Chapter 7: Hartshorne and Peirce: Individuals and Continuity by Manley Thompson

Existence and Actuality: Conversations with Charles Hartshorne
by John B. Cobb, Jr. and Franklin I. Gamwell (eds.)

Chapter 7: Hartshorne and Peirce: Individuals and Continuity by Manley Thompson

Manley Thompson is professor philosophy at the University of Chicago..

Peirce scholars are indebted to Charles Hartshorne not only for his work in coediting with Paul Weiss the first six volumes of the Collected Papers of Charles Sanders Peirce,1 but also for three stimulating papers on Peirce’s theory of categories.2 In the second of these papers (1964) Professor Hartshorne argues that ‘Peirce’s greatest single mistake . . was his ‘Synechism’, which consisted in trying to make continuity the key principle to every relationship, both of actuality and possibility" (MR, 467). This same theme is argued again in the most recent paper (1980). I want to explore briefly Peirce’s use of continuity in his account of individual existence and then to review this account in the light of Professor Hartshorne’s criticisms.


"Our initial hypothesis,’’ Hartshorne declares, "should be that actuality is discrete, but with our minds open among the unlimited conceptual, but mutually incompatible possibilities for discontinuity,"; Peirce, on the contrary, "wanted actuality . . . to be continuous" (M, 286). Yet as Hartshorne, of course, realized, Peirce clearly wanted it both ways. Actuality is in a sense discrete and in a sense continuous. As Pierce developed his position, actuality or existence is the mode of being of individuals as opposed to reality, which is the mode of being of universals. According to his preferred definition, "an individual is something which reacts" (3.6l3).3 Actuality (existence, secondness) consists in reactions, and reactions as instantaneous must be discrete. After giving his preferred definition of an individual, Peirce remarks that it is no objection to the definition that it makes an individual unintelligible, for an individual is unintelligible in the sense proclaimed by the definition. As he declares about this time (1902-3), in another context, "An existing thing [an individual] is simply a blind reacting thing to which not merely all generality, but even all representation is utterly foreign" (5.107).

The unintelligibility of individuals as discrete existences is emphasized again and again in Peirce’s later writings, and he was well aware that with this position he was left with the problem of explaining how we can ever talk about individuals -- how we can ever represent them. We experience them through sensations of brute reaction, and these sensations are not re-presentable. I am groping my way about in the dark. My outstretched hand meets a solid object that resists further forward movement of my arm. The resistance that I feel -- the sensation of reaction -- is something absolutely discrete and individual. When I put my withdrawn arm forward a second time, I may say I feel it again, but the "it" in this case refers to the object I take to be causing the resistance and not to the sensation of reaction I felt a moment before. In judging that I feel the object again, I assume that the object, unlike my initial sensation of reaction, continued to exist during the interval between my first and second sensations. I say that I had different sensations of the same individual object. I have thus said something about an individual and not merely experienced it through sensations of reaction, but I have done so only by invoking continuity as well as discreteness. I represent the individual as having continued existence through time while my sensations of reacting with it remain instantaneous and discrete. My representation is cognitive, intelligible, judgmental. It may be false. The object I felt the second time may not be the object I felt the first time, no matter how short the interval between my two sensations. But my sensations are noncognitive, unintelligible, nonjudgmental. They are neither true nor false; they simply are. An individual taken simply as that which reacts is simply that which is experienced in a sensation of reaction. As such it is unintelligible, unrepresentable.

Peirce seems to have had considerations like the above in mind when, after defining an individual as something which reacts, he went on to proclaim that "everything whose identity consists in a continuity of reactions will be a single logical individual" (3.613). If the identity of an individual consists in its reactions, it retains its identity -- remains one and the same individual -- only to the extent that it continually reacts. My judgment that I felt the same individual twice can be tine only if the individual retains its identity during the interval that separates my two sensations. But I can represent it as thus retaining its identity only by thinking of it as continuing to react during the interval, even though it is not reacting with me. For my judgment implies that if I had put my arm forward at any point during the interval I would have reacted with the object at that point. The object was then reacting with something (with the air or other objects in its surroundings) and it would still have been reacting with me if I had been in an appropriate position. If I think of the object as having ceased to react during the interval, I think of it as having ceased to exist, and I must then judge that my second sensation is of a different object.

