The Actual, The Possible And What's Real : 13.7: Cosmos And Culture Stuart Kauffman is beginning to think of a dualism, Res Extensa and Res Potentia.  It cannot kill us, he says, to think about it and it may be important.

The Actual, The Possible And What's Real

We have lived with scientific “monism” since Newton.

Monism is the view, shared by virtually all scientists, that the world is made of one kind of “stuff,” the Actual world of matter and energy and with some question marks, space and time and information.

There are very good grounds to accept monism. And it has an ancient history. No less an ancient philosopher, Empedocles said, “What is real in the universe is what is actual.”

Aristotle was less sure, he toyed with the idea that both the Actual and the Possible were “Real."  He called the Possible “potentia” and meant a variety of things by Potentia. And no less a mathematician and philosopher than Alfred North Whitehead, he of Principia Mathematica in the early 20th Century, written with Bertrand Russell, moved on to think of both Actuals and Possibles as “real,” or “ontologically real,” meaning two kinds of “stuff”, Actuals and Possibles in the universe.

I’m beginning, to my surprise to think Aristotle and Whitehead may have been right. If so, the implications seem pretty radical.  I’m beginning to think of a dualism, Res Extensa and Res Potentia.  It cannot kill us to think about it, and it may be important.

Yet the dominant view, the overwhelming view, the probably correct view of the world is the monism we have lived with since Newton.

We have arrived at our monist views by the enormous successes of classical physics, starting with stunning Newton himself. Consider:

  1. Aristotle gifts us a model of scientific explanation: deduction.  All men are mortal, Socrates is a man, therefore Socrates is a mortal.  I ask you to feel the logical force driving you from premises to conclusions, for this very logical force in part underlies our sometimes belief that the laws of nature “force” how nature behaves, they “govern” the universe.
  2. Newton invents his famous three laws of motion, invents the differential calculus, whose solutions require the initial conditions of, say, the billiard balls on the table and the boundary conditions, the edges of the table.  Given the initial positions and momenta of the balls, and the boundary conditions, we integrate Newton’s three laws  of motion, where integration is precisely deduction, to derive from the initial Actual positions and momenta of the balls, the Actual positions and momenta of the balls and any future or past moment of time.  There are Possibles in Newton’s world. Given the present position and momenta of all the balls, the future and past positions and momenta are in a weak sense Possibles, but since the equations are determinsitic, there is only one possible future or past position and momenta of all the balls at any moment.  As Laplace said: Given sufficient information about the positions and momenta of all the particles in the universe, and Newton’s laws, the entire future and past of the universe is determined.
  3. Einstein’s probable culmination of classical physics is the gigantic General Relativity. In a whirlwind triumph of courage, imagination, and mathematics, Einstein constructs a world view of a four dimensional spacetime block universe in which there are no Possibles at all. All that exist are four dimensional “world lines” spanning the block universe.  No Possibles at all, Empedocles triumphant 2700 years later.

But is it so?  A powerful doubt was raised before Newton by Descartes, whose invention of analytical geometry paved the way for the calculus.  Descartes thought the world consisted of two substances, mind stuff and matter stuff, Res Cogitans and Res Extensa.   If you are reading this blog, you know perfectly well what mind stuff is, it is your awareness of what you are seeing and understanding....whatever that is.

Well, Descartes’ dualism, Res cogitans and Res Extensa have not fared well given classical physics and its vast successes.  No, nothing but Actual Res Extensa, thank you.

Please do not get “metaphysical” on us.

But maybe Descartes was not entirely wrong?

I begin to suspect that Rene’ Desdartes was on to something we live with, Res Potentia, the Possible.  The rest of this blog spells out why I suspect this.  
A central reason to suspect that Res Potentia is real, ontologically real, is Quantum Mechanics itself.

However, I want to begin with a point made in a different context by American philosopher, Charles Sanders Pierce in the 19th Century  Pierce noted three “modalities”, the Actual, the Possible, the Probable.  All this bears on Aristotle and his famous “law of the excluded middle”. Consider the statements “A” and “Not A”. There is nothing, said Aristotle, that is in the “middle” of A and Not A.  One or the other, please.

