“One consequence of the Occidental obsession with transcendence… is a physics that is forever pompously asserting that it is on the verge of completion. The contempt for reality manifested by such pronouncements is unfathomable. What kind of libidinal catastrophe must have occurred in order for a physicist to smile when he says that nature’s secrets are almost exhausted? If these comments were not such obvious examples of megalomaniac derangement, and thus themselves laughable, it would be impossible to imagine a more gruesome vision than that of the cosmos stretched out beneath the impertinently probing fingers of grinning apes. Yet if one looks for superficiality with sufficient brutal passion, when one is prepared to pay enough to systematically isolate it, it is scarcely surprising that one will find a little. This is certainly an achievement of sorts; one has found a region of stupidity, one has manipulated it, but this is all. Unfortunately, the delicacy to acknowledge this – as Newton so eloquently did when he famously compared science to beach-combing on the shore of an immeasurable ocean requires a certain minimum of tast, of noblisse.”
– Nick Land, A Thirst for Annihilation (34)
That most scientists are not philosophers is to the detriment of philosophy. Yet we must not forget the success of science which philosophers seem to gloss over (except within the confines of the Philosophy of Science). As Land tells it the damage has been done, philosophy has even come to the point, the stage of obsolesence that “it has lost all confidence in its power to know … For at least a century, and perhaps for two, the major effort of the philosophers has simply been to keep the scientists out. How much defensiveness, pathetic mimicry, crude self-deception, crypto-theological obscurantism, and intellectual poverty is marked by the name of their recent and morbid offspring…” (35).
My notes follow:
The idea that any group of scientists could totalize the untotalizable dynamism we call the multiverse or universe (in the old parlance) is in itself mythology pure and simple. The Idealism that pretends to mathematize Nature, Being, etc., to reduce it to a subset of set-theory, or any advanced mathematical theorem is in itself a delusionary pursuit. Yet, this form of physics is only a subset of Science and Scientists that see this ToE as even relevant to physics itself.
As Freeman Dyson once stated “Gödel’s theorem implies that pure mathematics is inexhaustible. No matter how many problems we solve, there will always be other problems that cannot be solved within the existing rules. […] Because of Gödel’s theorem, physics is inexhaustible too. The laws of physics are a finite set of rules, and include the rules for doing mathematics, so that Gödel’s theorem applies to them.”
Yet, the conclusions of Gödel’s theorems are only proven for the formal theories that satisfy the necessary hypotheses. Not all axiom systems satisfy these hypotheses, even when these systems have models that include the natural numbers as a subset. For example, there are first-order axiomatizations of Euclidean geometry, of real closed fields, and of arithmetic in which multiplication is not provably total; none of these meet the hypotheses of Gödel’s theorems. The key fact is that these axiomatizations are not expressive enough to define the set of natural numbers or develop basic properties of the natural numbers. Regarding the third example, Dan E. Willard (Willard 2001) has studied many weak systems of arithmetic which do not satisfy the hypotheses of the second incompleteness theorem, and which are consistent and capable of proving their own consistency.
No physical theory to date is believed to be precisely accurate. Instead, physics has proceeded by a series of “successive approximations” allowing more and more accurate predictions over a wider and wider range of phenomena. Some physicists believe that it is therefore a mistake to confuse theoretical models with the true nature of reality, and hold that the series of approximations will never terminate in the “truth”. Einstein himself expressed this view on occasions. Following this view, we may reasonably hope for a theory of everything which self-consistently incorporates all currently known forces, but we should not expect it to be the final answer.
There is a philosophical debate within the physics community as to whether a theory of everything deserves to be called the fundamental law of the universe. One view is the hard reductionist position that the Theory of Everything(ToE) is the fundamental law and that all other theories that apply within the universe are a consequence of the ToE. Another view is that emergent laws, which govern the behavior of complex systems, should be seen as equally fundamental. Examples of emergent laws are the second law of thermodynamics and the theory of natural selection. The advocates of emergence argue that emergent laws, especially those describing complex or living systems are independent of the low-level, microscopic laws. In this view, emergent laws are as fundamental as a ToE.
Lee Smolin regularly argues that the layers of nature may be like the layers of an onion, and that the number of layers might be infinite.This would imply an infinite sequence of physical theories.
Yet others submit that this argument is not universally accepted or valid, because it is not obvious that infinity is a concept that applies to the foundations of nature. The results of quantum theory strongly suggest that nature is not infinite in its foundations, because space and time have been shown to break down at smaller quantities than the “Planck” values.
Steven Weinberg points out that calculating the precise motion of an actual projectile in the Earth’s atmosphere is impossible. So how can we know we have an adequate theory for describing the motion of projectiles? Weinberg suggests that we know principles ( Newton’s laws of motion and gravitation) that work “well enough” for simple examples, like the motion of planets in empty space. These principles have worked so well on simple examples that we can be reasonably confident they will work for more complex examples. So a ToE must work for a wide range of simple examples in such a way that we can be reasonably confident it will work for every situation in physics.
Even Stephen Hawking who was originally a believer in the Theory of Everything after considering Gödel’s Theorem, concluded that one was not obtainable. “Some people will be very disappointed if there is not an ultimate theory, that can be formulated as a finite number of principles. I used to belong to that camp, but I have changed my mind.”