Derrida Contra Austin – Irreducible Polysemy…

Architecture-of-the-grapheme-to-phoneme-converter-in-TTS-applications-be-reduced-to-a

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…

ctyp_81080777bb827_feature_1840-d4cdc4ac73759fde

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…

sunset-100367_1920-825x510

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…

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:

Screen Shot 2019-10-03 at 5.07.29 AM

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.

Screen Shot 2019-10-03 at 5.17.40 AM

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.

With Every Dream Denied…

Unknownlonely

With every road I move,
With every destination I choose,
With every love knocks me out,
With every emotion destiny’s a doubt,
I find myself in a labyrinth of life.
With every attempt to unwind,
With every soul that’s most unkind,
With every passing day and night,
With every teardrop that blinds my sight,
I sink into the morass of life.
With every word dismantled,
With every sentence entangled,
With every lyric the Heart utters,
With every Other the time fritters,
I discover all my dreams denied…

Kashmir, The Broken Soul…

imageskk

Stifled and Suffocated Under Occupation,

Confined to a Life in a Brazen Act of Annexation,

Subjected to a Toxicity by the Rest of the Confederacy, 

Paying the Price of Some Cooked and Some Raw Conspiracy.  

Counting Days and Nights Cut off From the Near and Dear Ones, 

By the Apathy and Atrophy of the Power that Runs, 

Into a Corner and Forced Underground, 

By the Despicable Vulgarity and Obscenity of the Dictatorial Sound. 

Who’d Turn a Messiah to the Multiplying Affliction, 

To Arrest the Basic Arithmetic of Division by Constriction, 

To a Unity Imposed by Self-Rule and Determination, 

By a Despot Shambolic and Ostentatious in Bringing Forth Malediction. 

We are People With Indomitable Rights, 

Sacrificed at the Altar of Rituals and Rites, 

Chanted on by a Population that doesn’t seem to Care, 

Legitimizing the Deeds of the Fundamentalists’s as an Internal Affair. 

Nuclear Winter…What if India and Pakistan Were to Engage Here?

2lqGMOV

We split the sub-continent with atomic burn,

The population is dead, we seal the urn,

Negotiations are over, we’re off the beaten track,

Civilizations en masse are interred through the crack.

 

Skies are turning to a horrific crimson,

The smoking bodies hide the moon and the sun,

The nuclear winter descends from the stratosphere,

Scorched earth is the writing on the wall everywhere…

Man Proposes OR Woman Proposes – “Matches” Happen Algorithmically and are Economically Walrasian Rather than Keynesian. Note Quote & Didactics.

Consider a set M of men and a set W of women. Each m ∈ M has a strict preference ordering over the elements of W and each w ∈ W has a strict preference ordering over men. Let us denote the preference ordering of an agent i by i and x ≻i y will mean that agent i ranks x above y. Now a marriage or matching would be considered as an assignment of men to women such that each man is assigned to at most one woman and vice versa. But, what if the agent decides to remain single. This is possible by two ways, viz. if a man or a woman is matched with oneself, or for each man or woman, there is a dummy woman or man in the set W or M that corresponds to being single. If this were the construction, then, we could safely assume |M| = |W|. But, there is another impediment here, whereby a subversion of sorts is possible, in that a group of agents could simply opt out of the matching exercise. In such a scenario, it becomes mandatory to define a blocking set. As an implication of such subversiveness, a matching is called unstable if there are two men m, m’ and two women w, w’ such that

  1. m is matched to w
  2. m’ is matched to w’, and
  3. w’ m w and m ≻w’ m’

then, the pair (m, w’) is a blocking pair. Any matching without the blocking pair is called stable.

Now, given the preferences of men and women, is it always possible to find stable matchings? For the same, what is used is Gale and Shapley’s deferred acceptance algorithm.

So, after a brief detour, let us concentrate on the male-proposal version.

