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.

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Hypostatic Abstraction. Thought of the Day 138.0

Hypostatic abstraction is linguistically defined as the process of making a noun out of an adjective; logically as making a subject out of a predicate. The idea here is that in order to investigate a predicate – which other predicates it is connected to, which conditions it is subjected to, in short to test its possible consequences using Peirce’s famous pragmatic maxim – it is necessary to posit it as a subject for investigation.

Hypostatic abstraction is supposed to play a crucial role in the reasoning process for several reasons. The first is that by making a thing out of a thought, it facilitates the possibility for thought to reflect critically upon the distinctions with which it operates, to control them, reshape them, combine them. Thought becomes emancipated from the prison of the given, in which abstract properties exist only as Husserlian moments, and even if prescission may isolate those moments and induction may propose regularities between them, the road for thought to the possible establishment of abstract objects and the relations between them seems barred. The object created by a hypostatic abstraction is a thing, but it is of course no actually existing thing, rather it is a scholastic ens rationis, it is a figment of thought. It is a second intention thought about a thought – but this does not, in Peirce’s realism, imply that it is necessarily fictitious. In many cases it may indeed be, but in other cases we may hit upon an abstraction having real existence:

Putting aside precisive abstraction altogether, it is necessary to consider a little what is meant by saying that the product of subjectal abstraction is a creation of thought. (…) That the abstract subject is an ens rationis, or creation of thought does not mean that it is a fiction. The popular ridicule of it is one of the manifestations of that stoical (and Epicurean, but more marked in stoicism) doctrine that existence is the only mode of being which came in shortly before Descartes, in concsequence of the disgust and resentment which progressive minds felt for the Dunces, or Scotists. If one thinks of it, a possibility is a far more important fact than any actuality can be. (…) An abstraction is a creation of thought; but the real fact which is important in this connection is not that actual thinking has caused the predicate to be converted into a subject, but that this is possible. The abstraction, in any important sense, is not an actual thought but a general type to which thought may conform.

The seemingly scepticist pragmatic maxim never ceases to surprise: if we take all possible effects we can conceive an object to have, then our conception of those effects is identical with our conception of that object, the maxim claims – but if we can conceive of abstract properties of the objects to have effects, then they are part of our conception of it, and hence they must possess reality as well. An abstraction is a possible way for an object to behave – and if certain objects do in fact conform to this behavior, then that abstraction is real; it is a ‘real possibility’ or a general object. If not, it may still retain its character of possibility. Peirce’s definitions of hypostatic abstractions now and then confuse this point. When he claims that

An abstraction is a substance whose being consists in the truth of some proposition concerning a more primary substance,

then the abstraction’s existence depends on the truth of some claim concerning a less abstract substance. But if the less abstract substance in question does not exist, and the claim in question consequently will be meaningless or false, then the abstraction will – following that definition – cease to exist. The problem is only that Peirce does not sufficiently clearly distinguish between the really existing substances which abstractive expressions may refer to, on the one hand, and those expressions themselves, on the other. It is the same confusion which may make one shuttle between hypostatic abstraction as a deduction and as an abduction. The first case corresponds to there actually existing a thing with the quality abstracted, and where we consequently may expect the existence of a rational explanation for the quality, and, correlatively, the existence of an abstract substance corresponding to the supposed ens rationis – the second case corresponds to the case – or the phase – where no such rational explanation and corresponding abstract substance has yet been verified. It is of course always possible to make an abstraction symbol, given any predicate – whether that abstraction corresponds to any real possibility is an issue for further investigation to estimate. And Peirce’s scientific realism makes him demand that the connections to actual reality of any abstraction should always be estimated (The Essential Peirce):

every kind of proposition is either meaningless or has a Real Secondness as its object. This is a fact that every reader of philosophy should carefully bear in mind, translating every abstractly expressed proposition into its precise meaning in reference to an individual experience.

This warning is directed, of course, towards empirical abstractions which require the support of particular instances to be pragmatically relevant but could hardly hold for mathematical abstraction. But in any case hypostatic abstraction is necessary for the investigation, be it in pure or empirical scenarios.

Valencies of Predicates. Thought of the Day 125.0

Since icons are the means of representing qualities, they generally constitute the predicative side of more complicated signs:

The only way of directly communicating an idea is by means of an icon; and every indirect method of communicating an idea must depend for its establishment upon the use of an icon. Hence, every assertion must contain an icon or set of icons, or else must contain signs whose meaning is only explicable by icons. The idea which the set of icons (or the equivalent of a set of icons) contained in an assertion signifies may be termed the predicate of the assertion. (Collected Papers of Charles Sanders Peirce)

Thus, the predicate in logic as well as ordinary language is essentially iconic. It is important to remember here Peirce’s generalization of the predicate from the traditional subject-copula-predicate structure. Predicates exist with more than one subject slot; this is the basis for Peirce’s logic of relatives and permits at the same time enlarging the scope of logic considerably and approaching it to ordinary language where several-slot-predicates prevail, for instance in all verbs with a valency larger than one. In his definition of these predicates by means of valency, that is, number of empty slots in which subjects or more generally indices may be inserted, Peirce is actually the founder of valency grammar in the tradition of Tesnière. So, for instance, the structure ‘_ gives _ to _’ where the underlinings refer to slots, is a trivalent predicate. Thus, the word classes associated with predicates are not only adjectives, but verbs and common nouns; in short all descriptive features in language are predicative.

This entails the fact that the similarity charted in icons covers more complicated cases than does the ordinary use of the word. Thus,

where ordinary logic considers only a single, special kind of relation, that of similarity, – a relation, too, of a particularly featureless and insignificant kind, the logic of relatives imagines a relation in general to be placed. Consequently, in place of the class, which is composed of a number of individual objects or facts brought together by means of their relation of similarity, the logic of relatives considers the system, which is composed of objects brought together by any kind of relations whatsoever. (The New Elements of Mathematics)

This allows for abstract similarity because one phenomenon may be similar to another in so far as both of them partake in the same relation, or more generally, in the same system – relations and systems being complicated predicates.

But not only more abstract features may thus act as the qualities invoked in an icon; these qualities may be of widely varying generality:

But instead of a single icon, or sign by resemblance of a familiar image or ‘dream’, evocable at will, there may be a complexus of such icons, forming a composite image of which the whole is not familiar. But though the whole is not familiar, yet not only are the parts familiar images, but there will also be a familiar image in its mode of composition. ( ) The sort of idea which an icon embodies, if it be such that it can convey any positive information, being applicable to some things but not to others, is called a first intention. The idea embodied by an icon, which cannot of itself convey any information, being applicable to everything or nothing, but which may, nevertheless, be useful in modifying other icons, is called a second intention. 

