Logic, Thought, and Action 16

Chapter 16

PRAGMATIC AND SEMIOTICPREREQUISITES FOR PREDICATION

A Dialogue Model

Kuno LorenzSaarbrucken University¨

Rather than starting my presentation of how to construe predicationwith a discussion about propositions, and independent of the ongoingdebate whether propositions should be understood as propositional ker-nels of full sentences (having a force, expressing a thought , and denotinga truth-value) or should themselves be considered as a particular forceof a sentence, i.e., its constative force as an assertion, I would like toinvite you to a journey into the prepropositional state where the task toprovide for propositions or sentences is still to be accomplished.

The primary means for changing one’s state, or for realizing thatsuch a change has occurred, I consider to be a dialogue, better still: adialogue-situation. This is a situation where, using a Peircean term, a>habit-change< occurs which should be construed as the acquisition ofan action-competence.1 It turned out that such an acquisition proce-dure will most profitably be modelled using the conceptual frame of atwo-person-game, and such a game may be considered as a generalizedWittgensteinean language-game or, rather, its pragmatic basis, not yetwith an explicit linguistic activity. In the beginning the game is not anobject of study but a means of study .

1Cf. K. Lorenz, Pragmatics and Semiotic: The Peircean Version of Ontology and Epistemol-ogy, in: G. Debrock/M. Hulswit (eds.), Living Doubt. Essays Concerning the Epistemologyof Charles Sanders Peirce, Dordrecht: Kluwer. 1994, 103-108.

D. Vanderveken (ed.), Logic, Thought & Action, 343–357.©c Springer. Printed in The Netherlands.2005

344 LOGIC, THOUGHT AND ACTION

Before giving a sketch of the dialogical constructions,2 which leadfrom modelling simple activity to modelling the growth of more com-plex activities up to elementary verbal utterances, at first a few generalremarks are in order to put my suggestions into a broader perspective.

IIn accordance with C. S. Peirce, I consider pragmatics to have be-

come the modern heir of ontology with semiotics being its counterpartas the modern heir of epistemology. Yet, in this context both disciplinesshould not be understood as two newly established empirical sciences,but as ways of investigation where empirical procedures are combinedwith reflexive procedures. Using such a broader perspective both actionsand sign-actions are not only treated as objects of research and repre-sentation, as, e.g., in Ch. Morris’ and U. Eco’s approach, but also asa means or tool of research and representation. You not only observeand describe these entities according to certain standards, but you alsoproduce them in a perspicuous fashion in order to arrive at some kind ofapproximating reconstruction of what you take to be available, already.Wittgenstein has used the term ‘language-game’ for this kind of activ-ity which aims at disclosure of what is going on by providing tools ofcomparison, though in his description of language-games pragmatic andlinguistic activity is not accounted for by separate steps.

Hence, the constructions serve cognitive purposes in the sense of de-lineating the very areas of (particular) objects one proceeds afterwardsto investigate in the more usual way. Language-games as well as thegeneralized ones of acquiring simple action competences have to countas paradigm cases of perceptual knowledge, because they exhibit a sig-nificative function if understood as icons in the sense of Peirce. An areaof internally structured objects is found by inventing a prototype.It should be obvious, therefore, that even the distinction of action andsign-action – a special case of the basic and embarrassing distinction be-tween world and language – which still is prevalent in Wittgensteinianlanguage-games where simple action competence is presupposed, has tobe relativized in view of a purely functional account of both what it

2For further details, cf. K. Lorenz, Artikulation und Pradikation, in: M. Dascal/D. Ger-¨hardus/K. Lorenz/G. Meggle (eds.), Sprachphilosophie.Philosophy of Language.La philoso-phie du langage. Ein internationales Handbuch zeitgenossischer Forschung II, Berlin-New¨York: de Gruyter 1995, 1098-1122; K. Lorenz, Rede zwischen Aktion und Kognition, in: A.Burri (ed.), Sprache und Denken. Language and Thought, Berlin-New York: de Gruyter 1997,139-156; K. Lorenz, Sinnbestimmung und Geltungssicherung. Ein Beitrag zur Sprachlogik,in: G.-L. Lueken (ed.), Formen der Argumentation, Leipzig: Leipziger Universistatsverlag¨2000, 87–106.