First, each man proposes to his top-ranked choice. Next, each woman who has received at least two proposals keeps (tentatively) her top-ranked proposal and rejects the rest. Then, each man who has been rejected proposes to his top-ranked choice among the women who have not rejected him. Again each woman who has at least two proposals (including ones from previous rounds) keeps her top-ranked proposal and rejects the rest. The process repeats until no man has a woman to propose to or each woman has at most one proposal. At this point the algorithm terminates and each man is assigned to a woman who has not rejected his proposal. No man is assigned to more than one woman. Since each woman is allowed to keep only one proposal at any stage, no woman is assigned to more than one man. Therefore the algorithm terminates in a matching.

IMG_20190909_141003

Consider the matching {(m1, w1), (m2, w2), (m3, w3)}. This is an unstable matching since (m1, w2) is a blocking pair. The matching {(m1, w1), (m3, w2), (m2, w3)}, however, is stable. Now looking at the figure above, m1 proposes to w2, m2 to w1, and m3 to w1. At the end of this round, w1 is the only woman to have received two proposals. One from m3 and the other from m2. Since she ranks m3 above m2, she keeps m3 and rejects m2. Since m3 is the only man to have been rejected, he is the only one to propose again in the second round. This time he proposes to w3. Now each woman has only one proposal and the algorithm terminates with the matching {(m1, w2), (m2, w3), (m3, w2)}.

The male propose algorithm terminates in a stable matching.

Suppose not. Then ∃ a blocking pair (m1, w1) with m1 matched to w2, say, and w1 matched to m2. Since (m1, w1) is blocking and w1m1 w2, in the proposal algorithm, m1 would have proposed to w1 before w2. Since m1 was not matched with w1 by the algorithm, it must be because w1 received a proposal from a man that she ranked higher than m1. Since the algorithm matches her to m2 it follows that m2w1 m1. This contradicts the fact that (m1, w1) is a blocking pair.

Even if where the women propose, the outcome would still be stable matching. The only difference is in kind as the stable matching would be different from the one generated when the men propose. This would also imply that even if stable matching is guaranteed to exist, there is more than one such matching. Then what is the point to prefer one to the other? Well, there is a reason:

Denote a matching by μ. The woman assigned to man m in the matching μ is denoted μ(m). Similarly, μ(w) is the man assigned to woman w. A matching μ is male-optimal if there is no stable matching ν such that ν(m) ≻m μ(m) or ν(m) = μ(m) ∀ m with ν(j) ≻j μ(j) for at least one j ∈ M. Similarly for the female-optimality.

The stable matching produced by the (male-proposal) Deferred Acceptance Algorithm is male-optimal.

Let μ be the matching returned by the male-propose algorithm. Suppose μ is not male optimal. Then, there is a stable matching ν such that ν(m) ≻m μ(m) or ν(m) = μ(m) ∀ m with ν(j) ≻j μ(j) for at least one j ∈ M. Therefore, in the application of the proposal algorithm, there must be an iteration where some man j proposes to ν(j) before μ(j) since ν(j) ≻j μ(j) and is rejected by woman ν(j). Consider the first such iteration. Since woman ν(j) rejects j she must have received a proposal from a man i she prefers to man j. Since this is the first iteration at which a male is rejected by his partner under ν, it follows that man i ranks woman ν(j) higher than ν(i). Summarizing, i ≻ν(j) j and ν(j) ≻i ν(i) implying that ν is not stable, a contradiction.

Now, the obvious question is if this stable matching is optimal w.r.t. to both men and women? The answer this time around is NO. From above, it could easily be seen that there are two stable matchings, one of them is male-optimal and the other is female-optimal. At least, one female is strictly better-off under the female optimality than male optimality, and by this, no female is worse off. If the POV is men, a similar conclusion is drawn.  A stable marriage is immune to a pair of agents opting out of the matching. We could ask that no subset of agents should have an incentive to opt out of the matching. Formally, a matching μ′ dominates a matching μ if there is a set S ⊂ M ∪ W such that for all m, w ∈ S, both (i) μ′(m), μ′(w) ∈ S and (ii) μ′(m) ≻m μ(m) and μ′(w) ≻w μ(w). Stability is a special case of this dominance condition when we restrict attention to sets S consisting of a single couple. The set of undominated matchings is called the core of the matching game.

The direct mechanism associated with the male propose algorithm is strategy-proof for the males.