What Peirce distinguishes in these scholastic standard notions borrowed from Aquinas via Scotus, is, in fact, the difference between Husserlian formal and material ontology. Formal qualities like genus, species, dependencies, quantities, spatial and temporal extension, and so on are of course attributable to any phenomenon and do not as such, in themselves, convey any information in so far as they are always instantiated in and thus, like other Second Intentions, in the Husserlian manner dependent upon First Intentions, but they are nevertheless indispensable in the composition of first intentional descriptions. The fact that a certain phenomenon is composed of parts, has a form, belongs to a species, has an extension, has been mentioned in a sentence etc. does not convey the slightest information of it until it by means of first intentional icons is specified which parts in which composition, which species, which form, etc. Thus, here Peirce makes a hierarchy of icons which we could call material and formal, respectively, in which the latter are dependent on the former. One may note in passing that the distinctions in Peirce’s semiotics are themselves built upon such Second Intentions; thus it is no wonder that every sign must possess some Iconic element. Furthermore, the very anatomy of the proposition becomes just like in Husserlian rational grammar a question of formal, synthetic a priori regularities.

Among Peirce’s forms of inference, similarity plays a certain role within abduction, his notion for a ‘qualified guess’ in which a particular fact gives rise to the formation of a hypothesis which would have the fact in question as a consequence. Many such different hypotheses are of course possible for a given fact, and this inference is not necessary, but merely possible, suggestive. Precisely for this reason, similarity plays a seminal role here: an

originary Argument, or Abduction, is an argument which presents facts in its Premiss which presents a similarity to the fact stated in the conclusion but which could perfectly be true without the latter being so.

The hypothesis proposed is abducted by some sort of iconic relation to the fact to be explained. Thus, similarity is the very source of new ideas – which must subsequently be controlled deductively and inductively, to be sure. But iconicity does not only play this role in the contents of abductive inference, it plays an even more important role in the very form of logical inference in general:

Given a conventional or other general sign of an object, to deduce any other truth than that which it explicitly signifies, it is necessary, in all cases, to replace that sign by an icon. This capacity of revealing unexpected truth is precisely that wherein the utility of algebraic formulae consists, so that the iconic character is the prevailing one.

The very form of inferences depends on it being an icon; thus for Peirce the syllogistic schema inherent in reasoning has an iconic character:

‘Whenever one thing suggests another, both are together in the mind for an instant. [ ] every proposition like the premiss, that is having an icon like it, would involve [ ] a proposition related to it as the conclusion [ ]’. Thus, first and foremost deduction is an icon: ‘I suppose it would be the general opinion of logicians, as it certainly was long mine, that the Syllogism is a Symbol, because of its Generality.’ …. The truth, however, appears to be that all deductive reasoning, even simple syllogism, involves an element of observation; namely deduction consists in constructing an icon or diagram the relation of whose parts shall present a complete analogy with those of the parts of the objects of reasoning, of experimenting upon this image in the imagination, and of observing the result so as to discover unnoticed and hidden relations among the parts. 

It then is no wonder that synthetic a priori truths exist – even if Peirce prefers notions like ‘observable, universal truths’ – the result of a deduction may contain more than what is immediately present in the premises, due to the iconic quality of the inference.

Complete Manifolds’ Pure Logical Necessity as the Totality of Possible Formations. Thought of the Day 124.0

In Logical Investigations, Husserl called his theory of complete manifolds the key to the only possible solution to how in the realm of numbers impossible, non-existent, meaningless concepts might be dealt with as real ones. In Ideas, he wrote that his chief purpose in developing his theory of manifolds had been to find a theoretical solution to the problem of imaginary quantities (Ideas Pertaining to a Pure Phenomenology and to a Phenomenological Philosophy).

Husserl saw how questions regarding imaginary numbers come up in mathematical contexts in which formalization yields constructions which arithmetically speaking are nonsense, but can be used in calculations. When formal reasoning is carried out mechanically as if these symbols have meaning, if the ordinary rules are observed, and the results do not contain any imaginary components, these symbols might be legitimately used. And this could be empirically verified (Philosophy of Arithmetic_ Psychological and Logical Investigations with Supplementary Texts).

In a letter to Carl Stumpf in the early 1890s, Husserl explained how, in trying to understand how operating with contradictory concepts could lead to correct theorems, he had found that for imaginary numbers like √2 and √-1, it was not a matter of the possibility or impossibility of concepts. Through the calculation itself and its rules, as defined for those fictive numbers, the impossible fell away, and a genuine equation remained. One could calculate again with the same signs, but referring to valid concepts, and the result was again correct. Even if one mistakenly imagined that what was contradictory existed, or held the most absurd theories about the content of the corresponding concepts of number, the calculation remained correct if it followed the rules. He concluded that this must be a result of the signs and their rules (Early Writings in the Philosophy of Logic and Mathematics). The fact that one can generalize, produce variations of formal arithmetic that lead outside the quantitative domain without essentially altering formal arithmetic’s theoretical nature and calculational methods brought Husserl to realize that there was more to the mathematical or formal sciences, or the mathematical method of calculation than could be captured in purely quantitative analyses.

Understanding the nature of theory forms, shows how reference to impossible objects can be justified. According to his theory of manifolds, one could operate freely within a manifold with imaginary concepts and be sure that what one deduced was correct when the axiomatic system completely and unequivocally determined the body of all the configurations possible in a domain by a purely analytical procedure. It was the completeness of the axiomatic system that gave one the right to operate in that free way. A domain was complete when each grammatically constructed proposition exclusively using the language of the domain was determined from the outset to be true or false in virtue of the axioms, i.e., necessarily followed from the axioms or did not. In that case, calculating with expressions without reference could never lead to contradictions. Complete manifolds have the

distinctive feature that a finite number of concepts and propositions – to be drawn as occasion requires from the essential nature of the domain under consideration –  determines completely and unambiguously on the lines of pure logical necessity the totality of all possible formations in the domain, so that in principle, therefore, nothing further remains open within it.

In such complete manifolds, he stressed, “the concepts true and formal implication of the axioms are equivalent (Ideas).

Husserl pointed out that there may be two valid discipline forms that stand in relation to one another in such a way that the axiom system of one may be a formal limitation of that of the other. It is then clear that everything deducible in the narrower axiom system is included in what is deducible in the expanded system, he explained. In the arithmetic of cardinal numbers, Husserl explained, there are no negative numbers, for the meaning of the axioms is so restrictive as to make subtracting 4 from 3 nonsense. Fractions are meaningless there. So are irrational numbers, √–1, and so on. Yet in practice, all the calculations of the arithmetic of cardinal numbers can be carried out as if the rules governing the operations are unrestrictedly valid and meaningful. One can disregard the limitations imposed in a narrower domain of deduction and act as if the axiom system were a more extended one. We cannot arbitrarily expand the concept of cardinal number, Husserl reasoned. But we can abandon it and define a new, pure formal concept of positive whole number with the formal system of definitions and operations valid for cardinal numbers. And, as set out in our definition, this formal concept of positive numbers can be expanded by new definitions while remaining free of contradiction. Fractions do not acquire any genuine meaning through our holding onto the concept of cardinal number and assuming that units are divisible, he theorized, but rather through our abandonment of the concept of cardinal number and our reliance on a new concept, that of divisible quantities. That leads to a system that partially coincides with that of cardinal numbers, but part of which is larger, meaning that it includes additional basic elements and axioms. And so in this way, with each new quantity, one also changes arithmetics. The different arithmetics do not have parts in common. They have totally different domains, but an analogous structure. They have forms of operation that are in part alike, but different concepts of operation.