Murray Murphey finds Peirce’s declaration that individual identity consists in a continuity of reactions to be inconsistent with ‘‘either the definition of reaction or of continuity -- there cannot be a continuum of instantaneous events."4 Peirce, of course, entertained different definitions of continuity, and his views on the subject changed. When he gave his definition of individual identity, the view of continuity he had in mind would seem to be the "common sense" one he came to through a modification of Kant’s definition ‘‘that a continuum is that of which every part has itself parts of the same kind" (6.168). While this definition, Peirce adds, "seems to be correct . . . it must not be confounded (as Kant himself confounded it) with infinite divisibility." For it "implies that a line, for example, contains no points until the continuity is broken by marking the points." It thus ‘‘seems necessary to say that a continuum, where it is continuous and unbroken, contains no definite parts; that its parts are created in the act of defining them and the precise definition of them breaks the continuity.’’ Peirce ends the paragraph by remarking that this ‘‘common sense idea of continuity" is not that found in "the calculus and theory of functions," according to which continuity "is only a collection of independent points."5

Whatever Peirce meant by declaring individual identity to consist in a continuity of reactions, he did not mean that it consists in a collection of independent reactions. The point is not that each reaction consists of shorter reactions, or that between any two reactions there is always a shorter. Infinite divisibility in this context can never yield more than a collection of independent reactions. The point is rather that indicated by a remark he makes to underscore his contrast between the common-sense idea of continuity and that found in the calculus and theory of functions. "Breaking grains of sand more and more will only make the sand more broken. It will not weld the grains into unbroken continuity" (6.168). Peirce wants a notion of individual identity according to which reactions are welded into unbroken continuity.

The inconsistencies Murphey finds in Peirce’s attempt to define individual identity are unavoidable if one begins with the assumption that the identity of an individual consists in a collection of independent reactions. The infinite divisibility of every item in the collection will not weld the items into an unbroken continuity that constitutes the identity of an individual. Peirce, as I read him, never made this assumption. The assumption he made instead is that the existence of an individual, but not its individual identity, consists simply in reaction, opposition, pure secondness. "[T]he mode of being of the individual thing is existence; and existence lies in opposition merely" (1.458). An individual in its mode of being is thus unintelligible; it is experienced, bumped up against, reacted with, but never cognized as an identical object. Cognition always involves thirdness, the mode of being of a universal or general idea. While ‘‘a reaction may be experienced . . . it cannot be conceived in its character of a reaction; for that element evaporates from every general idea" (3.613). Yet this is not to say that we have no concept of individual existence, that we cannot conceive of it in general. ‘Existence, though brought about by dyadism, or opposition, as its proper determination, yet, when brought about, lies abstractly and in itself considered, within itself" (1.461, Peirce’s emphasis). We thus come to the concept of "numerical identity, which is a dyadic relation of a subject to itself of which nothing but an existent individual is capable." This identity, unlike that "of a quality with itself" is not "empty verbiage" but "a positive fact." Red is always red and never anything else, but an individual that is now red may change its color. Yet, no matter how much its qualities change, an individual does not lose its numerical, its individual, identity. "Throughout all vicissitudes its oppositions to other things remain intact, although they may be accidentally modified; and therein is manifest the positive character of identity."6

The subtle point Peirce seems to be urging here is the difference between experiencing individuality (existence, actuality) and conceptualizing that experience. As experienced, individuality is simply a sensation of brute reaction, and as such it is unintelligible. As conceptualized it is simply that which reacts, an individual, and as such it is intelligible as that which remains numerically one and the same throughout its reactions. This is not to say, however, that since an individual retains its identity whatever its reactions may be, its identity is intelligible without reference to its reactions. Existence consists in reaction, and an individual maintains its identity only as long as it exists. But since it always exists through a time and reactions are instantaneous, its identity is not that of a single reaction. But then how is a collection of reactions welded into a single individual?

