The motives which led Democritus and Plato to postulate an Objective-Reality, supposed to be in relation to empirical-Existence while being radically distinct from it, and which does not determine in either of them the structure that both assigned to this Reality were, in fact and for us, the same. Namely, the desire to replace the fluctuating discourse that speaks of fluid phenomena, by a discourse that is definitively stabilised or valid as it is everywhere and always, while connecting it, if only to contradict it, to the contradictory discourse referring to empirical Existence in all the diversity of its extended duration. However, as a Philosopher, Plato was discursively aware of these motives, while the Physicist Democritus was not aware of them, at least explicitly. Furthermore, Plato’s religious attitude compelled him to relate ‘objective’ or ‘true’ discourse to the “mystical Silence” revealing the supra-real Beyond, while Democritus’ scientific attitude would have allowed him to be satisfied with the sole affirmation of the objective reality of what he was talking about, the ineffable Beyond being for him only pure nothingness (from which he distinguished, moreover, the “non-being” of the Emptiness, which was opposed in an irreducible way to the being of the Full within Objective-Reality). In fact, both Democritus and Plato were mistaken in believing that they could speak in the literal sense of what, according to them, Objective-Reality was. For us, the “theoretical” Physics inaugurated by Democritus was finally completed in and by the explicitly pseudo-discursive development of Energometry, which is content to measure objective-Reality, by putting a “mathematical relationship” (logos) for the results of these measurements, while renouncing to say what the “nature” of this measurement is. As for the Platonic Ideo-logy, we will see that by developing discursively, it ends in and through the Silence of para-thetical contra-diction. But if the the discursive (“exclusive”) element of Energo-metry is nothing other or more than the impasse of Dogmatism founded on silent scientific Experimentation, Platonic Ideo-logy opened up a perspective (through the Kantian Criticism of the Synthetic Para-thesis of Philosophy) on the (“synthetic”) discourse of the Hegelian System of Knowledge which, no longer excluding any discourse, no longer implies any “dogmatic” silence. [religious (theological), scientific or moral (ethical)]. Because in imagining his Ideo-logy, Plato emphasised from the beginning not what he was (more often than not, intended) to talk about there, but on the fact of being able to say it, in the proper sense of this word, that is to say, in a de-finite or definitive way, that is, in and by a discourse (supposed to be coherent) finished or completed in itself, but indefinitely reproducible. Now, it is precisely such a discourse that is the System of Knowledge which implies, as an integrant-element, the trans-formed Platonic Ideology (with a view to its entirely discursive and non-contradictory completion) in an Authentic energy.
Be that as it may, in this subsequent trans-formation of Plato’s Ideo-logy, the fact is that the latter developed it starting from the postulate of the definitive or de-finite Discourse. On the one hand, Plato shared the common opinion that there is (discursive) Truth only where (the meaning of) what is said “relates” to (the essence of) that of which one speaks, or that what one speaks of ‘corresponding’ to what one says of it (in truth) while being something other than the discourse which speaks of it. On the other hand, Plato realised that a discourse could only be said to be true on the condition of being defined or finished by ending itself in itself (without contradicting itself) and of not being able to continue indefinitely: being able to continue thus only by reproducing itself as it is from the beginning to the end (the other discourses being supposed to have to cancel each other out by developing indefinitely, since each of them was forced to contradict itself sooner or later). Now, if objective (“ideal”) Reality must, by its very Platonic definition, correspond to an (“ideological”) discourse which relates to it, the “subjective” structure of Discourse as such must also be “objective”, by being that of Reality. In fact and for us, the structure of the Discourse as such is irreducibly duplicated in itself or essentially dyadic.
Without having been the discoverer of this discursive Duality (of which Parmenides and Heraclitus have already spoken explicitly), Plato seems to have been the first (guided perhaps by Socrates to fully account for it (in and by his philosophical discourse, which he himself calls dialectic) to draw explicitly from it “logical consequences”. At least we can, it seems, explain in the following way the Platonic dialectic, which is to be found in a more or less implicit and different form in all Plato’s dialogues.
