Appendix IV

Prolegomena to Any Future Noumenology

David C. Braun

© 2006 David C. Braun

Appendix IV

[Studies de nihilo:  I.  Kant on the nothing, and on ex nihilo nihil fit in relation to substance v. cause:]

I wish to begin with a quote from Kant, Critique of Pure Reason (translated by Norman Kemp Smith), Transcendental Doctrine of Judgment, chapter II, section 3, (3), Second Analogy, proof (in pertinent part):

…When something happens, the mere coming to be, apart from all question of what it is that has come to be, is already in itself a matter for enquiry.  The transition from the not-being of a state to this state, even supposing that this state [as it occurs] in the [field of] appearance exhibited no quality, of itself demands investigation.  This coming to be, as was shown above in the First Analogy, does not concern substance, which does not come to be out of nothing.  For if coming to be out of nothing is regarded as effect of a foreign cause, it has to be entitled creation, and that cannot be admitted as an event among appearances since its mere possibility would destroy the unity of experience.  On the other hand, when I view all things not as phenomena but as things in themselves, and as objects of the mere understanding, then despite their being substances they can be regarded, in respect of their existence, as depending upon a foreign cause.  But our terms would then carry with them quite other meanings, and would not apply to appearances as possible objects of experience.

B251-52/A 206 (Kemp Smith at 229-30).  Here I note that Kant never dealt with whether coming to be out of nothing were to be regarded as not an effect of any cause but simply an eventuation where there was no cause.  Kant assumes here, in that comment, the application of a law telling us to look for a cause wherever we have a “coming out of nothing.”  In fact, there must be such a law, for A=A+0, and indeed not only would the “unity of experience” be destroyed but also the harmony of the states involved.  And in as many words Kant must assume this.

            How the possibility of creation “ex nihilo” as caused by God could destroy the unity of experience Kant has not here explained; that he had previously covered (for which cause I will quote another block paragraph).  But true eventuations ex nihilo, eventuations that are without cause would destroy, or rather run counter to, A=A+0.  Yet that in turn does not require a confining of faith in creation (!) by God to the purely nounenal.

            I note also that Kant had a place in his system for the maxim ex nihilo nihil fit, albeit one applying again only within and for phenomena:

… The proposition, that nothing arises out of nothing, is still another consequence of the principle of permanence, or rather of the ever-abiding existence, in the appearances, of the subject proper.  For if that in the [field of] appearance which we name substance is to be the substratum proper of all time-determination, it must follow that all existence, whether in past or in future time, can be determined solely in and by it.  We can therefore give an appearance the title “substance” just for the reason that we presuppose its existence throughout all time, and that this is not adequately expressed by the word permanence, a term which applies chiefly to future time.  But since the inner necessity of persisting is inseparably bound up with the necessity of always having existed, the expression [principle of permanence] may be allowed to stand.  Gigni de nihilo nihil, in nihilum nil posse reverti, were two propositions which the ancients always connected together, but which are now sometimes mistakenly separated owing to the belief that they apply to things in themselves, and that the first would run counter to the dependence of the world – even in respect of its substance – upon a supreme cause.  But such apprehension is unnecessary.  For we have here to deal only with appearances in the field of experience; and the unity of experience would never be possible if we were willing to allow that new things, that is, new substances, could come into existence.  For we should then lose that which alone can represent the unity of time, namely, the identity of the substratum, wherein alone all change has thoroughgoing unity.  This permanence is, however, simply the mode in which we represent to ourselves the existence of things in the [field of] appearance.

Id. at First Analogy, B228-29/A185-86 (Kemp Smith at 215-16).   Hereon several notes:

1.  Is the unity of the substratum not the unity of the “I think” on which Kant made the categories depend?  But all that is needed is a relative permanence in general, not an absolute permanence, and a relative permanence of some substance vis-à-vis the subject as observer, or the subject’s own relative permanence.  But the harmony of A=A is ground of permanence as to the noumenal, specifically that of the being-sustained-by-God if there be creation and a God other than the I-think.

2.  The maxim of the ancients (gigni ex nihilo nihil, or ex nihilo nihil fit), rightly understood, in no wise refutes the doctrine of creation “ex nihilo” if the latter is also rightly understood.  It refers only to the divine power to cause an entity to be that otherwise in no sense would be, and that ordinally previously was not.  Ex nihilo nihil fit means really A=A+0, 0=0, 0=~(~0), A=A, and A=~(~A).

