For instance, Scriptures include both commandments (free will) and prophecies (predestination.) Under bivalence, if everything is predetermined, commandments are illogical and conversely, if nothing is predetermined, prophesies are illogical. My assertion in the present sidebar is “non-classical logic” – i.e. that both predestination and free will are Truth for the simple reason that God has spoken both. Or to put it more broadly, we cannot apply formal logic (esp. Aristotlean logic) to God because of the observer problem.What you said!
We should add a caveat. The concept that you call bivalence is itself the product of logical analysis. This means that while we may easily posit the concept bivalence, this act does not reveal the depth of the synaptic relation between the associated elements. More care is needed to understand it. Plus, the association varies when a third or more element becomes involved. Given that the world is a multitudinous plurality of things, we can become shortsighted by simplifying the relation into a nondescript dualism.
Another note. The idea of nonclassical logic is not that profound, but easily overlooked. For any system to work, we have to agree on first principles. The most important of these is one of scope (which is often presupposed, and thus often not considered a first principle). The observer phenomena is one that designates scope.
In this regard, we can say that the law of non-contradiction also applies for nontraditional logical analysis. Again, this bears out the fact that the concept of non-contradiction does little to reveal the scope of the system. But the law does require limit. There is no principle of noncontradiction apart from limit.
(For some reason this reminds me of Porphory's Isagoge and the classification terms genus and species.)
Scope!... Hmmmm... Observing the Trees or the Forest?..
or even Observing the planet... Yes, I agree.. scope is important to the Observers vista..
Limits; rejecting this solar system, galaxy, universe and BEYOND might be wise.. cause that would all be hear-say evidence.. Scope is very important to an Observer.. unless he's day-dreaming in a 2nd reality..
It seems that many wish to ignore scope altogether and apply an observation which can only be made with reference to a system to any thing or event which may exist beyond that system. It is a common error especially related to second realities.
A simple example is that one cannot say a thing is random in the system if he doesn't know what the system "is." For instance, a string of numbers extracted from the extension of pi would appear random when they are in fact highly determined.
Likewise in mathematics the concept of infinity is a useful construct which does not translate well to physics because infinity is boundarylessness whereas physical reality (the geometry of space and time) has boundaries. Moreover, neither mathematics nor physics translate to spacelessness and/or timelessness - both of which are properties of the "void" from which there was a beginning in all cosmologies. IOW, timelessness and spacelessness apply to the Creator not the Creation.
And more to the point of this sidebar, laws such as logic or physical laws which apply to us as observers in physical reality cannot be projected "beyond" our boundaries "in" Creation to apply to the Creator as well.
For Lurkers:
Porphyry wrote a commentary on Aristotle's Categories that is extant and another longer one that is lost except for some fragments. And he wrote the Isagoge, which is an introduction to Aristotle's logical works in general. Through these logical writings Porphyry established himself as an important figure in the history of logic. The Isagoge in particular served as a standard introductory text in Byzantium, the Arabic world and in the Latin West through Boethius' translation and commentary. These texts served as a basic introductory texts in philosophy for at least 1000 years.
Platonists before Plotinus differed in their attitude towards Aristotle. Porphyry belongs to those who believed that Plato and Aristotle were essentially in agreement, and he refers to Aristotle for support throughout his writings. Plotinus too showed such reconciliatory attitudes but Porphyry takes this trend even further. The question arises how such an attitude can be reconciled with those passages in Aristotle that seem to disagree with Plato, sometimes expressly. We do not know how Porphyry dealt with others of these, besides Aristotle's Categories, which appears to modern readers in many respects to be an anti-Platonic work. This is especially notable in its claim that particulars are prior to universals. Porphyry solves this dilemma by insisting that the so-called Aristotelian categories—substance, quality, quantity etc. dealt with in the work Categories are “significant expressions”. That is to say, the Categories is not a work in primary ontology but rather a work about the expressions used to signify the sensible things around us. The class of beings signified by a universal term of this sort is indeed prior to the universal term, e.g., the class of pale things to the universal term ‘pale’. As Strange 1987, 1992 notes, this, however, does not affect the basic ontology. So interpreted the Categories is innocuous from a Platonic point of view: The realm of Platonic intelligible Forms, which are universals of a different kind than the expressions involved in the Categories, can be kept intact.
The Isagoge does not claim originality but on the contrary Porphyry says in his introductory note that in it he will rehearse “what the ancient masters say” and avoid the deep questions. As an example of the latter, he mentions questions about the ontological status of genera and species—whether they exist or depend on thought; and if they exist, whether they are bodies or incorporeal; and if the latter, whether they are sensible items or exist separately from such. These questions Porphyry wishes to shun. Nevertheless, his formulations of them constitute the most influential part of his work, since it was these questions that formed the basis of medieval debates about the status of universals.