Pragmatic and Semiotic Prerequisites for Predication 345

means to be an object and what it means to be a sign (of an object).In fact, it belongs to one of the basic tenets of, e.g., Nelson Goodman’sapproach that the seemingly clear-cut division of world and language– non-verbal language included – as a division between the given andthe constructed, between that which is found and that which is made,between the fact and the artefact, is outdated, and that it has even beenchallenged once and again since the time of the pre-socratics. But, onlyrarely is history looked at in this way. Any matter we are concernedwith, Goodman tells us, is dependent on some manner as the meansby which we deal with it. So worlds are but versions and worldmakingbegins with one version and ends with another. The message we shouldlearn runs thus: “never mind mind, essence is not essential, and mat-ter doesn’t matter”.3 Goodman goes on in claiming that we choose thefacts as much as the frameworks, though this statement should betterbe split into two complementary statements: We produce the facts asmuch as the frameworks and we experience the frameworks as much asthe facts. Constructions, when serving cognitive purposes, are alwaysreconstructions.

The last two Aristotelian categories, and , which seemedforgotten throughout most of modern philosophy in the tradition ofDescartes, though they play an important role both in Spinoza and Leib-niz, will enjoy a lively comeback as the two sides we are concerned withwhen doing something: you do it yourself (active) and you recognizeothers (including yourself!) doing the same (passive [with respect to thecontent of recognition]). In fact, the two sides reoccur in the model ofan elementary dialogue-situation with two agents being engaged in theprocess of acquiring an action-competence. At each given instant justone of the agents is active – a >real< agent – and the other agent – the>potential< agent or >patient< – is passive. The agent in active role isperforming an action, i.e., he is able to produce different tokens of thesame type, while the agent in passive role is recognizing an action, i.e.,he sees different tokens as belonging to the same type. One has learnedan action, if one is able to play both roles: while acting you know whatyou are doing, or, conversely, if you don’t know what you are doing, youdon’t act. Another way of saying this would be: Each action appearsin two perspectives, in the I-perspective by performing the action (=producing an action token) – it should be called the pragmatic side ofan action, or its >natural< side – and in the You-perspective when rec-ognizing the action (= witnessing an action type) which should be called

3N. Goodman, Ways of Worldmaking, Hassocks (Sussex): The Harvester Press 1978, p 96.


its semiotic or >symbolic< side. We have come across the first step toexecute the program of >naturalizing language< and other symbol sys-tems, and, at the same time, of >symbolizing world<, in order to bridgethe gap between the two.

For further guidance we may turn to Peirce again. He sketches a wayof deriving signs out of objects in more or less the same manner as I justdid, the difference being that he proceeds upside down.

“If a Sign is other than its Object, there must exist, either in thought orin expression, some explication or argument or other context, showinghow – upon what system or for what reason the Sign represents theObject or set of Objects that it does. Now the Sign and the Explanationtogether make up another Sign, and since the Explanation will be a Sign,it will probably require an additional explanation, which taken togetherwith the already enlarged Sign will make up a still larger Sign; andproceeding in the same way, we shall, or should, ultimately reach a Signof itself, containing its own explanation and those of all its significantparts; and according to this explanation each such part has some otherpart as its Object. According to this every Sign has, actually or virtually,what we may call a precept of Explanation according to which it is tobe understood as a sort of emanation, so to speak, of its Object.”4

