained by mathematics; rather, it is itself mathematics. To contrast, Karl Jaspers, summarizing Nietzsche, wrote:

We cannot say what the world as a whole is. It is false to change all processes into a familiar world of our own, and then say: “All is will (everything wills); all is pleasure or pain (everything endures); all is motion (everything flows); all is tone (everything sounds); all is spirit (everything thinks); all is number (everything reckons).” Nietzsche warns us against all notions of the whole: “Let us guard against thinking that the world is a living being…or that the universe is a machine…Let us guard against saying that there are laws of nature…Let us guard against thinking that the world eternally creates novelties.” All these “shadows of God” darken actuality. We are within the world, and the whole of the world is, as a whole, not accessible to us.
Karl Jaspers, Nietzsche: An Introduction to the Understanding of His Philosophical Activity, Henry Regnery Company, 1966, p. 293

Notice in the paragraph quoted above that Nietzsche specifically excludes reducing everything to numbers, in opposition to Tegmark and the simulation hypothesis.

Robert Kanigel describes Srinivasa Ramanujan as “the man who knew infinity” in his biography of the same title, but mathematicians disagree on the ontological status and utility of infinity. The discussion of applying Ramanujan’s sum to arrive at -1/12 is very intricate and complex.

To make things even more puzzling, math students are confronted with the Gaussian integral, with its positive and negative infinities.

You can gain additional insight into infinity with:

Cauchy and Weierstrass had eliminated infinitely small and infinitely great numbers from analysis and replaced them by limits. But the theory of limits that thereby became so central required a clearer theory of the real line, that is to say, a theory of the irrational numbers. And that theory promptly reintroduced the infinite into analysis. The old infinity of infinitesimal and infinite numbers was simply replaced by the new infinity of infinitely large collections.¹²

In 1831 Carl Friedrich Gauss said [Kli72, p. 994], “I protest against the use of an infinite quantity as an actual entity; this is never allowed in mathematics. The infinite is only a manner of speaking, in which one properly speaks of limits to which certain ratios can come as near as desired, while others are permitted to increase without bound.” But only 52 years later, we find this in Cantor’s Grundlagen [Can76, p. 75]: “The idea of considering the infinitely large not only in the form of the unlimitedly increasing magnitude and in the closely related form of convergent infinite series…but to also fix it mathematically by numbers in the definite form of the completed infinite was logically forced upon me, almost against my will since it was contrary to traditions which I had come to cherish in the course of many years of scientific effort and investigations.”

12 See Russell’s Principles of Mathematics [Rus03, p. 304] for a related sentiment.
Shaughan Lavine, Understanding the Infinite, Harvard University Press, 1994, pgs. 38-39

In 1961, the great Russian physicist George Gamow’s popular math and physics overview was republished to great acclaim among science and math aficionados. Intriguingly titled One, Two, Three…Infinity, the book gives you a hint that the relationship of numbers and integers to the concept of infinity is still intriguing even after the intricate analyses of Cauchy, Weierstrass et al.

Let us conclude by considering Zeno’s dichotomy paradox of motion, in which “That which is in locomotion must arrive at the half-way stage before it arrives at the goal.” As the goal is divided into halves, one must complete an infinite number of tasks, which Zeno maintains is an impossibility.

[read the previous essay on this topic]

Kierkegaard and Existence

There are various striking intuitions about human existence. For example, in his brilliant memoirs, Speak, Memory, Nabokov begins with the deep reflection where human existence is compared to a baby in a cradle, rocking, completely vulnerable and uncertain. All of this is bracketed by two episodes of infinite darkness. The first episode took place before you were born and the second takes place after you’re gone. Your existence is a temporary flame, like that of a lit match.

A MetaIntelligent comment on this would be that the profound ingenuity of the 19th century mathematicians analyzing the size and nature of infinity (e.g., Richard Dedekind or Georg Cantor) cannot in the last analysis wrestle down human existence into mathematics.

The modern progenitor of this kind of human existence-watching is the Danish genius Søren Kierkegaard. In one of his masterpieces, Concluding Unscientific Postscript to Philosophical Fragments (1846), he makes the claim that knowledge, theory, speculative thinking and infinity-watching à la Dedekind and Cantor, cannot possibly explain human existence, because it subsumes all of these.

In 2025, this would mean that the Kierkegaard sense of things would tell you that neuroscience can never really explain how existence is sensed by a living person.

Kierkegaard writes, “in my view the misfortune of the age was precisely that it had too much knowledge, had forgotten what existence means, and what inwardness signifies.” He continues, “for a knowledge-seeker, when he has finished studying China he can take up Persia; when he has studied French he can begin Italian; and then go on to astronomy, the veterinary sciences, and so forth, and always be sure of a reputation as a tremendous fellow.”