For Husserl, formal constraints banning meaningless expressions, meaningless imaginary concepts, reference to non-existent and impossible objects restrict us in our theoretical, deductive work, but that resorting to the infinity of pure forms and transformations of forms frees us from such conditions and explains why having used imaginaries, what is meaningless, must lead, not to meaningless, but to true results.

Metaphysical Continuity in Peirce. Thought of the Day 122.0

Continuity has wide implications in the different parts of Peirce’s architectonics of theories. Time and time again, Peirce refers to his ‘principle of continuity’ which has not immediately anything to do with Poncelet’s famous such principle in geometry, but, is rather, a metaphysical implication taken to follow from fallibilism: if all more or less distinct phenomena swim in a vague sea of continuity then it is no wonder that fallibilism must be accepted. And if the world is basically continuous, we should not expect conceptual borders to be definitive but rather conceive of terminological distinctions as relative to an underlying, monist continuity. In this system, mathematics is first science. Thereafter follows philosophy which is distinguished form purely hypothetical mathematics by having an empirical basis. Philosophy, in turn, has three parts, phenomenology, the normative sciences, and metaphysics. The first investigates solely ‘the Phaneron’ which is all what could be imagined to appear as an object for experience: ‘ by the word phaneron I mean the collective total of all that is in any way or in any sense present to the mind, quite regardless whether it corresponds to any real thing or not.’ (Charles Sanders Peirce – Collected Papers of Charles Sanders Peirce) As is evident, this definition of Peirce’s ‘phenomenology’ is parallel to Husserl’s phenomenological reduction in bracketing the issue of the existence of the phenomenon in question. Even if it thus is built on introspection and general experience, it is – analogous to Husserl and other Brentano disciples at the same time – conceived in a completely antipsychological manner: ‘It religiously abstains from all speculation as to any relations between its categories and physiological facts, cerebral or other.’ and ‘ I abstain from psychology which has nothing to do with ideoscopy.’ (Letter to Lady Welby). The normative sciences fall in three: aesthetics, ethics, logic, in that order (and hence decreasing generality), among which Peirce does not spend very much time on the former two. Aesthetics is the investigation of which possible goals it is possible to aim at (Good, Truth, Beauty, etc.), and ethics how they may be reached. Logic is concerned with the grasping and conservation of Truth and takes up the larger part of Peirce’s interest among the normative sciences. As it deals with how truth can be obtained by means of signs, it is also called semiotics (‘logic is formal semiotics’) which is thus coextensive with theory of science – logic in this broad sense contains all parts of philosophy of science, including contexts of discovery as well as contexts of justification. Semiotics has, in turn, three branches: grammatica speculativa (or stekheiotics), critical logic, and methodeutic (inspired by mediaeval trivium: grammar, logic, and rhetoric). The middle one of these three lies closest to our days’ conception of logic; it is concerned with the formal conditions for truth in symbols – that is, propositions, arguments, their validity and how to calculate them, including Peirce’s many developments of the logic of his time: quantifiers, logic of relations, ab-, de-, and induction, logic notation systems, etc. All of these, however, presuppose the existence of simple signs which are investigated by what is often seen as semiotics proper, the grammatica speculativa; it may also be called formal grammar. It investigates the formal condition for symbols having meaning, and it is here we find Peirce’s definition of signs and his trichotomies of different types of sign aspects. Methodeutic or formal rhetorics, on the other hand, concerns the pragmatical use of the former two branches, that is, the study of how to use logic in a fertile way in research, the formal conditions for the ‘power’ of symbols, that is, their reference to their interpretants; here can be found, e.g., Peirce’s famous definitions of pragmati(ci)sm and his directions for scientific investigation. To phenomenology – again in analogy to Husserl – logic adds the interest in signs and their truth. After logic, metaphysics follows in Peirce’s system, concerning the inventarium of existing objects, conceived in general – and strongly influenced by logic in the Kantian tradition for seeing metaphysics mirroring logic. Also here, Peirce has several proposals for subtypologies, even if none of them seem stable, and under this headline classical metaphysical issues mix freely with generalizations of scientific results and cosmological speculations.

Peirce himself saw this classification in an almost sociological manner, so that the criteria of distinction do not stem directly from the implied objects’ natural kinds, but after which groups of persons study which objects: ‘the only natural lines of demarcation between nearly related sciences are the divisions between the social groups of devotees of those sciences’. Science collects scientists into bundles, because they are defined by their causa finalis, a teleologial intention demanding of them to solve a central problem.

Measured on this definition, one has to say that Peirce himself was not modest, not only does he continuously transgress such boundaries in his production, he frequently does so even within the scope of single papers. There is always, in his writings, a brief distance only from mathematics to metaphysics – or between any other two issues in mathematics and philosophy, and this implies, first, that the investigation of continuity and generality in Peirce’s system is more systematic than any actually existing exposition of these issues in Peirce’s texts, second, that the discussion must constantly rely on cross-references. This has the structural motivation that as soon as you are below the level of mathematics in Peirce’s system, inspired by the Comtean system, the single science receives determinations from three different directions, each science consisting of material and formal aspects alike. First, it receives formal directives ‘from above’, from those more general sciences which stand above it, providing the general frameworks in which it must unfold. Second, it receives material determinations from its own object, requiring it to make certain choices in its use of formal insights from the higher sciences. The cosmological issue of the character of empirical space, for instance, can take from mathematics the different (non-)Euclidean geometries and investigate which of these are fit to describe spatial aspects of our universe, but it does not, in itself, provide the formal tools. Finally, the single sciences receive in practice determinations ‘from below’, from more specific sciences, when their results by means of abstraction, prescission, induction, and other procedures provide insights on its more general, material level. Even if cosmology is, for instance, part of metaphysics, it receives influences from the empirical results of physics (or biology, from where Peirce takes the generalized principle of evolution). The distinction between formal and material is thus level specific: what is material on one level is a formal bundle of possibilities for the level below; what is formal on one level is material on the level above.