For Peirce, this is like asking how a collection of points is welded into a single line. The question is put the wrong way round. One begins with the notion of a line and asks how it consists in a collection of points. The answer then is that the identity of a line consists in an unbroken continuity of points, but that none of its properties is determined until certain of its points are actually fixed, e.g., by specifying numbers or laying down certain conditions for a geometrical construction. There is no question about how the points once they are fixed are welded into a line. One begins with the concept of line identity and fixes points in order to determine properties of a particular line. When two points are fixed, the identity of the line connecting them consists in an unbroken continuity of intervening points. As such, the points on the line are already welded into a line and actually fixing any of them simply breaks the continuity. It is senseless to ask how these fixed points are welded into a line, for there is no question of constructing the line out of fixed points but only of fixing points on the line. It is of course impossible actually to fix them all, even with the completion of an infinite enumeration, since their multitude is nondenumerable. The properties of a line are determined only by fixing points. But its identity as a line does not consist in a continuity of fixed points; it consists in the unbroken continuity of all the points on the line.

In this geometrical illustration, a point by itself apart from the concept of a line is unintelligible. It is the geometrical analogue of a reaction. Just as one has first the concept of line identity and then fixes points in order to determine properties of a particular line, one has first the concept of individual identity and then experiences a reaction that determines properties of a particular individual. When my outstretched hand meets a solid object as I grope my way about in the dark, the reaction fixes a "point" in my spatial environment. I already have the concept of individual identity. The reaction I experience is individual and discrete; as such it is unintelligible. But through the concept of individual identity, I conceptualize the experience as an encounter with an individual existent.

It is not necessary for this conceptualization that I experience more than a single reaction and then judge that I encountered the same object twice. The conceptualization is not simply an objectification of the sensation of reaction, merely the conceiving of this sensation as a single instantaneous object. The sensation itself is not the object with which I react, but something in me and not something outside of my consciousness that opposes me. To take the conceptualization in question here as simply the objectification of the sensation would be to conflate what Peirce called ‘‘the feeling-element of sense with ‘‘the compulsion, the insistency, that characterizes experience" (6.340). With conceptualization merely of the feeling-element, I could say only that I felt hardness or solidity. I could not say that I felt a hard or solid individual object. In conceptualizing the object I cannot take its individual identity to consist in its hardness, solidity, or any other quality. The qualities of an individual, "however permanent [and peculiar] they may be, neither help nor hinder its individual existence . . . they are but accidents, that is to say, they are not involved in the mode of being of the thing; for the mode of being of the individual thing is existence; and existence lies in opposition merely" (1.458).

To conceptualize the object merely as that which stands in opposition to me -- to my sensation -- I must conceive of it as opposed to sensation in a respect that is both basic to sensation and yet has nothing to do with sensory qualities. The only thing basic to sensation apart from its feeling-element is the respect in which it involves a sense of reaction, and in this respect "it does not involve the sense of time (i.e. not of a continuum)" (8.41). It is sensed as discrete and instantaneous. The respect in which I conceive of an individual object as distinct from my reaction with it is then that I conceive of the former but not the latter as retaining an identity through time. When I judge on the basis of a single reaction that there is an object there in the dark I have bumped against, I must apply the concept of individual identity as consisting in a continuity of reactions. I cannot conceive of the identity of the object as consisting in the single reaction I experienced, for a single reaction as such is unintelligible. Individual existence is intelligible, as opposed to being merely experienceable, only as something that persists through time. And this persistence is intelligible only as a continuity of reactions; a collection of discrete reactions can never be welded into an individual identity.

