Black Hole Entropy in terms of Mass. Note Quote.

If M-theory is compactified on a d-torus it becomes a D = 11 – d dimensional theory with Newton constant

G_D = G₁₁/L_d = l⁹₁₁/L_d —– (1)

A Schwartzschild black hole of mass M has a radius

R_s ~ M^(1/(D-3)) G_D^(1/(D-3)) —– (2)

According to Bekenstein and Hawking the entropy of such a black hole is

S = Area/4G_D —– (3)

where Area refers to the D – 2 dimensional hypervolume of the horizon:

Area ~ R_s^D-2 —– (4)

Thus

S ~ 1/G_D (MG_D)^(D-2)/(D-3) ~ M^(D-2)/(D-3) G_D^1/(D-3) —– (5)

From the traditional relativists’ point of view, black holes are extremely mysterious objects. They are described by unique classical solutions of Einstein’s equations. All perturbations quickly die away leaving a featureless “bald” black hole with ”no hair”. On the other hand Bekenstein and Hawking have given persuasive arguments that black holes possess thermodynamic entropy and temperature which point to the existence of a hidden microstructure. In particular, entropy generally represents the counting of hidden microstates which are invisible in a coarse grained description. An ultimate exact treatment of objects in matrix theory requires a passage to the infinite N limit. Unfortunately this limit is extremely difficult. For the study of Schwarzchild black holes, the optimal value of N (the value which is large enough to obtain an adequate description without involving many redundant variables) is of order the entropy, S, of the black hole.

Considering the minimum such value for N, we have

N_min(S) = MR_s = M(MG_D)^1/D-3 = S —– (6)

We see that the value of N_min in every dimension is proportional to the entropy of the black hole. The thermodynamic properties of super Yang Mills theory can be estimated by standard arguments only if S ≤ N. Thus we are caught between conflicting requirements. For N >> S we don’t have tools to compute. For N ~ S the black hole will not fit into the compact geometry. Therefore we are forced to study the black hole using N = N_min = S.

Matrix theory compactified on a d-torus is described by d + 1 super Yang Mills theory with 16 real supercharges. For d = 3 we are dealing with a very well known and special quantum field theory. In the standard 3+1 dimensional terminology it is U(N) Yang Mills theory with 4 supersymmetries and with all fields in the adjoint repersentation. This theory is very special in that, in addition to having electric/magnetic duality, it enjoys another property which makes it especially easy to analyze, namely it is exactly scale invariant.

Let us begin by considering it in the thermodynamic limit. The theory is characterized by a “moduli” space defined by the expectation values of the scalar fields φ. Since the φ also represents the positions of the original DO-branes in the non compact directions, we choose them at the origin. This represents the fact that we are considering a single compact object – the black hole- and not several disconnected pieces.

The equation of state of the system, defined by giving the entropy S as a function of temperature. Since entropy is extensive, it is proportional to the volume ∑³ of the dual torus. Furthermore, the scale invariance insures that S has the form

S = constant T³∑³ —– (7)

The constant in this equation counts the number of degrees of freedom. For vanishing coupling constant, the theory is described by free quanta in the adjoint of U(N). This means that the number of degrees of freedom is ~ N².

From the standard thermodynamic relation,

dE = TdS —– (8)

and the energy of the system is

E ~ N²T⁴∑³ —– (9)

In order to relate entropy and mass of the black hole, let us eliminate temperature from (7) and (9).

S = N²∑³⁽(E/N²∑³))^3/4 —– (10)

Now the energy of the quantum field theory is identified with the light cone energy of the system of DO-branes forming the black hole. That is

E ≈ M²/N R —– (11)

Plugging (11) into (10)

S = N²∑³(M²R/N²∑³)^3/4 —– (12)

This makes sense only when N << S, as when N >> S computing the equation of state is slightly trickier. At N ~ S, this is precisely the correct form for the black hole entropy in terms of the mass.