3.  Is it really the consequence of mere permanence that one can put the dictum ex nihilo nihil fit, or is it rather owing to the difference between the nothing and the something?

So now I must consider Kant’s lore in this part regarding the nothing, as it should be important alike to his thought and mine in contrast with his:

… The principle which anticipates all perceptions, as such, is as follows:  In all appearances sensation, and the real which corresponds to it in the object (realitas phaenomenon), has an intensive magnitude, that is, a degree.  Consequently there is also possible a synthesis in the process of generating the magnitude of a sensation from its beginning in pure intuition = 0, up to any required magnitude.  Since, however, sensation is not in itself an objective representation, and since neither the intuition of space nor that of time is to be met within it, its magnitude is not extensive but intensive.  This magnitude is generated in the act of apprehension whereby the empirical consciousness of it can in a certain time increase from nothing = 0 to the given measure.

Id., B208/A167 (Kemp Smith at 200-02).  Is the nothing here what Kant will later in the text call ens imaginarium (i.e., the third of the four types of nothing)?  [See, incidentally hereto, the note below at his discussion of the division.]

… Apprehension by means merely of sensation occupies only an instant, if, that is, I do not take into account the succession of different sensations. As sensation is that element in the [field of] appearance the apprehension of which does not involve a successive synthesis proceeding from parts to the whole representation, it has no extensive magnitude.  The absence of sensation at that instant would involve the representation of the instant as empty, therefore as = 0.

Id., B209/A 167 (Kemp Smith at 202-03).  As also here is the nothing ens imaginarium?  Or should I not rather wonder whether one should notice here, not a form of intuition without content (ens imaginarium), nor, on the other hand, a concept of the absence of the object (nihil privativum), but the fifth nothing I have identified, the “nothing of dreamless sleep” I have elsewhere discussed?  But notice that, even here, until Kant arrives as his discussion of the fourfold sense of “nothing,” he made no particular point of keeping any distinctions among them but treated them as if they were fungible or nearly so.

Now what corresponds in empirical intuition to sensation is reality (realitas phaenomenon); what corresponds to its absence is negation = 0.

Id., B209/A167-68 (Kemp Smith at 203).  But here the nothing is, is it not, in Kant’s terminology, nihil privativum (i.e., the second of the four)?

Every sensation, however, is capable of diminution, so that it can decrease and gradually vanish.  Between reality in the [field of] appearance and negation there is therefore a continuity of many possible intermediate sensations, the difference between any two of which is always smaller than the difference between the given sensation and zero or complete negation.

Id., B209-10/A168 (Kemp Smith, ibid.).  Here I should even find perhaps the first (i.e., ens rationis), or perhaps even an absolute void of the type not on Kant’s fourfold table.

In other words, the real in the [field of] appearance has always a magnitude.  But since its apprehension by means of mere sensation takes place in an instant and not through successive synthesis of different sensations, and therefore does not proceed from the parts to the whole, the magnitude is to be met with only in the apprehension.  The real has therefore magnitude, but not extensive magnitude.  A magnitude which is apprehended only as unity, and in which multiplicity can be represented only through approximation to negation = 0, I entitle an intensive magnitude.

Ibid.  Here has Kant not again invoked the nihil privativum, second of his fourfold table?

… The quality of sensation, as for instance in colours, taste, etc., is always merely empirical, and cannot be represented a priori.  But the real, which corresponds to sensations in general, as opposed to negation = 0, represents only that something the very concept of which includes being, and signifies nothing but the synthesis in an empirical consciousness in general.

Id., B217/A175-76 (Kemp Smith at 207-08).  Here Kant must mean nihil privativum.

Empirical consciousness can in inner sense be raised from 0 to any higher degree, so that a certain extensive magnitude of intuition, as for instance of illuminated surface, may excite as great a sensation as the combined aggregate of many such surfaces has illumiated.  [Since the extensive magnitude of the appearance thus varies independently], we can completely abstract from it, and still represent in the mere sensation in any one of its moments a synthesis that advances uniformly from 0 to the given empirical consciousness. 

Id., B217-18/A176 (Kemp Smith at 208).  But does he here now refer to the third one, or ens imaginarium, i.e., the form of time without content?  But see the note below regarding ens imaginarium.

