Grammar and Logic (3): Grammar and Metaphysics

The first instance of metaphysics is found in grammar. If a verb “to begin” merely marks a division, it is metaphysically devoid of content. If it marks a process or even just a period of transition, this implies a universe where the possibility of change is taken for granted; what becomes of issue is the nature of change, e.g., whether it is brought about through agency, as an act, or whether it occurs passively, as an inevitability somehow embedded as possibility in the matter of the universe.
Thomas Aquinas for instance devoted a small but highly important text to an attempt to unravel the usage of the copula so that it could be used to imply activity, agency, act. His effort failed, because the usage of a single word or its cognates does not determine grammar; rather, the case is the other way around. On some level, this would seem to be obvious; but then of course, we are forced to confront the difficulty in articulating the structures of grammar that determine the usage of words. There is no point in this matter, in turning to text books, handbooks, manuals, of proper grammar, of standard grammar, written by professional, or otherwise expert, grammarians – such handbooks lay down rules for ” proper ” usage, the authors blissfully unaware that the structures of their grammar predetermine the manner in which such rules can be articulated. This means that the supposed rules of grammar can only themselves articulate a portion of the structures of grammar and thus cannot explain the relationships between grammar and the usage, and therefore the meaning, of various words or terms, or even such trivial symbols of mere rhythm such as pauses and punctuation.

Over the past five hundred years, thinkers in the West have either attempted to put an end to the study of metaphysics or they have claimed that they have ended the study of metaphysics. We see this in the denial of metaphysics in the work of the Americans William James and John Dewey, as well as in the effort to ” deconstruct ” the grammar of all Western metaphysics, such as we see in the texts of Martin Heidegger or Jacques Derrida. such efforts are doomed to failure. there is no “fact” found in our statements lacking metaphysical implications. There is a no original or originary experience to which to return, at least not for one who has learned the use and comprehension of language. There is no reason as yet, that is, no concrete evidence, for believing that language is genetically encoded in our brains. But once language is learned, it cannot be unlearned, although we have ample evidence discovered in the study of dementia that not only language but the fundamental structure of language can be forgotten in the process of the general erosion of neurons throughout the brain that occurs in dementia. I suppose that in the study of the language expressed by the demented, we will at last discover linguistic structures devoid of metaphysical implications; but I doubt we shall ever do so otherwise.

To learn language is to learn metaphysics but not all languages have the same grammatical structures. This in itself indicates that grammar it is not only open to variance, but open to change. It is not my purpose here to speculate concerning the process of such change. But we must note that it is impossible to articulate history without a sense that such change occurs.

This means that the supposed “rules” of grammar are not everywhere at all times the same, nor are they at all reducible to the same. Further, we find that metaphysics cannot be discovered to be true at all times and everywhere, despite the fact that it is impossible to engage in the study of grammar without making this assumption, since this is a fundamental teleology of metaphysics, to discover the reality that can be expressed as everywhere and at all times the same. I do not have and cannot offer a solution to this evident quandary; perhaps it is a paradox, perhaps everywhere at all times the same paradox, perhaps it is the fundamental reality beneath and above our existence.

Metaphysics is our truth, the truth expressible in language, what we can say, both grammatically and logically, as everywhere and at all times true.

Unfortunately, this “truth”, dependent on the possible expressions of our language, of any given language, is neither eternal nor universal. This certainly comes as a disappointment; but the frustration we feel over this matter is not the sign of the futility of human intellect, but the defining ground from which it arises. The human capacity for intellect develops from the effort to adapt intelligently to the discovery that what once was “true” is so no longer, and what never previously existed now exists as “true”.

There is a rather childish sophistry in our present language (21st century English) that can make this more clear. It would be well worth our effort to discuss what it may have been like to live in the Ptolemaic universe which had the immovable earth at its center, rather than the post-Copernican universe of orbiting masses, one of which just happens to be the earth; but we need to drive to the heart of the real issue here. So let us address the seemingly simple problem of number.

As we all know, “2+2=4”. Thus, if a person were to argue, “yes, but two zeros plus two zeros only adds up to zero,” we should recognize that person to be engaging in a bit of sophistry; specifically the obfuscation of certain mathematical terms. One cannot add zeros.

And if another person were to say, “well, but two ounces of mud plus two white shirts just gives us two mud-stained shirts,” we would recognize that the term “plus” here is used in place of a more precise usage of a verb, e.g., “applied to” or “smeared on”, or something of the sort. That is, we would recognize that this person is not really referring to an arithmetical process or mathematical formula at all, but a physical activity generating a physical realty.

Mere sophistry; yet the fact is, although not all mathematics derives from counting [it is not the case that all mathematics can be abstracted from some counting process], all mathematics historically begins with counting; it is really impossible to assume otherwise, since the artifactual evidence for this from the earliest moments of written number doesn’t leave any room for interpretation.

In a general overview of the history of number, we find strategic moments of real embarrassment. “1+2=3”; in Roman numerals we express this as: “I+II=III”. Which means that we are adding one straight vertical line to two vertical lines to get three vertical lines. But if that’s the case, why can we not add one circle to two circles to get three circles, in this fashion: “0+00=000”? Which, after all, we can express as “one zero plus two zeros equals three zeros”.

More sophistry; I am clearly confusing the symbols for the numerical contents they are held to symbolize.

The problem is, at the beginning of number as written articulation of a process of counting, there could not have been such a sophisticated distinction. All written number systems appear to have had, near their point of origin, some grammar of number similar to that of the Romans; that is, representing three as, say, three straight lines, three wavy lines, three horizontal lines, three vertical lines, etc. And it is worth remarking, in this context, that few such systems have any symbol for “nothing”, which we now articulate in the use of the symbol “0”. Why should they? If there is nothing to count, one merely states the fact, “there is nothing to count,” why bother symbolizing this in the domain of number? In this respect, the invention of the symbol “0” must have been as radical an innovation in the mathematics of its day as that of calculus in our own.

This means that one can really imagine [or perhaps even discover] a culture where one can state “one zero plus two zeros equals three zeros”. In our culture, a sophistry; in that culture a statement of fact.

We want to say to this, “but really, the confusion between symbol and numerical content remains; there really cannot be two nothings or three nothings, and all the zero symbolizes is nothing!”

But this is not necessarily the case; one can construct a binary mathematic wherein the zero counts a pause in temporal sequence; a nothingness to be sure, surrounded by some material events or entities, but a measured nothingness, and, as such, an identifiably discrete nothingness which can be counted. And I am here discussing known mathematics: the binary code of the I-Ching, and that of computer logic. Perhaps, still, the confusion between symbol and numerical content remains the same as in our sophistries; unfortunately, there may yet be a metaphysical content underlying such grammars that may yet be discovered, making all our sophistries statements of fact. [We are, after all, temporal beings; nothingness may itself be determined as having temporal limits.]


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