The Antichrist of Language: Grammar and Logic

ANTICHRISTIME

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Let’s consider how language can determine what we can know of the world and how we can know it. The discussion following is somewhat technical, although it is nothing compared to the technicalities of professional philosophy texts. But perhaps it doesn’t need to be.

This is constructed from notes I wrote while reading a book by a 15th century logicians. Unfortunately, I have since lost that book, which included translation from the original Latin. Luckily I noted the Latin passages I needed, but unluckily not the translation. So I have had to translate anew. I trust my reading of the original text, but my ability to translate Latin into English not so much, so I am open to correction.

The issue has to do with the relationship between grammar and logic.

Within a social setting we are trained to deploy three primary tools of linguistic communication, grammar, rhetoric, and logic. somewhere in the conjunction of these three we find the construction of metaphysics. This of course ultimately must be expressed logically. Grammar determines ahead of time the limitations of possible expression within a given culture. If it can’t be said, it cannot be said as true. Grammar constructs the House in which metaphysics dwells.

Let Entity X be any material entity, that, qua X, comes into being; that is, there is an indefinite period of time when there is no such entity as X, which we’ll call Period A; and then there comes a moment when X exists (and for the present, we will not establish any further temporal limits on the existence of X). This moment when X comes fully into its own existence, we will call Event B; the immediately following moment we will call Moment C. Let us say that we are in that period of time before the existence of X, A. At A, what true statement can we make concerning the existence of X?

There are two possible scenarios which may determine our first response to this question; in the First Scenario, we know that Event B is a certainty, which means we know the future existence of X is inevitable, it also is a certainty. The Second Scenario has us less certain of the future; in this case, we know that Event B, and the consequent existence of X, is highly probable; but not quite an inevitability, some unknown event could occur prior to Event B, or at the same moment, that cancels out the possibility of the existence of X.

Now we want the possible responses to the question to be evident prima facie; if we know that Event B will occur, then we can state, as a knowable truth, “X will exist”. and in the Second Scenario, we want to ‘hedge our bet’, so to speak; we only claim that Event B is likely to occur, and that therefore X will most likely exist from that point on.

I devised these hypotheses while reading the Logica Magna of the master 15th century logician, Paul of Venice, specifically his Treatise on Contingency and Necessity. Paul had certain theological conditions which Modern logicians have not needed to confront. According to the doctrine of the Roman Church, there were some events, promised in the Bible (via divine inspiration of the authors), that were to be taken for granted as inevitable, such as the Apocalypse, that is, Judgment Day. Now, Paul seems to have recognized the problem with such a doctrine; nonetheless, unable to confront it directly, he seems to torture his arguments into what appear to us as mere tautologies; in fact, they are the most refined instance of logical subtlety I’ve seen outside the texts of the Buddhist atomists who argued against Shankara’s Vedanta disciples.

The fundamental problem Paul appears to attempt to unravel [with limited success], is that if an expected event of the future is held to be absolutely true in the same manner as the existential event of entities that already do exist [their very existence is itself an event, at every moment of their existence – a fact the medieval Latins seemed to understand better than we Moderns], then logically, any true statement that one could make concerning it should be reducible to the exact same logical structures of true statements concerning events and entities which are already in existence all around us, or even those merely in our heads [e.g. geometrical forms]. Unfortunately, this is not possible. One way to think of this, as a problem of pure logic, is to ask the simple question, does any verb projecting an existence (of any kind) into the future (e.g.: must, will, shall, etc.) have the same grammatical status as the logical copula, the verb “to be”? No. But, why not? Let us go back to our hypotheses.

We’ll start with the Scenario with the least complications for this discussion, the Second. In this scenario, we do not have absolute certainty that Event B will occur and thus X will exist. If we just say “X will exist”, this sentence has no truth-value, since it concerns a non-existent entity that, according to the Scenario, may possibly never come into being. However, should we assert merely that “probably X will exist”, this sentence seems to have greater validity, and thus greater claim to a truth-value, than the first assertion; but, that is so only within the domain of probability theory. In practical application, really, it does not. Both sentences are contingent; that is, both claims can only be verified by an Event B occurring. (Should B never occur, then the probability of such occurrence is moot; and if it does occur, then obviously, at some point in the past, it possessed the possibility of being probably determined.) But the occurrence of B leading to the existence of X is not really what is at issue here.