… Similarly, the second state as reality in the [field of] appearance differs from the first wherein it did not exist, as b from zero.  That is to say, even if the sate b differed from the state a only in magnitude, the alteration would be a coming to be of b – a, which did not exist in the previous state, and in respect of which it = 0.  The question therefore arises how a thing passes from one state = a to another = b.

            … All alteration is thus only possible through a continuous action of the causality which, so far as it is uniform, is entitled a moment.  The alteration does not consist of these moments, but is generated by them as their effect.  That is the law of the continuity of all alteration.  Its ground is this:  that neither time nor appearance in time consists of parts which are the smallest [possible], and that, nevertheless, the state of a thing passes in its alteration through all these parts, as elements, to its second state.  In the [field of] appearance there is no difference of the real that is the smallest, just as in the magnitude of times there is no time that is the smallest; and the new state of reality accordingly proceeds from the first wherein this reality was not, through all the infinite degrees, the differences of which from one another are all smaller than that between 0 and a.

Id., B253-54/A208-09 (Kemp Smith at 231).  Kant appears in the above to distinguish an imaginary abstract nothing from a nothing that is really a sort of primeval content of the interstices of experiences – anticipating what I have noted about “dreamless sleep.”  Here one can see a contrast between what Kant stated about the nothing in the above and what he stated below:

            Before we leave the Transcendental Analytic we must add some remarks which, although in themselves not of special importance, might nevertheless be regarded as requisite for the completeness of the system.  The supreme concept with which it is customary to begin a transcendental philosophy is the division into the possible and the impossible.  But since all division presupposes a concept to be divided, a still higher one is required, and this is the concept of an object in general, taken problematically, without its having been decided whether it is something or nothing.  As the categories are the only concepts which refer to objects in general, the distinguishing of an object, whether it is something or nothing, will proceed according to the order and under the guidance of the categories.

            1.  To the concepts of all, many, and one there is opposed the concept which cancels everything, that is, none.  Thus the object of a concept to which no assignable intuition whatsoever corresponds is = nothing.  That is, it is a concept without an object (ens rationis), like noumena, which cannot be reckoned among the possibilities, although they must not for that reason be declared to be also impossible; or like certain new fundamental forces, which though entertained in thought without self-contradiction are yet also in our thinking unsupported by any example from experience, and are therefore not to be counted as possible.

            2.  Reality is something; negation is nothing, namely, a concept of the absence of an object, such as shadow, cold (nihil privativum).

            3.  The mere form of intuition, without substance, is in itself no object, but the merely formal condition of an object (as appearance), as pure space and pure time (ens imaginarium).  These are indeed something, as forms of intuition, but are not themselves objects which are intuited.

            4.  The object of a concept which contradicts itself is nothing, because the concept is nothing, is the impossible, e.g., a two-sided rectilinear fiture (nihil negativum).

            The table of this division of the concept of nothing would therefore have to be drawn up as follows.  (The corresponding division of something follows directly from it):

Nothing as

1.      Empty concept without object, ens rationis.

2.      Empty object of a concept, nihil privativum.

3.      Empty intuition without object, ens imaginarium.

4.      Empty object without concept, nihil negativum.

We see that the ens rationis (1) is distinguished from the nihil negativum (4), in that the former is not to be counted among possibilities because it is mere fiction (although not self-contradictory), whereas the latter is opposed to possibility in that the concept cancels itself.  Both, however, are empty concepts.  On the other hand, the nihil privativum (2) and the ens imaginarium (3) are empty data for concepts.  If light were not given to the senses we could not represent darkness, and if extended beings were not perceived we could not represent space.  Negation and the mere form of intuition, in the absence of a something real, are not objects.

Id., Appendix after chapter III, B346-49/A298-92 (Kemp Smith at 294-96).

            In relation to the third part of the table, note a problem.  Kant had earlier, in the Transcendental Aesthetic, put it that [space and] time did not exist in se, but alone as condition of the perception of intuitions of the senses.  See, e.g., id., Transcendental Aesthetic, §5, Conclusions from the Foregoing Concepts, a.  Is he not in this part contradicting part of what he had put in the Transcendental Aesthetic?