The argument of Peirce calls for something which is a sign of itself,that is, which combines object status and sign status, or better: whichfunctions in both ways. The basic point of his pragmatic foundation ofsemiotics was to give an account of the process of separation betweensign and its object within the framework of his Pragmatic Maxim.5 Andthe arguments used for this purpose are themselves to be understood assections of an open sign-process on the level of reconstruction. And itis these sections that may be looked at as conceptualizations of general-ized Wittgensteinian language-games. Now, the descending sequence ofinterpretants ends with an ultimate logical interpretant6 which is iden-tified as a habit-change. As stated in the beginning, already, such ahabit-change, in contemporary terminology, is nothing else but the ac-quisition of an action-competence such that all the ways of dealing withthe object in respect of what is signified by the initial sign are included.And within the process of acquisition, if it is modelled as an elemen-tary dialogue-situation, the two perspectives of agent and patient maycount, respectively, as action on the object-level in performing the ac-tion, and action on the sign-level in recognizing the action through the

4C. S. Peirce, Meaning [1910], in: Collected Papers of Charles Sanders Peirce I-VI, C.Hartshorne/P. Weiss (eds.), Cambridge Mass.: Harvard University Press 1931-1935, 2.230.5Cf. B. M. Scherer, Prolegomena zu einer einheitlichen Zeichentheorie: Ch. S. PeircesEinbettung der Semiotik in die Pragmatik, Tubingen: Stauffenburg Verlag 1984.¨6Cf. C. S. Peirce, Collected Papers 5.476.


performance functioning as a representative of any other performance.Thus, habit-changes are, indeed, entities which are signs of themselves.We may finally conclude that a verbal sign of an object signifies a rangeof possibilities of dealing with that object. Even more generally, bydeleting the dummy term ‘object’, it might be said that having the com-petence for such a sign-action – being a verbal sign-action, it functionssymbolically – is tantamount to >knowing<, by that very action, of awhole range of further actions which may be said to be signified by the(symbolic) sign-action.We arrive at the following equivalence: Knowing an action, in the senseof being acquainted with it, is knowing ways of dealing with that action.And this implies that knowing an arbitrary object is equivalent to treat-ing this object as a sign of its distinctions, i.e., of its internal structurewhich is exhibited step by step in an open sign-process.

IINow, within the model of acquisition of an action-competence by an el-

ementary dialogue-situation it is important to make some further distinc-tions. They are based on the observation that producing an action-tokenand witnessing an action-type, i.e., I-perspective and You-perspective ofan action, are inseparably bound together and cannot be treated in isola-tion from each other. The model of acquisition of action-competence is amodel of actions as a means and not yet of actions as objects which, in or-der to be accessible, will in turn be dependent on other actions as a meansof dealing with objects. Dialogical construction as a means of study asksfor self-application such that the interdependence of the status of being-a-means and the status of being-an-object, hence of >epistemology< and>praxeology< on the one hand, and of >ontology< on the other hand,is laid bare. Actions as a means are characterized by their two sidesas they arise from the two perspectives, from singular performance inI-perspective and universal recognition in You-perspective. Yet, whenperforming is understood to be a case of producing (an action-token)and, analogously, recognizing to be a case of witnessing (an action-type),the action in question is treated as an object, in fact, sometimes eventwo objects, the token as an external or >corporeal< particular and thetype as an internal or >mental< particular. But, even if action particu-lars, i.e., individual acts, are treated uniformly without being split intoexternal and internal entities, particularity is to be kept strictly distinctfrom singularity and universality. Usually, in the terminology of typeand token, where types are treated logically as generated >by abstrac-tion< out of tokens, and where tokens originate >by concretion< from


types (rather than looking at the relation of tokens to types in a psy-chological fashion as a relation of external to internal particulars), bothtypes and tokens are (individual) objects, yet of different logical order,which are related in standard notation as sets to their elements. At thelowest level, if there is one, the final universe of discourse is located,i.e., a world of elementary individual objects, the particulars, to whicheverything else will have to be reduced. Such an account, by neglectingthe distinction between particularity and singularity as well as univer-sality, violates the inseparability of (producing a) token and (witnessinga) type in the context of actions as a means, or, rather, it exhibits anequivocation in the use of ‘type’ and ‘token’. It is necessary to relinquishboth the equivalence of ‘performing an action’ with ‘producing an actiontoken’ and the equivalence of ‘recognizing an action’ with ‘witnessing anaction type’.