Any authentically discursive assertion (and not “degenerated” into para- or pseudo-discourse) can be reduced to the verbal formula S is P. The word “is” establishes a significant relation between the word S and the word P, in that meaning that in this relation, the first is brought into relation with the second. We can specify the nature of the discursive or ‘logical’ relation by saying that as ‘relation is’, it is a relation of inclusion. Which can be made explicit by saying that the fact of this relationship, the word S, which has no meaning in itself, receives one on the condition that the word P is “meaningful”, the meaning of S thus being the same as that of P, although these two meanings differ from each other insofar as one of the two words does not coincide with the other. Neither S nor anything in general has any meaning, if P has none. Now, the fact is that P can only have one on the condition of also having another and therefore of having a hard one, or, more exactly, of being able to signify one OR the other of these two meanings. For the fact is still, that if P were to signify both one AND the other, its “double meaning” would only show that it no longer has any, thus signifying sign neither one NOR the other. We can define each of these two combined meanings by saying that one is the opposite of the other, by designating them, in order to distinguish them, P and Not-p.
Since any “double meaning” P AND Not-p is equivalent to the absence of any meaning whatsoever, it also makes no sense to say S is P and Not-p. In this case, the relation is no longer a discursive relation. But since S and P have a meaning only because P has one and since P is only one of inclusive meaning if Not-p is also one (namely the opposite meaning”), S is Non-p has just as much a meaning as S is P. And one of these expressions can be said to have a meaning (and is thus only discursive) to the extent that both have meaning, each having the opposite meaning of the ‘other. However, S does have a meaning, for example, P, only on the condition that it does not have the opposite meaning Not-p. Moreover, one cannot say (without contradicting oneself) S is P unless one can also say S is not Non-p. Saying one is therefore equivalent to saying the other. But to account for the fact that we can indifferently say not only one OR the other, but also one AND the other at the same time, thus saying the same thing twice, we can distinguish, within the discursive relation, between the relation of inclusion which is said to be and that of exclusion which is said to be not. But the discursive relation attributes to S the meaning P, whatever this meaning may be: P or Not-p. Therefore, it makes just as much sense, say, to affirm (by the relation of inclusion) that S is P or Not-p as, say, to deny (by the relation of exclusion ) whether S is one or the other.
- We will thus have four discursive relations (of which, moreover, each one is discursive only on condition that the four are discursive) or, more exactly, two relations (of inclusion and exclusion), each of which is duplicated into a couple of assertions having opposite meanings:
S is P I affirmation I I positive I
S is Not-p I affirmation I I negative |
S is Not-p. I negation I I positive I
S is-not Not-p I negation I. I negative I
Given that the relation loses its meaning or ceases to be discursive either if S is put in an affirmative relation with P AND not-p at the same time, or if it is put in relation of NEITHER with the one NOR with the other (or, which amounts to the even, if it is put in relation niante [negierende] with both) and that it has a positive meaning only on the condition of also having the opposite meaning to the negative, it follows that the discursive relation as such is irreducibly double, the Discourse being therefore essentially dyadic. Therefore, if we want to make someone understand that we affirm (positively) that S is P, we must not prevent him from saying the opposite, by affirming (negatively) that S is No -p. No doubt one can (if one has understood) answer him by denying (negatively) what he is saying, that is to say, by saying that S is not Non-p. But if we want to be understood by him, we must not prevent him from answering in his turn that S is not P, thus denying (positively) what he has understood.
Now, if to affirm (positively or negatively) anything has neither more nor less meaning than to deny (positively whatever is nevertheless other than that of affirmation or negatively) anything, the meaning of an assertion to the contrary is its negation. We note it “immediately, that is, from the mere fact of having understood the meaning of an affirmation or any negation or, if you prefer, at the very moment we do it.