            I notice that Kant left out altogether any discussion of “dreamless sleep” or anything analogous thereto.  I should wonder, then, whether it fit the “empty intuition without an object” (ens imaginarium) or some other type.  Similarly, where does the 0 in his consideration of intension of sensations fit?  This is one place where Kant failed to explain what he ought.  (For that reason I supplied notes and noticed certain fungibilities in his consideration thereof.)  And, to the extent “dreamless sleep” (for example) does not fit here, is it within or without his fourfold schema of the nothing?  On the other hand, the nihil negativum is really a self-contradiction, not merely a nothing, and an impossibility.  But is not also the 0 ex quo something also an impossibility?

            I note that there is a common thread among the absolute nothing, the nothing of “dreamless sleep” and the 0 of A=A+0, a common thread that Kant appears neither to intuit nor to recognize.  Is that common thread one of intuition or sensation or only of thought?  My own further comment is that the common thread among them is that of congruence.  An absolute physical void (of the type Christianity or Judaism presuppose with the notion of creation ex nihilo), on getting anything into it, is no longer a totally empty void but now has still points of emptiness about it, which one can still denominate 0, and which has a non-contradictory continuity with the originary 0 in the physical sense.

[II.  Legitimacy of the concept in relation to positivism:]

                [A.  The set-up:]

            Let us suppose a child wonders what the nothing would be like.  She first thinks of blackness, utter darkness; but even that was a content of vision (after a fashion), whereas the absolute absence of experience would nave not even that quality to it.  All this questioning might arise in the context of a Weltvernichtung not in the theoretical sense, as in some speculation by the phenomenologist Husserl, see E. Husserl, Ideas (I), §49, but in the practical sense of what might happen if the Bomb wiped out all life.  (This presupposes that consciousness does not survive bodily death.)

            Kant protested also against the idea that any sensations could be found to correspond to the concept “which annihilates every thing,” to-wit, nothing (in the first of four senses in which he used ,,[das] Nichts“)[Kritik der reinen Vernunft, I, pt. I, bk. II, ch. III, app., B: 347/A: 290f].  Now in the sense of my being able to point out a particular positive (!) experience onto which I could “hang the hat” and say, “Here is the nothing,” I might be willing to play along.  But within the stream of my conscious life I can point to the discontinuities, or near-discontinuities like dreamless sleep, the event of the tuning-out of consciousness, and there have near enough the event I would analogize to das Garnichts.  I refer the reader to §3 of the main text of the Prolegomena to Any Future Noumenology.

[B.  The neo-positivist complaint against “the nothing” in philosophy:]

                                [1.  Prologue:  Avoiding Heidegger’s lore in translating the main text:]

Consideration of how I would translate my text into (e.g.) German led me to note that I can translate the words “the nothing of a moment ‘doth naught’” (§4) into German only by the words ,,das Nichts eines Moments ,tut nichts‘“, never by the words ,,das Nichts eines Moments ,nichtet‘“, as I wish in no way to express Heidegger’s sense in the following text:

            In dread there is a retreat from something, though it is not so much a flight as a spell-bound (gebannt) peace.  This “retreat from” has its souce in Nothing.  The latter does not attract:  its nature is to repel.  This “repelling from itself” is essentially an “expelling into”:  a conscious gradual relegation to the vanishing what-is-in-totality (das entgleitenlassende Verweisen auf das versinkende Seiende im Ganzen).  And this total relegation to the vanishing what-is-in-totality – such being the form in which Nothing crows around us in dread – is the essence of Nothing:  nihilation.  Nihilation is neither an annihilation (Vernichtung) of what-is, nor does it spring from negation (Verneinung).  Nihilation cannot be reckoned in terms of annihilation or negation at all.  Nothing “nihilates” (nichtet) of itself.

            Nihilation is not a fortuitous event; but, understood as the relegation to the vanishing what-is-in-totality, it reveals the latter in all its till now undisclosed strangeness as the pure “Other” –  contrasted with Nothing.

            Only in the clear night of dread’s Nothingness is what-is as such revealed in all its original overtness (Offenheit):  that it “is” and is not Nothing.  This verbal appendix “and not Nothing” is, however, not an a posteriori explanation but an a priori which alone makes possible any revelation of what-is.  The essence of Nothing as original nihilation lies in this:  that it alone brings Dasein face-to-face with what-is as such …

Heidegger, What is Metaphysics, published in English translation by Werner Brock in Existence and Being, 325-66, at 338f.  