We can see this better by reviewing the First Scenario. In this, we have absolute certainty that X will come into existence at Event B. So we want the sentence “X will exist” somehow to have the same truth- value as “there is at least one entity X”. But that is not the case. The problem is that the sentence “X will exist” only states a present truth about our certainty, not about the existence of X, since at that time X has no existence, and no truth claim can be made of it. It cannot even be said “X is that which will exist”, because at that point X is not anything, or to put it as simply as Parmenides, X is not.

The manner in which Paul confronts this problem is rather interesting. He addresses the question, what can be said of a soul that comes into existence at a certain instance of time; he chooses to use as his example the soul of the AntiChrist. This is because the AntiChrist is a soul destined to come into existence at a specific moment in the events leading up to Apocalypse, as has been promised (according to Church doctrine) in the Book of Revelations. In other words, its inevitable existence has to be taken for granted by Paul.

[Here, for the sake of consistency, I will transpose our value symbols onto Paul’s text, so that our “Event B” represents that moment when he speaks of the instant when the soul – the Anti-Christ – now represented for the sake of discussion by “X” – comes into existence; moment “C” is that moment following the entity’s coming into existence. However, it should be noted that, while Moment B is clearly an event – the coming into existence of the AntiChrist – Moment A and Moment C are better thought as ‘durations.’ A is the duration of human existence from the Fall to the coming of the AntiChrist; C is the duration between the appearance of the AntiChrist to Judgment Day. The duration of A is predetermined by God, but unknown to humans; the duration of C is predetermined by its end in Judgment Day. But B is simply the instant when the AntiChrist appears. This might seem an odd usage of the notion ‘moment,’ but from the Catholic theological view, determined by Augustine, the events of human history were pretty much valueless, while the value of events directly leading up to Judgment Day was decided by Judgment Day as the fulfillment of prophesy, and the culmination of the narrative of the relations between God and humans. From the view of God – existing beyond all time and history – only the latter mattered.]

We pick up Paul’s discussion at the point where he addresses the issue of the entity’s coming into existence:

Immo, bene concedo quod haec anima [X] incipet esse necessario post [B]; quia in [B] instanti haec anima incipet esse necessario post [B]. Nam in [B] instanti haec anima non erit necessario post [B], quia tunc non erit post [B], et immediate post [B] instans ipsa necessario post [B]. Probatur:
In quolibet instanti post [B] ipsa necessario erit post; igitur immediate post [B] ipsa necessario erit post.

(It may be well to concede that this soul, X, is necessary after moment B;
because it is in moment B that this soul is necessary.
For in moment B the immanence (possibility) of this soul will not be necessary after B,
because in that case there will be no moment after for the possibility of B.
Proof: At every instant after B, B is made necessary as a given for what follows.)

Which argument he buttresses with another:

In [C] illa anima [X] erit post [B]; et in [C] non poterit esse quin illa anima [X] erit post [B]; igitur in [C] illa anima [X] necessario erit post [B].
Antecedens probatur: quia, si non, detur aliquod instans post [B] in quo non necessario erit post A, et sit illud [C]; tunc agitor quod in [C] illa anima [X] necessario erit post A, quia
In [C] illa anima [X] erit post [B]; et in [C] non poterit esse quin illa anima [X] erit post [B]; igitur in [C] illa anima [X] necessario erit post [B].

(In moment C the being of X ends moment B;
and at C, X will not be unless B is at an end;
therefore at C, X will necessarily be after B.
The antecedent is proved, because,
if not, let it be given B not necessarily following moment A, there is moment C;
it is then in moment C, that the soul, X, needs to exist after moment A.
Then at C X exists, beginning existence after A,
thus that moment C follows X beginning existence (moment B).
So at C X necessarily exists after B.)

Paul has a problem here; he has not read Hegel, and thus lacks the grammar of “becoming” with which our modern metaphysics is embedded [and I am not trying to get witty here]. And he hasn’t read Darwin, so he has no grammar of historical evolution. He certainly hasn’t read Einstein, so the relativity of time is unknown to him; he knows nothing of quantum physics, so statistical ‘history over time’ never enters his head.