And looking more closely, we will see what Plato saw, namely that the difference in question is that the Positive is “simple” or one in itself, while the negation is “composite”, being in itself split or double. But if we look even closer, we will see that the discursive double in question is less simple than it seems at first sight. Be that as it may, this first Platonic view can be expressed discursively as follows. In the discursive relation of the positive affirmation (relation of inclusion in the Positive), namely S is P; S has simply or only the meaning P and it alone, this meaning not only being unique in its kind, but also one in itself. On the other hand, in the discursive relation by the negative affirmation (relation of inclusion in the Negative) S is not P, S has a double meaning or, if one prefers, a split meaning, which is also unique in its kind, but which is so by being not one in itself, but two.
Indeed, S has meaning in S is-not P (just as in S is P, for that matter) only insofar as P has one. For if P had no meaning, S is not P would not have any either (just as little, moreover, as S is P). There is therefore “on the one hand” of S is-not P, the meaning P. But, on the other hand, there must be yet another or a second meaning, so that S is-not P has a meaning of its own, which must be other than that of S is P for the two expressions to have any meaning. This other meaning of S is not P, this meaning other than P, is that of No or of Negation as such. Without the meaning P, S is-not P would have no meaning at all. But the meaning Not-s is-not P would have no meaning other than that of S is P. S is-not P therefore does not have a meaning of its own, which is its own meaning; and it has a meaning insofar as it has a double meaning, namely a “particular” meaning P (“positive”) whatever and the (“negative”) meaning of the No “in general” or of the Negative, even of the Negation as is. Now, if the meaning of S is P is finite in itself or defined by itself, that of S is-not P is in-definite (even “infinite”, if we admit wrongly, but with Heraclitus and Kant/ the infinity of the set of senses as such).
This character, one could argue, is unique to the (“negative”) meaning of the No (or of the not-is-not). We can therefore say that only a split discourse is not finite (or is in-finite), that the Discourse is in-definite only insofar as it is double or two. As source or origin (principle) of the discursive In-definite, the Two can thus effectively be called (“definite”), with Plato, in-definite Dyad (aoristos Dyas).
However, if the discourse S is not P is in-definite, if it is in-finite in the sense of non-finite, it is not “infinite” in the proper sense [?] of the term, it is i.e. indefinable. Indeed, because of not being P, S is not just anything. On the contrary, the very fact of not being P renders it forever incapable of being anything of what is P. The relation of exclusion of S with P limits S just as much as its relation of inclusion with this same P. And the limit of S comes in both cases from one and the same P, even from the finite or de-finite character of the latter. Only, the (“positive”) relation of inclusion of the S in the P de-finishes the notion S itself, in and by its “definition” which is the discourse S is P, also de-fined by the de-finite P that it implies. On the other hand, the notion S is and remains in-definite in the discourse that is the (“negative”) relation of exclusion S is-not P, this discourse itself being in-definite because of the implication of the indefinite No. But the implication of the de-finite P limits this discourse and, suddenly, the S that it also implies. Without being de-finite (because of the inclusion of the No), this discourse is therefore de-finishable and it is so as limited (by the inclusion of the P from which S is excluded). And one can say, with Plato, that if S is defined by P (in the “definition” S is P) insofar as it “is” this P defined (being nothing else), it is only definable insofar as it only ‘participates in this P while being excluded or ‘separated’ from it (in indefinite but definable discourse S is not P). It is only if an S (“any”) did not “participate” at all in a definite P (whatever it is) that this S would be “infinite” in the sense of indefinable or not developable into a discourse, finished or defined. But the “participation” of an indefinite or “infinite” S in a P defined whatever it may be, limits this S by thus making it definable, or virtually defined, even if it does not actually de-finish it.
In other words, the “participation” of S in P in and through the (negative) discourse S is-not-P is a “definition” of the S “in the process of becoming”. It is a “definition” which has begun, but which is not finished. We already know that S is not P, but we do not yet know what S “is”. But since the “participation” of the S in the P which is being “separated” from it (or from which it is excluded) limits this S, this one is a “finite” in the sense of being “definable”. Now, we de-finish the S by saying what it ״is”. Let us say then, to de-fine S “in act” or to complete its “virtual” definition which says that S is-not P, we need to add (/ better yet, to replace it in the) claim that S is Not-p. The discourse S is Not-p is no longer a negation, as S is-not P was. It is an affirmation, just as S is P. But while this was a positive affirmation, S is Not-p is a negative statement. That is to say that the discourse remains split or double in itself. Because it involves both the senses of P and No. But the discursive relation is no longer that of the in-definite relationship of exclusion; it is that of the definite relation of inclusion. We can just as easily say that we have finished defining P, or that we are defining it “in action”. For one says what S is by saying that it “is” Non-p. And we can bring out this completed or actual character of the definition by saying that S “is” Q (Q being equivalent to Not-p, having the same meaning as the latter).