                                [2.  The complaint of the neo-positivists; the answer:]

It was precisely against Heidegger’s dictum, das Nichts nichtet, that Rudolf Carnap, the logical positivist, vented his spleen in an article published under the title “The Language of Physics as the Universal Language of Science,” in the journal Erkenntnis, vol. II, pp. 219-41 (1931), specifically at 229-33.  But I suspect his analysis boiled down solely to this, as put by the Polish [Dominican friar and] logician, J. M. Bochenski:

            Another example:  a philosopher says, “Nothing nothings” (“das Nichts nichtet”).  Here “Nothing” is the argument of “nothings”; this last expression is obviously a monadic, statement-generating and name-determining functor.  But how can it be name-determining in this statement?  For what, considered syntactically, is “Nothing”?  It is evidently not a name although it seems to be something like one.  When we say “there is nothing”, we are really trying to say “for any x it is not the case that x is here and now”.  “Nothing” is therefore an abbreviation for the negation.  The negation, however, is not a name but a functor.  What the philosopher means may be right, but what he says must be regarded as syntactic nonsense.  It is not a statement and means nothing.

            By appealing to such examples the supporters of the neopositivist school have tried to show up the whole of philosophy as meaningless.  They have, however, mistaken syntactic nonsense for something quite different, namely semantic nonsense.  With the passage of time it has become clear that they have gone much too far.  All the same their attacks have contributed to the general awareness today that a poetic language can be used for the communication of scientific ideas only with great caution, since it can so easily conceal syntactic nonsense.  Hence the syntactic analysis of meaning has a far greater significance in philosophy today than was formerly the case.

Bochenski, The Methods of Contemporary Thought, 47 (New York 1968).  And it was to answer the criticism above set forth that I had inserted section 3 into the first chapter of the Prolegomena to Any Future Noumenology.

            Someone could notice that A=A+0 has nothing (sic!) to do with the “dreamless-sleep” state of “for every value, there is no x whatsoever” in section 3 of the Prolegomena to Any Future Noumenology, and that the 0 is simply a notational shorthand for “no value of x such that x=A, or that x=B, etc.”  Perhaps then a follower of Carnap might essay to twit me about the continued usage in discussing “causation” and the old Aristotelian rule ex nihilo nihil fit.  But perhaps one should at this point make resort to the Carnap of the Erkenntnis article(s), who sought to base his starting-point not in psychical language (as in Der logische Aufbau der Welt, passim) but in physicalist language, as alleged in H. Küng, Does God Exist, at 98 (Garden City, N.Y. 1981).  Quid ergo de vacuo?  Science allows the hypothesis of a vacuum into which are produced or radiate (as appropriate) photons of light (or other radiation-waves), quarks, subatomic particles, atoms, molecules, physical objects, etc.  So is there not still the zero of the vacuum plus A?

            [Or does Carnap attack the vacuum even as discussed in science?  Oy . . .  And I suppose “thought-experiments” – in which, e.g., a nearly absolute vacuum could be conceived, along the lines of Husserl’s Weltvernichtung in another context – should next be banned from scientific physics.  There would go not only important parts of relativity-theory dem Einstein nach but also indeed the concept of “absolute zero” and Lord Kelvin’s thermometric scale.]

            I would admit a fundamental analogical congruence, or at least resemblance, among “dreamless sleep,” the vacuum/Weltvernichtung, and the ”zero of the vacuum plus A,” to allow the 0 of A=A+0, 0=0, 0=~(~0), etc.

                                [3.  Return to consideration of problems specific to Heidegger’s notion of Nothing:]

            Heidegger’s nothing is an unclarified concept.  How does it repel?  As (e.g.) a positively charged ion repels a like-charged ion?  Or is this a sort of emotional repelling?  [As it were, it is repulsive to contemplate?]  And how does the “what-is-in-totality” vanish?  What (or who) relegates what (or whom) to this alleged “vanishing what-is-in-totality” under what circumstances?  Does Heidegger mean to credit to Nothingness the power to relegate entities to the point of fading away until there is no entity at all?  And yet the Nothing cannot annihilate (!).  Now, frankly, I am confused.  Was it Heidegger’s intent to confuse?  There is something indeed to be said for requiring a writer on metaphysics to define terms clearly.

