Tag: Gödel’s incompleteness theorems

Is It Good to Be a Detached Observer?

The famous Dutch historian, Pieter Geyl, in his Napoleon, for and against (Dutch, Napoleon: voor en tegen in de Franse geschiedschrijving) teaches us that there are “arguments without end.” One example is the question surrounding the concept of detachment. Aristotle, in his Nicomachean Ethics, proposes “eudaimonia,” a Greek word literally translating to the state or condition of good spirit coming from imperturbability. This sense of things is all over the Western tradition. Think of the line from the British poet, Alexander Pope, “For Fools rush in where Angels fear to tread.” (An Essay on Criticism, 1711). You see from this that fools lack detachment and act on impulse.

We get a confirmation of Geyl’s arguments without end when we remember that almost every love song recommends the opposite. For example, “Fools Rush In (Where Angels Fear to Tread)” originally made famous by Frank Sinatra and later Elvis Presley, offers us the line “But wise men never fall in love / So how are they to know.” From this, we can interpret that wise men can be foolish and foolish people can be wise. You may also have in the back of your mind Tennyson’s “Tis better to have loved and lost / Than never to have loved at all.” It is not wise to be careful always.

We get a twist on this in the Rodgers & Hammerstein musical South Pacific. Think of “Some Enchanted Evening”:

Who can explain it?
Who can tell you why?
Fools give you reasons—
Wise men never try.

Fools give you reasons because they think everything can be explained, where wise men realize this is not always true. The larger point, from existential thinker Gabriel Marcel, is that all the phenomena of life that are explainable are themselves wrapped up in a larger mystery. He discusses the question of detachment in Being and Having: An Existentialist Diary, which we covered in “Existence and the Problem of Separability” and “Is the World Broken?”.

Marcel says:

March 8th [1929]

I am more and more struck by the difference between the two modes of detachment: the one is that of the spectator, the other of the saint. The detachment of the saint springs, as one might say, from the very core of reality; it completely excludes curiosity about the universe. This detachment is the highest form of participation. The detachment of the spectator is just the opposite, it is desertion, not only in thought but in act. Herein, I think, lies the kind of fatality which seems to weigh on all ancient philosophy—it is essentially the philosophy of the spectator.

But one thing must be noted: the belief that one can escape pure spectatorship by devotion to a practical science, which cannot quite clearly formulate it as yet. I should express it by saying that the modifications which such a science imposes on reality have no other result (metaphysically of course than of making that science in some sense a stranger to reality. The word ‘alienation’ exactly expresses what I mean. ‘I am not watching a show’—I will repeat these words to myself every day. A fundamental spiritual fact.

The interdependence of spiritual destinies, the plan of salvation; for me, that is the sublime and unique feature of Catholicism.

I was just thinking a moment ago that the spectator-attitude corresponds to a form of lust; and more than that, it corresponds to the act by which the subject appropriates the world for himself. And I now perceive the deep truth of Bérulle’s theocentrism. We are here to serve; yes, the idea of service, in every sense, must be thoroughly examined.

Also perceived this morning, but still in a confused way, that there is profane knowledge and sacred knowledge (whereas previously I have wrongly tended to assert that all knowledge was pro-fane. It isn’t true, profane is a supremely informative word). Inquire on what conditions knowledge ceases to be profane.

Incredible how thronged these days are spiritually! My life is being illuminated right into the depths of the past, and not my life only.

Every time we give way to ourselves we may unawares be laying an additional limitation on ourselves, forging our own chain. That is the metaphysical justification for asceticism. I never understood that till now.

Reality as mystery, intelligible solely as mystery. This also applies to myself.

Gabriel Marcel, Being and Having: An Existentialist Diary, Harper Torchbooks, 1965, pages 20-21.

Notice this discussion starts by analyzing modes of detachment and concludes with Marcel talking about reality and himself as mystery. This brings us full circle to Geyl and his concept of arguments without end because trying to define pros and cons of detachment and what is a mystery is ultimately undecidable. This may remind you of Gödel’s incompleteness theorems, that finding a complete and consistent set of axioms for all mathematics is impossible.