If one abstracts from any meaning whatsoever, one transforms the discursive formula S is Q into a symbolic (“mathematical”) formula, which no longer says that S “is” Q in the sense that it a signifies the same thing as Q. It is therefore better to write S Q (or Q, as moreover S and =, can be = replaced by any other morpheme, for example by P), to show that the formula no longer makes sense at all. But we can content ourselves with “formalising” the formula as “formal logic” does, that is, by preserving the meaning of Q, but understanding it as any meaning whatsoever. In this case, it makes sense to say S is Q, the sense in question signifying that S “is” Q, Q being, moreover, “some”. Only, the meaning of P being already arbitrary, by definition to say that S “is” Q therefore has no other meaning than to say that it is “P. And this is why “formal logic” confuses these two discursive formulas, in a single one, which is that of the “affirmative judgment”, as opposed to the formula of the negative judgment S is not P.
We also see that this “separation” distinguishes Q from P in the sense that the S which is P “is” P only and nothing else, while the S which is Q “is” on the contrary something other than P, while being not just anything, but only Not-p. In other words, the discursive formula S is P is one in itself, having one and the same meaning, the meaning of S being the same as that of P, which is (single and) one. On the other hand, the discursive formula S is Q (-Not-p) is itself double and it therefore de-doubles “indefinitely” in itself, thus being multiple (because of the Not that Q implies at the same title as it implies P). Now, if the unity of S is P is explicit, the multiplicity that S is Q implies is not explicit. In other words, if the positive affirmation S is P is an explicit actual “definition”, the negative affirmation S is Q is also actual, but it is so only as implicit. The whole question is whether the implicit meaning of Q (and therefore that of S as in S is Q, as well as the meaning of this formula itself) is “infinite” or not in the sense that it cannot be made explicit in and by a “finished” or “completed” discourse (meaning: in a limited time, or in an extended duration which has a end and therefore a beginning proper). In other words: by saying that S “is” Q (-Not-p), we actualized the virtual “definition” of S which said that this S “is” not P: because we have now said what “is” S, namely Q and nothing else. Only, this Q is not one in itself, but double, even “indefinitely” doubled or multiple. It would therefore be necessary to say several things in order to be able to say explicitly what “is” the S in question. Now, only one thing has been said about it, namely that it is Q. The question is therefore to know whether we can say explicitly all that the S which is Q “is”, by saying it in a ‘finished’ or completed discourse, or if one must speak endlessly while trying to do so, without ever arriving anywhere at the end of this discourse which is also its goal as an explicit definition. In fact and for us, the answer to this question is “positive”. Indeed, if Q = Not-p were “infinite” in the sense of the indefinable (as is sometimes claimed), Q would have no meaning at all. It would therefore make just as little sense to affirm that S “is” Q as to deny it, by saying that S “is” not Q. And to say that S is not “is” Q is to say that S is not Non-p. Now, de-doubled into P and No, the S which does not “is” would be non-only- (-Not-p), namely, not “infinite” (in the sense indicated) because it would have one and the same sense that one could call P. Thus, to say it as “finite” or de-finite, but still one in itself, not having S is-not Not-p is equivalent to saying S is P.
And since the S which “is P can only have one meaning (namely P), S is P must have the same meaning as S is-not Not-p. For there to be Discourse, Non-p must therefore be a finite or have a de-finite meaning “in action.” Now, the meaning of S n’est-pas Non-p (maybe it is better this way…?) is the same as that of S is P. If the latter is explicit, the former must be too. But S is-not Not-p cannot have an explicit meaning, if the implicit meaning of Not-p (=Q) is never made explicit anywhere. It must therefore be one day somewhere, in and by a “finished” or completed discourse.