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Derrida Contra Searle – Intentionality – Part 2…

Part 1 is here

Another acerbic criticism by Searle concerns meaning as utterance meaning attributed to Derrida, where the positionality of intentions is confined to entities that are mysterious in nature and lying behind these utterances. The only way to smash this criticism is by showing that Derrida does respect the existence of distinction that mirrors Searle’s distinction between speaker’s utterance meaning and literal meaning. In accepting such a distinction, the seemingly apparent gulf becomes non-existent, and the irreducible polysemy or dissemination of Derrida lands on the same level as the literal ambiguity of Searle. Searle highlights the category mistake in underlying the supposition that the utterance of the token and the token are identical and the mistake only proliferates when the token acquires a different meaning from type in the case of utterance meaning as differing from sentence meaning. For him, excepting diachronic changes, special codes, and the like, the token’s meaning is always the same as the meaning of the type, and the only distinction worthy of name is the one between speaker’s utterance meaning from sentence meaning, type or token (John R. Searle – Expression and Meaning _ Studies in the Theory of Speech Acts). This can mean nothing more and nothing less than the fact that one’s use of token has no impact upon token’s type. Even if utterances and tokens are different from one another, utterances lose their existential status without tokens, implying that nothing rules out the possibility of utterances and token having different meanings, with the condition of utterance meaning as not affecting token’s literal meaning being strictly adhered to.¹ In order to establish the nexus between literal meaning and the issue of intentionality, Searle takes a recourse to fungible intentionality that highlights the conventionality of intentionality when trying to connect to the notion of literal meaning. This introduces about-ness in intentions or intentional states. The word “fungible” is used to designate a literal meaning that can do the work of a state of mind that is about something. Searle’s vagaries are once again evident when he simply broaches this concept of fungible intentionality in his reply to Derrida, as the essay circulates around argument of the iterability of linguistic forms as facilitating a necessary condition for particular forms of intentionality as characterizing speech acts. This is so, primarily due to the status enjoyed by us human beings at mastering recursive rules that help in the proliferation of speech acts thus generating infinite number of new things, meanings in its wake. And this is true even in case of remainder or when the sentence gets alienated, weaned from its origin. As Searle points out,

There is no getting away from intentionality, because a meaningful sentence is just a standing possibility of the corresponding intentional speech act. To understand it, it is necessary to know that anyone who said it and meant it would be performing that speech act determined by the rules of the languages that give the sentence its meaning in the first place.

Another complication that surfaces in Searle is his insistence on the dissimilarity between utterance meaning’s context dependency vis-à-vis sentence meaning’s context dependency², which incidentally is even accepted by Derrida. But, the problem lies in the non-clarity in Searle when he is trying his hand at distinguishing between meaning attached to the sentence and meaning attached to the utterance in his critique of Derrida in relation to Austin. To take an example, Derrida invokes a puzzling example from Nietzsche, “I forgot my umbrella”. This quote simply means ‘I forgot my umbrella’, even if one is unaware of the context underlying the remark. This quote also gives rise to a duality in that, on the one hand, one is aware of what is intended, whereas, on the other, one is not aware of the intention behind the statement. If this duality is considered, and if what Searle claims about intentionality as missing from writing holds true, then there is nothing that goes against Searle, for the consequence that a sentence would undergo would always be dictated by fungibility of intentions. But the point is missed for the thinker in question fails to apprehend what Derrida might have meant, that is, writer’s intention rather than fungible intention. The Derridean argument thereafter goes on to prove that intentions as such are never fully actualized. In a highly insightful passage, Derrida (Limited Inc 38) comments,

On the one hand, I am more or less in agreement with Sarl’s statement, “…there is no getting away from intentionality, because a meaningful statement is just a standing possibility of the corresponding intentional speech act”, I would, on the other hand, add, placing undue and artificial emphasis on -ful, that for reasons just stated, there cannot be a sentence that can be fully and actually meaningful and hence (or because) there can be no ‘corresponding (intentional) speech act’ that would be fulfilled, fully present, active and actual.

So, even if there are some traces of agreement between the two thinkers, Derrida rejects the thesis that intentions could be fully present within the text, thus proving his dissemination or irreducible polysemy as holding firm grounds. Moreover, his affirmation gets all the more strengthened because, iterability keeps account of dissemination, thus preventing intentions from ever getting actualized. Furthermore, if dissemination is to mark its presence, it is possible only with and within iterability. This goes on to prove the untenability of Searle’s “ideal hypothesis”, since the very structure of the mark excludes the hypothesis of idealization.