            A good way farther into his essay, Heidegger wrote the following:

            Since ancient times metaphysics has expressed itself on the subject of Nothing in the highly ambiguous proposition:  ex nihilo nihil fit – nothing comes from nothing.  Even though the proposition as argued never made Nothing itself the real problem, it nevertheless brought out very explicitly, from the prevailing notions about Nothing, the over-riding fundamental concept of what-is.

            Classical metaphysics conceives Nothing as signifying Not-being (Nichtseiendes), that is to say, unformed matter which is powerless to form itself into “being” [i.e., in contrast with “not-being”] and cannot therefore present an appearance (eidos).  What has “being” is the self-creating product (Gebilde) which presents itself as such in an image (Bild), i.e., something seen (Anblick).  The origin, law and limits of this ontological concept are discussed as little as Nothing itself.

What is Metaphysics?  [Brock, op. cit. at 344f.]  I daresay that Heidegger’s interpretation of the Greek metaphysical tradition would very likely draw dispute.  As witness therefor I cite the position of Parmenides that the nothing simply did not exist, hence there was but a plenum entis and motion was impossible.  (So also would have held Zeno of Elea, his disciple and the framer of the famous paradoxes on motion and distance, etc.)  I would greatly doubt that even the Aristotelian [and Thomist] concept of potency answers to “the ancients’ concept” of nothing.

            But in his next paragraph Heidegger exposed an old misunderstanding, one it appears he had adopted as his own:

            Christian dogma, on the other hand, denies the truth of the proposition ex nihilo nihil fit and gives a twist to the meaning of Nothing, so that it now comes to mean the absolute absence of all “being” outside God:  ex nihilo fit – ens creatum:  the created being is made out of nothing.  “Nothing” is now the conceptual opposite of what truly and authentically (eigentlich) “is”; it becomes the summum ens, God as ens increatum.  Metaphysical discussion of what-is, however, moves on the same plane as the enquiry into Nothing.  In both cases the question concerning Being (Sein) and Nothing as such remains unasked.  Hence we need not be worried by the difficulty that if God creates “out of nothing” he above all must be able to relate himself to the Nothing.  But if God is God he cannot know Nothing, assuming that the “Absolute” excludes from itself all nullity (Nichtigkeit).

Id. [at 345].  My first impression is that Heidegger committed the same misapprehension, the same misunderstanding of “creation ex nihilo” that is evident in the text of Fredegisus of Tours, De nihilo et tenebris [Patrologia Latina, vol. 105, coll. 751-56], where Fredegisus took “nothing” to be a kind of existent, the first of God’s creatures, from which God formed other creatures.  But the Christian doctrine of creatio “ex nihilo” supposes only that God by omnipotence creates a new entity where but for that act there would be nothing and without fashioning it out of any thing real.  It is precisely the intent of the Church to teach that there is not some pre-existing stuff out of which God makes the creature.  And hence the nothing is not any kind of stuff at all, and bears no relation at all to the creative process by which God creates the creature.  By the same token, the Catholic Christian in no wise denies the truth of the Aristotelian dictum, ex nihilo nihil fit, provided that what is being discussed is relative to the question of effects’ requiring some real cause.

            But then Heidegger’s text moved onward to show something at once clarifying and perhaps alarming:

            This crude historical remainder shows Nothing as the conceptual opposite of what truly and authentically “is,” i.e., as the negative of it.  But once Nothing is somehow made a problem this contrast not only undergoes clearer definition but also arouses the true and authentic metaphysical question of the Being of what-is.  Nothing ceases to be the vague opposite of what-is:  it now reveals itself as integral to the Being of what-is.

            “Pure Being and pure Nothing are thus one and the same.”  This proposition of Hegel’s (“The Science of Logic,” I, WW III, p. 74) is correct.  Being and Nothing hang together, but not because the two things – from the point of view of the Hegelian concept of thought – are one in their definiteness and immediateness but because Being itself is finite in essence and is only revealed in the Transcendence of Da-sein as projected into Nothing.

What is Metaphysics?  [op. cit. at 346].  Now one might legitimately ask if real clarity were achieved herein.  The “Nothing” cannot be integral to the “Being of what-is” if the entity, the being is understood as the not-nothing, except in altogether a negative sense, by a kind of apophatic definition.  But precisely such an apophatic definition makes the pronouncement of Hegel absolutely incorrect, and negates the “motor of the dialectic.”  What is achieved is that Heidegger could be willing to sacrifice the rule A=~(~A) in his discussion of Being, Nothing, and the “Transcendence of Dasein.”

