Leibniz constructed time as a simple ordering of the moments of a static “nature,” whereas the time constructed by Whitehead is a much more dynamic one. Whitehead’s construction is based on his method of extensiveabstraction and makes time the extensive continuum that results from the connection of all real potentialities. The two fundamental properties of that continuum are infinite divisibility and unboundedness (PR 103).
In the description of verbal tenses by some linguists, the relational aspect is especially emphasized. Nicolas Beauzée, a French mathematician and grammarian (1717–1789), was the first to argue that verbal tenses express deep relations between temporal locations of particular events—relations between moments such as the moment of utterance, the moment of a term of comparison, and the period in which the process comes into being (1789). These moments have been independently rediscovered and formalized by Hans Reichenbach (1947) with his “three points of time” (speech (S), reference (R) and event (E)), and the two relations of concomitance and succession. When dealing with the indicative mood, Reichenbach represents time as a line: a linear unbounded continuum is divided by the “present” point into two unbounded parts, a left part, representing the dimension of the past, and a right part, representing the future:
Fig. 1: Physical time
Traditionally, the structures used for the formal representation of time are based on the set of real numbers. We have argued that (1) in qualitative linguistics, temporality does not need physical time to be expressed; (2) that for any aspectual values of the process concerned (punctual, periodic or iterative), calculation is always done on points or sequences of points, with the two fundamental relations of simultaneity and precedence; and (3) that the formalism of the S-languages, as developed by Schwer (2002), is an adequate framework for such a calculation. This model is in accordance with the model of time obtained with the method of extensive abstraction by Whitehead. Note that Whitehead was only concerned with theories of physical time (PNK, CN, R, PR).
There are already several linguistic studies that take inspiration from Whitehead’s philosophy, notably those by Firth (1957), Halliday, and Fortescue (2001). Here, however, we will not offer another such study, but will rather compare aspects of Whitehead’s thought with the theory of tense and aspect of the French linguist Gustave Guillaume (1883-1960) who founded the discipline of linguistic psychomechanics. Whitehead was concerned with the links between mind and nature, while Guillaume studied those between mind and language. They both evince a shared respect for exact reasoning, careful definitions of terms, and the need to examine actual real facts, whether of the natural world, as in Whitehead’s case, or of languages and discourse, as in Guillaume’s. They both used the method of abstraction in order to have a good understanding of the objects of their study, a relational and process-oriented way of thinking. In addition, they were both ostracized to a certain extent by their contemporaries. Since Firth, Halliday and Fortescue do not refer to Guillaume in their work that draws on Whitehead, we will first provide a short biography of the man. Next we compare some of the ideas of Whitehead and Guillaume, and outline Guillaume’s theory of tense and aspect. We end by showing how it is possible to construct time starting from temporal linguistic information: namely, we offer a linguist’s approach to time, based on a linear sequence, and inspired by Whitehead’s overall vision.
1. Gustave Guillaume: A Short Biography
Gustave Guillaume was born in Paris on December 16, 1883. Forced at an early age to earn a living and provide for his mother, he gave French lessons mainly to Russian immigrants. Although he had never attended university, he taught himself mathematics, philosophy, physics, literature, and was very curious about linguistic matters. In 1909, when working as a bank clerk, he met Antoine Meillet who was impressed by him and invited him to attend his lectures. Guillaume began to publish in 1911. His first works are based on the thought that the use of grammatical forms derives from an unconscious universal mathematical logic that precedes conscious logic. He showed later, that the unconscious logic was not the erudite logic of mathematics, but a logic sui generis.
His major ideas were made more widely known in his two most famous publications, Le problème de l’article (1919) and Temps et verbe (1929). In the first, he employed the clear distinction between two levels of linguistic activity: the potential level, or langue and the actualized level, or parole (i.e. “discourse” or actual individual utterances). The article is a part of language that permits one to move from the first level to second. In Temps et verbe, he introduced the notion of operating time, the time which is necessary for the brain to move between the two levels, since “a psychic fact, whatever it is, requests time to achieve itself.” He studied language as a system, which he termed architecture. His theory links closely both structural and cognitive linguistics. He became lecturer in l’Ecole Pratique des Hautes Etudes in 1938, where, during more than twenty years, he elaborated his theory. He died on February 3, 1960 and was buried in the cemetery of Montparnasse in Paris. All his lectures were preserved and have been published by Roch Valin.
2. Guillaume as a Whiteheadian Thinker
In The Concept of Nature, Whitehead argues that
the primary task of a philosophy of natural science is to elucidate the concept of nature, considered as one complex fact for knowledge, to exhibit the fundamental entities in terms of which all laws of nature have to be stated, and to secure that the entities and relations thus exhibited are adequate for the expression of all the relations between entities which occur in nature (CN 46).