There is a nuance associated with irreducible polysemy, despite Searle’s thesis of vagueness and literal ambiguity that is no different than Derrida’s dissemination. Searle holds ambiguity to be finite, whereas, Derrida holds polysemy to be determinable, since irreducible polysemy never makes the arrogant claim on signs, words and sentences as having indeterminate meanings.³ Even a cursory look at the positions of the two thinkers  is enough to reach a conclusion that on the issue of meaning of sentences, these thinkers do not differ greatly, since both regard meaning as relatively contextual and meta- contextual, in addition to holding contexts as unchanging, and showing hardly any nuance amongst themselves in considering polysemy a characteristic feature of sentences. Well, this judgment appears to be slightly neutral laden or prejudiced with the usage of the word “nuance”, and could eventually mean as if the word is used rather strongly. But, this ain’t the sense in which it is employed here. There is a difference, and it lies in iterability, which, for Derrida, lends a polysemic status to sentential meanings, whereas the deviation wrought about by Searle lends legitimacy to the existence of univocal sentences.

Before getting into the discussion on parasitic discourses that formed a real contentious issue between Searle and Derrida, on the latter’s reading of Austin, it is necessary to provide a brief recapitulation. The major criticisms provided by Searle on Derrida’s take on Austin’s parasitic/normal/abnormal discourse are,

1. a misplaced conflation of iterability, citationality and parasitism that slides into a misplaced accusation of Austin as implicitly denying quotability,
2. a misplaced conflation of non-fiction/fiction distinction with speech/writing distinction as attributed to Austin,
3. a mistaken understanding of Austin’s exclusion of parasitic discourse and,
4. attaching an ethical status to this exclusion.

What is confounding for Searle is his understanding of Derrida, who according to former denies Austin any possible expressibility of quotations, since, Austin analyses serious speech acts before undertaking studies on parasitic ones. So, if Searle thinks of parasitism as not a matter of quotability on the one hand, he also considers Derrida’s position of commitment to parasitism as citationality on the other. Thus nothing differentiates citationality from quotability for Searle, whereas, for Derrida, quotation is just one aspect of citation. This Searlean argument falls flat on face, and a further decimation of it occurs, when one notes that Derridean parasitism is only an utterance, or a citation of an utterance in contexts that happen to be extraordinary. If non-serious citations were “the determined modification” of general citationality, it could only imply for non-serious utterances as a certain type of utterance in general⁴. One of the themes of Signature Event Context is to show that Austin excludes the determined modification of citationality, and with this exclusion, a successful performative misses its mark. So, it appears that there is a trade-off of exclusion for one type of citationality in favor of the other, viz, serious citation. This is a clear case of Searle misinterpreting citationality as mere quotability. Now, if there is a suggestion to the effect of non-serious citations as determined modifications of citationality, this could only be deciphered on the basis of conventionality, in that, whenever, these features are noticed, they should always be taken as utterances of a certain kind. If this is where Searle’s criticism aims at, Derrida takes a recourse to counter it by an augmented track to hit straight at former’s notions of idealization and semantic rules. This is to be accomplished in order to prove whether a distinction that is not sharp enough is a legitimate conceptual distinction in the first place. Derrida carries no qualms in admitting that it is not, whereas Searle insists on it being a legitimate conceptual distinction. The questions concerning the legitimate conceptual distinction is again a deviated path for the thinkers in question, since, both of them at least agree upon the premiss that a normal speech act is only comprehensible as a fiction following an aporetic situation in which a sharp distinction between normal and parasitic speech acts is encountered, thus considering these distinctions as nothing short of idealizations.

