Dialectical Theology

In The Will to Believe (1897), William James, marshalling arguments for the defensibility of theistic belief, writes (p. 61):

God himself may draw vital strength and increase of very being  from our fidelity.

We may christen this  the Tinkerbell Theory of the nature of God.

[Note:  Not making fun of James’ idea,  just naming it.]

For:  Recall when Tinkerbell, having herself imbibed the poison potion, that Peter might be spared, was fading fast;  and Peter Pan, stepping boldly outside the frame of footlit fiction, turns to address the audience, bidding all who “believe in fairies” to demonstrate their faith by some sign, such as clapping or shouting or tossing five-dollar bills onto the stage.   The audience complies, and the sprite recovers -- at least, that was the drill in 1956, the year I saw the play on Broadway (with Mary Martin in the title role).   Who knows what kids today would do, their minds rotted by brutish masscult -- probably drown the little cross-dressing actress out with vuvuzelas.

Anyhow.

The thought, thus limited, is plausible, on the analogy of the inner strength which parents gain while laboring to nurture their babies.  But the parents are fully present before the baby arrives.  Quite otherwise is a variant whereby the creatures themselves somehow bring the Creator -- or the invisibilia -- into being.  We might call this the “…chicken begat the egg begat the chicken begat the egg begat…” Hypothesis (again, just to give it a name).

Thus, we recur to Michael Dummett, “Truth” (1959), repr. in Truth and other enigmas (1978), who (as we saw earlier) wrote, on p. 18: “Intuitionists speak of mathematics in a highly anti-realist (anti-platonist) way:  for them it is we who construct mathematics; it is not already there”, and contrasted this with the full-bore Realist “Fregean notion of a mathematical reality waiting to be discovered”:  Intermediate between these opposing views, Dummett offers a compromise (to my mind, incoherent):

If we think that mathematical results are in some sense imposed on us from without, we could have instead the picture of a mathematical reality  not already in existence, but as it were  coming into being as we probe.  Our investigations bring into existence  what was not there before, but what they bring into existence  is not of our own making.

Here is another spin on this surprising idea:   John McDowell, in Evans & McDowell, eds., Truth and Meaning (1976), p. 48:

The alternative conception of sense would require a novel, anti-realist conception of the world:  if truth is not independent of our discovering it, we must picture the world  either as our own creation, or, at least, as springing up in response to our investigations.

And indeed, one of our own readers -- not a professional philosopher by any means -- recently commented:

God and Man are both Necessary and Contingent. The existence of one depends upon the other. The mind of man evolved to recognize and name God, therefore, God's existence is contingent upon man. God is also necessary because, logically, if Man, and the Mind of Man exist, then so too must God exist. And vice-versa. Man, or rather the mind of man, is necessary to recognize God and therefore bring God into existence.

The only thing I can make of these various related statements, is that they are conflating the notions of Reality or (Existence) and Reality(Existence)-for-us, a move to which I took exception here.

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            This general style of thinking would seem to cohere with the contemporary complexus of attitudes which we may group under the rubric of “Gaia”.  These appear in many different forms.  Thus from Richard Rorty, Philosophy and the Mirror of Nature (1979), p. 297, commenting on the views of Wilfrid Sellars, Jay Rosenberg, and C.S. Peirce:

Sellars wants to substitute a way of looking at human inquiry which views “fated to be agreed upon” as a description of a causal process which leads to the creation of self-representings by the universe.  Thus we find Rosenberg echoing the later Peirce’s idealistic metaphysics of evolutionary love:

We must come to see the physical universe as an integrated physical system which necessarily “grows knowers” and which thereby comes to mirror itself within itself.

If you prefer that to simple Realism, fine.  “Fated to be agreed upon” sounds like an awfully roundabout way to avoid uttering the forbidden word true, but hey, de gustibus.

 

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Note:  That mealy-mouthed “fated to be agreed upon” crap  is isomorphic to the celebrated formula of John Stuart Mill, to the effect that actual objects (like a cat) are “permanent possibilities of sensation”.  This was intended to avoid the agnostic absurdity of “it’s all just colour-patches and raw feels”, while skirting the forbidden Realism. -- To which I reply:  That’s the cat.  It’s on the mat.  Deal with it.

Babylonian mathematics

In The Character of Physical Law (1965), the physicist Feynman presents an informal dichotomy between the “Greek” and the “Babylonian” approach to science.  The Greek: axiomatic, systematic.  The Babylonian: ad-hoc bricolage.  I satirized the latter in the parable of the humble woodchuck (“Constructivist Angelology”).

In this morning’s reading, I happened upon this:

Shlomo Sternberg, Celestial Mechanics (1969), p. 1:

In most popular accounts, the contributions of the Babylonians …  are consistently underestimated.  The Babylonians, in addition to having accumulated impressive observational data, based their tables and predictions on a form of Fourier analysis (using what are now known as “spline functions” instead of trigonometrical series).

!!! -- I stand corrected.

