On the Nature of Logic: Solicitations.
July 14th, 2009 | 
Author: Based on several years of research/thinking/lit review, I’ve come up with some opinions on the subject of logic et cetera. Since it’s mostly been myself talking to eccentric though lovable phil profs and a lot of old dead white men, I’d like to ask you, dear reader, for any thoughts or opinions on the final paragraph of mind-altering questions (the first few paragraphs intended to provide definitions and context):
Logic is defined here as the study of valid demonstration and inference, or the principles of correct reasoning. It concerns the structure of statements and arguments, and rules of inference in both formal systems and natural language. Formal logical systems consist of:
- a formal language, and
- a deductive system (or deductive apparatus) which consists of a set of inference rules and/or axioms.
Formal systems derive statements from prior statements in the system. A derived statement is called a theorem, whereas axioms are statements that are assumed to be true without proof (self-evidence).
Some of the desired properties possible for logical systems are: consistency (none of the system’s theorems contradict one another), soundness (the system’s rules of proof will never allow a false inference from a true premise), and completeness (that there are no true sentences in the system that cannot be proved in the system). Not all systems achieve all three virtues (e.g. Godel’s incompleteness theorems state no useful system of arithmetic can be both consistent and complete).
There are many types of logic – first-order logic, second-order logic, informal logic, interpretability logic, intuitionistic logic, quantum logic, categorical logic, clocked logic, linear logic, college logic, combinatorial logic, affine logic, Boolean logic, ternary logic, monotic logic, non-monotic logic, multivalued logic, paraconsistent logic, non-Aristotelian logic, relevant logic, temporal logic, sequential logic, scholastic logic, term logic — the list goes on. There are local and global logics, which hold different axioms or rules of inference. Despite its long history, the nature of logic is obscured by a number of disturbing questions that have yet to be satisfactorily answered.
Is there a single true logic, or are many logics equally correct? Is it possible to have genuine disagreements about the correctness of a logical principle? What makes a logical constant? What are the proper accounts of logical concepts (e.g. logical consequence, quantification, etc)? What is the scope of logic (e.g. does it encompass mathematics)? Is logic a matter of convention? What is the nature of logical necessity? What is the relationship between the verbal rules of logic and the mental ability to reason logically? Is logic subject to empirical revision?
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Yes, there is a single true logic, of which all valid logics can only be specializations. The 20th century’s hostility to metaphysics has led people to confuse formalizations with the thing being formalized, as if logic were about nothing but self-consistent manipulation of symbols, rather than about deduction of truth.
Most of your questions are about the ontology of logic. They can only be answered in the context of a broader metaphysics. The standard metaphysics these days is a nominalistic materialism in which thought is just computation. This doctrine is actually riddled with holes, but it’s very difficult for scientifically literate people to conceive of anything else, and if they do, they tend to swing to the opposite extreme of mystical crypto-platonism, e.g. “the universe is a computer program” or “reality is made of mathematics”.
My own personal formula for ontological progress is transcendental phenomenology in matters of mind, Aristotelian realism regarding universals and their relation to particulars, and a new monadology in which the self is an irreducible quantum tensor factor in the entangled brain, rather than a fuzzy coalition of discrete computational units. If you interpret the elementary aspects of physics in terms of proto-psychological properties, rather than vice versa, then I can see the possibility of eventually saying something about the relationship between reason, cause and effect, why the laws of nature operate, and how they operate within the mind. I don’t at all insist that I’m on the right path, just that the mainstream is on the wrong path. Unfortunately, it seems to be extremely difficult to come up with substantial new ideas - just pointing out that there’s a problem is not in itself enough to suggest the answer.
“My own personal formula for ontological progress is transcendental phenomenology in matters of mind, Aristotelian realism regarding universals and their relation to particulars, and a new monadology in which the self is an irreducible quantum tensor factor in the entangled brain, rather than a fuzzy coalition of discrete computational units.”
This.
Is that a request for more details?
I’ll try to say a little more about how to turn that into a thesis about the nature of logic. But it may take a while.
I can’t help but feel that there is a rather, well, flexible “true” logic. If the study of our universe has yielded anything of value, it is that large systems do seem to bear a resemblance to smaller systems, rather like a fractal. If we assume that this holds true then it would seem to me that there is something like empirical truth, but it has a tendency to change. Not to say that the previous iteration wasn’t true, simply that something changed and now a different set of givens is now “true”.
I think that human perception brings in a whole new set of problems tChough. I have begun to despair that the human mind is so ruthlessly flawed that it cannot but perceive things differently, as though light were passing through a prism.
After this bending of the Light, forgive my use of analogy, the truth becomes something far more subjective. Within the given realm of any single humans cognition the truth and how it is perceived is different but just as subjectively true. After all, we all function under the assumption that what we know is true, whether this is empirically true is a different beast all together, but at the very least it is useful.
Let me give an example. If what I understand about the Big Bounce theory is correct, then it may very well be quite possible other “universes” exist within the same space/time continuum, which is supposed to be particulate in nature in this theory.
If there were other points on the Map of the universe where other Big Bangs occurred then it is quite possible other, universes, exist, however if there were even minute difference things would come out drastically different. As a result all the natural laws we hold to be empirically true here would be vastly different in these other Big Bang universes.
In fact they might be so strange to our set of truth that we might not even be able to interact with them in any meaningful or intelligible way, even if we passed right through one another.
So that is my view of logic. As for your questions.
Is there a single true logic, or are many logics equally correct? I think there are many equally correct logics dependent upon the circumstance.
Is it possible to have genuine disagreements about the correctness of a logical principle? Absolutely given the environment in which the priciple functions
What makes a logical constant? Being true for a given set tasks, though not all.
What are the proper accounts of logical concepts (e.g. logical consequence, quantification, etc)? This descends into semantics, I would gauge it to be a matter of utility.
What is the scope of logic (e.g. does it encompass mathematics)? As hideous as a response as it is, the scope it can fit in. Logic can encompass mathematics, but most likely not emotion, or love. I have yet to find anything logical about love.
Is logic a matter of convention? It can be, it just depends on what the conventions are.
What is the nature of logical necessity? Utility.
What is the relationship between the verbal rules of logic and the mental ability to reason logically? Chess.
Is logic subject to empirical revision? Yes, depending on the determinate sets of empirical truths.
I feel like these answers would be a decent starting point. Nothing is ever right on the first go.