Aleksandar Mikovic on Platonic Metaphysics

Godel's Incompleteness Theorems and Platonic Metaphysics

A law of Nature can be easilly understood within a platonic metaphysics. It is a postulate in a mathematical theory we use to describe the Nature. On the other hand, explaining the laws of Nature within a materialistic metaphysics, is more complicated. If one accepts that the natural laws are different entities from space, time and matter, and are irreducible, then for a materialist it does not seem to be a problem to add a finite set of such objects to his ontology. In this case the natural laws are the postulates of a finite TOE. However, any TOE has to include the aritmethics, so that Goedel's theorems imply that there can not be a finite number of laws which completely explain the universe and one must introduce an infinite number of natural laws. This means that in addition to space, time and matter, one has to introduce an infinite number of other entities, which are not reducible to space, time and matter, and hence one is back at platonism.

In order to avoid introducing an infinite number of non-material entities in a materialistic metaphysics, one then has to give up the idea of a natural law as a mathematical concept (i.e. a postulate in a mathematical theory). Then the only explanation for a natural law in a materialistic metaphysics is that a natural law represents a regular pattern which appears in the fundamentaly chaotic motion of matter. This regularity appears at random and lasts for a very long time. In this case one accepts the view that at the fundamental level there is no order and the particle trajectories and field configurations are completely arbitrary. This doctrine is a logical possibility, but it is highly implausible. The standard example for this type of implausibility is to find a string of letters in a random sequence of letters which corresponds to a well-known novel; or to construct a functioning airplane by using a tornado passing through a junk yard. Also, if the natural laws are finite-duration random regularities, then the Earth can stop orbiting the Sun tomorrow, which means that our reality can disintegrate at any time in the future.

Another problem in a materialistic metaphysics is how an observer will recognize a natural law given that the ideas of order do not exist. This is also a problem in a platonic metaphysics, see [6], but it is a less severe problem, because the basic elements from which one can construct a solution already exist, see [2] for a possible solution.

"[2]" is this paper:

Temporal Platonic Metaphysics

We have presented a Platonic metaphysics where time plays the essential role: it serves to distinguish between real and abstract universes. This role of time together with our proposed mind-brain connection resolves the epistemological problem in platonism [1]. Namely, if the abstract ideas are outside of spacetime, then how can we do mathematics? According to our approach, the answer is that our mind, which is a temporal sequence of ideas contained in our brain, will contain the copies of these abstract ideas.

An important consequence of the assumption that passage of time is a non-mathematical idea, is that mind is not a mathematical structure. This is because we can imagine processes in time, so that the idea of passage of time is contained in our mind. Hence our mind is not a mathematical structure. This then implies that a mind cannot be simulated on a computer.

Note that our approach represents a generalization of von Neumann’s idea to formulate QM as a theory of evolving objective universe interacting with human consciousness, see [9]. In theories with global time, the conflict with relativity can be a voided if one postulates that the label is not the same as a clock reading and that a clock reading depends on the clock trajectory. On the other hand, it is clear that is related to the age of the universe. Since always increases, then the time travel will be impossible within our framework.

From the platonic perspective, existence of multiple universes is natural, since all possible universes exist as objects in the World of Ideas. Further more, by assuming that the passage of time is a fundamental and a non-emergent concept, one can divide all possible universes into the temporal ones and the timeless ones. The temporal universes can be then considered as real, i.e. like the universe we live in, while the timeless universes can be considered as abstract.