Instead, performation is performation of something singular and recog-nition is recognition of something universal, whereas producing (a token)together with its twin activity of witnessing (a type) occur with respectto something particular. Now, if types and tokens are not in this wayconstrued as particulars that are produced or witnessed, respectively,they should be identified, in tune with action as a means, with universalfeatures and singular ingredients of particulars that are exhibited by ac-tions which deal with them. Particulars together with the situations (ofacting) of which they occupy the foreground are appropriated by per-forming an action which deals with them, and they are objectified byrecognizing such an action. It should be noted that neither universalfeatures nor singular ingredients have object status by themselves; theyremain means with respect to (particular) objects. Universals cannotbe appropriated and singulars cannot be objectified. Hence, in perfor-mances of an action that is dealing with a particular you (pragmatically)present one of the (singular) token ingredients of this particular, whereasin recognitions of an action that is dealing with a particular you (semi-otically) represent one of its (universal) type features. Switching fromthe language of means – pragmatic means are singular, semiotic meansare universal – to the language of objects (= particulars) you may saythat it is individual acts that provide both services, of presentation withrespect to its performance perspective and of representation with respectto its recognition perspective. With recourse to a traditional terminol-ogy it may be said, in a >spiritualistic< version, that an individual acthas been >aimed at< in a singular performance and will >originate< froma universal recognition, but it could as well be said, in a >naturalistic<version, that an individual act was >caused< by a singular performanceand is >conceived< by a universal recognition. In appropriation as well


as in objectivation of particulars of arbitrary category, like individualacts, individual things or events, groups of individuals or other non-individual particulars, etc., the actions of dealing with particulars areused as a means, of presentation (of singular tokens – the way a par-ticular is present) in the case of appropriation and of representation(of universal types – the way a particular is identified) in the case ofobjectivation.

Particulars may be said to act as appearances of >substances<, i.e.,some part of the whole out of like singular tokens is a part of the particu-lar, and as carriers of >properties<, i.e., the particular is an instance of auniversal type.7 Therefore, in order to avoid misunderstandings, insteadof ‘perform’ we will, henceforth, say ‘actualize’, and we say ‘schematize’instead of ‘recognize’. Within the model of an elementary dialogue-situation where two agents are engaged in the process of acquiring anaction-competence, the activities of actualizing and schematizing shouldnot be understood as performances of two separate actions; it is oneaction the competence of which is acquired by learning to play boththe active and the passive role. Active actualization makes the actionappear in I-perspective, passive schematization lets it appear in You-perspective. Any action as a means is characterized by its pragmatic andits semiotic side, and it doesn’t make sense as yet to speak of the actionas an >independent< object(-type) split into particulars, i.e., some set ofindividual acts. In order to achieve the switch from action as a meansto action as object, it is essential to iterate the process of acquiring anaction-competence by turning the two sides of an action into proper ac-tions by themselves, i.e., into actions of dealing with the original actionunder its two perspectives such that the (secondary) action-competencesadditionally required will have to be modelled in turn by means of (nownon-elementary) dialogue-situations. Such a further step may be lookedat as an application of the principle of self-similarity.