1 Kevin Halion correctly summarizes this with his reading of Searle as delineating two fundamental and separate distinctions viz, sentence/utterance and type/token. Speaker’s utterance meaning and sentence meaning are both context dependent. Over and above the context dependence of the utterance of ‘The cat is on the mat’ (where its indexicals are only determined relative to the context of utterance which decides which cat it is and where the mat is), there is a contextuality of its literal meaning. This dependence on contextual or background assumptions is easily shown. For instance, it would be problematic to speak of a cat’s being on a mat outside some gravitational field. However it might still be said and Searle gives an example to show this: looking from a space-ship window, mats float past with cats near them in such a relation that, relative to the ship, it can be said that in some cases the cat is on the mat and in the others the mat is on the cat. And there are innumerable other contexts to which the statement about the cat is also relative.

2 For to understand this opposition and differing kinds of context dependencies, it is worthwhile to have a look at the quote by Searle (Expression and Meaning 133f, linked above) below,

A … skeptical conclusion that I explicitly renounce is that the thesis of the relativity of literal meaning destroys or is in some way inconsistent with the system of distinctions … that centers around the distinction between the literal sentence meaning and the speaker’s utterance meaning, where the utterance meaning may depart in various ways from literal sentence meaning. …The modification that the thesis of relativity of meaning forces on that system of distinctions is that in the account of how context plays a role in the production and comprehension of metaphorical utterances, indirect speech acts, ironical utterances, and conversational implications, we will need to distinguish the special role of the context of utterance in these cases from the role that background assumptions play in the interpretation of literal meanings.

This clearly indicates the distinction made by Searle between utterance meaning and sentence meaning, even if they are both determined by context.

3 A couple of quotations from ‘Afterword: Toward an ethic Discussion’ (Limited Inc 115) lends legitimacy to Derrida’s views here.

I never proposed ‘a kind of “all or nothing” choice between pure realization of self-presence and complete freeplay or undecidability.’ I never believed in this and I never spoke of ‘complete freeeplay or undecidability’.

And again on page 148,

From the point of view of semantics…’deconstruction’ should never lead either to relativism or to any sort of indeterminism.

The quotations within the above quotes are from Searle (Caution: Subscribers’ only), that were reproduced by Gerald Graff in putting across his questions.

4 So it is not true that Derrida held that ‘the phenomenon of citationality’ (with citationality understood as quotability in the sense of mention but not of use) was ‘the same as the phenomenon of parasitic discourse’.

Derrida Contra Searle – Part 1…

The three most essential features of writing for Derrida happen to be remainder, rupture and spacing, of which the first is mirrored in weaning of a text from its origin and the second finds its congruence in severance of expression from its meaning, and all of the three happen to be graphematic. Remainder could also be thought of as writing that absents itself from the original context, while rupture is to be seen primarily as the unlikelihood of a proper context that arrests it, or confines it. Even if weaning of a text from its origin fits the bill of being graphematic, Searle’s rejects rupture as being one. This implies that the status of permanence is accorded to writing, as unlike speech, it remains in its archival form even in the absence of speaker-writer. This position is non- Derridean, as it argues against all language use as characterized by the absence of the sender. Therefore, severance of meaning from the expression is denied any special status for writing by an advantageous denomination of quotability, which, even if, not a normal purpose of quotation¹, could still be a possible one. Searle’s reading of severance of meaning from an expression or rupture goes for a tailspin here, for, rupture implies a signifier to be grafted onto innumerable contexts in which sense could be derived, rather than boundations imposed upon graphemes and phonemes as simple considerations of marks and sounds respectively, and alienated from any significations they might carry when considered as mere signifiers.

Derrida most patiently and appropriately, ironically launches into his own defense against these Searlean criticisms. Irony and/or mockery rules the roost in Limited Inc., for the style is a deliberate attempt to deal with the serious/non-serious distinction in response to Searle’s tone of high disdain. In the words of Spivak (Revolutions That As Yet Have No Model), Searle’s essay is brusque and all too brief, whereas, Derrida’s is long and parodistically courteous and painstaking.