On his own terms, he has run himself aground in an attempt to identify the moment of the entity’s “beginning to exist” with the occurrence of its actual existence. If at Event B, X comes into existence, then at Moment C it cannot possibly follow “beginning to exist”, since at that moment it simply does exist; “beginning” doesn’t add anything to it.

Making this mistake is the only way for Paul to elude the obvious implications of the argument which Paul considers immediately following the above:

Et si ex concluditur quod haec anima necessario erit, negatur consequentia. Quia licet tunc poterit non esse, ipsa tamen poterit non esse. Quia continua ante [B] poterit non esse, cum numquam ante [B] erit, Similiter non sequitur:
In [B] instanti haec anima [X] necessario erit; igitur haec anima [X] necessario erit [B] instanti,
quia post [B] instans non necessario erit in [B] instanti, cum numquam post [B] instans erit in [B] instanti.

(And if it be concluded that this soul (X) will not be of necessity, I deny the inference.
Because before B it is not, then it would be able not to be.
That can hold if B will be able to not occur;
(but that) X never follows but as B shall come to pass,
it does not follow the same way:
in B, this is the instant the soul, X, needs to be present;
then, the soul of X needs to be given, in the instant B,
since after B, the immanence (possibility) of X is not necessary (since it will already be in existence.)

(Short form:
If event B doesn’t happen, X does not exist, so its possibility prior to B is irrelevant.
But at B X must exist, therefore B will occur
(since X will certainly exist).
Once B occurs, any question concerning the possibility of the existence of X is irrelevant.)

For Paul, who has no theory of probability he can employ here, existence implies prior possibility. Should X exist, it’s prior possibility to exist is assured (but irrelevant); should it not exist, then if it can exist, there is a possibility for it to exist and a contiguous possibility for it not to exist. In which case the moment it comes into existence is similarly contingent. But doctrine assures that it will exist. So the moment it comes into existence is assured.

We moderns say that if it does not exist then logically its future existence as a possibility is a matter of complete indifference. This is of course within the realm of absolute logic; however, we have been able to elaborate an entire mathematical theory of probability by which to address precisely this issue. The possibility of the existence of the entity is indifferent, yet we can still compute the probability of its existence. For Paul the possibility of the existence of the Antichrist could not be indifferent; the hope of the final redemption of Judgment Day depended on it.

At any rate, for Paul it cannot be said with absolute certainty within the domain of logic that “the Antichrist will exist” prior to B; but it is assured doctrinally; thus the event of the Antichrist’s coming into existence [B] is a certainty. At that point (B) the claim that the entity exists will be true; and it will also be true to say that X exists at B. But once B has passed, this sentence “X exists at B” cannot be true because we are then at moment C, and event B is no longer possible (it occurred, now it is mooted).

But to grasp the problematic relationship between Paul’s logic and Modern logic more firmly, let us resurrect Hegel here. According to Paul, the sentence “X exists at B” is a true statement at B. This is the event of X coming into existence. Yet, exactly because X is in the process of coming into existence, of ‘becoming a real X’, it cannot be at that moment considered in existence or having existence. In some very real sense (to Hegel, anyway), X exists only in the process of ‘becoming X’, it is not yet a real X. It does not exist, it does not not-exist; it is becoming.

(A seed is not a tree; a shoot from a seed is not yet a tree, neither is it a seed. It is in the process of becoming a tree. There is obviously a paradox of category here, resolved only by resort to denying that what we are talking about are real universal categories, but instead, our conceptualizations of those categories: In the shoot, the seed no longer exists, the tree does not yet exist; yet the concept “tree” necessitates the shoot as part of the process of the becoming “tree,” which also includes both seed and tree.)

Throughout Period A, no true statement can be said concerning the future existence of X. We cannot say that ‘X will exist at B,’ because that isn’t quite the case, it will only ‘become’ at B, and we as yet have no language with which to articulate this, despite monumental efforts to do so in such sciences as Physics and Biology. Do caterpillars exist? Obviously. Do they exist as butterflies? Obviously not. Biologists tell us that they exist as a certain stage of transformation within the existence of the entity as member of a certain species of insect. This is actually useful only within the domain of biological theory; a “member of a certain species of insect” just does not exist in the material universe; there is a caterpillar, or there is not.

