Derrida Contra Austin – Irreducible Polysemy…

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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.”

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Ruminations on Philosophy of Science: A Case of Volume Measure Respecting Orientation

Let M be an n–dimensional manifold (n ≥ 1). An s-form on M (s ≥ 1) is a covariant field αb1…bs that is anti-symmetric (i.e., anti-symmetric in each pair of indices). The case where s = n is of special interest.

Let αb1…bn be an n-form on M. Further, let ξi(i = 1,…,n) be a basis for the tangent space at a point in M with dual basis ηi(i=1,…,n). Then αb1…bn can be expressed there in the form

αb1…bn = k n! η1[b1…ηnbn] —– (1)

where

k = αb1…bnξ1b1…ξnbn

(To see this, observe that the two sides of equation (1) have the same action on any collection of n vectors from the set {ξ1b, . . . , ξnb}.) It follows that if αb1…bn and βb1…bn are any two smooth, non-vanishing n-forms on M, then

βb1…bn = f αb1…bn

for some smooth non-vanishing scalar field f. Smooth, non-vanishing n-forms always exist locally on M. (Suppose (U, φ) is a chart with coordinate vector fields (γ⃗1)a, . . . , (γ⃗n)a, and suppose ηib(i = 1, . . . , n) are dual fields. Then η1[b1…ηnbn] qualifies as a smooth, non-vanishing n-form on U.) But they do not necessarily exist globally. Suppose, for example, that M is the two-dimensional Möbius strip, and αab is any smooth two-form on M. We see that αab must vanish somewhere as follows.

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A 2-form αab on the Möbius strip determines a “positive direction of rotation” at every point where it is non-zero. So there cannot be a smooth, non-vanishing 2-form on the Möbius strip.

Let p be any point on M at which αab ≠ 0, and let ξa be any non-zero vector at p. Consider the number αab ξa ρb as ρb rotates though the vectors in Mp. If ρb = ±ξb, the number is zero. If ρb ≠ ±ξb, the number is non-zero. Therefore, as ρb rotates between ξa and −ξa, it is always positive or always negative. Thus αab determines a “positive direction of rotation” away from ξa on Mp. αab must vanish somewhere because one cannot continuously choose positive rotation directions over the entire Möbius strip.

M is said to be orientable if it admits a (globally defined) smooth, non- vanishing n-form. So far we have made no mention of metric structure. Suppose now that our manifold M is endowed with a metric gab of signature (n+, n). We take a volume element on M (with respect to gab) to be a smooth n-form εb1…bn that satisfies the normalization condition

εb1…bn εb1…bn = (−1)nn! —– (2)

Suppose εb1…bn is a volume element on M, and ξi b (i = 1,…,n) is an orthonormal basis for the tangent space at a point in M. Then at that point we have, by equation (1),

εb1…bn = k n! ξ1[b1 …ξbn] —– (3)

where

k = εb1…bn ξ1b1…ξnbn

Hence, by the normalization condition (2),

(−1)nn! = (k n! ξ1[b1 …ξbn]) (k n! ξ1[b1 …ξbn])

= k2 n!2 1/n! (ξ1b1 ξ1b1) … (ξnbn ξnbn) = k2 (−1)n

So k2 = 1 and, therefore, equation (3) yields

εb1…bn ξ1b1…ξnbn = ±1 —– (4)

Clearly, if εb1…bn is a volume element on M, then so is −εb1…bn. It follows from the normalization condition (4) that there cannot be any others. Thus, there are only two possibilities. Either (M, gab) admits no volume elements (at all) or it admits exactly two, and these agree up to sign.

Condition (4) also suggests where the term “volume element” comes from. Given arbitrary vectors γ1a , . . . , γna at a point, we can think of εb1…bn γ1b1 … γnbn as the volume of the (possibly degenerate) parallelepiped determined by the vectors. Notice that, up to sign, εb1…bn is characterized by three properties.

(VE1) It is linear in each index.

(VE2) It is anti-symmetric.

(VE3) It assigns a volume V with |V | = 1 to each orthonormal parallelepiped.

These are conditions we would demand of any would-be volume measure (with respect to gab). If the length of one edge of a parallelepiped is multiplied by a factor k, then its volume should increase by that factor. And if a parallelepiped is sliced into two parts, with the slice parallel to one face, then its volume should be equal to the sum of the volumes of the parts. This leads to (VE1). Furthermore, if any two edges of the parallelepiped are coalligned (i.e., if it is a degenerate parallelepiped), then its volume should be zero. This leads to (VE2). (If for all vectors ξa, εb1…bn ξb1 ξb2 = 0, then it must be the case that εb1 …bn is anti-symmetric in indices (b1, b2). And similarly for all other pairs of indices.) Finally, if the edges of a parallelepiped are orthogonal, then its volume should be equal to the product of the lengths of the edges. This leads to (VE3). The only unusual thing about εb1…bn as a volume measure is that it respects orientation. If it assigns V to the ordered sequence γ1a , . . . , γna, then it assigns (−V) to γ2a, γ1a, γ3a,…,γna, and so forth.

Metric. Part 1.

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A (semi-Riemannian) metric on a manifold M is a smooth field gab on M that is symmetric and invertible; i.e., there exists an (inverse) field gbc on M such that gabgbc = δac.

The inverse field gbc of a metric gab is symmetric and unique. It is symmetric since

gcb = gnb δnc = gnb(gnm gmc) = (gmn gnb)gmc = δmb gmc = gbc

(Here we use the symmetry of gnm for the third equality.) It is unique because if g′bc is also an inverse field, then

g′bc = g′nc δnb = g′nc(gnm gmb) = (gmn g′nc) gmb = δmc gmb = gcb = gbc

(Here again we use the symmetry of gnm for the third equality; and we use the symmetry of gcb for the final equality.) The inverse field gbc of a metric gab is smooth. This follows, essentially, because given any invertible square matrix A (over R), the components of the inverse matrix A−1 depend smoothly on the components of A.