For these reasons, the single step on the ladder of sciences is only partially independent in Peirce, hence also the tendency of his own investigations to zigzag between the levels. His architecture of theories thus forms a sort of phenomenological theory of aspects: the hierarchy of sciences is an architecture of more and less general aspects of the phenomena, not completely independent domains. Finally, Peirce’s realism has as a result a somewhat disturbing style of thinking: many of his central concepts receive many, often highly different determinations which has often led interpreters to assume inconsistencies or theoretical developments in Peirce where none necessarily exist. When Peirce, for instance, determines the icon as the sign possessing a similarity to its object, and elsewhere determines it as the sign by the contemplation of which it is possible to learn more about its object, then they are not conflicting definitions. Peirce’s determinations of concepts are rarely definitions at all in the sense that they provide necessary and sufficient conditions exhausting the phenomenon in question. His determinations should rather be seen as descriptions from different perspectives of a real (and maybe ideal) object – without these descriptions necessarily conflicting. This style of thinking can, however, be seen as motivated by metaphysical continuity. When continuous grading between concepts is the rule, definitions in terms of necessary and sufficient conditions should not be expected to be exhaustive.

The Second Trichotomy. Thought of the Day 120.0

The second trichotomy (here is the first) is probably the most well-known piece of Peirce’s semiotics: it distinguishes three possible relations between the sign and its (dynamical) object. This relation may be motivated by similarity, by actual connection, or by general habit – giving rise to the sign classes icon, index, and symbol, respectively.

According to the second trichotomy, a Sign may be termed an Icon, an Index, or a Symbol.

An Icon is a sign which refers to the Object that it denotes merely by virtue of characters of its own, and which it possesses, just the same, whether any such Object actually exists or not. It is true that unless there really is such an Object, the Icon does not act as a sign; but this has nothing to do with its character as a sign. Anything whatever, be it quality, existent individual, or law, is an Icon of anything, in so far as it is like that thing and used as a sign of it.

An Index is a sign which refers to the Object that it denotes by virtue of being really affected by that Object. It cannot, therefore, be a Qualisign, because qualities are whatever they are independently of anything else. In so far as the Index is affected by the Object, it necessarily has some Quality in common with the Object, and it is in respect to these that it refers to the Object. It does, therefore, involve a sort of Icon, although an Icon of a peculiar kind; and it is not the mere resemblance of its Object, even in these respects which makes it a sign, but it is the actual modification of it by the Object. 

A Symbol is a sign which refers to the Object that it denotes by virtue of a law, usually an association of general ideas, which operates to cause the Symbol to be interpreted as referring to that Object. It is thus itself a general type or law, that is, a Legisign. As such it acts through a Replica. Not only is it general in itself, but the Object to which it refers is of general nature. Now that which is general has its being in the instances it will determine. There must, therefore, be existent instances of what the Symbol denotes, although we must here understand by ‘existent’, existent in the possibly imaginary universe to which the Symbol refers. The Symbol will indirectly, through the association or other law, be affected by those instances; and thus the Symbol will involve a sort of Index, although an Index of a peculiar kind. It will not, however, be by any means true that the slight effect upon the Symbol of those instances accounts for the significant character of the Symbol.

The icon refers to its object solely by means of its own properties. This implies that an icon potentially refers to an indefinite class of objects, namely all those objects which have, in some respect, a relation of similarity to it. In recent semiotics, it has often been remarked by someone like Nelson Goodman that any phenomenon can be said to be like any other phenomenon in some respect, if the criterion of similarity is chosen sufficiently general, just like the establishment of any convention immediately implies a similarity relation. If Nelson Goodman picks out two otherwise very different objects, then they are immediately similar to the extent that they now have the same relation to Nelson Goodman. Goodman and others have for this reason deemed the similarity relation insignificant – and consequently put the whole burden of semiotics on the shoulders of conventional signs only. But the counterargument against this rejection of the relevance of the icon lies close at hand. Given a tertium comparationis, a measuring stick, it is no longer possible to make anything be like anything else. This lies in Peirce’s observation that ‘It is true that unless there really is such an Object, the Icon does not act as a sign ’ The icon only functions as a sign to the extent that it is, in fact, used to refer to some object – and when it does that, some criterion for similarity, a measuring stick (or, at least, a delimited bundle of possible measuring sticks) are given in and with the comparison. In the quote just given, it is of course the immediate object Peirce refers to – it is no claim that there should in fact exist such an object as the icon refers to. Goodman and others are of course right in claiming that as ‘Anything whatever ( ) is an Icon of anything ’, then the universe is pervaded by a continuum of possible similarity relations back and forth, but as soon as some phenomenon is in fact used as an icon for an object, then a specific bundle of similarity relations are picked out: ‘ in so far as it is like that thing.’

Just like the qualisign, the icon is a limit category. ‘A possibility alone is an Icon purely by virtue of its quality; and its object can only be a Firstness.’ (Charles S. PeirceThe Essential Peirce_ Selected Philosophical Writings). Strictly speaking, a pure icon may only refer one possible Firstness to another. The pure icon would be an identity relation between possibilities. Consequently, the icon must, as soon as it functions as a sign, be more than iconic. The icon is typically an aspect of a more complicated sign, even if very often a most important aspect, because providing the predicative aspect of that sign. This Peirce records by his notion of ‘hypoicon’: ‘But a sign may be iconic, that is, may represent its object mainly by its similarity, no matter what its mode of being. If a substantive is wanted, an iconic representamen may be termed a hypoicon’. Hypoicons are signs which to a large extent makes use of iconical means as meaning-givers: images, paintings, photos, diagrams, etc. But the iconic meaning realized in hypoicons have an immensely fundamental role in Peirce’s semiotics. As icons are the only signs that look-like, then they are at the same time the only signs realizing meaning. Thus any higher sign, index and symbol alike, must contain, or, by association or inference terminate in, an icon. If a symbol can not give an iconic interpretant as a result, it is empty. In that respect, Peirce’s doctrine parallels that of Husserl where merely signitive acts require fulfillment by intuitive (‘anschauliche’) acts. This is actually Peirce’s continuation of Kant’s famous claim that intuitions without concepts are blind, while concepts without intuitions are empty. When Peirce observes that ‘With the exception of knowledge, in the present instant, of the contents of consciousness in that instant (the existence of which knowledge is open to doubt) all our thought and knowledge is by signs’ (Letters to Lady Welby), then these signs necessarily involve iconic components. Peirce has often been attacked for his tendency towards a pan-semiotism which lets all mental and physical processes take place via signs – in the quote just given, he, analogous to Husserl, claims there must be a basic evidence anterior to the sign – just like Husserl this evidence before the sign must be based on a ‘metaphysics of presence’ – the ‘present instant’ provides what is not yet mediated by signs. But icons provide the connection of signs, logic and science to this foundation for Peirce’s phenomenology: the icon is the only sign providing evidence (Charles S. Peirce The New Elements of Mathematics Vol. 4). The icon is, through its timeless similarity, apt to communicate aspects of an experience ‘in the present instant’. Thus, the typical index contains an icon (more or less elaborated, it is true): any symbol intends an iconic interpretant. Continuity is at stake in relation to the icon to the extent that the icon, while not in itself general, is the bearer of a potential generality. The infinitesimal generality is decisive for the higher sign types’ possibility to give rise to thought: the symbol thus contains a bundle of general icons defining its meaning. A special icon providing the condition of possibility for general and rigorous thought is, of course, the diagram.