What has to be done is to schematize and to actualize the elemen-tary dialogue-situation, i.e., to create a He/She-perspective towards theI/You-situation such that, on the one hand, He/She becomes a (sec-ondary) You-perspective with respect to I/You as I, and, on the otherhand, He/She becomes a (secondary) I-perspective with respect to I/Youas You. In the first case you gain an >exterior view< of the originalaction by acquiring a second level action (with respect to the original

7A particular wooden chair, for example, acts as a carrier of all the properties conceptualizedby ‘wooden’, and as an appearance of the substance >wood<, inasmuch as a part of >thewhole wood< may be considered to be a part of the particular wooden chair; cf. the entry‘Teil und Ganzes’ in: Enzyklopadie Philosophie und Wissenschaftstheorie¨ IV, J. Mittelstraß(ed.), Stuttgart-Weimar: Metzler 1996, 225-228.


action) which functions as one of the indefinitely many aspects of theoriginal action: The You-perspective is turned into the schema of a sec-ond level action out of an indefinite series of second level actions. Inthe second case you gain an >interior view< of the original action by ac-quiring a second order action (with respect to the original action) whichfunctions as one of the indefinitely many phases of the original action:The I-perspective is turned into an actualization of a second order ac-tion out of an indefinite series of second order actions. The semioticside of an action is split into a multiplicity of aspects or (secondary)You-perspectives, and the pragmatic side of an action likewise into amultiplicity of phases or (secondary) I-perspectives.

By (dialogical) construction, it is in its active role that an aspect-action is I-You-invariant and, in this sense, >objective<, whereas a phase-action is I-You-invariant in passive role, only. Hence, by applying theprinciple of self-similarity once again to both aspects and phases, thepragmatic side of an aspect-action is split into a multiplicity of objectivearticulations or sign-actions, and the semiotic side of a phase-action intoa multiplicity of objective mediations or partial actions. Any one of thesign-actions is a means to designate the original action, and any one ofthe partial actions is a means to partake of the original action, where des-ignating and partaking function with the proviso that the original actionitself is turned from a means into an object. In fact, an action as object– things, events, and other categories of entities are included among ac-tions by identifying an entity[-type] with the action[-type] of dealing withthe entity – is constituted, on the one hand >formally<, by identificationof the schemata of the aspect-actions, i.e., of their >subjective< semioticside (when turned into a multiplicity of full-fledged actions, one wouldget perceptual actions), and, on the other hand >materially<, by summa-tion of the actualizations of the phase-actions, i.e., of their >subjective<pragmatic side (when turned into a multiplicity of full-fledged actions,one would get poietic actions). On the one side, through identifica-tion, an action as object is a semiotic (abstract) invariant of which onepartakes by means of a partial action, and on the other side, throughsummation, it is a pragmatic (concrete) whole which one designatesby means of a sign-action. With respect to the additional dialogue-situations modelling the acquisition of second-order-action-competencesas well as second-level-action-competences the original action as objectoccurs within a situation which, in fact, is responsible for individuatingthe original action as object. The move of objectivation from actionas a means to action as object is accompanied by a split of the ac-tion into (action-)particulars such that the respective invariants may betreated as kernels of the schemata of aspects (= universalia), and the


respective wholes correspondingly as closures of the actualizations ofphases (= singularia). An objectival foreground together with a situa-tional background will semiotically be a constant foreground against avariable background (= the same particular in different surroundings,i.e., its varying external structure), and it will pragmatically be a vari-able foreground against a constant background (= different particulars[of the same kind] by their varying internal structure, in the same sur-rounding). Both together, kernel and closure – >form< and >matter< inphilosophical tradition8 – make up a particular within a situation. Work-ing backwards again, i.e., making the countermove of appropriation, theschemata of the kernel and the actualizations of the closure, are realizedin representations and presentations, respectively, by schematizing andactualizing a particular (in a situation) as explained above.