And in Process and Reality, he begins with the following definition of speculative philosophy: “[It] is the endeavour to frame a coherent, logical, necessary system of general ideas in terms of which every element of our experience can be interpreted” (PR 3). “Speculative” thought does not remain on the level of the experiment, but uses all the resources of rationality to build a scheme to account for the essence of the universe and to reach first principles. The same concerns are found throughout Guillaume’s linguistic work; they led him to a structural analysis of language and to his theory of linguistic psychomechanics. In his lecture of November 11, 1943, he explained that “the highest sciences in the hierarchy of sciences are those which can use best, in any useful proportion, both attentive observation of the concrete and abstract speculation.” Just as natural laws are not subject to sense perception, so too the important relations that structure linguistic phenomena cannot be actually observed. “The linguist must combine the fine observation of the facts and abstract thinking. Abstract thinking brings power and acuity to the observation of the concrete.”
For Whitehead, “nature is a process” (CN 53). Nature is always moving on but its principles and the rules are eternal. Analogously, Guillaume’s views have been summarized as follows (Hirtle 1975, 4): “language is a process” on the one hand, and a “system of systems” on the other (PLTGG, 25) language is both “inherited from the past and a human and transcendental organization of that heritage.” The whole system has its image inside each subsystem, and the same is true at any level of the hierarchy. The “word” is a system, the “article” is a system, the “verb” is a system, and so forth.
On the basis of the fundamental distinction between thought and the power that thought has to understand itself, Guillaume identifies language with the power that thought has to understand in itself its own activity. Thought is free, but the means by which it understands itself are systematized and organized in a restricted number; the structure of language offers a faithful image of these means. What the attentive observer discovers in language, considered in itself, are these mechanisms. This is the set of means that thought has systematized and instituted to give to itself the permanent possibility of attaining a fast, clear understanding of what is happening within it.
Psychosystemic, as it is termed by Guillaume, studies these mechanisms. It aims to understand two phenomena—potentiality or conceivability, at the level of langue, and the outcome of this, at the level of actual parole. In his lecture of November 26, 1948, he argued that
langue is the result of constructive operations whose goal is to divide the thinkable into a definite number of representations bringing with them, by their division, the power to express every thought. This division is oriented from the particular to the universal. The universal is here comprised of all that is thinkable. Discourse [parole] is the result of operations of thought that consist in making use of the resulting representations of langue, all of which are parts of the thinkable, in order to provide a momentary expression of a narrow and singular thought (PLTGG, 171).
Hence, the fact of langue is a formal instituted representation, while the fact of discourse is a free running of what is instituted inside the langue. Thus, fact of discourse is associated with one fact of langue. The fact of discourse should never transgress the definition of its corresponding fact of langue that allows it with a whole freedom of interior play (PLTGG, 171).
3. Guillaume’s Theory of Mode, Aspect and Tense
Time cannot be represented by itself but needs space to be represented. The representation of time differs depending on which langue is used. Germanic languages, such as English, do not represent time in the same way as Romance ones. The expression of time is more recent than its representation. The verb is of course a part of the system but is also a system in its own. It is associated with a notion with duration that is called a process. A process can be situated in time and has its proper time. The path from the mental notion of a process to the word employed also needs some time duration. We get, then, three types of time which Guillaume claims refer to Mode, Aspect and Tense. In other words, Mode, Aspect and Tense refer to the same phenomenon: a stretch of time which is the extension of some events or acts, with a duration and some temporal relationships. But they are related to different kinds of temporality.
Within any extension there are three epochs—beginning, end and a middle point. The beginning is characterized by the fact that the act is about to be realized, the middle by the fact that the act has a part realized and a part not yet realized (and which will perhaps not be realized), and the end by the fact that the act is done. This epochal theory of time is applied first to the mental operation of drawing a time-figure: namely, physical time is usually represented by a line. This line is cut in two parts, the past and the future, which meet in the present, as illustrated in Figure 1.
There is no expression of time at the level of langue, only a representation. This representation allows an expression in the discourse. The passage from the representation in the langue into an expression in a discourse needs some time; Guillaume calls this the operating-time supporting the process of chronogenesis: “Mind needs time to think time” (Lecture, March 4, 1939). The first epoch (the beginning) of the chronogenesis is named time in posse: an indivisible time-figure, it is the moment where the mind is about to draw the time-figure. At this moment, the verb is very close to the noun. The second (middle) epoch is the time in fieri: it is the moment when the mind is drawing the time-figure; there is not yet the division of Past/Present/Future. For the French representation of time, the line drawn at this level is like an eternal present, without past or future. The third epoch is named time in esse: it is the moment when the mind has achieved its time-figure in the state shown in Figure 1. These three epochs are related to the verbal mood: quasi-nominal mood for the first epoch, subjunctive mood for the second, and indicative mood for the third. This last epoch is the only one that inserts the cut of the present, dividing physical time into two unbounded periods, the past and the future. Hence, the mode refers to the stage where the speaker has stopped, inside the chronogenesis, when he made the utterance.
