Education: Linguistic and Arithmetic Elusiveness

We wish to sensitize the student to the obvious-but-hard-to-see truth that both language and arithmetic have slippery natures built into them and seeing this clearly is a part of deeper education, our mission here.

Take four simple statements and see that they’re entwined and “confusing.”

  1. You can count (i.e., numeracy).
  2. You can count (depend) on me.
  3. You don’t count (i.e., importance).
  4. Count (include) me in.

When a person says, “you can count on me” do they mean that you will be standing on me and then go, “one apple, two apples, three apples” (i.e., count in the everyday sense). No, obviously not. “On” in this context is not physical or locational, but figurative. Ask yourself: how is it that you know the difference and nuances of all these meanings given that the word count and the preposition “on” seem straightforward but are really “polyvalent.”

Wittgenstein tells us that philosophy and its conundrums are ultimately based on “language games.”

When Gadamer (Heidegger’s student) tells us that “man is a linguistic creature” he means, among other things, that man “swims” in this ambiguity ocean every moment and puns and jokes aside, handles these ambiguities automatically, somehow. How does a child acquiring language get the sense of all this? It’s difficult to understand and explain. Language is both our nature and somehow beyond our grasp.

The same slipperiness, in a different way, holds for arithmetic and numbers. You can immediately see that the square root of 16 is 4 (plus or minus) but if you are asked, “what is the square root of seventeen?” you’d be “at sea” without a calculator. If you’re now asked, what is the square root of -17 (negative seventeen), you would probably be lost.

These would seem to be very basic “operations” and yet are baffling in their way and parallel the “sudden difficulties” in language use and orientation and clarity.

Deep and “meta-intelligent” education, which we promote here, begins by seeing, among other things, that both our ability to function while “swimming” among words and numbers is puzzling if you look at them “freshly.”

It’s also not so easy to define exactly what reading and writing are in the first place or why exactly the smile in Leonardo da Vinci’s Mona Lisa painting is enigmatic.

When one glimpses the truth that we are surrounded by obvious things that are never really obvious, one pauses and thinks. This is where (self) “re-education” begins, especially if “enchantment” (genuine magical fascination) accompanies the thinking.

Essay 37: 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.