This does not mean that the discourse S is Q, which makes explicit the meaning of Q= Not-p, cannot develop “indefinitely”, contrary to the discourse S is P. The discourse which defines Q can be more explicit, and this is so “indefinitely”: Q can be explained as Q1, Q1- – as Q2, etc. But it is necessary and sufficient that each of these discourses be “reasoned” in and by the preceding one (which it only develops “in detail”), so that all of these discourses can be summed up in one and the same (implicit) definition that says that S “is” Q.
But such is not the opinion of Plato. According to him, the so-called “discourse” which develops the meaning of the Q, which is Non-p, is nothing else than the Heraclitean Discourse-river, which flows endlessly and has neither beginning nor end. This pseudo-discourse is “infinite” in the sense that it does not return anywhere to its point of departure and is therefore never “summarised”. One could only say what Q (- Not-p) is by saying that it is Q₁; but one can only say what “is” Q1, by saying that it “is” Q2, which “is” Q3.; and so on indefinitely or “ad infinitum”.
Only this discursive River without beginning or end or, rather, this cataract which pours into a bottomless abyss while falling from nowhere, does not frighten Plato and does not make him dizzy. For he fixes his gaze on the fixed and stable rainbow, one, albeit diverse, which the light of the sun causes in the cloud of drops of water (moreover always new), which are constantly occurring above the current new and frightening vertigo.
To speak without images, Plato believes he has established the possibility of discursive Truth, that is to say, of finite or de-finite (indefinitely repeatable) Discourse that one cannot deny (without contradicting oneself), while believing to note that the Philosopher can be satisfied with speaking about P, opposing the profane ones, even the héracliteans, by questioning the dubious pleasure to speak without end and thus without goal, nor term, of all that is Non-p. And this is because of the famous “separation” between P and Non-p (charismos) that Aristotle will reproach.
TO BE CONTINUED. EDITED, ETC.
At any rate, the following notes can facilitate the understanding of the text so far: We begin by Kant, which we indeed mentioned…the third note takes us to what should continue this very partial text…
- Infinite Judgment. Science is, perhaps, for Kant, one and the same “infinite” discourse, that is to say, an indefinitely developable discourse, but also one that can be summed up at any time. But the synthetic para-thesis that is Kantian philosophy is more sceptical than that. In any case, the term infinite judgment introduced by Kant is very ambiguous. He has clearly seen that for Philosophy, the formal S is Non-p (==q) is something other than the formula S is P of the affirmative judgment to which formal Logic brings it back and that it is not to be confused with the formula S ‘is’ not P of the negative judgement’, but he was wrong to speak of infinite judgment, by specifying that the S which is ‘Not-p’ can be an infinity of things other than P, instead of having to be the finite set of all that is not P. In addition, great confusion reigns in the terminology distinguishing between the contradictory and the opposite [so far!]. Let us try to help. Certainly, we “contradict” S is P by saying S is not P and we say the “opposite” when we say S is Non-p or S is Q (== Non-p). In other words: S which is not P is anything except P; but S which is ‘Non-p’ can only be ‘of the same kind’ as P, while not being P. For example, if S is not red, S may be blue, etc., or colourless as a number, etc. But if S is Non-red, S must be coloured (or colourable), while having any colour other than red (including white as the absence of any colour, but not black, if this is the set of all colours). Now, we generally say that S is Q is “contrary” to S is P, if Q is Not-p; but we do not say it, if Q is simply something other than P or only a different from P: Red is the “opposite” of Non-red, but Red is only “different” from Blue (if White is the absence of any colour and Black the presence of all, White and Black are not “opposites; but White and Colored are; for what is Non-white has at least one colour and can have them all, that is- i.e. being black). Now, if the Non-red is not only blue, it is also blue; by explaining its implicit definition, sooner or later, we will end up defining it (also) as blue. It would therefore be necessary to say that Red and Non-red are “opposites” insofar as the definition of Non-red remains sufficiently implicit not to make blue explicit, but that they are only different as soon as Non-red is made explicit as blue. Be that as it may, Plato does not seem to have been concerned with these things. Aristotle was, but what he says about it has remained very confusing. At any rate, qua logic, as philosophy qua logic, all this is very stupid indeed. On the other, there is something gymnastic here in Hegelian terms, yet implicit to the non-Hegelian. [Things I do when it is obvious that there is a cake 🎂in the kitchen: not to see the second obvious: I am too lazy to go get it.].