The second type of time is the process time. A verb need also a temporal extension, which can be named process’s coming-to-be. There are two positions for the speaker to look at the process: from its outside, which is the transcendent aspect or from its inner, which is the immanent aspect. The immanent aspect has three divisions, depending of the position inside the process’s coming-to-be: (1) at its beginning; (2) in the middle, that cut the process’s coming-to-be in two parts (one already achieved and one remaining to be achieved); and (3) the end of the process’s coming-to-be. Hence, with respect to process time, the immanent aspect consists in viewing the process as a transparent box, whereas the transcendent aspect consists in viewing the process as a black box. Figure 2 summarizes the situation.
Fig. 2: Immanent/transcendent aspect
The third type of time is the physical time corresponding to the tenses. The process is then situated inside the time-figure (in posse, in fieri or in esse) with respect to some other process(es): the point of speech and/or an other process’s coming-to-be.
We argue that these times are just a support for a linear ordering of the different epochs—that are points on the line—situated with respect to some vision intercepting points, using the two fundamental qualitative (i.e. without measure of any duration) temporal relationships—precedence and simultaneity. We do not get all nature (potential and actual) because we are not able to speak about all the processes. We only get a portion of nature. The equivalence classes of the simultaneity relation over epochs are “perceptible” instants of physical time, ordered by the precedence relation. The order is not linear when future or potential processes are referred to, but there is only one effective linear order. Between two perceptible instants, there can be inserted as many instants as there appear in the discourse. A line can be drawn from one perceptible instant to its follower. Hence the physical time-line can be rebuilt from these perceptible instants, whatever their number be.
4. Guillaume’s and Whitehead’s Construction of Time
Whitehead had, by 1914, applied his method of extensive abstraction to time, presented first in RTS and developed later in PNK and CN.  He showed how a bridge could be constructed between the data immediately given to sensory awareness through a slice of time, which Whitehead called durations, and the temporal moments of conceptual awareness. This method consists in using the relation of inclusion between durations, particularly on some family of durations, named an abstractive class of durations, which is such that (1) of any two of its members, one includes the other; and (2) there are no members that are included in every duration of the collection. Hence, an abstractive set provides the meaning of convergence to an ideal limit (which is not a duration) that yields the fundamental conceptual temporal components, moments.
We claim that Guillaume’s construction of the present as a separation between the past and the future, obtained at the end of the chronogenesis, follows such a method of ideal convergence. We claim also that each point of interception, related to the aspectuality, corresponds to a moment that contains the simultaneity of the perceiver event with the chosen part of the perceived process. Hence, physical time can be constructed from those significant moments, ordered by all the temporal information conveyed by linguistic marks: verb forms, some nouns (predecessor, day), adjectives (earlier, next), adverbs (yesterday, twice), prepositional phrases (at 5:00 pm, for two days), and subordinate clauses (while I was waiting for them), and also with the help of some knowledge of the world (a cause always precedes its effect). These moments forms a linear sequence, which is a chronology, among which any other event can be inserted: either inside an already given moment (in the case this event is simultaneous to one inside this moment) or between two already given moments. We can iterate this insertion of events ad libitum. Hence, physical time is obtained by an iterative procedure of inserting new elements inside a sequence which can begin with only one moment, which is naturally the moment associated with the event of speech, as far as we presuppose a linear ordering of all moments. Any other moment, determined by a temporal relation with the speech, will be either before, after or itself. Two moments of the sequence determine a duration they bound. These durations are qualitative until a system of measurement is given. We have then constructed time from the events described, as Whitehead did in CN and PNK.
Our claim is that this construction has built a linear unbounded dense time, fitting the definition required by Whitehead for the ether, which is a continuum, but that it is not necessary to get the mathematically continuous set of the real numbers, since the set of rational numbers is sufficient for modeling purposes. Moreover, I suggest that Whitehead stayed within Weierstrass’ theory of convergence because of the non-existence of a strongly satisfying theory of infinitesimal, in Leibniz’ sense. This theory was developed exactly one century after Whitehead’s birth, in 1961 by Robinson, and is known as non-standard analysis. In this theory, every standard number—the naturals, rationals and reals—is surrounded by a neighborhood of infinitesimally small numbers, which are smaller than any positive real number. The multiplication of an infinitesimal with any real, no matter how large, is still an infinitesimal. This theory thus provides a notion of moment which is neither punctual nor durative (its diameter is not a real number) but which has a thickness. I believe that this point of view provides a new and fruitful context for Whitehead’s work on time and space.
 Schwer, Traitement de la Temporalité des Discours: une Analysis Situs (forthcoming).