Dialogical construction of particulars being dependent on identifica-tion of schemata of aspects and on summation of actualizations of phases,implies the establishment of mutual independence between objectivalforeground and situational background. In order to achieve this, a spe-cially chosen articulation has to act as a substitute for arbitrary aspectswith respect to some partial action – such a function of substitution maybe articulated by rules of translation among aspects – and will be calledsymbolic articulation. Constant foreground and variable background willthus become independent of each other. Analogously, any mediation willhave to acquire the function of having the phase to which it belongs ex-tended by arbitrary other phases with respect to some sign-action –such a function of extension may be articulated by rules of constructionfor phases – and will be called comprehensive mediation. In this case,constant background and variable foreground are made independent ofeach other. Both constructions together guarantee that particulars con-trast with their surroundings.9 By symbolic articulation, a symbolicsign-action, you arrive at a semiotically determined particular in actu-alized situations, i.e., the particular is symbolically represented , whereasby comprehensive mediation, a comprehensive partial action, you arriveat pragmatically determined particulars in a schematized situation, i.e.,the particulars are symptomatically present.

The semiotic side of partial actions (>what you do<) and the prag-matic side of sign-actions (>how you speak<), together they make up theways of life (of the agents). Correspondingly, the pragmatic side of par-

8The treatment of particulars as mixta composita out of or forma, and ormateria, is due to Aristotle as explained, e.g., in the commentary of Alexander of Aphrodisiason Aristotle’s Metaphysica, cf. Comm. in Arist. Graeca I, p 545, line 30ff; 497, line 4ff.9For an explicit dialogical construction of both identification and summation, cf. my ‘Redezwischen Aktion und Kognition’, op.cit. [note 2], p 145ff.


tial actions (>how you act<) and the semiotic side of sign-actions (>whatyou say<), together they make up the world views (of the agents).

IIIArticulation is signified canonically by the result of a sign-action, an

articulator (= >signifiant< in the sense of F. de Saussure); articulationhas a pragmatic side, i.e., it is a sign-action in its being an action, anda semiotic side, i.e., it is a sign-action in its being a sign. Semiotically,articulation is effected by uttering an articulator that has to be takenas a (verbal) type, in a speech situation; and if it is treated as function-ally equivalent with any other way of articulation, including non-verbalones, it acts as a symbolic articulator . Again semiotically, i.e., as a sign(-action), it shows its two sides, a pragmatic one and a semiotic one. Thepragmatic one is to be called communication, or the side with respect topersons or subjects, and the semiotic one is to be called signification, orthe side with respect to particulars or objects (these two sides in theirfunction being reminiscent of Plato’s and ). By itera-tion, communication splits into (content of) predication on the semioticside, and mood (of predication) on the pragmatic side, whereas signifi-cation splits into (intent of) ostension on the pragmatic side, and modeof being given on the semiotic side. Any predication can take place onlyby using a mood, and any ostension is effected only by using a mode ofbeing given. We have strictly to distinguish: content and mood of pred-ication, intent and mode of ostension. The moods of predication are,of course, speech acts, and only with respect to a mood a predicationcontains a claim, e.g., a truth claim.

Articulation of a mood of predication yields performators on the semi-otic side of the articulation, whereas articulation of a mode of ostensionyields perceptions (= Wahrnehmungsurteile) on the pragmatic side ofthe articulation. Without such a second order articulation of mood andmode, we have arrived at one-word sentences ‘P’ (in a mood and usinga mode of being given) by uttering the articulator ‘P’.

With the next step we introduce the separation of significative andcommunicative function, two functions that coincide with showing andsaying in the terminology of Wittgenstein’s Tractatus. Separation withrespect to predication, i.e., the semiotic side of communicative function,yields: δPεP (this P [= something done] is P[-schematized]), or, alterna-tively, σPπP (the universal P [= something imagined] is P-actualized),whereas separation with respect to ostension, i.e., the pragmatic sideof significative function, yields: δPζP (this P belonging to P), or κPξP(the whole P [= something intuited] being P-exemplified).