For us, as for Plato, the discourse S is not P (“negative judgement”) is a discourse properly speaking, that is to say, having a “definite” meaning, only insofar as it ” participates “a definite meaning” P, as a discursive relation of S to P by a relationship of exclusion between P and S. We can also say, with Plato, that S has no meaning that belongs to it in own but receives one by the “participation” in the proper sense of P, while remaining “separate” from this P and being in-definite or “infinite” in and by this very “separation”. Now, we understand better what Plato has in view when we consider the degenerate (“negative”) verbal formula: S is not. Here, P has completely disappeared (“has been annihilated”): there is no longer any “participation” of S to P. Suddenly, S is absolutely “undefined”, in the sense of indefinable; we can say, if we want, that S is then “infinite”, in the sense that we can no longer say what it is > in any finite or defined discourse. We can express it by saying that S is then nothing at all or that it is not. No doubt we can call this “Infinite” S “Nothingness” in the sense of indefinable. But it must then be said that NOTHING is a symbol, that is to say a morpheme of an ex-notion deprived of its meaning. And since every morpheme is, by definition, unspecified or “arbitrary”, we can replace this one by others, for example by oo, 0, etc. But by simply changing the morpheme of a symbol, we do not transform it into a notion: none of the morphemes of the symbol will have a meaning properly speaking, that is to say, discursively defined or -what definable in and by a finite discourse. Moreover, the “degeneracy” of S is not purely apparent. For if the P is no longer made explicit there, it is nevertheless implicitly present there. S is not is equivalent to S is-not P, insofar as P signifies Being as such or the totality of what is, indeed all that “is” something. Here again, the “participation” in P limits the S by assigning to it a discursive meaning properly so-called, if only definable. ‘Nothingness’ then means (everything) of which one will never be able to say anywhere what it is”. What we can also say by saying that Nothingness means (everything) that which is not. Which amounts to saying that Nothingness is ineffable, being (all) that which cannot be spoken of or (all) that which is revealed in and by (even as) Silence. Now, we in no way contradict ourselves when we speak of something only to say that we cannot or do not want to speak about it.
One might wonder why Plato did not see that the Being-given implies, as the third and middle term of its totality, not implication or conjunction, even juxtaposition by AND, but exclusion by Difference. (or Negation). Perhaps the notion of Difference-from-the-Identical was “logically” too shocking? Yet Plato knew very well that the meaning of this notion is that of the notion Spatiality (of which it is the first discursive development or the first definition). Would he have been reluctant to spatialize (ideal) Being as such? This is what Aristotle seems to insinuate, when he says that we must ask Plato why Ideas are not in Place (cf. Phys., 209b in fine). But it may be that Plato saw that the Difference-of-the-identical, which is Spatiality, implied the Identity-of-the-different, which is nothing other than Temporality, and that he taught less spatialization of ideal-Being than its temporalization. If he saw himself obliged to reject Parmenides’ Eternity in the beyond of Discourse by contenting himself with admitting the discursivity of the only eternal Concept, he did not want in any case to temporalize the latter. It seems that from a “psychological” point of view, he had religious reasons to oppose it. But from the “systematic” point of view, the exclusion of the AND or of Difference, that is to say, the reduction of the Being-three or of the Trinity-which-is Hegelian to the Being-two or to the Heraclitean Dyad, is an integral part of the correct discursive development of the Thetical Para-thesis of Philosophy. This Para-thesis is Platonic only because it was Plato who first refused to take into account the difference between what is and what is not or between what is spoken of in any way and what one was silent by saying nothing.