There is another strategy which modern logicians frequently employ to resolve this problem [and hopefully evade the Hegelian paradox as well], and that is an insistent resort to conditional sentence structures, what the Latins knew as the modus ponens: e.g., “If X, then B”, or “B if and only if X”, and the like. Many an undergraduate has passed an introductory course in modern logic a confirmed cynic. The fact that the sentence “B if and only if X” can be run through a “truth-table” means precisely that it can only be contingently true, dependent on certain conditions. In the immediate case, the condition is obvious, that in Event B there appears the given entity X. But then it is the condition which is necessary for the determination of the truth of the sentence, not the possibility nor the probability of the existence of X. Which means that this sentence is neither true nor false, it is simply a limitation-sentence, determining the valid grounds for stating a truth that is, paradoxically, forbidden within the domain of Modern logic, “X exists”. In terms of Classical logic, “B if and only if X” means precisely that “X possibly will exist at B”. (‘If’ means if, even when it excludes other possibilities; it is still merely possible.) Its function is therefore grammatical, not yet logical.

(I fail to see the great advance in reasoning Moderns claim for such restructuring of logic in claims concerning ontic reality. We remain in the domain of what can be said of the possible, as Aristotle, 2300 years ago, suggested we would be.)

So I suggest that Paul’s real problem is one of grammar, and there is evidence in his text that he is aware of this; for instance, he frequently draws on grammar to resolve logical problems, yet he also remarks the necessity of using logic to clarify grammatical problems. This is not entirely self-contradicting behavior; Paul does not ascribe to the Modernist faith that somehow grammar is entirely subordinate to logic. He couldn’t, because much of Church doctrine, at the time, presumed Biblical statements to be true prima facie, e.g., “God exists.“

(By the way, not only do moderns not understand this sentence in the way the Latins did, but, since Kant, we can no longer hold it to be a logically valid statement; which means, technically, that it can not be determined either true or false logically, so it is simply “nonsense.”)

Because of Church doctrine, Paul is not burdened with problems arising from the Modern faiths that the universe is either perfectly logical in its functioning, or that the universe is simply unknowable chaos. Although he doesn’t really have the language with which to express it, this is what he really believes: that the universe is knowable grammatically. Ultimately, although Paul as a logician distrusts “grammarians,” his theology is bending his mind toward a final resolution of his problems by perfecting logic as a supplement to grammar, and not the other way around. (But of course he has problems of his own.)

The primary issue now confronting us has to do with how Paul understands the usage of the term “beginning”. This is a grammatical, not a logical, problem, because logical definition of the term, which Paul certainly gives to it in a logically valid manner, proves to be entirely ineffective. The problem thus stands revealed as the limitations the grammatical usage of the term imposed on Paul‘s text, and thus on his logic. Although the Roman Christian Bible opens with the Book of Genesis, the first line of which is frequently translated into English as “In the beginning, God created the heavens and the earth,” Paul’s Church did not understand “beginning“ as a verb identifying a process. On the contrary. implicit in traditional Church Doctrine, back to Augustine, is that whatever begins does so in the shortest amount of time possible – shorter, in fact, when the power of God is involved. In other words, the term “beginning” does not really identify a process, not even an event; it simply remarks a temporal division between something not being the case and something being the case. One way to conceive this is to imagine being born a full-grown adult with a college education; nothing happened before this; then suddenly everything is.

So the only moment when it becomes logically permissible to claim that “X begins to exist at B,“ is precisely at the very moment that is B; unfortunately, at precisely this moment, nothing actually happens: X is just there, it‘s formative beginning can not be articulated, so it simply won‘t occur; X never “begins,“ it just is. We have been translating Paul’s term for it, ‘Instanti B,’ as “Event B“; now we must confront a grammatical fact with logical implications. For Paul, there actually is no “event“ occurring at our “B,“ as we understand the term. This allows Paul to claim that X exists at B, and then also to claim that X continues to “begin“ at our moment “C” (since the verb “begin“ is really a formally empty term of art; which means that it has no truth-value status anything like that of the logical copula, “to be“).

However, although Paul obviously does not recognize it, this denies B any possible logical significance. At A, X does not exist, at C it exists, and between these two moments, there is B. However nothing happens at B; if X exists at B it does so in precisely the same manner in which it exists at C; which means that C is merely a temporal duplication of B. Therefore, logically, the only moments of concern, metaphysically, are A and B; technically, what this really does is to merge C into B; the whole notion of an Event B or Moment C stands revealed as an unnecessary multiplication of terms. This reduces Paul’s argument to near incoherence. Paul develops his text with such refined subtlety as a writing strategy for evading confrontation with this fact.