The index connects the sign directly with its object via connection in space and time; as an actual sign connected to its object, the index is turned towards the past: the action which has left the index as a mark must be located in time earlier than the sign, so that the index presupposes, at least, the continuity of time and space without which an index might occur spontaneously and without any connection to a preceding action. Maybe surprisingly, in the Peircean doctrine, the index falls in two subtypes: designators vs. reagents. Reagents are the simplest – here the sign is caused by its object in one way or another. Designators, on the other hand, are more complex: the index finger as pointing to an object or the demonstrative pronoun as the subject of a proposition are prototypical examples. Here, the index presupposes an intention – the will to point out the object for some receiver. Designators, it must be argued, presuppose reagents: it is only possible to designate an object if you have already been in reagent contact (simulated or not) with it (this forming the rational kernel of causal reference theories of meaning). The closer determination of the object of an index, however, invariably involves selection on the background of continuities.

On the level of the symbol, continuity and generality play a main role – as always when approaching issues defined by Thirdness. The symbol is, in itself a legisign, that is, it is a general object which exists only due to its actual instantiations. The symbol itself is a real and general recipe for the production of similar instantiations in the future. But apart from thus being a legisign, it is connected to its object thanks to a habit, or regularity. Sometimes, this is taken to mean ‘due to a convention’ – in an attempt to distinguish conventional as opposed to motivated sign types. This, however, rests on a misunderstanding of Peirce’s doctrine in which the trichotomies record aspects of sign, not mutually exclusive, independent classes of signs: symbols and icons do not form opposed, autonomous sign classes; rather, the content of the symbol is constructed from indices and general icons. The habit realized by a symbol connects it, as a legisign, to an object which is also general – an object which just like the symbol itself exists in instantiations, be they real or imagined. The symbol is thus a connection between two general objects, each of them being actualized through replicas, tokens – a connection between two continua, that is:

Definition 1. Any Blank is a symbol which could not be vaguer than it is (although it may be so connected with a definite symbol as to form with it, a part of another partially definite symbol), yet which has a purpose.

Axiom 1. It is the nature of every symbol to blank in part. [ ]

Definition 2. Any Sheet would be that element of an entire symbol which is the subject of whatever definiteness it may have, and any such element of an entire symbol would be a Sheet. (‘Sketch of Dichotomic Mathematics’ (The New Elements of Mathematics Vol. 4 Mathematical Philosophy)

The symbol’s generality can be described as it having always blanks having the character of being indefinite parts of its continuous sheet. Thus, the continuity of its blank parts is what grants its generality. The symbol determines its object according to some rule, granting the object satisfies that rule – but leaving the object indeterminate in all other respects. It is tempting to take the typical symbol to be a word, but it should rather be taken as the argument – the predicate and the proposition being degenerate versions of arguments with further continuous blanks inserted by erasure, so to speak, forming the third trichotomy of term, proposition, argument.

Husserl’s Flip-Flop on Arithmetic Axiomatics. Thought of the Day 118.0

Husserl’s position in his Philosophy of Arithmetic (Psychological and Logical Investigations with Supplementary Texts) was resolutely anti-axiomatic. He attacked those who fell into remote, artificial constructions which, with the intent of building the elementary arithmetic concepts out of their ultimate definitional properties, interpret and change their meaning so much that totally strange, practically and scientifically useless conceptual formations finally result. Especially targeted was Frege’s ideal of the

founding of arithmetic on a sequence of formal definitions, out of which all the theorems of that science could be deduced purely syllogistically.

As soon as one comes to the ultimate, elemental concepts, Husserl reasoned, all defining has to come to an end. All one can then do is to point to the concrete phenomena from or through which the concepts are abstracted and show the nature of the abstractive process. A verbal explanation should place us in the proper state of mind for picking out, in inner or outer intuition, the abstract moments intended and for reproducing in ourselves the mental processes required for the formation of the concept. He said that his analyses had shown with incontestable clarity that the concepts of multiplicity and unity rest directly upon ultimate, elemental psychical data, and so belong among the indefinable concepts. Since the concept of number was so closely joined to them, one could scarcely speak of defining it either. All these points are made on the only pages of Philosophy of Arithmetic that Husserl ever explicitly retracted.

In On the Concept of Number, Husserl had set out to anchor arithmetical concepts in direct experience by analyzing the actual psychological processes to which he thought the concept of number owed its genesis. To obtain the concept of number of a concrete set of objects, say A, A, and A, he explained, one abstracts from the particular characteristics of the individual contents collected, only considering and retaining each one insofar as it is a something or a one. Regarding their collective combination, one thus obtains the general form of the set belonging to the set in question: one and one, etc. and. . . and one, to which a number name is assigned.

The enthusiastic espousal of psychologism of On the Concept of Number is not found in Philosophy of Arithmetic. Husserl later confessed that doubts about basic differences between the concept of number and the concept of collecting, which was all that could be obtained from reflection on acts, had troubled and tormented him from the very beginning and had eventually extended to all categorial concepts and to concepts of objectivities of any sort whatsoever, ultimately to include modern analysis and the theory of manifolds, and simultaneously to mathematical logic and the entire field of logic in general. He did not see how one could reconcile the objectivity of mathematics with psychological foundations for logic.

In sharp contrast to Brouwer who denounced logic as a source of truth, from the mid-1890s on, Husserl defended the view, which he attributed to Frege’s teacher Hermann Lotze, that pure arithmetic was basically no more than a branch of logic that had undergone independent development. He bid students not to be “scared” by that thought and to grow used to Lotze’s initially strange idea that arithmetic was only a particularly highly developed piece of logic.

Years later, Husserl would explain in Formal and Transcendental Logic that his

war against logical psychologism was meant to serve no other end than the supremely important one of making the specific province of analytic logic visible in its purity and ideal particularity, freeing it from the psychologizing confusions and misinterpretations in which it had remained enmeshed from the beginning.

He had come to see arithmetic truths as being analytic, as grounded in meanings independently of matters of fact. He had come to believe that the entire overthrowing of psychologism through phenomenology showed that his analyses in On the Concept of Number and Philosophy of Arithmetic had to be considered a pure a priori analysis of essence. For him, pure arithmetic, pure mathematics, and pure logic were a priori disciplines entirely grounded in conceptual essentialities, where truth was nothing other than the analysis of essences or concepts. Pure mathematics as pure arithmetic investigated what is grounded in the essence of number. Pure mathematical laws were laws of essence.

He is said to have told his students that it was to be stressed repeatedly and emphatically that the ideal entities so unpleasant for empiricistic logic, and so consistently disregarded by it, had not been artificially devised either by himself, or by Bolzano, but were given beforehand by the meaning of the universal talk of propositions and truths indispensable in all the sciences. This, he said, was an indubitable fact that had to be the starting point of all logic. All purely mathematical propositions, he taught, express something about the essence of what is mathematical. Their denial is consequently an absurdity. Denying a proposition of the natural sciences, a proposition about real matters of fact, never means an absurdity, a contradiction in terms. In denying the law of gravity, I cast experience to the wind. I violate the evident, extremely valuable probability that experience has established for the laws. But, I do not say anything “unthinkable,” absurd, something that nullifies the meaning of the word as I do when I say that 2 × 2 is not 4, but 5.

