Part III. The Second Miracle: The evolution of the biosphere is a propagating, non-deducible construction, not an entailed deduction. There is no Law. Evolution is ever-creative.

All classical physics, the physics of Newton, lives within the Newtonian Paradigm: i. State the relevant variables, for example position and momentum. ii. State the Laws of Motion in differential form connecting the relevant variables. Newton’s three laws of motion are an example. iii. Define the boundary conditions. These define the phase space of all possible combinations of values of the relevant variable. iv. State the initial conditions. v. Integrate the equations of motion to obtain the entailed determined single trajectory in the system’s phase space, (41,42,43).

\ The Newtonian Paradigm is unchanged in Quantum Mechanics. Schrödinger’s wave equation is integrated to obtain the entailed trajectory of a probability distribution. Then measurement, typically held ontologically random, occurs, (42,43).

\ It is fundamental to the entire Newtonian paradigm, hence of all modern physics, that the phase space must be specified beforehand, (42,43).

\ We show next that the evolving biosphere of Kantian Wholes persistently creates novel phase spaces that cannot be deduced or determined ahead of time. The entire Newtonian paradigm collapses. The evolving biosphere cannot be explained by physics alone. Appeal to “function” is necessary.

\ These issues are basic, (42,43):

\ i. Once we have defined a Kantian Whole, the non-circular definition of the “function” of a Part is clear. The function of a part is that subset of its causal consequences that sustains the Whole. The function of your heart is to pump blood, not make heart sounds or jiggle water in your pericardial sac.

\ ii. Selection acts at the level of the Kantian Whole organism, not its Parts. Selection does not directly select for hearts that are more efficient at pumping blood. Organisms that inherit such improved hearts are more likely to have offspring, thus improved hearts are indirectly selected.

\ iii. Because the function of a Part is that subset of its causal properties that sustains the Whole, the function of the very same part can change. Some new, unused, subset of causal properties of the same Part can come to sustain the Whole. These are called Darwinian pre-adaptations, or by Gould and Verba, exaptations, (44). Examples include the co-opting of scales that evolved for thermoregulation on some dinosaurs to evolve into flight feathers on birds. Other examples include the co-opting of normal enzymes to become transparent lens proteins. A superb example is the evolution of swim bladders from the lungs of lung fish, (43).

\ iv. A remarkable and fundamental feature of such exaptations is that they cannot be deduced. Consider a hypothetical example. An engine block can be used as a paper weight. The same engine block has sharp corners that can be used to crack open a coconut. But from the fact that an engine block is being used as a paper weight, it cannot be deduced that “This object can be used to crack open coconuts”. This object might have been a banana peel.

\ v. Such new uses of the same object are “Jury Rigging.” There is no deductive theory of Jury Rigging.

\ vi. The truly profound implication is that such non-deducible jury-rigged exaptations are the source of functional novelty and the open-ended evolution of the biosphere. The evolution of the biosphere is a non-deducible construction not an entailed deduction. No entailing laws govern the evolution of the biosphere, (42,43).

\ vii. The further implication is equally profound. We cannot list all the uses of an engine block alone or with other things. We also cannot list all the uses of a screwdriver alone or with other things. Therefore, we cannot use Set Theory or any mathematics based on set theory: The First Axiom of Set Theory is the Axiom of Extentionality, (45): “Two sets are equal if and only if they contain the same members”. But we cannot prove that the un-listable uses of an engine block are identical to the un-listable uses of a screwdriver. More the Axiom of Choice fails as well. The implication is huge: We can use no mathematics based on Set Theory – essentially all of mathematics – to deduce the future evolution of the biosphere.

\ viii. No union and intersection of Sets. No First Order Logic. No numbers via Russell, (43, 46). No numbers via Peano, (43, 47). No equations. No real numbers. No real line. No manifolds. No topology. No equations on manifolds. No integration of the equations we cannot write.

\ ix. The entire Newtonian Paradigm that is the basis of all physics, requires a prestated phase space. But we can neither deduce nor prestate the evolving phase space of the evolving biosphere, (42,43). Evolution is beyond the Newtonian Paradigm.

\ x. We cannot explain the evolving biosphere with physics alone. The heart evolved by virtue of its function pumping blood. Natural selection of heritable variation acts on the Kantian Whole, not directly on its Parts. Such selection is Downward Causation. Here, the explanatory arrows point upward.

\ xi. Strong reductionism, the dream of many, fails. If the Final Theory to be inscribed on the famous T-shirt is to include the deduction of the evolving biosphere, there is no final theory.

\ xii. Heisenberg’s demonstration of the Uncertainty Relation demanded that we abandon Classical Physics, (48).

\ xiii. If we must abandon Set Theory with respect to biological evolution, what are the implications? We hardly begin to know.

\ xiv. We now enter the Third Transition in Science, (43). The new fundamental questions surely include: How does the evolving biosphere create, and seize by heritable variation and Natural Selection, or genetic drift, the ever-new bubbles of possible ways organisms can co-exist for some period as the burgeoning wave of life flowers onward.

:::info This paper is available on arxiv under CC BY 4.0 DEED license.

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