But wait, said Pierce, “A is True”, “A is possibly true”, “A is false”.   The “Possible” evades the law of the excluded middle, indeed it is smack in the middle between “A is True” and “A is False”.

Now consider the famous two slit experiment with its well known photon gun squirting photons at one per minute at a barrier with two open slits and a photo-detector screen on the far side. We all know the results: One sees the famous interference banded pattern of light and dark bands spanning the detector screen between where bullets would hit the screen if passing via slit 1 or via slit 2.  So light is behaving as a wave.  And, in the Copenhagen interpretation, upon which I will depend, we can say of the photon that it is possible that the photon went through slit 1 and also at the same time it is possible that the photon went through slit 2.  Indeed, in R. Feynman’s wonderful “sum over all possible histories formulation of quantum mechanics, we say that the single photon simultaneously took all possible pathways at the same sequence of time moments, from the photon gun, through both slits, to the detector screen. We cannot say the photon “really” went through slit one or slit two.

Quantum Mechanics, it seems safe to say, evades the law of the excluded middle! Classical physics does not!

But things get worse with the famous Bell’s inequalities, now very well established experimentally, and which grow out of the 1935 Einstein, Podolsky, Rosen paper. Bell’s inequalities have to do with “entangled quantum particles” and it is fun to read about it. For now, the conclusion is my focus.  Given the experimental results, we are forced either to abandon “locality” in physics, or we are forced to abandon “the Definiteness of CounterFactual Statements!”.  Now giving up locality, ie non-locality, is generally not welcomed by physicists, who want to believe that Actual events have spatially local Actual casual consequences.

Well, what about giving up "The definiteness of counter-factual statements?"  A counterfactual statement is something like this: "A caused B, and if A had not occurred (contrary to fact), B would not have occurred."

But the definiteness of counterfactual statements rests on the law of the excluded middle. Try the above with “A occurred and B possibly occurred and (contrary to fact) A did not occur so it is not possible that B  occurred.  Not so.

Possibles evade the definiteness of counterfactual statements.

So what?

Maybe a lot.

“If you think you understand quantum mechanics, you have not thought about it.” said Feynman.  Yes, and I am not a physicist, so caveat lector.  
But we have tried rather desperately for 70 years to come to terms with Quantum Mechanics based solely on an ontologically real Actual, we children of Newton.  We have the Multiple World interpretation, the non-local Bohmian interpretation, and the Copenhagen interpretation abetted by a transition between the quantum and classical world via decoherent acausal loss of phase information from the Schrodinger wave equation.

And we have 70 years of struggle to meld General Relativity with Quantum Mechanics, so far to no clear success.  The general claim is that General Relativity is nonlinear and Quantum Mechanics is a linear theory so it is hard to meld the two. Yes. But also, I now want to claim, General Relativity is based only on ontological Actuals. Quantum Mechanics, it seems to me, is fully interpretable in terms of ontologically real Possibles. Res Potentia.  Quantum Mechanics is consistent with a different ontology than General Relativity, one that allows Res Extensa and Res Potentia!

On this new dualism, Res Extensa and Res Potentia, what is then waving in the mathematical formalism of Quantum Mechanics is exactly what physicists say, but don’t mean, the waves are waves of “possibilities” (wink wink), and when you square the amplitudes of the waves you get probabilities, Born’s rule, and thank goodness Probabilities obey the law of the excluded middle. We are back on safe turf.

Maybe, just maybe, we have an ontological dualism. We have Res Extensa, the Actual. And we have Res Potentia, the Possible. Both are real as Aristotle hinted and Whitehead insisted.

If you think about it, our entire awake lives are guided by the Possibles we live with and act to create. (See my blogs: Toward a Responsible Free Will, and The Hard Problem Consciousness.)  I begin to suspect that what I call the “Adjacent Possible” that grows forever out of the nexus of what is Actual, as in technological evolution, cultural evolution and history, is an ontologically real Possible.

A final thought: If the Possible is real, then constructive and destructive interference in the Schrodinger time dependent wave equation constitute real possibilities that interact with one another as real possibilities to create the famous two slit banding interference patterns.  Res Extensia, of course. Res Potentia? What happens in Res Potentia?  Perhaps Quantum Mechanics and much of the universe.