Husserl taught that every judgment either is a truth or cannot be a truth, that every presentation either accorded with a possible experience adequately redeeming it, or was in conflict with the experience, and that grounded in the essence of agreement was the fact that it was incompatible with the conflict, and grounded in the essence of conflict that it was incompatible with agreement. For him, that meant that truth ruled out falsehood and falsehood ruled out truth. And, likewise, existence and non-existence, correctness and incorrectness cancelled one another out in every sense. He believed that that became immediately apparent as soon as one had clarified the essence of existence and truth, of correctness and incorrectness, of Evidenz as consciousness of givenness, of being and not-being in fully redeeming intuition.

At the same time, Husserl contended, one grasps the “ultimate meaning” of the basic logical law of contradiction and of the excluded middle. When we state the law of validity that of any two contradictory propositions one holds and the other does not hold, when we say that for every proposition there is a contradictory one, Husserl explained, then we are continually speaking of the proposition in its ideal unity and not at all about mental experiences of individuals, not even in the most general way. With talk of truth it is always a matter of propositions in their ideal unity, of the meaning of statements, a matter of something identical and atemporal. What lies in the identically-ideal meaning of one’s words, what one cannot deny without invalidating the fixed meaning of one’s words has nothing at all to do with experience and induction. It has only to do with concepts. In sharp contrast to this, Brouwer saw intuitionistic mathematics as deviating from classical mathematics because the latter uses logic to generate theorems and in particular applies the principle of the excluded middle. He believed that Intuitionism had proven that no mathematical reality corresponds to the affirmation of the principle of the excluded middle and to conclusions derived by means of it. He reasoned that “since logic is based on mathematics – and not vice versa – the use of the Principle of the Excluded Middle is not permissible as part of a mathematical proof.”

Triadomania. Thought of the Day 117.0

Peirce’s famous ‘triadomania’ lets most of his decisive distinctions appear in threes, following the tripartition of his list of categories, the famous triad of First, Second, and Third, or Quality, Reaction, Representation, or Possibility, Actuality, Reality.

Firstness is the mode of being of that which is such as it is, positively and without reference to anything else.

Secondness is the mode of being of that which is such as it is, with respect to a second but regardless of any third.

Thirdness is the mode of being of that which is such as it is, in bringing a second and third into relation to each other.

Firstness constitutes the quality of experience: in order for something to appear at all, it must do so due to a certain constellation of qualitative properties. Peirce often uses sensory qualities as examples, but it is important for the understanding of his thought that the examples may refer to phenomena very far from our standard conception of ‘sensory data’, e.g. forms or the ‘feeling’ of a whole melody or of a whole mathematical proof, not to be taken in a subjective sense but as a concept for the continuity of melody or proof as a whole, apart from the analytical steps and sequences in which it may be, subsequently, subdivided. In short, all sorts of simple and complex Gestalt qualities also qualify as Firstnesses. Firstness tend to form continua of possibilities such as the continua of shape, color, tone, etc. These qualities, however, are, taken in themselves, pure possibilities and must necessarily be incarnated in phenomena in order to appear. Secondness is the phenomenological category of ‘incarnation’ which makes this possible: it is the insistency, then, with which the individuated, actualized, existent phenomenon appears. Thus, Secondness necessarily forms discontinuous breaks in Firstness, allowing for particular qualities to enter into existence. The mind may imagine anything whatever in all sorts of quality combinations, but something appears with an irrefutable insisting power, reacting, actively, yielding resistance. Peirce’s favorite example is the resistance of the closed door – which might be imagined reduced to the quality of resistance feeling and thus degenerate to pure Firstness so that his theory imploded into a Hume-like solipsism – but to Peirce this resistance, surprise, event, this thisness, ‘haecceity’ as he calls it with a Scotist term, remains irreducible in the description of the phenomenon (a Kantian idea, at bottom: existence is no predicate). About Thirdness, Peirce may directly state that continuity represents it perfectly: ‘continuity and generality are two names of the same absence of distinction of individuals’. As against Secondness, Thirdness is general; it mediates between First and Second. The events of Secondness are never completely unique, such an event would be inexperiencable, but relates (3) to other events (2) due to certain features (1) in them; Thirdness is thus what facilitates understanding as well as pragmatic action, due to its continuous generality. With a famous example: if you dream about an apple pie, then the very qualities of that dream (taste, smell, warmth, crustiness, etc.) are pure Firstnesses, while the act of baking is composed of a series of actual Secondnesses. But their coordination is governed by a Thirdness: the recipe, being general, can never specify all properties in the individual apple pie, it has a schematic frame-character and subsumes an indefinite series – a whole continuum – of possible apple pies. Thirdness is thus necessarily general and vague. Of course, the recipe may be more or less precise, but no recipe exists which is able to determine each and every property in the cake, including date, hour, place, which tree the apples stem from, etc. – any recipe is necessarily general. In this case, the recipe (3) mediates between dream (1) and fulfilment (2) – its generality, symbolicity, relationality and future orientation are all characteristic for Thirdness. An important aspect of Peirce’s realism is that continuous generality may be experienced directly in perceptual judgments: ‘Generality, Thirdness, pours in upon us in our very perceptual judgments’.

All these determinations remain purely phenomenological, even if the later semiotic and metaphysical interpretations clearly shine through. In a more general, non-Peircean terminology, his phenomenology can be seen as the description of minimum aspects inherent in any imaginable possible world – for this reason it is imaginability which is the main argument, and this might point in the direction that Peirce could be open to critique for subjectivism, so often aimed at Husserl’s project, in some respects analogous. The concept of consciousness is invoked as the basis of imaginability: phenomenology is the study of invariant properties in any phenomenon appearing for a mind. Peirce’s answer would here be, on the one hand, the research community which according to him defines reality – an argument which structurally corresponds to Husserl’s reference to intersubjectivity as a necessary ingredient in objectivity (an object is a phenomenon which is intersubjectively accessible). Peirce, however, has a further argument here, namely his consequent refusal to delimit his concept of mind exclusively to human subjects (a category the use of which he obviously tries to minimize), mind-like processes may take place in nature without any subject being responsible. Peirce will, for continuity reasons, never accept any hard distinction between subject and object and remains extremely parsimonious in the employment of such terms.

From Peirce’s New Elements of Mathematics (The New Elements of Mathematics Vol. 4),

But just as the qualities, which as they are for themselves, are equally unrelated to one other, each being mere nothing for any other, yet form a continuum in which and because of their situation in which they acquire more or less resemblance and contrast with one another; and then this continuum is amplified in the continuum of possible feelings of quality, so the accidents of reaction, which are waking consciousnesses of pairs of qualities, may be expected to join themselves into a continuum. 