Derrida in Signature Event Context thematically points out the exclusion of writing from speech act theory, and talks about the essential predicates that minimally determine the classical notion of writing. He does this through his reading of Husserl’s Logical Investigations and The Origin of Geometry, where Husserl had indicated a suspicion on speech as underlining certain of these predicates of writing, by supposing writing to imitate speech, but unable to share in the immediate link between speech and its context of production. Even if Signature Event Context considers every sign as cited without the quotation marks, a possibility of a break with every given context leading to illimitable new contexts cannot be ruled as a crisis ridden possibility in itself. Such a crisis has resolution in Husserl through his phenomenological reduction, and in Austin through a programmatic, initial, and initiating exclusion. For Searle, writing is nothing more than a transcription of speech, and his refutation of Derrida’s take on speech and writing is too quick a translation that finds its bottom in a standard and trivial idiom. For instance, Searle clearly misinterprets Derrida by noting some marks to be only iterable by citations exemplified in quotations. It is without any doubt that Derrida considers quotation as a form of iteration or citation, but is only one such form, since for him, use of any such mark is equally a case of/for citation and iteration.²

This is misinterpretation on Searle’s part primarily due to his treating/interpreting graphematic in the classical notion of writing.

When Searle reads Signature Event Context, he reads in it the absentia of intention from writing altogether, which he bases upon the mark as separated from its origin and context of production and is clearly stated in his reply to Derrida. He (Reiterating the Differences {linked in the footnotes}) says,

Intentionality plays exactly the same role in written as well as spoken communication. What differs in the two cases is not the intentions of the speaker but the role of the context of the utterance in the success of the communication.

So, if intentions are present in writing, and contexts differentiate themselves with respect to speech and writing, leading to speech as more implicit in its form as compared to writing that happens to be explicit, one can only adduce to the fact of Searle being caught up in the classical notion of writing, with writing relegated to a lower form of language vis-à-vis speech. This is despite the fact of classical notion holding writing as dependent on speech, with Searle breaking away from it marginally by holding this dependence to be a matter of contingency in the history of human languages, rather than construed as a logical matter, and simultaneously unsubscribing from the classical notion of intentions as somehow absent from writing. Derrida sees a problem with this particular take on intentions that have hitherto sought to actualize and totalize intentionality into self-presence and self-possession.³ One cannot miss the teleological overtones of classical notions of intentionality, and the resolution lies in problematizing this notion. One such solution lies in leveling the privileged status bestowed upon writer-reader’s presence brought about by deconstruction to call back to the center the necessary possibility of the absence of sender and receiver as the positive condition of possibility of communication.⁴ Such a critique should not be taken to mean in Searlean style that intentionality should be done away with, or effaced, but would only lay importance to its deployment as against disappearance. Intentions could very well themselves be the effects of a desire that lead to self-identical intentions in order to produce interpretations. A limit is imposed upon such desires to prevent it from being thought in terms of a fully intending subject. These limitations, however accentuate the very functionality of intentions, lest it should only focus on Derrida’s project as absurdly nihilist. According to Derrida (Limited Inc),

What is valid for intention, always differing, deferring, and without plenitude, is also valid correlatively, for the object (qua signified or referent) thus aimed at. However, this limit, I repeat (“without” plenitude), is also the (“positive”) condition of possibility of what is thus limited.

In short, in Derrida the originary self-division of intention “limits what it makes possible while rendering its rigor or purity impossible” (Revolutions that as yet have no model). Derrida sees intention as part of the total context⁵ that somehow carries the ability to intrinsically determine utterances, and is rigorously put forward, when he (Limited Inc) says,

Intention, itself marked by the context, is not foreign to the formation of the total context…to treat context as a factor from which one can abstract for the sake of refining one’s analysis, is to commit oneself to a description that cannot but miss the very contents and object it claims to isolate, for they are intrinsically determined by context.

This point of understanding intentionality is crucial here, for writer’s intending is bracketed by the same context as the actual production of graphemes, and Searle, who at times vehemently rejects any distinction between intention and context invokes it in his criticism of Derrida, thus exhibiting his own conflictual stance. To achieve explicitness, writing must be able to function without the presence of the writer, and the way this is attained is when something meaningful is being said, the intention behind it exhibits its non-presence. This helps clarifying the distinction between the intention to be meaningful and intention itself, or the intended meaning. The phrase “non-presence” is misleading however, and it is loaded with absence. In actuality, these are not to be employed synonymously.⁵ Non-presence entails intentions as never actualized, or made fully present in the language due to dissemination. Derrida (Limited Inc) explicitly never questions intentionality, but only its teleological aspirations through his text, since these aspirations orient the movements towards the possibility of fulfilling, realizing, and actualizing in a plenitude that would be present to and identical with itself. And this is precisely the reason why Derrida calls intention as not being present wholly. This position is bound to raise suspicion in Searle, when it is largely misinterpreted that radical absence of the receiver in general should connote the absence of trace of any sender. The confusion builds up around “radical absence”, as it is taken to mean the absence of intention, which, however, is not the case. What is really communicated here is the absence of consciousness of what one intended, as is clear from the fact that if a conscious act needs to be intentional, it does not assume intention as conscious.

