Before we can evaluate the logic of some statement or theory, we must first have a system of logic that serves as the standard of evaluation. Logic is a fundamental tool for validating statements relative to their content. Classical (Aristotelian) logic introduced the fundamental principles of any applied logic: 1. The law of identity. 2. The law of non-contradiction 3. The law of the excluded middle. These principles are axiomatic based on the natural universe, a universe that has identity. Thus the law of identity holds that everything that is, is what it is; it has a specific nature that defines its capabilities and limits. The law of non-contradiction holds that an assertion cannot be both true and false about the same existent in the same respect. The law of the excluded middle holds that any assertion about existents must be either true or false; there is no middle ground of truth.
Clearly logic, a tool of epistemology (which answers such questions as 'What is knowledge, and how is knowledge achieved') must rest on a system of metaphysics (which answers such questions as: 'What is being and what is the nature of being qua being. What do we know from the sheer fact that something 'is'?
Classical physics is based on a metaphysics that views the world as having a non-contradictory identity and on an epistemology that views knowledge as the process of identification and integration of the facts of existence, through the power of reason, using its tools of induction and deduction constrained by the laws of classical logic.
Based on my layman understanding of it, quantum logic appears to be an inherently ambiguous concept. It generally refers to the special nature of quantum 'facts'. These include 1. That no absolute mathematical facts about instances of existents are possible at the quantum mechanical level, since all facts about the measurable properties of existents are stochastic (defined entirely and exclusively in terms of probabilities, not actualities), 2. Probability, in the QM view permeates the universe thoroughly and metaphysically, implying that at the QM level (which quantum theory holds to be the foundational level of all existence) nothing has an ontological determinate value, all properties of existents being absolutely ontologically stochastic, 3. Human knowledge (including scientific knowledge) of concrete existents requires measurement (that is any form of epistemological 'looking') and that the very act of 'looking' causes the quantum phenomenon under observation to collapse its probabilistic wave into an determinate transient 'fact'.
This QM epistemological view is, of course, in direct contradiction to classical views of knowledge that hold that facts are neither caused by nor influenced by acts of consciousness (perceiving, thinking, wishing, etc.). So here is where the epistemology/ ontology of QM jars the rational mind: The assertion that looking or measuring alters the state of the physical world and causes facts to come into (as well as their contraries go out of) existence. This view is a species of the primacy of consciousness, which holds that consciousness, on its own without body, can cause reality to come into existence. This is the basis of theories of God as the Creator of the Universe. Modern science has, until QM theory, repudiated the primacy of consciousness doctrine. Now it is part of QM doctrine. No wonder theologians are now encouraged by QM!
Part of the problem in understanding QM logic is that QM theory does not seem to embrace the established meaning of the concept of probability. Probability is an epistemological not an ontological concept. It refers to limitations of knowing about a fact in a given context (such as a coin toss), where the initial conditions could result in any one of a number of possible (potential) outcomes (actualizations). Probability is a mathematical tool for quantifying the uncertainty of stochastically determined potential outcomes. Probability, in this view, is not an ontological statement about facts of existence in the objective world (independent of consciousness). The world itself and its existents are what they are at any moment. What is possible to entities as an outcome of their previous states is determined by their internal determinate nature. The view that the universe embodies natural laws means that the universe is determinate and that any fact about the universe that we care to study has a determinable nature. This part of what it means to say that facts (not our ability to know them in a given cognitive context) are determinate and not merely probable. This is what Einstein meant by his assertion: 'God does not play dice with the universe.'
For an excellent discussion of Einstein's views on Quantum Theory and its relationship to reality, see Quantum: Einstein, Bohr, and the Great Debate about the Nature of Reality by Manjit Kumar, W. W. Norton & Company, 2008. See especially Chapter 13 Quantum Reality for a full discussion of the ERP (Einstein, Rosen, Podolsky) critique of QM as incomplete in its lack of correspondence mapping between its concepts and the physical (real) world.
From my blog article: http://bioperipatetic.com/aristotle-and-the-philosophical-crisis-of-quantum-theory/
This problem of ‘becoming’, of process and temporal continuity of being is relevant to quantum mechanics and attempts to overcome the static reality view of the Copenhagen interpretation. The Copenhagen interpretation of quantum mechanics is not the only embraced interpretation. There are others, equally or even more bizarre. Some have reduced the degree of strangeness by introducing explicitly Neoplatonic ideas into their interpretation. Most prominent and widely embraced, and least paradoxical, is the ingenious theory of David Bohm, which is based on the Cusanian idea of the universe as the unfolding (explicatio) of a transcendent enfolded (implicatio) world whose nature is fundamentally mathematical. This is the fundamental vision underlying Bohm’s ‘implicate order’, illustrated by his famous thought experiment: the Glycerine Machine. What make David Bohm’s model of ‘the implicate order’ so significant is that it introduces the fundamental missing element of quantum mechanics: process and continuity, what Arran Gare would call the dimension of ‘becoming’. Here are David Bohm comments about the absence of the concepts of movement, process and continuity in quantum mechanics:
You see, the present quantum mechanics does not have any concept of
movement or process or continuity in time. It really deals with one
moment only, one observation, and the probability that one observation
will be followed by another one. But there is obviously process in the
physical world. Now I want to say that that process can be understood
from the implicate order as this activity of re-projection and
re-injection. So, the theory of the implicate order, carried this far,
goes quite beyond present quantum mechanics. It actually deals with
process, which quantum mechanics does not, except by reference to an
observing apparatus which in turn has to be referred to something
else. — from Morphic Fields and the Implicate Order: A dialogue with
David Bohm, p. 7.