Since, then an accidental reaction is a combination or bringing into special connection of two qualities, and since further it is accidental and antigeneral or discontinuous, such an accidental reaction ought to be regarded as an adventitious singularity of the continuum of possible quality, just as two points of a sheet of paper might come into contact.

But although singularities are discontinuous, they may be continuous to a certain extent. Thus the sheet instead of touching itself in the union of two points may cut itself all along a line. Here there is a continuous line of singularity. In like manner, accidental reactions though they are breaches of generality may come to be generalized to a certain extent.

Secondness is now taken to actualize these quality possibilities based on an idea that any actual event involves a clash of qualities – in the ensuing argumentation Peirce underlines that the qualities involved in actualization need not be restrained to two but may be many, if they may only be ‘dissolved’ into pairs and hence do not break into the domain of Thirdness. This appearance of actuality, hence, has the property of singularities, spontaneously popping up in the space of possibilities and actualizing pairs of points in it. This transition from First to Second is conceived of along Aristotelian lines: as an actualization of a possibility – and this is expressed in the picture of a discontinuous singularity in the quality continuum. The topological fact that singularities must in general be defined with respect to the neighborhood of the manifold in which they appear, now becomes the argument for the fact that Secondness can never be completely discontinuous but still ‘inherits’ a certain small measure of continuity from the continuum of Firstness. Singularities, being discontinuous along certain dimensions, may be continuous in others, which provides the condition of possibility for Thirdness to exist as a tendency for Secondness to conform to a general law or regularity. As is evident, a completely pure Secondness is impossible in this continuous metaphysics – it remains a conceivable but unrealizable limit case, because a completely discon- tinuous event would amount to nothing. Thirdness already lies as a germ in the non-discontinuous aspects of the singularity. The occurrences of Secondness seem to be infinitesimal, then, rather than completely extensionless points.

Husserl’s Melodies of the Absolute Flux. Note Quote.

Husserl elaborates the basic problem of time-consciousness by taking the simple example of a melody. Observing that what we perceive endures – i.e., a melody is experienced as a unity of discrete tones, with each tone and the melody as a whole grasped as unified enduring objects – he sets out to examine how this can occur. Clearly, more than one tone must be retained in consciousness, since if each disappeared entirely after it had sounded then their succession, and therefore the melody as a whole, could never be grasped: “in each moment we would have a tone, or perhaps an empty pause in the interval between the sounding of two tones, but never the representation of a melody.” And each tone must also undergo some form of modification in consciousness, enabling it to appear “as more or less past, as pushed back in time, as it were,” since otherwise “instead of a melody we would have a chord of simultaneous tones, or rather a disharmonious tangle of sound, as if we had struck simultaneously all the notes that had previously sounded“. It is in order to account for our ability to experience such temporally extended objects as temporally extended that Husserl takes an immanent tone as his phenomenological datum.

In the characteristic phenomenological move Husserl proposes, at the outset of his lectures, “the complete exclusion of every assumption, stipulation and conviction with respect to objective time”. This suspension of the “natural attitude” towards time leaves – as the phenomenological residue – the indisputable immanent time (succession and duration) of lived experience (erlebnis). And immanent temporal objects within the immanent time of the flow of consciousness will enable reflection of the phenomenon of temporal experience free of all transcendent presuppositions. Husserl can therefore declare his task as being to “exclude all transcendent apprehension and positing and take the tone purely as a hyletic datum”.

Posing the question of “How, in addition to ‘temporal objects,’ immanent and transcendent, does time itself – the duration and succession of objects – become constituted?” Husserl points out that these are “different lines of description….” For example: “When a tone sounds … [we] can make the tone itself, which endures and fades away, into an object and yet not make the duration of the tone or the tone in its duration into an object”. Focusing on the latter, we can observe that the tone appears in “a continuity of ‘modes’ in a ‘continual flow'” – that is, appears in the mode of (as) ‘now’ or as ‘immediately past’ – even though “‘Throughout’ this whole flow of consciousness, one and the same tone is intended as enduring, as now enduring”. Because the tone itself is the same but the manner in which it appears is continually different, then description of the tone itself must be distinguished from description of “the way in which we are ‘conscious’ of … the ‘appearing’ of the immanent tone”. It is this latter that the phenomenology of time-consciousness will analyze.

Husserl accounts for our experience of the duration of the tone by distinguishing the intended temporal determinations of ‘now,’ ‘just-past,’ and ‘about-to-be’ from the consciousness that intends them: the impressional, retentional and protentional consciousness which constitute present, past, and future, respectively. As he describes it, the “source-point” (Quellpunkt) of the enduring object in the flowing stream of consciousness is the “primal impression” – consciousness of the (constantly changing) “tone-now” (Tonjetzt). And as this ‘tone-now’ is modified into ‘something that has been,’ so the primal impression passes over into retention: “the tone-now changes into a tone-having-been; the impressional consciousness, constantly flowing, passes over into an ever new retentional consciousness”. Retention not only “holds in consciousness what has been produced and stamps on it the character of the ‘just-past'” – ensuring that consciousness is always “consciousness of what has just been and not merely consciousness of the now-point of the object that appears as enduring” – but each retention is also retention of the elapsed tone retention, including in itself “the entire series of elapsed intentions in the form of a chain of mediate intentions”. In this way, retention “extends the now-consciousness” such that the “now-apprehension is, as it were, the head attached to the comet’s tail of retentions”.

This description of the extended moment is completed with the addition of protention as the symmetrical futural counterpart of retention. Protention, the intuition of the immediate future, is “just as original and unique as the intuition of the past,” Husserl writes. “Every process that constitutes its object originally is animated by protentions that emptily constitute what is coming as coming”. Retention and protention together combine to form “the living horizon of the now,” for every primal impression “has its retentional and protentional halo” ensuring that “The now point … [always] has for consciousness a temporal fringe”. The punctual now is therefore only an ideal limit, which cannot be phenomenologically given or encountered. And this description of the now as an ideal abstraction therefore applies equally to the primal impression of which it is the correlate: “In the ideal sense … perception (impression) would be the phase of consciousness that constitutes the pure now…. But the now is precisely only an ideal limit, something abstract, which can be nothing by itself”.

The temporal phases of the immanent object are, then, on a different stratum of analysis than the consciousness of those phases; the impressional, retentional, and protentional consciousness which, in intending the object as ‘now,’ ‘just-past,’ or ‘about-to-be’ “constitute the very differences belonging to time”. Husserl reaches the heart of his phenomenological account of time-consciousness with his description of how these “acts that create time” – primal impression, retention, and protention – “can be understood as time-constituting consciousness, as moments of the flow”. The ‘flow’ is made up of these partial intentions which are not fully fledged acts as such because their correlates are not objects but the temporal phases of objects. Retention, for example, “is an intentionality” but it “is not an ‘act’ (that is, an immanent duration-unity constituted in a series of retentional phases)”. The intentionality of these elements of the primal flux differs from that of apprehending or perceptual acts – they in fact constitute as a unity the apprehending act: “In perception a complex of sensation-contents, which are themselves unities constituted in the original temporal flow, undergo unity of apprehension. And this unitary apprehension is again a constituted unity”.