Actuality or existence is thus discrete in the sense that "the compulsion, the insistency, that characterizes experience" is discrete, but it is continuous in the sense that an individual existent retains its identity through time. It seems to me that Peirce’s use of continuity in his account of individual existence as I have sketched it is open to some but not to all of the criticisms Hartshorne has urged against it. I turn now to these criticisms.


Hartshorne objects (1) that although Peirce "had an ontology of relations in the idea of relative actualities, he lacked any definite terms or subjects for the relations. There seems to be a succession of experiences, but (if the succession is a continuum) there are no single experiences" (M, 286); (2) that Peirce "fell into a subtle but complete mistake" when he held that since "continuity leaves open possibilities which discontinuity excludes . . . the burden of proof is upon discontinuity" (MR, 467-68); (3) that ‘‘he could not, in the continuum of becoming which he posited, give meaning to the idea of a definite single event" (M, 287).

(1) The first objection, I think, is the one against which Peirce has the clearest defense. The succession of experiences is discrete as a succession of sensations of reactions, and there are single experiences in this sense. But as single the experiences are unintelligible. Intelligibility is obtained through the concept of individual identity as consisting in a continuity of reactions. With this concept Peirce could account for definite singular terms in general, though he could not with his "pragmaticistic"7 theory of meaning distinguish one such term from another as he could distinguish one general term from another. ‘[I]t must be admitted," he wrote, "that pragmaticism fails to furnish any translation or meaning of a proper name, or other designation of an individual object" (5.429). Yet this failure does not prevent the pragmaticist from granting "that a proper name . . . has a certain denotative function peculiar to that name and its equivalents’’ and ‘‘that every assertion contains such a denotative or pointing-out function." While this function "in its peculiar individuality" must be excluded from "the rational purport of the assertion . . . the like of it, being common to all assertions, and so, being general and not individual, may enter into the pragmatistic purport." The generality intended here is supplied by Peirce’s concept of individual identity. His next sentence is: "Whatever exists, ex-sists, that is, really acts upon other existents, so obtains a self-identity, and is definitely individual.’’

The denotative function of a proper name that enters into the pragmaticistic purport (the intelligibility) of every assertion is the function performed in quantificational logic by individual variables. When a variable is replaced by a proper name or other designation of an individual, no new element of intelligibility is added. The function performed by individual variables in general is then performed by one symbol in particular. It is the function of singling out a subject of which a certain general term or predicate is true. The function is the same whether the subject is any, at least some one or other, or only a single individual. What is singled out is intelligible not as an individual in its individuality (what Peirce sometimes called a "hecceity"8 but only as that which continually reacts through a period of time and thereby remains one and the same.

With this denotative function common to all assertions Peirce has a way of accounting for definite terms or subjects for relations. Complications arise when an individual is considered to be spatial as well as temporal. But these complications relate to Hartshorne’s third objection, and I will postpone consideration of them here.

(2) Peirce’s defense against the second objection, that he fell into a subtle but complete mistake when he thought the burden of proof was with discontinuity, lies in his use of Kant’s distinction between what is constitutive and what is merely regulative of experience. In the passage Hartshorne cites, Peirce is concerned with proclamations of discontinuity as assumptions that "block the road of inquiry" (1.170). His examples are the questions of how one mind can act on another and how one particle of matter can act on another at a distance from it. He objects to what he calls the "nominalistic" assumption that, because there is ultimate discontinuity between one mind and another, and between one particle and another, these questions are absolutely unanswerable. He acknowledges that, with the state of physics at the time of his writing (c. 1897), we can only say "that we know that one thing does act on another but that how it takes place we cannot very well tell." But this uncertainty in no way licenses the assumption that, since we have not succeeded in telling exactly how they act on each other at a distance, particles of matter must be ultimately discontinuous. Such an assumption blocks the road of inquiry, whereas the assumption that all particles of matter may be continuous leaves the road open to the possibility of eventually explaining action at a distance, starting with the hypothesis "that one portion of matter acts upon another because it is in a measure in the same place."