 Linguists are not concerned with the problem of the “now” moment, and of simultaneity with respect to the theory of relativity, since the speeds relevant to linguistic phenomena are far less than that of light. But simultaneity and the notion of “granularity” do give rise to some questions. At a given level of granularity, two processes can be viewed as punctual and simultaneous, but at some finer level of granularity, one process can be viewed as punctual and the other as enduring. Hence, simultaneity comes to include a point inside an interval. Reichenbach used punctual formalism, but this does not mean that he thought every process to be punctual.
 There is a contemporary community of linguists, principally in France, Belgium and Canada who work within the framework of linguistic psychomechanics and are affiliated with the Association Internationale de Psychomécanique du Langage. There is an international congress every three years, the last in Montpellier France, in June 2006.
 The linguist Antoine Meillet (1866-1936) succeeded Ferdinand de Saussure at the Ecole Pratique des Hautes Etudes in 1891 and taught at the College the France from 1906 until 1932. Among his students were Emile Benveniste, Marcel Cohen, Georges Dumézil, Lucien Tesnière, and Joseph Vendryes.
 Leçons de linguistique de Gustave Guillaume, edited by R. Valin, W. Hirtle and A. Joly.
 Principes de linguistique théorique de Gustave Guillaume (henceforth referred to as PLTGG), p. 101.
 Lesson of November 11, 1943.
 Psychosystemics combined with psychosemiotics constitute the psychomechanics of language.
 Guillaume, Temps et verbe, 9. The present has a duration but can be very narrow, and contains a past part (accomplished) and a future part (to come). In the French language, tenses are related to these three periods: Past/Present/Future. In English language, there are only two periods: Past/non-Past, this last covering present and future.
 For this description of the time event, see Hirtle 1975, 26.
 The arrow represents the location of the interception (the speaker’s position) inside the process’ coming-to-be, or outside, in the result phase.
 We here are interested only in the indicative mood. The other moods can be formalized in a similar way and are related to the notion of “point of view” or “reference universe.”
 For details of Whitehead’s developing thought on this theme, see Hurley 1985, 93.
 Of course no one can experience the full scope of the passage of nature, as what we experience are temporally (and spatially) thick chunks of this passage, which Whitehead calls “events.”
Works Cited and Further Readings
Beauzée, Nicolas. 1789. Grammaire générale.
Firth, J. R. 1957a . “Sounds and prosodies,” in Papers in Linguistics 1934-1951 (London, Oxford University Press), 121-28.
Firth, J. R. 1957b . “The semantics of linguistic science,” in Papers in Linguistics 1934-1951 (London, Oxford University Press), 139-47.
Firth, J. R. 1957c . “Personality and language in society,” in Papers in Linguistics 1934-1951 (London, Oxford University Press), 177-89.
Firth, J. R. 1957d . “Modes of meaning,” Papers in Linguistics 1934-1951 (London, Oxford University Press), 190-215.
Fortescue, Michael. 2001. Pattern and Process. A Whiteheadian Perspective on Linguistics (Amsterdam and Philadelphia, John Benjamins Publishing).
Guillaume, Gustave. 1919 Le problème de l’article et sa solution dans la langue Française (Paris, Hachète).
Guillaume, Gustave. 1929. Temps et verbe (Paris, Champion).
Guillaume, Gustave. Leçons de linguistique de Gustave Guillaume, 19ab-19a (b+1), edited by R. Valin, W. Hirtle et A. Joly (Québec, Presses de l’Université de Laval; Lille, Presses universitaires de Lille). These lecture notes are now available online at http://nlip.pcu.ac.kr/gustave/.
Hirthe, Walter H. 1975. Time, Aspect and the Verb (Québec, Presses Université Laval-Québec).
Hurley, Patrick. 1985. “Time in the earlier and Later Whitehead,” in Physics and the Ultimate Significance of Time, edited by David R. Griffin (Albany, SUNY Press).
Reichenbach, Hans. 1947. Element of Symbolic Logic (New York, Macmillan).
Schwer, R. Sylviane. 2002. “S-arrangements avec répétitions,” Comptes Rendus de l’Académie des Sciences de Paris, Série I 334 261-66.
Schwer, R. Sylviane. Forthcoming. Traitement de la Temporalité des Discours: une Analysis Situs (Cahiers Chronos).
Sylviane R. Schwer
Laboratoire d’Informatique de l’université Paris-Nord, UMR CNRS 7030
Institut Galilée/Université Paris-Nord
How to Cite this Article
Schwer, Sylviane R., “Whitehead’s Construction of Time: A Linguistic Approach”, last modified 2008, The Whitehead Encyclopedia, Brian G. Henning and Joseph Petek (eds.), originally edited by Michel Weber and Will Desmond, URL = <http://encyclopedia.whiteheadresearch.org/entries/thematic/language/whiteheads-construction-of-time/>.