E8: a Riposte (concluded)

Let us examine a bit more closely  Synge’s picture of physics as bricolage,  where theories have the intellectual status of just-so stories, and are really little more than pragmatic techniques, or tools -- Newtonian mechanics and relativistic mechanics each useful in its own sphere, like screwdrivers and spoons, but of little interest in their own right.   Now, this is not to knock the status of a toolkit -- my respect for competent carpenters and electricians borders on reverence -- but fundamental physics is not like that.

            Synge presents the Newtonian view as having not been replaced or refuted by relativity;  it rules as before in its own realm.  Newton’s good for some things, Einstein for others, and Wiccan no doubt for others still.   But this view assumes a confusion.  For it is not the case that Newtonism and relativity are independently valid in their own way but incompatible;  rather, Newtonism is the limiting case of relativity, in a way very familiar in mathematics;  its continued use in everyday life is simply a calculational convenience, a shortcut.   To continue the tool metaphore:  Einstein and Newton are not like screwdriver and pliers, but like a hammer, and an old shoe used as a hammer, good enough for the task at hand.

            Furthermore, it is a good thing, not a bad thing, when initially separate paths converge.  If you only know one way to climb a thing,  perhaps it is only a Potemkin mountain -- a paper-maché façade, hollow behind the north slope.   It is quite a relief -- and an ontological ratification -- to meet another mountaineering party that has scaled up the other side.

            The reader may be familiar with the story of how Schrödinger and Heisenberg separately found Rome by different roads.  Let George Gamow tell it, in Thirty Years that Shook Physics (1966), p. 3:

The simultaneous appearance of Schrödinger’s and Heisenberg’s papers  in two different German magazines … astonished the world of theoretical physics.  These two papers looked as different as they could be, but led to exactly the same results concerning atomic structure and spectra.

We are, in hindsight, not overly surprised by this, since by now we most of us accept that there is something there at the quantum level, something real, something other than subjective, to be described.   It is describable by two quite different mathematical approaches, much as our peak may be scaled by walking up the north face  or rappelling up the southern cliffs.    Nor is such ‘duplication of effort’ a waste of time, for  in this instance, not only the factual success, but even the approaches themselves retained their usefulness -- for determining energy levels, Schrödinger’s wave mechanics was calculationally more convenient; and Heisenberg’s matrix methods had the edge when it came to calculated the intensities of the radiated frequencies.   Or, alternately, P.A.M. Dirac, The Principles of Quantum Mechanics (4^th edn. 1958), p. viii:

Quantum mechanics … is known under one or other of the two names ‘Wave Mechanics’ and ‘Matrix Mechanics’, according to which physical things receive the emphasis in the treatment, the states of a system or its dynamical variables.

And (p. 115):

The Schrödinger form is the more useful one for practical problems, as it provides the simpler equations. … Heisenberg’s form for the equations of motion  is of value in providing an immediate analogy with classical mechanics.

Or again (R. F. Streater & A. S. Wightman, PCT, Spin & Statistics, and All That (1964), p. 4):

Throughout this book, states will be described in the Heisenberg picture of quantum mechanics.  The Schrödinger picture is much less convenient for the description of a relativistic theory, because it treats the time coordinate on a very different footing from the space coordinates.

And:

P.A.M. Dirac, The Principles of Quantum Mechanics (4^th edn. 1958), p. 311:

The Schrödinger picture is unsuited for dealing with quantum electrodynamics, because the vacuum fluctuations play such a dominant role in it. … They get bypassed when one uses the Heisenberg picture, and one is then able to concentrate on qualities that are of physical importance.

Dr. Matrix

Dr. Wave

Approaching an abstract but genuine reality from two different theoretical complexes  has its counterpart in different experiments, or different means of calculation, strengthen each other when they arrive at the same result.   Thus Einstein, in his annus mirabilis of 1905, when not inventing Relativity, found it worth his while  to “develop theoretically  three independent methods for finding Avogadro’s number.” (Abraham Pais, Subtle is the Lord (1982), p. 55.)   It was worth his while because, independently of our endeavors, this number is indeed there.

Summarizing:  For epistemology, the fact that two or more radically different approaches each manages to describe the phenomenon of interest, reassures us that we really do have our arms around this thing.   The lesson goes over, I would submit, in cases where what is being described is nothing so tangible as an atom (which Rutherford reportedly saw in front of his face as plainly as a spoon), but rather a four-manifold, or a simple Lie group.

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Afterword.

I recently happened across the following curious passage:

The algebras G_2, […] E_8  are called exceptional.  In 1945, Chevalley remarked  that the existence of these algebras  is a brutal act of Providence  which we must accept blindly.  Perhaps this should be revised today  to assert that the source of these algebras  is the wisdom of the Deity  in allowing the Cayley numbers to exist.

-- Irving Kaplansky, “Lie Algebras”; in: T. L. Saaty, ed.  Lectures on Modern Mathematics, vol. I (1963), p. 126

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There’s one further type of brane in M-theory  that is really surprising.  This brane is the edge of spacetime. … The photons at the edge of spacetime participate in supersymmetric E₈ gauge theory.

-- Steven Gubser, The Little Book of String Theory (2010), p. 95