1 Searle talks about the normal and the possible purpose of quotation in a note that follows his remark (Reiterating the Differences),

We can always consider words as just sounds and marks and we can always construe pictures as just material objects. But…this possibility of separating the sign from the signified is a feature of any system of representation whatever: there is nothing especially graphematic about it at all.

2 If every ark is iterable, then no mark belongs to language strictly speaking. Languages could be thought of as reifications, that for someone like Donald Davidson, help us construct theories of meaning, while at the same time engaging with consistent and idiomatic speech behaviors. This might seem like loose semantic conventions and habits, but nonetheless direct towards some sort of an engagement with the likes of Joyce and Mrs. Malaprop and inculcating in us the revisionary exercise towards the theory of what language our interlocutor is speaking in line with the principle of charity. 

3 This is one of the reasons why Derrida calls his critique as ethico-political in nature.

4 This is reviewed by Spivak (Revolutions that as yet have no model {linked above}), and she calls attention to an extensive quote attributed to Derrida on the same page, that I find very insightful and hence worth reproducing it here.

To affirm…that the receiver is present at the moment when I write a shopping list for myself, and , moreover, to turn this into an argument against the essential possibility of the receiver’s absence from every mark, is to settle for the shortest, most facile analysis. If both sender and receiver were entirely present when the mark was inscribed, and if they were thus present to themselves-since, by hypothesis, being present and being-present-to- oneself are here the same-how could they even be distinguished from one another? How could the message of the shopping list circulate among them? And the same hold force, a fortiori, for the other example, in which sender and receiver are hypothetically considered to be neighbors, it is true, but still as two separate persons occupying two different places, or seats…But these notes are only writable or legible to the extent that…these two possible absences construct the possibility of the message at the very instant of my writing or his reading.

5 This confusion is ameliorated when one sees non-presence as designating a less negated presence, rather than getting caught up in the principally binary presence/absence opposition that is usually interpreted.

Derrida Contra Austin – Irreducible Polysemy…

The position of Austin seems to relegate writing vis-à-vis speech, even if he maintains that certain aspects of speech are imperfectly captured by writing. Even Searle joins his mentor in admitting the implicit context of speech when compared with the explicit context of writing. Another thematic insistence between speech and writing in Austin is an utterance that is tied to origin. When an utterance is not in the present indicative active, then the utterer is not typically referred to by name or personal pronoun ‘I’ but by the fact that it is he who is speaking and thus the origin of the utterance, and when he happens to be absent and does not use his name or the personal pronoun ‘I’, he will often indicate in the written document that it is he who is the origin by signing it with his name. Derrida voices his criticism on this position for the speaker’s intended meaning isn’t any more unequivocal, if he is present, than, if he would have written. This point is cogently argued by Derrida because for him the presence of the speaker is analogous to the one who signs. He says in Signature, Event, Context,

The signature also marks and retains [the writer’s] having-been present in a past now or present which will remain a future now or present…general maintenance is in some way inscribed, pinpointed in the always evident and singular present punctuality of the form of the signature…in order for the tethering to the source to occur, what must be retained is an absolute singularity of a signature-event and a signature-form: the pure reproducibility of a pure event.