Well, but Paul wrote in the 15th century. Only a century later, Descartes would turn this world inside out. Thus Paul wrote in an era when the grammar of Church Doctrine, that of Medieval Latin, was, as a viable medium of intellectual communication, was beginning to come – becoming in its final realization – to an end.

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5 thoughts on “The Antichrist of Language: Grammar and Logic

  1. I’ll leave this for tomorrow. Its fryday evening, after a hard week of work (as a computer programmer, so I have had my share of formal stuff for the day), and I just poured myself a glass of red wine 😉

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  2. That was a really interesting read, but I didn’t quite follow everything. I wonder if you could clarify something. You said:

    “The problem is that the sentence “X will exist” only states a present truth about our certainty, not about the existence of X, since at that time X has no existence, and no truth claim can be made of it. It cannot even be said “X is that which will exist”, because at that point X is not anything, or to put it as simply as Parmenides, X is not.”

    I’m not a philosopher, I’m a linguist, and when I first read this, this was my immediate reaction: I would agree that statement like “X will be fruit-flavoured” might lack a truth value because X doesn’t exist at utterance time (in the same way that ‘The King of France is bald’ lacks a truth value). The situation is different with the specific predicate ‘exist’ combined with the modal ‘will’. In fact, the ONLY time it is felicitous to utter ‘X will exist’ is if X doesn’t exist yet. Once X comes into existence, such a statement is infelicitous. Given what you’re saying, it seems there would *never* be an appropriate time to utter ‘X will exist’, making it a totally vacuous piece of language. Or have I really misunderstood this?

    Then as I read on and you described Paul’s argument…am I basically falling into the same trap?

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    • The sentence “X will exist” is a grammatically proper sentence (and is most appropriately asserted when X does not exist). In modern logic, however, it has limited value in modal logic systems.

      As I noted in passing, propositional logic, “p if q,” is embedded with contingencies, but these are not understood to be temporal contingencies. So in a probabilistic universe, propositional logic must be supplemented with modal logics in order to express temporally contingent statements with definable truth-values.

      So we moderns have been developing logical systems out of the grammars of contingencies and change developed in the 17th, 18th and 19th centuries – in which truth can come to us contingently, gradually, probably, historically. But neither such grammar nor such logic were available to Paul of Venice. To make the *logical* claim that “X will exist” needed a level of certitude that we can no longer give it, usually provided by some deductive methodology or most frequently some authority – doctrine, dogma, the Bible. However, given the certitude provided, the claim reduces to a copula – “X exists at time B, whenever B occurs” (because the Bible says it must).

      The Medievals had a quirky understanding of time, derived from Augustine’s insistence that God existed outside of time. For instance “eternity” actually had a beginning (that described in Genesis) and an end (Judgment Day) since time is entirely a property of the material universe of creation. Also, since God is outside of time, he knows everything that occurs in time, all at once, as it were. So it is entirely appropriate to say “X is at time B” since God already ‘knows’ X at B, even if B hasn’t occurred for us (but God has assured us that it will happen).

      Paul’s real problem starts when he has to determine a difference between the moment of the event of the Antichrist’s appearance from the period between that appearance and Judgment day (C). There has to be this difference in order to talk about ‘the last days,’ but there is no logical distinction between the Antichrist existing at B and its existence in any moment after B.

      It would be interesting to imagine how Paul might have addressed these issues by deploying history (‘historical conditions leading up to the Antichrist’), but, per Augustine, human history was irrelevant. Nor could Paul discuss how someone – or something – could *become* Antichrist, since the Antichrist either is or is not, there would be no ‘becoming.’ Nor could he even fall back on the logical contingencies allowed via Aristotle, ‘possibility’ and ‘potentiality,’ since the appearance of the Antichrist was Biblically assured.

      So Paul’s language effectively predetermines what he can discuss, what he can say about it, and how he is going to say this, and effectively digs a pit for him that can only be seen through the prism of a different language. (In his own world, given the allowable language and its presumed knowledge base, Paul’s argument was entirely correct.)

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