By way of contrast, “inwardness in love does not consist in consummating seven marriages with Danish maidens, then cutting loose on the French, the Italian, and so forth, but consists in loving one and the same woman, and yet being constantly renewed in the same love, making it always new in the luxuriant flowering of the mood.” (Concluding Unscientific Postscript to Philosophical Fragments, page 232.)

Kierkegaard’s kind of existence-watching can be understood as a turning-upside-down of the famous phrase from Descartes, “I think, therefore I am.” For Kierkegaard, “I am, therefore I think.” Notice that “I think” is an epistemological statement or knowledge-watching. “I am” is an ontological statement.

This existentialist tradition of putting ontology before epistemology finds its culmination in Heidegger. As he says in his opus, Being and Time (1927), “human being is ultimately the being for whom being itself is an issue.”

The Language Phenomenon in Education

Wittgenstein (1889–1951) identifies language as the principal “confusion-machine” within philosophy:

“Philosophy is a battle against the bewitchment of our intelligence by means of language.”

The philosopher’s treatment of a question is like the treatment of an illness.

“What is your aim in philosophy?—To show the fly the way out of the fly-bottle.”

Education if deep and meaningful would put language itself in front of a student to understand the “bewitchment” and to perhaps “escape from the fly-bottle.” The fly-bottle is roughly “the captive mind syndrome” described by Czesław Miłosz, the Polish poet-thinker.

There are various aspects of this language-watching:

Hans-Georg Gadamer (Heidegger’s successor, who died in 2002) writes:

“It is not that scientific methods are mistaken, but ‘this does not mean that people would be able to solve the problems that face us, peaceful coexistence of peoples and the preservation of the balance of nature, with science as such. It is obvious that not mathematics but the linguistic nature of people is the basis of civilization.’”

(German Philosophy, Oxford University Press, 2000, pages 122/123)

This is readily seeable. Imagine Einstein and Kurt Gödel walking near the Princeton campus. They speak to each other in German, their native tongue which they both “inhabit.” Gödel communicates the limits to logic and Einstein the limits to modern physics such as quantum mechanics. They bring in Bohr and Heisenberg and the “Copenhagen Interpretation” as a counter-view. They refer to equations and experiments and conjectures and puzzles, current papers and conferences.

They take “communicative action” by use of speech using German as a means.

There are two levels here that are always confused: the ontological (i.e., all the why-questions people ask using language) and the ontic level, all the how-questions people pose using mathematics and laboratory results (e.g., Higgs boson).

Gödel once made the observation that if you look at language as a kind of logical system, it’s absolutely puzzling that people can communicate at all since language is so utterly ambiguous and “polyvalent.”

Take the sentence: “Men now count.” Out of context, does it mean count as in the sense of numeracy, one, two, three apples in front of me or do you mean perhaps that men in a certain country were given the right to vote and now “count” politically. Without the context and the ability to contextualize, no sentence by itself makes certain sense at all.

This is partly why Wittgenstein sees philosophy problems as “language games.”

Heidegger coming from “being-in-the-world” as foundational, and calls language “the house of being.”

You inhabit a native language the way you “inhabit” a family home or a home town. You flow through.

When a child of ten plays marbles (as analyzed by Piaget) and his native language (say French) comes pouring out of him in a spontaneous gusher, how can we really explain it since the child doesn’t look up syntactical rules and grammatical definitions when he speaks. The words flow.

Heidegger retorts that language speaks you in other words, you’re channeling the language in a way a songwriter explains how a song comes to him. In the end, it’s something spontaneous and not propositional like grammar is.

A moment’s reflection shows you how “slippery” language is:

A man driving to New York says to you, “the car died on me halfway there.” He does not mean the car was “on” him physically. To die on doesn’t really mean perish forever, it means, on average, stopped to function in a way that usually can be fixed in the garage. It means this reparable conking out of the car gave him a big headache and aggravation as he waited for the Triple A people to get there and do the paperwork. You visualize all these layers and twists.

Again, without a human context, the sentence “the car died on me” makes little sense. Without a human context, “the sky is blue” makes incomplete sense too. Does a camel or cricket see a blue sky?

A full education would explore these dimensions of language and this has nothing to do with bringing back Latin or Greek or studying a foreign language to meet a Ph.D. requirement. Formal linguistics à la Chomsky, Fodor, Katz, etc. is not what’s being discussed, as interesting as all that might be.

It also is not about language genes such as FAP-2 or how vocal cords work since these questions are ontic (i.e., how does it work?) and not ontological (i.e., what does something mean or imply?). Thinking about language in an engineering sense with the human mouth as a “buccal cavity” is quite legitimate and a voice coach might do well to do that. We are talking about something else: the centrality of language in human self-understanding, functioning and the making of meaning.