The requirement that a metric be invertible can be given a second formulation. Indeed, given any field gab on the manifold M (not necessarily symmetric and not necessarily smooth), the following conditions are equivalent.

(1) There is a tensor field gbc on M such that gabgbc = δac.

(2) ∀ p in M, and all vectors ξa at p, if gabξa = 0, then ξa =0.

(When the conditions obtain, we say that gab is non-degenerate.) To see this, assume first that (1) holds. Then given any vector ξa at any point p, if gab ξa = 0, it follows that ξc = δac ξa = gbc gab ξa = 0. Conversely, suppose that (2) holds. Then at any point p, the map from (Mp)a to (Mp)b defined by ξa → gab ξa is an injective linear map. Since (Mp)a and (Mp)b have the same dimension, it must be surjective as well. So the map must have an inverse gbc defined by gbc(gab ξa) = ξc or gbc gab = δac.

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In the presence of a metric gab, it is customary to adopt a notation convention for “lowering and raising indices.” Consider first the case of vectors. Given a contravariant vector ξa at some point, we write gab ξa as ξb; and given a covariant vector ηb, we write gbc ηb as ηc. The notation is evidently consistent in the sense that first lowering and then raising the index of a vector (or vice versa) leaves the vector intact.

One would like to extend this notational convention to tensors with more complex index structure. But now one confronts a problem. Given a tensor αcab at a point, for example, how should we write gmc αcab? As αmab? Or as αamb? Or as αabm? In general, these three tensors will not be equal. To get around the problem, we introduce a new convention. In any context where we may want to lower or raise indices, we shall write indices, whether contravariant or covariant, in a particular sequence. So, for example, we shall write αabc or αacb or αcab. (These tensors may be equal – they belong to the same vector space – but they need not be.) Clearly this convention solves our problem. We write gmc αabc as αabm; gmc αacb as αamb; and so forth. No ambiguity arises. (And it is still the case that if we first lower an index on a tensor and then raise it (or vice versa), the result is to leave the tensor intact.)

We claimed in the preceding paragraph that the tensors αabc and αacb (at some point) need not be equal. Here is an example. Suppose ξ1a, ξ2a, … , ξna is a basis for the tangent space at a point p. Further suppose αabc = ξia ξjb ξkc at the point. Then αacb = ξia ξjc ξkb. Hence, lowering indices, we have αabc =ξia ξjb ξkc but αacb =ξia ξjc ξib at p. These two will not be equal unless j = k.

We have reserved special notation for two tensor fields: the index substiution field δba and the Riemann curvature field Rabcd (associated with some derivative operator). Our convention will be to write these as δab and Rabcd – i.e., with contravariant indices before covariant ones. As it turns out, the order does not matter in the case of the first since δab = δba. (It does matter with the second.) To verify the equality, it suffices to observe that the two fields have the same action on an arbitrary field αb:

δbaαb = (gbngamδnmb = gbnganαb = gbngnaαb = δabαb

Now suppose gab is a metric on the n-dimensional manifold M and p is a point in M. Then there exists an m, with 0 ≤ m ≤ n, and a basis ξ1a, ξ2a,…, ξna for the tangent space at p such that

gabξia ξib = +1 if 1≤i≤m

gabξiaξib = −1 if m<i≤n

gabξiaξjb = 0 if i ≠ j

Such a basis is called orthonormal. Orthonormal bases at p are not unique, but all have the same associated number m. We call the pair (m, n − m) the signature of gab at p. (The existence of orthonormal bases and the invariance of the associated number m are basic facts of linear algebraic life.) A simple continuity argument shows that any connected manifold must have the same signature at each point. We shall henceforth restrict attention to connected manifolds and refer simply to the “signature of gab

A metric with signature (n, 0) is said to be positive definite. With signature (0, n), it is said to be negative definite. With any other signature it is said to be indefinite. A Lorentzian metric is a metric with signature (1, n − 1). The mathematics of relativity theory is, to some degree, just a chapter in the theory of four-dimensional manifolds with Lorentzian metrics.

Suppose gab has signature (m, n − m), and ξ1a, ξ2a, . . . , ξna is an orthonormal basis at a point. Further, suppose μa and νa are vectors there. If

μa = ∑ni=1 μi ξia and νa = ∑ni=1 νi ξia, then it follows from the linearity of gab that

gabμa νb = μ1ν1 +…+ μmνm − μ(m+1)ν(m+1) −…−μnνn.

In the special case where the metric is positive definite, this comes to

gabμaνb = μ1ν1 +…+ μnνn

And where it is Lorentzian,

gab μaνb = μ1ν1 − μ2ν2 −…− μnνn

Metrics and derivative operators are not just independent objects, but, in a quite natural sense, a metric determines a unique derivative operator.

Suppose gab and ∇ are both defined on the manifold M. Further suppose

γ : I → M is a smooth curve on M with tangent field ξa and λa is a smooth field on γ. Both ∇ and gab determine a criterion of “constancy” for λa. λa is constant with respect to ∇ if ξnnλa = 0 and is constant with respect to gab if gab λa λb is constant along γ – i.e., if ξnn (gab λa λb = 0. It seems natural to consider pairs gab and ∇ for which the first condition of constancy implies the second. Let us say that ∇ is compatible with gab if, for all γ and λa as above, λa is constant w.r.t. gab whenever it is constant with respect to ∇.