Tag: logic

Existence and the Problem of Separability

In contracts and legal documents, there is a concept of “separability” which means that clause A is connected to clause B in a way that cannot be undone.

The great twentieth century French philosopher, Gabriel Marcel, has a profound non-separability analysis of existence itself. Marcel wrote:

…We cannot really separate:—

  1. Existence
  2. Consciousness of self as existing
  3. Consciousness of self as bound to a body, as incarnate.
Gabriel Marcel, Being and Having: An Existentialist Diary, Harper Torchbooks, 1965, page 10.

This leads to saying things that are very deep aspects of existential thinking governed by the points above. For example, Marcel wrote, “As I have said elsewhere, the moment I treat my body as an object of scientific knowledge, I banish myself to infinity.” Consider the end of the previous phrase. The very notion that someone, within themselves could go down a route to “banish themselves” in this way, shows you a door into very deep psychological problems. In other words, Marcel is telling you that some psychological problems could have a philosophical or existential root cause and are a type of blunder.

This is not to say that one should avoid scientific thought. Taking a drop of your blood and viewing it under a microscope is not a blunder. However, if you take this to the extreme of trying to analyze everything scientifically, to the exclusion of philosophy in daily life, this is Marcel’s warning.

Marcel’s context for this thinking is given here:

Notes for a Paper to the Philosophical Society

Undated, written in 1927 or 19281

When I affirm that something exists, I always mean that I consider this something as connected with my body, as able to be put in contact with it, however indirect this contact may be. But note must be taken that the priority I thus ascribe to my body depends on the fact that my body is given to me in a way that is not exclusively objective, i.e. on the fact that it is my body. This character, at once mysterious and intimate, of the bond between me and my body (I purposely avoid the word relation) does in fact colour all existential judgments.


What it comes to is this. We cannot really separate:—

  1. Existence
  2. Consciousness of self as existing
  3. Consciousness of self as bound to a body, as incarnate.

From this several important conclusions would seem to follow:

  1. In the first place, the existential point of view about reality cannot, it seems, be other than that of an incarnate personality. In so far as we can imagine a pure understanding, there is, for such an understanding, no possibility of considering things as existent or non-existent.
  2. On the one hand, the problem of the existence of the external world is now changed and perhaps even loses its meaning; I cannot in fact without contradiction think of my body as non-existent, since it is in connection with it (in so far as it is my body) that every existing thing is defined and placed. On the other hand, we ought to ask whether there are valid reasons for giving my body a privileged metaphysical status in comparison with other things.
  3. If this is so, it is permissible to ask whether the union of the soul and body is, in essence, really different from the union between the soul and other existing things. In other words, does not a certain experience of the self, as tied up with the universe, underlie all affirmation of existence?
  4. Inquire whether such an interpretation of the existential leads towards subjectivism.
  5. Shew how idealism tends inevitably to eliminate all existential considerations in view of the fundamental unintelligibility of existence. Idealism versus metaphysics. Values detached from existence: too real to exist.

Existential and personalist interests closely linked. The problem of the immortality of the soul is the pivot of metaphysic.

Every existent is thought of like an obstacle by which we take our bearings—like something we could collide with in certain circumstances—resistent, impenetrable. We think of this impenetrability, no doubt, but we think of it as not completely thinkable.2 Just as my body is thought of in so far as it is a body, but my thought collides with the fact that it is my body.

To say that something exists is not only to say that it belongs to the same system as my body (that it is bound to it by certain connections which reason can define), it is also to say that it is in some way united to me as my body is.

Incarnation—the central ‘given’ of metaphysic. Incarnation is the situation of a being who appears to himself to be, as it were, bound to a body. This ‘given’ is opaque to itself: opposition to the cogito. Of this body, I can neither say that it is I, nor that it is not I, nor that it is for me (object). The opposition of subject and object is found to be transcended from the start. Inversely, if I start from the opposition, treating it as fundamental, I shall find no trick of logical sleight of hand which lets me get back to the original experience, which will inevitably be either eluded or (which comes to the same thing) refused. We are not to object that this experience shews a contingent character: in point of fact, all metaphysical enquiry requires a starting-point of this kind. It can only start from a situation which is mirrored but cannot be understood.

Inquire if incarnation is a fact; it does not seem so to me, it is the ‘given’ starting from which a fact is possible (which is not true of the cogito).

A fundamental predicament which cannot be in a strict sense mastered or analysed. It is exactly this impossibility which is being stated when I declare, confusedly, that I am my body; i.e. I cannot quite treat myself as a term distinct from my body, a term which would be in a definable connection with it. As I have said else-where, the moment I treat my body as an object of scientific know-ledge, I banish myself to infinity.

This is the reason why I cannot think of my death, but only of the standstill of that machine (illam, not banc). It would perhaps be more accurate to say that I cannot anticipate my death, that is, I cannot ask myself what will become of me when the machine is no longer working.3

[1] This paper was never delivered.