Husserl can therefore distinguish and outline the three levels of his analysis of time and consciousness as follows: Firstly, “the things of empirical experience in objective time”; secondly, “the constituting multiplicities of appearance … the immanent unities in pre-empirical time”; and lastly, “the absolute time-constituting flow of consciousness” which, as that which “lies before all constitution,” is the ultimate stratum of the constitutive process. This absolute consciousness “is not itself content or object in phenomenological time”. It is a ‘flow’ of “continuous ‘change'” which cannot be described as having constancy or duration, nor even as a ‘process,’ since the concept of process presupposes persistence and a ‘something’ that persists and endures through change. However, the flow does possess, in a sense, something abiding: “What abides, above all, is the formal structure of the flow, the form of the flow”. This unchanging form of the absolute flux is the retentional/impressional/protentional structure by which “a now becomes constituted by means of an impression and … a trail of retentions and a horizon of protentions are attached to the impression”. The question remains, of course, of how we can know this flow which is neither content nor object:

Every temporal appearance, after phenomenological reduction, dissolves into … a flow. But I cannot perceive in turn this consciousness itself into which all of this is dissolved. For this new percept would again be something temporal that points back to a constituting consciousness of a similar sort, and so in infinitum. Hence the question arises: How do I come to know the constituting flow?

To deal with this question Husserl recalls the ‘double intentionality’ of retention. One of these is the “‘primary memory’ of the (just sensed) tone” which “serves for the constitution of the immanent object”. But there is also the other, the second retentional intentionality which “is constitutive of the unity of this primary memory in the flow”. This “retention of retention” ensures that “each past now retentionally shelters within itself all earlier stages” and also therefore that “there extends throughout the flow a horizontal intentionality [Längsintentionalität] that, in the course of the flow, continuously coincides with itself”. By means of this, the unity of the flow becomes itself “constituted in the flow of consciousness as a one-dimensional quasi-temporal order”. The absolute flux is, therefore, self-constituting. It constitutes the unity of immanent objects in a unitary immanent time and thereby, “as shocking (when not initially even absurd) as it may seem,” also its own unity:

two inseparably united intentionalities, requiring one another like two sides of one and the same thing, are interwoven with one another in the one, unique flow of consciousness. By virtue of on limits of language of the intentionalities, immanent time becomes constituted…. In the other intentionality, it is the quasi-temporal arrangement of the phases of the flow that becomes constituted…. This prephenomenal, preimmanent temporality becomes constituted intentionally as the form of the time-constituting consciousness and in itself.

And it is this second retentional intentionality that gives us our oblique self-awareness of the flux, removing the problem of infinite regress whilst simultaneously resolving the difficulty of knowing the flow. “The self-appearance of the flow does not require a second flow: on the contrary, it constitutes itself as a phenomenon in itself”. It requires no second flow because this is a non-objectivating awareness – experienced in the same way as we experience acts, in a perceptual objectivation, without thematizing them. Unlike such acts, however, it cannot itself be made an object of reflection. Because there is no object or substance that endures, and no ‘time’ here as such, our ability to speak of the absolute flux runs up against the limits of language and conceptual thought. “We can say nothing other than the following: This flow is something we speak of in conformity with what is constituted, but it is not ‘something in objective time.’ It is absolute subjectivity and has the absolute properties of something to be designated metaphorically as ‘flow’.” Husserl is blunt about the inescapable inadequacy of his vocabulary here: “For all of this, we lack names”.

In a sense Husserl’s project in the lectures on time-consciousness can be understood as an inquiry into the constitution of constitution; into the way in which intentional acts of consciousness are constituted as temporal unities able to have as their correlate the transcendent temporally extended object. As he observes: “It is certainly evident that the perception of a temporal object itself has temporality, that the perception of duration itself presupposes duration of perception, that the perception of any temporal form itself has temporal form”. Yet Ricoeur writes that “The fact that the perception of duration never ceases to presuppose the duration of perception did not seem to trouble Husserl“, implying that Husserl was blind to the significance of his own observation. This rather offhand remark plays little role in Ricoeur’s argument for the conflict between Kant and Husserl’s respective treatments of time, but given that Husserl was clearly sorely troubled by this ‘fact’ – that it is arguably the very observation that led him beyond Kant’s standpoint to explore the temporality of the constitutive act itself.

Phantom Originary Intentionality: Thought of the Day 16.0

Phantom limbs and anosognosias – cases of abnormal impressions of the presence or absence of parts of our body – seem like handy illustrations of an irreducible, first-person dimension of experience, of the sort that will delight the phenomenologist, who will say: aha! there is an empirical case of self-reference which externalist, third-person explanations of the type favoured by deflationary materialists, cannot explain away, cannot do away with. As Merleau-Ponty would say, and Varela after him, there is something about my body which makes it irreducibly my own (le corps propre). Whether illusory or not, such images (phantoms) have something about them such that we perceive them as our own, not someone else’s (well, some agnosias are different: thinking our paralyzed limb is precisely someone else’s, often a relative’s). One might then want to insist that phantom limbs testify to the transcendence of mental life! Indeed, in one of the more celebrated historical cases of phantom limb syndrome, Lord Horatio Nelson, having lost his right arm in a sea battle off of Tenerife, suffered from pains in his phantom hand. Most importantly, he apparently declared that this phantom experience was a “direct proof of the existence of the soul”. Although the materialist might agree with the (reformed) phenomenologist to reject dualism and accept that we are not in our bodies like a sailor in a ship, she might not want to go and declare, as Merleau-Ponty does, that “the mind does not use the body, but fulfills itself through it while at the same time transferring the body outside of physical space.” This way of talking goes back to the Husserlian distinction between Korper, ‘body’ in the sense of one body among others in a vast mechanistic universe of bodies, and Leib, ‘flesh’ in the sense of a subjectivity which is the locus of experience. Now, granted, in cognitivist terms one would want to say that a representation is always my representation, it is not ‘transferable’ like a neutral piece of information, since the way an object appear to me is always a function of my needs and interests. What my senses tell me at any given time relies on my interests as an agent and is determined by them, as described by Andy Clark, who appeals to the combined research traditions of the psychology of perception, new robotics, and Artificial Life. But the phenomenologist will take off from there and build a full-blown defense of intentionality, now recast as ‘motor intentionality’, a notion which goes back to Husserl’s claim in Ideas II that the way the body relates to the external world is crucially through “kinestheses”: all external motions which we perceive are first of all related to kinesthetic sensations, out of which we constitute a sense of space. On this view, our body thus already displays ‘originary intentionality’ in how it relates to the world.