One conclusion that could be favorably drawn from Derrida’s reading of Austin according to the above quote is that for the latter, a permanence is given to the signature that identifies the signer and his presence with/within the text. This also implies at the same time the reproducibility of the mark of signature to deduce that it is recognized as¹ his signature , thus proving not only originality of signature but also its iterability. Derrida’s general criticism of Austin rest upon the latter’s failing to acknowledge the graphematic nature of locutions in addition to performative/constative and serious/parasitic distinctions not being able to fit in, when applied to locutions. This is deducible by arguments that run against the notion of proper contexts thereby hindering the discernment between speech acts that qualify as normal or parasitic and happy or unhappy. A careful reading of Austin’s How To Do Things With Words establishes a thematic rule of classifying and/or categorizing speech acts that are resistant to being unambiguously accounted for one way rather than other, or, in other words, the book’s primary aim is to root out the thesis that context is absolutely determinable, even if there is a recognition of serious and non-serious speech acts with the cautionary treatment of leaving out the non-serious acts during the examination of the serious ones. Derrida, on the contrary gives a lot of seriousness to the “non-serious/non-literal”’ linguistic use, as for him, they are determinate of meaning. This stand of Derrida goes opposite to Austin’s, for who, speech acts, even if they harbor felicities and infelicities, could only be investigated about within ordinary circumstances. In an amazing reading² of Austin, Derrida claims non-serious citations of utterances qua citations, are nothing but instances of the iteration of the utterances that help determine its identity. Moreover, Derrida claims graphematic root of citationality as responsible for why Austin is unable to provide an exhaustive list of criteria to distinguish performatives with constatives, and also because Austin fails to take account of the structure of locution as already entailing predicates that blur the oppositions which are in turn unsuccessfully attempted to be established. Also, failure to recognize the necessity of impure performatives on Austin’s part made Derrida’s criticism more cogent, as for the latter, “impurities” are not just confined to performatives having a constative dimension, or constatives having a performative dimension, but, even normal and parasitic acts weren’t immune anymore to “impurities”. This criticism gains authority, since for Derrida, impurities are necessary and not any accidental facts, and in the absence of proper contexts, “hosts” maybe parasitic on “parasites” implying further that “normal” utterances are relatively normal and “parasitic” utterances are relatively parasitic, since the criterion invoked to differentiate them is the difference in contexts that is somehow missing or blurred in Austin. So, if the constative/performative distinction is an impure distinction in itself for Austin, then he is not successful in legitimizing the normal/parasitic distinction. Derrida claims that Austin’s work shows that the possibility of failure, or infelicity, is a permanent structural and/or necessary possibility of performative utterances, but Austin excludes the risk of such failures as accidental. In other words, Austin shows that performatives are characterized by an essential risk of failure and yet treats that risk as if it were accidental, which Derrida characterizes as a necessary impurity of performatives and constatives. Furthermore, Austin’s investigations of infelicities and total speech situations point to the fact that speakers and hearers can exercise control over speech situations in order to avoid infelicity and secure uptake, which meets its counter- argument in Derridean dissemination or irreducible polysemy by the establishing of locutions as graphematic, thus losing out on any such possibility of securing control on the speech act by either the speaker or the hearer.

In a nutshell, it is safe to say that Austin’s total speech act revolved around a dual notion of a possible elucidation within the total speech situations that left room for a generalized accountability for a formulation to comprehend parasitic deviations from the norm and speech acts construed as an exercise in exposing the lack of distinctions like parasitic/normal involved therein. Therefore, even if in his speech act theory, it is impossible for an utterance to take hold of normal and parasitic tones, it does not rule out the contingency of such distinctions from coming into being. The impossibility of distinctions for utterances in Austin’s case is what moves Searle away from his mentor, as for the latter, utterances could be tagged normal or parasitic due to his literal/utterance-meaning and representation/communication distinctions (his notion of intentionality achieves prominence here with the speaker-writer determining if her utterance is normal or parasitic). For Searle, sentences are loaded with literal ambiguities, since the possibilities of speaking literally or non-literally exist in some sort of a double bind, and this take of his has some parallels in Derrida’s citationality, iterability and dissemination. There is a difference though, in that, Derrida gives credence to the irreducible polysemy and parasitism and unhappiness as permanent and structural, that should in no way be counted as indeterminate or free play, but rather as mired in ambiguities, whereas Searle never thinks of all utterances as polysemic…

1 It should be noted that the ideal signature is one which can only be repeated by one individual, and for Derrida, it is the impossible ideal of something original that remains so even when it undergoes repetition. Effects of signature are the most common thing in the world, with the conditions of its possibility as simultaneously the conditions of its impossibility of a rigorous purity. Functionality is driven, when the signature enjoys repeatable, iterable and imitable forms, which is made possible, when a signature gets detached from its singular, intended production, or in other words, it is sameness which, by corrupting its identity and its singularity, divides its seal. 