Peirce remarks in the next paragraph: "The principle of continuity is the idea of fallibilism objectified. For fallibilism is the doctrine that our knowledge is never absolute but always swims, as it were, in a continuum of uncertainty and of indeterminacy. Now the doctrine of continuity is that all things so swim in continua" (I. 171, Peirce’s emphasis).

From these remarks, it would seem that fallibilism is the regulative principle that no hypothesis should be regarded as absolutely determinate and certain, while the doctrine of continuity, or "synechism," as Peirce usually called it, is the corresponding constitutive principle that the things constituting reality are never absolutely determinate and discrete. But this view conflicts with a later statement (1902): "Synechism is not an ultimate and absolute metaphysical doctrine; it is a regulative principle of logic, prescribing what sort of hypothesis is fit to be entertained and examined" (6.173). I do not think the conflict here is serious. The word ‘fallibilism’ occurs in the Collected Papers as the expression of a doctrine only in 1.171 and in another fragment (1.8-14) of the same date (c. 1897), and I have never seen the word used in this way in writings not included in the Collected Papers. Even in 1. 170 Peirce advocated the assumption of continuity in things (minds and particles of matter) because it avoided blocking the road of inquiry. He did not also claim that it was metaphysically true. So even here the assumption is, in the Kantian sense,9 regulative of inquiry rather than constitutive of experience. Constitutively, experience is discrete; it is constituted by sensations of brute reaction. But as such it is unintelligible. Intelligibility arises only when reactions are followed by judgments concerning what is experienced, and judgments as regulated by the principle of continuity are always fallible. The judgment that one particle of matter is spatially separated from another may be true in a sense but false when taken as implying an absolute separation in reality.

Although Peirce’s use of the regulative/constitutive distinction may provide a reason for his belief that the burden of proof is with discontinuity, I think there is more than a use of this distinction underlying Hartshorne’s charge that with the belief Peirce fell into a subtle but complete mistake. The further issue, however, seems to me best approached in the light of Hartshorne’s third objection.

(3) In discussing the first objection, I remarked that complications arise with Peirce’s account of definite terms or subjects for relations when an individual is considered to be spatial as well as temporal. After declaring that "everything whose identity consists in a continuity of reactions will be a single logical individual," Peirce explained: "Thus any portion of space, so far as it can be regarded as reacting, is for logic a single individual; its spatial extension is no objection" (3.613). But how is a portion of space to be determined, and how are we to decide when it can be regarded as reacting? A few sentences later Peirce remarks that "space is nothing but the intuitional presentation of the conditions of reaction, or of some of them." This remark suggests a Kantian position according to which space is the form of Outer sense. Whatever is outer, external to my consciousness, and therefore capable of reacting against me, is spatial. As long as my outstretched hand continues to encounter resistance as I move it about spatially, I determine a portion of space I regard as reacting and judge to be a single individual.

Peirce never accepted just this Kantian position, but he remained close to it. While he rejected the view that space and time are forms of intuition, he retained the Kantian notion of outer and inner sense corresponding, respectively, to space and time (cf. 8.41, 8.330). He thus was prevented by his philosophical position from conceiving of space-time as a four-dimensional continuum. Peircean individuals, like Newtonian and Kantian particles, are located in space and time, not in space-time. I see no defense for Peirce against Hartshorne’s third objection, that he could not give meaning to the idea of a definite single event. For the idea Hartshorne intends here, I think, is that of an event in space-time, and Peirce could give no meaning to this idea because in his philosophy he lacked any notion of space-time. I suggest that it is to the reason for this lack rather than, as Hartshorne avers, to an "uncritical love for continuity" (M, 286), that we should look when we want to account for Peirce’s failure to develop the idea of a definite single event. I will return to this point shortly.