            Perhaps the best policy is to refuse to discuss any writer who refused to define terms and adhere strictly thereto.

                                [4.  An objection from science to the nothing of the vacuum raised:]

            The objection to the vacuum as the nothing arises in consideration of space as “affected by gravitation,” and as in turn bending light.  But is it that mere “empty space” is what is bent, or is there a gravitational field?  Conceptually this has somewhat the feel of the quagmire.  But there would be still the at least hypothetical (and transcendent, naught-effecting) nothing, the conditions answering to the x for every value of which there is no x.  Conceptual purity is called for here.  [But, meanwhile, one must still explain what the gravitational field actually is, if one wishes to argue that empty space (!) is a thing (!) “bent” by large material objects, or that it is empty space that bends light.  I doubt this was what Einstein et al. had meant, especially to declare themselves partisans of Fredegisus of Tours!]

            In my previous discussion of the nothing, I had allowed that the nothing is what is analogically posited in the situation, “what if, for every value of x, there is no x,” and alluded to in the perceptual vacuity of dreamless sleep, but also still about in the notion of the physical world’s vacuum, as well as in the notation A=A+0, or its discursive development, ex nihilo nihil fit.  I want to note, however, that the 0 of the entire world’s vacuity (the absolute nothing of dreamless sleep as absolutized for all worlds in “for every value of x, there is no x”) does not with itself get contradicted because of the presence of some x, so as to render 0 of itself the not-0.  For, instead, it is the x whose presence and to its extent is a not-0, which is denominated a non-void and understood as being.  The x does not, in other words, cause the vacuity of the vacuum beyond x to be a self-contradicting vacuity.  So 0=0 still, for all that, even though, between the infinite God and the finite x, the range of the vacuum is yet limited.

            But the sentence A=A+0 expresses yet another shorthand truth:  A is not self-conflicted, either.  To change, A must get the change ab extra, as it were.  I should also admit that much of one’s concept of the nothing is shaped by relative vacuity such as is encountered in the empty room (e.g., other than air, there is seemingly nothing between me and that wall).  So there is a greater dimension for the 0 therein than solely to express some other truths about A in shorthand, or about A’s world in general in shorthand, even if the nothing or vacuum be but relative and taken within certain limitations.  [I am reminded of the problem of the light-bending properties accorded to “empty space” near large gravitational field-generating objects like the sun or certain planets.]

            Perhaps I should clarify one thing specifically in relation to the void or the vacuum and the Parmenidean objection.  Parmenides held that the nothing does not exist, and from that concluded that being is an infinite plenum in which motion is impossible.  But it seems Parmenides’ argument depends upon a confusion between the idea of something’s being an entity and of something as simply there (in the sense of the French expression “il y a . . .” or the English “there is . . .” or the German ,,es gibt [ein] . . . “).  The nought can never be an entity (Fredegisus of Tours to the contrary notwithstanding), but I can say it is there, in that quadrant of space.  “And what do you see there?”  “Nothing at all.”

            [A Parmenidean would have to conclude that the senses betrayed their owners by passing off illusions as verities.  But a follower of Democritus at least would have the senses defensible because, besides atomoi, that one also admitted the void, the vacuum.  That theory seems more empirically defensible.  I refer, among other things, to what Lucretius had noted in De rerum natura about how wet clothing hung out loses the water-weight altogether, the water being broken up to the point of invisibility and being borne away in the air.]

            What I am actually essaying to say of the nothing is that it is a total abstractive, or, better, subtractive.  That means that the abstract concept is yielded by subtracting, per hypothesin, every value of x of any sort, the empirical by considering dreamless sleep as a consciousness-related state where every value of x within consciousness is subtracted.  But note that being does not equal the nothing precisely because it is the non-void.  I note that the physical-empirical concept of the nothing is yielded by considering the vacuum.  I can mentally subtract every value of x while still noting the presence of some x and frame, legitimately, the expression x + 0, which does not alter x.  And the persistent x as not contradicted by its environment supports the equation x = x + 0 and the “harmony of the void,” either as pure abstract construct or considered as vacuum.