2 This reading is evident in the quote (Derrida),

“..ultimately, isn’t it true that what Austin excludes as anomaly, exception, ‘non-serious’ citation (on stage, in a poem, or a soliloquy) is the determined modification of a general citationality- or rather, a general iterability – without which there would not even be a ‘successful’ performative? So that- a paradoxical but unavoidable conclusion – a successful performative is ‘necessarily’ an impure performative, to adopt the word advanced later on by Austin when he acknowledges that there is no pure performative.”

The Jukebox…

The last coin found its way through the slot. the years wore strained and the ears that were trained to the notes in synchronized harmony. This time, however, nothing of the harmonic was sounded, nothing but silence pierced through the curtains, out in the moonless air, dissipated and buried in the dead souls of the city retiring endlessly from the chores for a living. The Jukebox stared at me blankly as the last of its mechanical life escaped as I sat looking into the void and crying silently….

An Unfinished Story…

No murmur ever rose from the bed of River of Silence that flowed eternally with a hushing influence over it’s pearly pebbles that we loved to gaze together far down within its bosom into a most contented pledge of till death do us part, until…..

And as the years grew heavily on my existence, I could no longer dwell in the valley of the River of Silence with a shadow palling over my mind of the life no more accompanying me, of the silence of togetherness no longer a quietude in solemnity, of the zephyr no longer dallying the tree that bore witness, and of glory long ago transformed into vain glory…

Sedition

I am a victim of Political Claustrophobia,
Suffocated by the Tyrant’s Myopia,
Chased by the Dictatorial Democracy,
Clobbered to Silence by Seditious Lunacy.

Catastrophe, Gestalt and Thom’s Natural Philosophy of 3-D Space as Underlying All Abstract Forms – Thought of the Day 157.0

The main result of mathematical catastrophe theory consists in the classification of unfoldings (= evolutions around the center (the germ) of a dynamic system after its destabilization). The classification depends on two sorts of variables:

(a) The set of internal variables (= variables already contained in the germ of the dynamic system). The cardinal of this set is called corank,

(b) the set of external variables (= variables governing the evolution of the system). Its cardinal is called codimension.

The table below shows the elementary catastrophes for Thom:

The A-unfoldings are called cuspoids, the D-unfoldings umbilics. Applications of the E-unfoldings have only been considered in A geometric model of anorexia and its treatment. By loosening the condition for topological equivalence of unfoldings, we can enlarge the list, taking in the family of double cusps (X₉) which has codimension 8. The unfoldings A₃(the cusp) and A₅ (the butterfly) have a positive and a negative variant A₊₃, A_-3, A₊₅, A_-5.

We obtain Thorn’s original list of seven “catastrophes” if we consider only unfoldings up to codimension 4 and without the negative variants of A₃ and A₅.

Thom argues that “gestalts” are locally con­stituted by maximally four disjoint constituents which have a common point of equilibrium, a common origin. This restriction is ultimately founded in Gibb’s law of phases, which states that in three-dimensional space maximally four independent systems can be in equilibrium. In Thom’s natural philosophy, three-dimensional space is underlying all abstract forms. He, therefore, presumes that the restriction to four constituents in a “gestalt” is a kind of cognitive universal. In spite of the plausibility of Thom’s arguments there is a weaker assumption that the number of constituents in a gestalt should be finite and small. All unfoldings with codimension (i.e. number of external variables) smaller than or equal to 5 have simple germs. The unfoldings with corank (i.e. number of internal variables) greater than two have moduli. As a matter of fact the most prominent semantic archetypes will come from those unfoldings considered by René Thom in his sketch of catastrophe theoretic semantics.