[2] It is thought of, but it is never resolved. The opacity of the world is in a certain sense insoluble. The link between opacity and Meinbeit. My idea is opaque to me personally in so far as it is mine. We think of it as an adherence. (Note written Feb. 24th, 1929.)

[3] ‘To be involved.’ (idée d’un engagement) Try to shew in what sense this implies the impossibility (or absolute non-validity of my representing my death. In trying to think of my death I break the rules of the game. But it is radically illegitimate to convert this impossibility into a dogmatic negation. (Note written Feb. 24th, 1929.)

It is evident that this whole train of thought is at the root of le Gouvernail: the first notes on the theme of le Gouvernail were composed a few days after these. (Note written April 13th, 1934.)

Gabriel Marcel, Being and Having: An Existentialist Diary, pages 10-12

The reader should not be afraid of converting this level of discussion to everyday life and everyday slang. For example, when Marcel uses phrases like, “I banish myself to infinity” that should resonate with phrases like “flipping out.”

Take this example from Kierkegaard. There’s a book-seller in Copenhagen and he greets a customer who has just entered his shop. The book-seller turns to his wife and says, “It is I who am speaking, isn’t it?” Kierkegaard’s book-seller seems to have “banished himself” and cannot return.

Heidegger vs. Marx as World Watchers

Marx (1818-1883) implies that the foundation of human reality is econo-technical, and on that basis society creates thoughts and philosophies, art and poems. This explanation seems appealing when we think of the economic development of China in our time, for example, or the rise of computers and software.

In a way, Heidegger (1889-1976) turns this upside down. At the basis of world history is society producing culture. You can make a simple “cartoon” and say that for Marx, economics shapes everything, and for Heidegger culture replaces economics.

For example, in his book, What Is Called Thinking? (English translation, 1968, Harper & Row), Heidegger argues the foundation of all Western thinking and culture comes from axioms such as logos [Ancient Greek: λόγος] (from which we have logic, cosmology, psychology, epistemology, etc.), as well as legein (the Greek verb λέγειν, “to speak”).

Heidegger states (on page 204), “Without the λέγειν of that logic, modern man would have to make do without his automobile. There would be no airplanes, no turbines, no Atomic Energy Commission.”

Our MI comment on this is that any monocausal explanation of how mankind went from Neanderthal to the Manhattan skyline is completely inadequate. You must create a “double-helix” of Marx and Heidegger, adding the dimensions of surprise and unintended consequences. Without the physics concepts of emergence and complexity, we have no possibility of understanding how we got to now. In the site tagline, we use the word “composite” as a reference to this kind of deeper understanding.

Education and Word and Number Hidden Vagueness

These mini-essays help students of any age to re-understand education in a deeper and more connected way.

They look for “circum-spective” intelligence. (Not in the sense of prudential or cautious but in the sense of “around-looking.”)

One of the things to begin to see is that explaining things in schools is misleading “ab initio” (i.e., from the beginning).

Let’s do an example:

In basic algebra, you’re asked: what happens to (x2 – 1)/(x – 1) as x “goes to” (i.e., becomes) 1.

If you look at the numerator (thing on top), x2 is also 1 (since 1 times 1 is 1) and (1 – 1) is zero. The denominator is also (1 – 1) and zero.

Thus you get 0 divided by 0.

You’re then told that’s a no-no and that’s because zeros and infinities lead to all kinds of arithmetic “bad behavior” or singularities.

You’re then supposed to see that x2 – 1 can be re-written as (x – 1)(x + 1) and since “like cancels like,” you cancel the x – 1 is the numerator and denominator and “get rid” of it.

This leaves simply x + 1. So, as x goes to 1, x + 1 goes to 2 and you have a “legitimate” answer and have bypassed the impasse of 0 acting badly (i.e., zero divided by zero).

If you re-understand all this more slowly you’ll see that there are endless potential confusions:

For example: you cannot say that (x2 – 1)/(x – 1) = x + 1 since looking at the two sides of the equal sign shows different expressions which are not equal.

They’re also not really equivalent.

You could say that coming up with x + 1 is a workaround or a “reduced form” or a “downstream rewrite” of (x2 – 1)/(x – 1).

This reminds us of the endless confusions in high school science: if you combine hydrogen gas (H2) with oxygen gas (O2) you don’t get water (H2O). Water is the result of a chemical reaction giving you a compound.

A mixture is not a compound. Chemistry is based on this distinction.

Math and science for that matter, are based on taking a formula or expression (like the one we saw above) and “de-cluttering” it or “shaking loose” a variant form which is not identical and not the same but functionally equivalent in a restricted way.