I remarked that I think there is more than a use of the regulative/constitutive distinction underlying the objection that Peirce places the burden of proof on discontinuity. The further issue is the basically epistemological and Kantian orientation of Peirce’s philosophy, early and late. Like Kant in his critical period, Peirce’s initial philosophical stance is that of a knower with human cognitive faculties for processing given input into cognitions of reality. Reality is then what is represented in the final output of the unlimited community of such knowers. But then how is the reality of the original unprocessed input to be explained? If this input has no contact with reality, if it is not in itself real, how can any processing of such input, even when indefinitely prolonged, result in a representation of reality?

These questions present no special difficulty if one’s philosophical stance is external to the human knowers one is considering as subjects; if, in other words, one speaks of knowers only in the third person. Original input is then simply the stimulation of a subject’s sensory receptors; there is no question of its reality because it is in direct causal contact with reality. Nor need there be a question of how the subject is conscious of the stimulations, since with a third-person perspective one may remain a radical behaviorist and agree with Quine: "What to count as observation now can be settled in terms of the stimulation of sensory receptors, let consciousness fall where it may."10 But the question of consciousness can of course not be dismissed when the philosophical stance is that of oneself as a human knower; and if cognitive consciousness is always the result of processing an input, as it appears to be with Kant’s doctrine of synthesis, consciousness of the input cannot be a cognition of reality. Any such cognition from this first-person perspective will be output. As Barry Stroud has put it recently, ‘‘In my own case I have nothing but ‘output’ to work with."11

In his early papers on cognitive faculties, Peirce held that every cognition was determined by a previous cognition. There was thus only output. He argued that the assumption of an absolutely first cognition (one not determined by previous cognitions) is no more required to account for the fact of cognition than the assumption of an absolutely first distance to be traversed is required to account for the fact that Achilles overtakes the tortoise (cf. 5.263). The argument leaves untouched the question of how a cognition is ever in contact with reality and not just with previous cognitions. With regard to this argument alone, it might seem plausible to think of Peirce as misled by an uncritical love for continuity. He seems to have seen only the logical problem of accounting for the completion in a finite time of a process for which it is impossible to specify an absolutely first beginning. He missed entirely the epistemological problem of explaining how cognition is initially in contact with reality. But if it was from an uncritical love of continuity that he missed the problem, it was also from a love of what he regarded, by the time had come to see the problem, as a confusion of infinite divisibility with tine continuity.12

In Peirce’s later philosophy, cognition is initially in contact with reality via a perceptual judgment, which is "the cognitive product of a reaction" (5.156). As we have already noted, reaction in its mode of being as an existent is unintelligible. What is intelligible is not its existence but its individual identity as consisting in a continuity of reactions. Yet the continuity here is not the infinite divisibility of discrete items in a collection but the unbroken continuity that welds the items into the identity of an individual. Continuity in this sense is regulative of experience which, constitutively, is discrete, being nothing but sensations of reactions. Input as input is simply the brute reaction of experience; its contact with reality is immediate, for existence simply consists in reaction. But any judgment as to individual identity is output and is regulated by its principle of continuity.

With a basically metaphysical stance, on the contrary, what is viewed constitutively is not experiential contact with reality but reality itself. Reality is then constitutively continuous as possibility or potentiality, but in actuality it is discrete. To place the burden of proof on the assumption that there is ever discontinuity is then tantamount to skepticism as to whether there is any ultimate actuality -- whether there is a real external world as opposed to the infinite possibilities realizable in thought. This attitude toward discontinuity inevitably appears as skepticism when one begins with a metaphysical stance that takes a real world of existing actualities as given. The reverse is the case, however, with Peirce’s epistemological stance. Nothing existential is given but sensations of reaction that give rise to cognition of reality. With this cognition, reactions are welded into a continuity of reactions constituting an individual identity, and an individual is cognized as instantiating a real universal or law. The reality of a law does not consist in a collection of independent individuals any more than a line consists in a collection of independent points. A real law, like a line, is an unbroken continuum.13 Ultimate discontinuity, with this epistemological stance, is ultimate inexplicability, brute facts unrelated by laws. Any hypothesis of ultimate discontinuity blocks the road of inquiry and appears as dogmatic skepticism -- -a proclamation of absolutely unknowable reality. Hypotheses of this sort are excluded from inquiry regulated by synechism.

