Then I learned symbolic logic which gave me insight into the formalism of language and mathematics. Here I saw that logic and mathematics rested on undefined terms and given rules that ultimately could not be proved through inference. This was because as soon as you tried to prove the terms and rules on which logic or mathematics were built, you had to develop another logic or math with undefined terms and given rules. The mathematician, Kurt Gödel, actually proved that the validity of a statement always rests on something outside the formalism of language, logic, mathematics. It cannot be proved in the symbolic system in which it is uttered.
That was a big deal. It actually knocked out the notion that truths were based in some objective realm of ideas out there. Good-bye Platonic heaven in tune with our souls. It also knocked out the notion that we who think through symbols can achieve some absolute truths by the workings of our minds.
Into-European languages are built and operate on the rule of non-contradiction. And this seems to be the rule of our common sense dealings in the world. But do all languages and mathematics need to assume this rule? Wonder if we create a logic with undefined terms and rules that do not include the rule of non-contradiction? Suppose we have a rule where something can be negative and positive at the same time. That's hard to imagine in our day to day Western world. Or is it?
Are there rules of thought that are natural; that is, built into the very structure of our organisms and brain? Since we think symbolically (and that does seem to be natural) and that does seem to be a universal factor for homo sapiens, that would seem to imply that there are invariable laws of thought. Indeed when we think we posit (i.e., affirm) a word or proposition that structures our environment. If it works, we affirm it. If it doesn't we negate it and try another. Discursive thought works that way including common sense, science, and philosophy.
But we have seen that there are other way of symbolically engaging our environment. In myth, religion, and art, the law of non-contradiction is not so important. We use words, propositions, symbols that seem to negate and affirm at the same time or at least very ambiguously. We use metaphors, figures of speech, suggestive metaphors to engage with our environment and structure our worlds. Mystics and artists have a certain insight into being as nothing and nothing as being.
Digital thinking is a matter of 0s and 1s--electric charge and withholding of charge, negatives and positives. And we know that the brain is electric. But analogical thinking is a bit "fuzzier." it is a matter of suggestion between images. Digital thinking can be expressed in the formalism of logic. But anagogic thinking is considered more "intuitive" or "evocative." Analogy is not a matter of clear, distinct ideas validly inferred. It is more a sense of "yes, that feels right."
So do we have a digital or analogical world? Another way to ask the question: Is engaging the world a digital or analogical enterprise? Well the answer seems to be both. Yet, we better recognize which mode of thinking we are engaging our world in.
Myth, religion, and art confuse and mislead us when they pretend to be science or vie with the conclusions of valid science. And science and the philosophy in tune with science are not the answer to life or the arbiter of absolute meaning.There are more things in heaven and earth, Horatio,
Than are dreamt of in your philosophy. - Hamlet (1.5.167-8)
In the evolved structure of symbolic behavior and thinking, we do discern the inward direction of the environment to the organism and the outward direction of the organism to the environment through symbols in the same moment. And so there is both a focal or conscious experience of objects in the world and a background or pre-conscious experience of the thinking body. We call one experience objective which we know is the pattern we give to our environment by commonly agreed upon symbols such as words or formulas. We call the other experience subjective or consciousness. The dual direction or experience of symbolic activity gives rise to the illusions of the individual self and the real thing.
Perhaps, I conjecture, in the domain of the objective where we consider things out-there and real is the place for formal and linear logic built on the principle of non-contradiction. In positing symbols we are affirming that these symbols apply or work. But we are also putting limits on them by saying that they work for these phenomena but not for those others. Saying no is what categorization, definition, distinction is all about. "This" implies "not-that." "Yes" implies "no." In science we even argue that a proposition or formula makes no sense if it cannot be falsified and then to work must be verified by peer reviewed evidence.
But as existential phenomenologists and pragmatists point out, the very act of positing aware of itself in consciousness, i.e. the subjective domain, has different rules. In fact the act of positing symbols in the world is a tension between the poles of the pre-symbolic lived world and the symbolically structured world, non-conscious and conscious, nothing and thing. The thing (symbolized and conscious object) comes from nothing (unformed and pre-conscious subjectivity). Science as a product is in the formal or objective domain. But science, and every mode of thinking, as an activity, a subjective thrust to the world, belongs to the informal, non-objective domain.
It is in the domain of non-objective background experience, which we might call the realm of the pre-conscious because it is not yet focalized through symbols, that the undefined terms, the assumptions, and given rules come from. It is in this domain that the "rules" of myth, religion, and aesthetics operate. It is the totality of the embrained organism prior to its being objectified with all the resources of pre-objective (un-formalized, unfocalized) consciousness in body and in memory, in genes and memes. Because this is the non-objective domain scoping, from the inside out, the whole of symbolic activity in its tension between nothing and something, it is not the place of clear and distinct ideas. It is the realm of the ambiguous.
So is there a logic of ambiguity? Perhaps, but unlike the ideal for logic, that's not quite clear.
Note on the Unconscious.
I guess because I am pointing to the non-objective and ambiguous realm of thinking, I am using the word consciousness to contain both the background non-conscious whole body/mind experience and the conscious focal experience defined by the symbol. I prefer not to use the word "Unconscious" because it evokes an additional mysterious realm to be explored by psycho-analysis. The information is there in our genes and memes and dreams, in our bodies, culture, and intentions, even when that information is not conscious, i.e. symbolized. It's already there in the nothing "before" the something.
Note on philosophy.
Is philosophy in the objective domain? Mostly, I would argue. And arguing is in the objective domain subject to the laws of formal logic. But then, what philosophy is trying to get a hold of is the act of symbolic thinking itself from the inside-out or, better, in its tension from nothingness to something. When the scientist reflects on his doing of science and inquires as to how it happens and how it relates to other modes of doing, he is engaging in philosophy. And so does the artist, the religionist, the mathematician, the economist. That's why philosophy is sometimes called "second reflection" or even "literary criticism." And because the philosopher is trying to catch human symbolic behavior or thinking in the act, prior to and in critique of his own formalization, he often has to resort to the ambiguous language of the informal, non objective, aesthetic domain of not so clear and distinct ideas. So if that's not clear, you try it.
Note on spirituality.
Earlier I discussed the relation of mindfulness to thinking. Mindfulness, I find, is a preparation for, component of, and even reflection on the act of thinking. Mindfulness can be assisted through exercises of meditation or contemplation where persons let their thoughts go to notice the flow of consciousness our of which thoughts come. This is not religion, just as it is not science or philosophy although many religious, scientific, and philosophic traditions recognize the inner flow or "nothingness" from which religious, scientific, and philosophical thoughts are constructed and emerge (e.g. mysticism in religion, psychology in science, phenomenology in philosophy). Since mindfulness is a letting go of thoughts, I suppose you could call spirituality "thought-less." But since the letting go of thoughts prepares the way for new, original, critical thinking, I find spirituality quite thoughtful and being in the mode of thoughtfulness.