Education and Wittgenstein “Language Games”

It is instructive for a student to get a grip on the whole question of “language games” à la Wittgenstein, who says that these “games” (i.e., ambiguities) are central to thinking in general and thinking about philosophy in particular.

Let’s make up our own example and step back from the meaning of the preposition “in.”

The comb is in my back pocket has nothing to do with the “in” of “he’s in a good mood” or “he’s in a hurry” or “he’s in a jam or pickle” or “he’s in trouble.” Furthermore, in modern deterministic neuroscience language, a good mood is a footnote to brain and blood chemicals so that means that a good mood is in you via chemicals and not you in it.

Does the word “jam” here mean difficulty or somehow the condiment called jam? You don’t know and can never without more information (i.e., meaningful context).

Imagine we take a time machine and are standing in front of the home of Charles Dickens in London in his time say in the 1840s. They say he’s working on a new novel called Oliver Twist.

Someone says: a novel by Dickens is a kind of “fictional universe.” Shall we say that because Dickens is in his home (at home) in London (though in London is itself confusing since London as a city is not like a pocket to a comb or wallet) his fictional universe is “in” the universe which might be a multiverse according to current cosmological speculations? That’s not what we mean. The fictional universe of Dickens is a shared cultural abstraction involving his stories, characters, people absorbing his tales, his mind and our mind, books and discussions. A fictional universe is as “weird” as the other universe. The preposition “in” does not begin to capture what’s going on which is socio-cultural and not “physicalistic.”

We begin to intuit that everyday language which we use and handle as the most obvious thing in the world in constant use, is completely confusing once you look at it more clearly.

Einstein’s friend at Princeton, Kurt Gödel, looked into language as a logical phenomenon and concluded that it’s entirely puzzling that two people could actually speak and understand one another given the ambiguities and open-endedness of language.

A language-game (German: Sprachspiel) is a philosophical concept developed by Ludwig Wittgenstein, referring to simple examples of language use and the actions into which the language is woven. Wittgenstein argued that a word or even a sentence has meaning only as a result of the “rule” of the “game” being played. Depending on the context, for example, the utterance “Water!” could be an order, the answer to a question, or some other form of communication.

In his work, Philosophical Investigations (1953), Ludwig Wittgenstein regularly referred to the concept of language-games. Wittgenstein rejected the idea that language is somehow separate and corresponding to reality, and he argued that concepts do not need clarity for meaning. Wittgenstein used the term “language-game” to designate forms of language simpler than the entirety of a language itself, “consisting of language and the actions into which it is woven” and connected by family resemblance (German: Familienähnlichkeit).

The concept was intended “to bring into prominence the fact that the speaking of language is part of an activity, or a form of life,” which gives language its meaning.

Wittgenstein develops this discussion of games into the key notion of a “language-game.”

Gödel saw that language has deep built-in ambiguities which were as puzzling as math and logic ones:

Gödel’s (died in 1978) incompleteness theorems are two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system capable of modeling basic arithmetic. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics.

Take any simple sentence: say, “men now count.”

Without a human context of meaning, how would you ever decide if this means count in the sense of numeracy (one apple, two apples, etc.) or something entirely from another domain (i.e. males got the vote in a certain country and now “count” in that sense).

When you say, “count me in” or count me out,” how does that make any sense without idiomatic language exposure?

If you look at all the meanings of “count” in the dictionary and how many set phrases or idioms involve the word “count,” you will immediately get the sense that without a human “life-world” (to use a Husserl phrase), you could never be sure of any message or sentence at all involving such a fecund word.

One task of real education is to put these difficulties on the student’s plate and not avoid them.

Linguistics as such is not what’s at issue but rather a “meta-intelligent” sense of language, written or spoken as highly mysterious with or without the research into vocal cords, language genes (FOXP2, say) or auditory science and the study of palates or glottal stops and fricatives, grammars and syntax.

Seeing this promotes deep education (i.e., where understanding touches holism in an enchanting way).