It is not enough with Peirce’s epistemology to say merely that "an individual is something which reacts." The essential point epistemologically is "that it might react, or have reacted, against my will" (3.613; cf. 8.41). It is only as it reacts against my will (e.g., my will to move straight ahead in the dark) that I receive input from which I construct cognitions that for me determine reality. As reacting against my will, an individual must exist external to me, and I must therefore conceive of it as located outside my consciousness. This location cannot be temporal, for its reaction against my will and the sensation I internally experience occur at the same time. As external to me, it must have spatial location; it must be "a portion of space" that ‘‘can be regarded as reacting." When I conceive of its individual identity as consisting in a continuity of reactions, I am conceiving of a portion of space continually reacting.14

If I were to say instead "a portion of space-time," I would have no way to draw the epistemological distinction between internal and external that is central to the Kantian orientation of Peirce’s philosophy. If I were to conceive of both myself and the object as world-lines in space-time that intersect on the occasions when the object reacts against me, I would view myself as an object in the world of existents and there would be nothing external to me in the epistemological sense of an external world. I would have no reason to conceive of the object as having an identity consisting in the continuity of the reactions of a portion of space while I conceived of my own identity quite differently.15 I would have the idea of a definite single event as an event in space-time, and I could conceive of both my own identity and that of the object as consisting in a collection of events. Though discrete, the events would not be independent but internally related, for unlike Peircean reactions and mathematical points they would not be in themselves unintelligible. Such events through their internal relations are "welded into an individual identity," to borrow Peirce’s language. There is no need to conceive of the identity as consisting in an unbroken continuity -- as something whose mode of being is distinct from the mode of being of the events. The fact that Peirce conceived of individual identity in this way is not, I would urge, simply the result of an uncritical love for continuity. It is rather the result of a basically Kantian orientation that permeated his philosophy and rendered the notion of space-time foreign to his thought.

I want to close with some brief comments in which I expand a bit on what I mean by a Kantian orientation and its philosophical consequences.


I do not intend by my remarks about space-time to imply that, if Peirce had known relativity physics, he would have given up his notion of individual identity as consisting in a continuity of reactions and accepted the idea of a definite single event as intelligible by itself. I do not know whether he would have done this or not, since I believe that with his pragmatism he might have accommodated relativity physics without altering his epistemology, though I cannot go into the question here.16 What seems to me clear is that the philosophical issues underlying Hartshorne’s criticisms of Peirce cannot be settled by theories of physics or the mathematics of continuity. I will try to give some indication of what I mean, starting with a few remarks by Whitehead.

In the Preface to Process and Reality Whitehead declared that "in the main the philosophy of organism is a recurrence to pre-Kantian modes of thought."17 Later in the work he explained: ‘‘The philosophy of organism is the inversion of Kant’s philosophy. The Critique of Pure Reason describes the process by which subjective data pass into the appearance of an objective world. . . . For Kant, the world emerges from the subject; for the philosophy of organism, the subject emerges from the world."18 With Peirce’s pragmatic definition of reality, the world emerges from the inquiry of the unlimited community. But such inquiry presupposes individual inquirers who process given input into cognitive output that to some extent represents a determination of reality. The concept of individual identity as consisting in a continuity of reactions functions as a regulative principle for the process that renders the output (ultimately the world) intelligible. In the pre-Kantian philosophy of Plato and Aristotle, individual substances have specific identity by participating in or being essentially constituted by intelligible form, and rational subjects emerge (are actualized) in the apprehension of such form. The apprehension constitutes the actualization of the subjects but not of the world.