A lot of students who fail to follow high school or college science sense these and other “language and number” problems of hidden vagueness.
School courses punish students who “muse” to themselves about hidden vagueness. This behavior is pre-defined as “bad woolgathering” but we turn this upside down and claim it is potentially “good woolgathering” and might lead to enchantment which then underlies progress in getting past one’s fear of something like math or science or anything else.

One is surrounded by this layer of reality on all sides, what Wittgenstein calls “philosophy problems which are really language games.”

Think of daily life: you say to someone: “you can count one me.” You mean trust, rely on, depend on, where count on is a “set phrase.” (The origin of the phrase and how it became a set phrase is probably unknowable and lost in the mists of time.)

“You can count on me” does not mean you can stand on me and then count something…one, two, three.

In other words in all kinds of language (English, say, or math as a language) one is constantly “skating over” such logic-and-nuance-and-meaning issues.

The genius Kurt Gödel (Einstein’s walk around buddy at Princeton) saw this in a deep way and said that it’s deeply surprising that languages work at all (spoken, written or mathematical) since the bilateral sharing of these ambiguities would seem deadly to any clarity at all and communication itself would seem a rather unlikely outcome.

You could also say that drama giants of the twentieth century like Pinter, Ionesco and Beckett, intuit these difficulties which then underlie their plays.

All of this together gives you a more “composite” “circum-spective” view of what is really happening in knowledge acquisition.

Education and the “Knowability” Problem

There was a wonderful PBS Nature episode in 2006 called “The Queen of Trees” [full video, YouTube] which went into details about the survival strategy and rhythms and interactions with the environment of one tree in Africa and all the complexities this involves:

This Nature episode explores the evolution of a fig tree in Africa and its only pollinator, the fig wasp. This film takes us through a journey of intertwining relationships. It shows how the fig (queen) tree is life sustaining for an entire range of species, from plants, to insects, to other animals and even mammals. These other species are in turn life-sustaining to the fig tree itself. It could not survive without the interaction of all these different creatures and the various functions they perform. This is one of the single greatest documented (on video) examples of the wonders of our natural world; the intricacies involved for survival and ensuring the perpetual existence of species.

It shows us how fragile the balance is between survival and extinction.

One can begin to see that the tree/animal/bacteria/season/roots/climate interaction is highly complex and not quite fully understood to this day.

The fact that one tree yields new information every time we probe into it gives you a “meta” (i.e., meta-intelligent) clue that final theories of the cosmos and fully unified theories of physics will be elusive at best and unreachable at worst. If one can hardly pin down the workings of a single tree, does it sound plausible that “everything that is” from the electron to galaxy clusters to multiverses will be captured by an equation? The objective answer has to be: not particularly.

Think of the quest of the great unifiers like the great philosopher–physicist Hermann Weyl (died in 1955, like Einstein):

Since the 19th century, some physicists, notably Albert Einstein, have attempted to develop a single theoretical framework that can account for all the fundamental forces of nature–a unified field theory. Classical unified field theories are attempts to create a unified field theory based on classical physics. In particular, unification of gravitation and electromagnetism was actively pursued by several physicists and mathematicians in the years between the two World Wars. This work spurred the purely mathematical development of differential geometry.

Hermann Klaus Hugo Weyl (9 November, 1885 – 8 December, 1955) was a German mathematician, theoretical physicist and philosopher. Although much of his working life was spent in Zürich, Switzerland and then Princeton, New Jersey, he is associated with the University of Göttingen tradition of mathematics, represented by David Hilbert and Hermann Minkowski.

His research has had major significance for theoretical physics as well as purely mathematical disciplines including number theory. He was one of the most influential mathematicians of the twentieth century, and an important member of the Institute for Advanced Study during its early years.

Weyl published technical and some general works on space, time, matter, philosophy, logic, symmetry and the history of mathematics. He was one of the first to conceive of combining general relativity with the laws of electromagnetism. While no mathematician of his generation aspired to the “universalism” of Henri Poincaré or Hilbert, Weyl came as close as anyone.

Weyl is quoted as saying:

“I am bold enough to believe that the whole of physical phenomena may be derived from one single universal world-law of the greatest mathematical simplicity.”

(The Trouble with Physics, Lee Smolin, Houghton Mifflin Co., 2006, page 46)

This reminds one of Stephen Hawking’s credo that he repeated often and without wavering, that the rational human mind would soon understand “the mind of God.”

This Weyl–Hawking–Einstein program of “knowing the mind of God” via a world-equation seems both extremely charming and beautiful, as a human quest, but potentially mono-maniacal à la Captain Ahab in Moby-Dick. The reason that only Ishmael survives the sinking of the ship, the Pequod, is that he has become non-monomaniacal and accepts the variegatedness of the world and thus achieves a more moderate view of human existence and its limits. “The Whiteness of the Whale” chapter in the novel gives you Melville’s sense (from 1851) of the unknowability of some final world-reality or world-theory or world-equation.