Suppose not. Then there is a profile of preferences π = (≻m1 , ≻m2 , . . . , ≻mn) for the men, such that man m1, say, can misreport his preferences and obtain a better match. To express this formally, let μ be the stable matching obtained by applying the male proposal algorithm to the profile π. Suppose that m1 reports the preference ordering ≻ instead. Let ν be the stable matching that results when the male-proposal algorithm is applied to the profile π1 = (≻, ≻m2 , . . . , ≻mn). For a contradiction, suppose ν(m1) ≻m1 μ(m1). For notational convenience let a ≽m b mean that a ≻m b or a = b.

First we show that m1 can achieve the same effect by choosing an ordering ≻̄ where woman ν(m1) is ranked first. Let π2 = (≻̄ , ≻m2 , . . . , ≻mn). Knowing that ν is stable w.r.t the profile π1 we show that it is stable with respect to the profile π2. Suppose not. Then under the profile π2 there must be a pair (m, w) that blocks ν. Since ν assigns to m1 its top choice with respect to π2, m1 cannot be part of this blocking pair. Now the preferences of all agents other than m1 are the same in π1 and π2. Therefore, if (m, w) blocks ν w.r.t the profile π2, it must block ν w.r.t the profile π1, contradicting the fact that ν is a stable matching under π1.

Let λ be the male propose stable matching for the profile π2. ν is a stable matching w.r.t the profile π2. As λ is male optimal w.r.t the profile π2, it follows that λ(m1) = ν(m1).

Let’s assume that ν(m1) is the top-ranked woman in the ordering ≻. Now we show that the set B = {mj : μ(mj) ≻mj ν(mj)} is empty. This means that all men, not just m1, are no worse off under ν compared to μ. Since ν is stable w.r.t the original profile, π this contradicts the male optimality of μ.

Suppose B ≠ ∅. Therefore, when the male proposal algorithm is applied to the profile π1, each mj ∈ B is rejected by their match under μ, i.e., μ(mj). Consider the first iteration of the proposal algorithm where some mj is rejected by μ(mj). This means that woman μ(mj) has a proposal from man mk that she ranks higher, i.e., mkμ(mj) mj. Since mk was not matched to μ(mj) under μ it must be that μ(mk) ≻mk μ(mj). Hence mk ∈ B , otherwise μ(mj) ≽ mkν(mk) ≽mk μ(mk) ≻mk μ(mj), which is a contradiction. Since mk ∈ B and mk has proposed to μ(mj) at the time man mj proposes, it means that mk must have been rejected by μ(mk) prior to mj being rejected, contradicting our choice of mj.

The mechanism associated with the male propose algorithm is not strategy-proof for the females. Let us see how this is the case by way of an example. The male propose algorithm returns the matching {(m1, w2), (m2, w3), (m3, w1)}. In the course of the algorithm the only woman who receives at least two proposals is w1. She received proposals from m2 and m3. She rejects m2 who goes on to propose to w3 and the algorithm terminates. Notice that w1 is matched with her second choice. Suppose now that she had rejected m3 instead. Then m3 would have gone on to proposes to w2. Woman w2 now has a choice between m1 and m3. She would keep m3 and reject m1, who would go on to propose to w1. Woman w1 would keep m1 over m2 and in the final matching be paired with a her first-rank choice.

Transposing this on to economic theory, this fits neatly into the Walrasian equilibrium. Walras’ law is an economic theory that the existence of excess supply in one market must be matched by excess demand in another market so that it balances out. Walras’ law asserts that an examined market must be in equilibrium if all other markets are in equilibrium, and this contrasts with Keynesianism, which by contrast, assumes that it is possible for just one market to be out of balance without a “matching” imbalance elsewhere. Moreover, Walrasian equilibria are the solutions of a fixed point problem. In the cases when they can be computed efficiently it is because the set of Walrasian equilibria can be described by a set of convex inequalities. The same can be said of stable matchings/marriages. The set of stable matchings is fixed points of a nondecreasing function defined on a lattice. 

Kashmir

Kashmir is the undefined unbecoming by the unprepared for the uninformed by way of the unceremoniously unspecified creation of this unruly mess.

I’d unsubscribe from this undemocratic, unparliamentary and unconstitutional uncertainties…