The operators: demonstrator ‘δ’ and attributor ‘ε’ (= copula), respec-tively, neutralize the communicative function and the significative one;‘δ’ keeps the significative function and ‘ε’ the communicative one, withthe result that ‘δP’ plays a singular role and ‘εP’ a universal one. In theterminology of logic or semiotics, ‘δP’, which is used to >ostend< P, is anindex of an actualization of the action articulated by ‘P’, whereas ‘εP’,which is used to >predicate< P, is a predicator serving as a symbol of theschema of action P. Predication εP and ostension δP with its respectiveassociates: form of a proposition ‘ εP’ and form of an indication ‘δP ’,are the modern equivalents of the traditional >forms of thinking< and>forms of intuition<. Proceeding dually with respect to the predicationoriented and, hence, semiotic distinction ‘singular-universal’, it is alsopossible to use another pair of operators, universalisator ‘σ’ and presen-tator ‘π’, where ‘σP’ has only significative function with universal roleand ‘πP’ only communicative function with singular role. In the sec-ond case which works with respect to the ostension oriented and, hence,pragmatic distinction ‘active-passive’, either demonstrator ‘δ’ and par-titor ‘ζ’, or, dually, totalisator ‘κ’ and exemplificator ‘ξ’, serve the samepurpose: ‘δ’ and ‘κ’ keep the significative function in active and passiverole, respectively, whereas ‘ζ’ and ‘ξ’ keep the communicative function,here in passive and active role, respectively.

What is not yet available up to now and what would not even makesense, are >propositions< of kind δPεQ and >indications< of kind δQζP.The reason why these expressions don’t make sense, is simply the fol-lowing: ‘δP’ is not the kind of expression to occupy the empty place ina propositional form ‘ εQ’ with Q�=P, and ‘�� ζP’ is not the kind of ex-pression to occupy the empty space in an indicational form ‘δQ ’ withQ�=P. Instead, we have to introduce�� individuators ‘ιP’ in order to refer toparticulars, i.e., the situation-dependent units of the action articulatedby ‘P’; >things< as well as objects of other categories, any one (type) ofthem being identified with the action(-type) of arbitrary dealings with anobject(-type), hence, any of the so-called >natural kinds<, are, of course,included among the P. Particulars, be they individual things or events,individual acts or processes, are composed out of kernels of schemata ofaspects: σ(ιP) (= invariants), together with closures of actualizations ofphases: κ(ιP) (= wholes). Hence, particulars may be considered to behalf thought and half action. Using individuators we, now, may writedown eigen-propositions ιPεP as well as eigen-indications δPιP (shortfor: δPζιP), and it is possible to render these versions of saying andshowing with the help of the four operators: demonstrator, attributor,universalisator, and totalisator, in the following traditional way:


(i) In the case of saying (ιPεP): the universal σP is predicated of aP-particular by means of ‘εP’ (or: within the proposition ιPεP,the individuator is a sign of an indication, and, hence, functionsas a nominator of a P-particular, i.e., within the proposition ιPεP,nomination by ‘ ιP ’ is shown), and

(ii) In the case of showing (δPιP): ostending the whole κP at a P-particular by means of ‘δP’ (or: within the indication δPιP, theindividuator is a sign of a proposition, and, hence, functions to saythat participation in a P-particular holds, i.e., within the indica-tion δPιP, participation in ιP is said).

Hence, reference to particulars ιP includes both nomination of κ(ιP),i.e., of the matter of ιP, and participation in σ(ιP), i.e., in the form ofιP. As a remark, it may be added that nominating is the articulation ofdesignating by symbolic articulation, and, analogously, participating isthe articulation of partaking by comprehensive mediation.

The composition of P, e.g., wood, and Q, e.g., chair, is a result of sepa-rating speech-situation and situation-talked-about. It can be realized byanalyzing and reconstructing what happens when, e.g., in a Q-situationyou are uttering ‘P’. In the foreground of the situation-talked-aboutwhich is articulated by ‘P’, there are two particulars to be welded. Itmay come about in either of two possible ways:

(i) An aspect (with its schema being) out of σ(ιP) coincides with aphase (actualizations of which being) out of κ(ιQ), e.g., sitting ona wooden chair as a phase-action with respect to chair is simulta-neously an aspect-action >sitting on the wood of the chair< withrespect to wood;

(ii) A phase out of κ(ιP) coincides with an aspect out of σ(ιQ).

In the first case you may articulate the coincidence predicatively byεPQ (= is a wood of [a] chair), in the second case ostensively by δ(QP)(= this wood with the form of [a] chair).Instead of δPQ ε PQ we may write ιQεP(= ιQ is P, or: this [particular]chair is wooden), and likewise, instead of δ(QP) ζ (QP), it is possible towrite δPιQ (short for: δPζιQ) (= δP at ιQ, or: this dealing with woodbelonging to this [particular] chair). Hence, ‘εP’ acts as a symbol for theresult of schematizing ιQ, whereas ‘δP’ acts as an index for the result ofactualizing ιQ.

Actualizations ostending κ(ιQ) are simultaneously actualizing the uni-versal σP [= δQεP; equivalent with: σPπQ]; schemata predicating auniversal out of σ(ιQ) exemplify simultaneously the whole κP [= δPζQ;


equivalent with: κPξQ] by being the form of an element of a partitionof κP into a class εP. Hence, σ(ιQ) is an appearance of the whole orsubstance κP, and κ(ιQ) is a carrier of the universal or property σP. Anindication δPιQ shows that the substance κP is ostended at ιQ by meansof ‘δP’; a proposition ιQεP says that the property σP is predicated ofιQ by means of ‘εP’.

Involution as transformation of phase-structures (= internal struc-ture) into aspect-structures (= external structure), and vice versa, cannow be proved to exist in a one-to-one way.10 So, it makes indeed senseto say: ιQ consists both of phases such that the closure of their actual-isations is κ(ιQ), and of aspects such that the kernel of their schematais σ(ιQ).And, taking our example, a phase-action with respect to chair which isthe pragmatic side of a dealing with chair, being turned into an indepen-dent action, can be mapped one-one onto (>seen as<) an aspect-actionwith respect to wood which is the semiotic side of a dealing with wood,being turned into an independent action.

As a historical remark, it may be added that the two sides of a partic-ular ιQ, the concrete whole κ(ιQ) and the abstract invariant σ(ιQ), cor-respond neatly to >body< or >phenomenon< and >soul< or >fundament<of a monad as it is conceived in the Monadologie of Leibniz.11 It mayalso be useful to observe that the identification of δPQ ε PQ with ιQεP,i.e., the introduction of (one-place) elementary propositions, is closelyrelated to Reichenbach’s transition from a thing-language to an event-language articulated with the help of an asterisk-operator which movesthe predicative ingredients of a subject term of an (one-place) elemen-tary proposition into its predicate term, e.g., from ‘this man is smoking’you arrive at ‘smoking of [this particular] man’, or: (ιQεP)*= PQ.12

Now, we have reached the usual account of (one-place) predicationwhere >general terms< ‘P’ – they should more appropriately and in linewith the Fregean analysis of general terms as propositional functions orpredicators be rendered as ‘εP’ – serve to attribute properties to particu-lars of an independently given domain of Q-objects, in the simplest casereferred to by deictic descriptions ‘ιQ’ that are special cases of >singularterms< [another use of ‘singular’ !] or nominators.

10Cf. K. Lorenz, On the Relation between the Partition of a Whole into Parts and theAttribution of Properties to an Object, in: Studia Logica 36 (1977), 351-362.11Cf. for further corroboration various essays in: Leibniz and Adam, M. Dascal/E. Yakira(eds.), Tel Aviv: University Publishing Projects 1993.12H. Reichenbach, Elements of Symbolic Logic, Toronto: Macmillan 1947, § 48.

LOGIC, THOUGHT AND ACTION356


Documents

Logic, Thought, and Action 16