There are, to be sure, aspects of Peirce’s philosophy that appear to represent a return to pre-Kantian modes of thought, notably his "scholastic realism." But his is a unique sort of scholastic realism; its orientation is epistemological rather than metaphysical. Real universals are defined with reference to the output of scientific inquiry rather than to the input that makes such inquiry possible. Pace Whitehead, Peirce has real universals emerging from inquiry rather than inquiry emerging from real universals. His "scholastic realism," despite appearances to the contrary, hardly represents a return to pre-Kantian modes of thought. I think a similar remark holds for his cosmic evolution, his logic of events, his objective idealism, and other parts of his metaphysics, although I admit that the point needs to be argued.

The notion of space-time is not difficult to fit into pre-Kantian modes of thought. In a recent elementary text on relativity physics, the author begins with space-time as "the collection of all possible events" and proceeds to develop the notion first in terms of what he calls "Aristotelianized spacetime."19 I have difficulty conceiving of Kantianized space-time, and I suspect Peirce would have too. But I do not think the philosophical issues concerning the epistemological role Kant assigned to space and time as forms, respectively, of outer and inner sense, are simply resolved by introducing the notion of space-time in physics. Whether in philosophy one should conceive of actuality as comprising individuals that maintain their identity in portions of space continually reacting through time, or as comprising events in space-time, is not a question of physics or of mathematics. Hartshorne’s criticisms of Peirce seem to me to assume that the second alternative is the philosophically sound one.


1. Charles Hartshorne and Paul Weiss, eds., The Collected Papers of Charles Sanders Peirce (Cambridge, Mass.: Harvard University Press, 1931-58). Volumes 7 and 8 were edited by Arthur W. Burks.

2. "The Relativity of Nonrelativity: Some Reflections on Firstness," Studies in the Philosophy of Charles Sanders Peirce, ed. Philip P. Wiener and Frederic H. Young (Cambridge; Mass.: Harvard University Press, 1952), pp. 215-24. "Charles Peirce’s ‘One Contribution to Philosophy’ and His Most Serious Mistake," in Studies in the Philosophy of Charles Sanders Peirce, second series, ed. Edward C. Moore and Richard S. Robin (Amherst, Mass.: University of Massachusetts Press, 1964), pp. 455-74. References to this paper are given in the text as MR followed by page number. "A Revision of Peirce’s Categories,’’ Monist 63, no. 3 (1980):277-89. References to this paper are given in the text as M followed by page number.

3. This reference is to volume 3, paragraph 613 of the Collected Papers of Charles Sanders Peirce. All references in the text to this work are given in this fashion. In contrast to his preferred definition, Peirce gave a "more formal’’ one: "an individual is an object (or term) not only actually determinate in respect to having or wanting each general character and not both having and wanting any, but is necessitated by its mode of being to be so determinate’’ (3.611). I have discussed these two definitions in "Peirce’s Conception of an Individual," in Pragmatism and Purpose: Essays Presented to Thomas A. Goudge (Toronto: University of Toronto Press, 1981), pp. 133-48.

4. Murray G. Murphey, The Development of Peirce’s Philosophy (Cambridge, Mass.: Harvard University Press, 1961), p. 398.

5. Peirce elsewhere referred to this mathematical idea of continuity as yielding a ‘‘pseudo-continuum." Cf. 6.176.

6. In his logical algebra and logical graphs, Peirce regarded identity as a second intentional relation (cf. 2.315, 2.548, 3.398, 3.490, 4.80 ff.). But he never confused this logical notion of identity ("things are identical" when every predicate is true of both or false of both’’ [3.398]) with the notion of individual identity through time, which is at issue here.

7. In his later writings (1905 and afterwards) Peirce sometimes referred to his own position as ‘‘pragmaticism" to distinguish it from what James and others were calling "pragmatism." Cf. 5.414.

8. Hecceities are "determinations not of a generalizable nature" (3.612).

9. That Peirce had Kant in mind when he spoke of a regulative principle is indicated by his reference to Kant in 3.612.

10. W. V. Quine, Ontological Relativity (New York: Columbia University Press, 1969), p. 84.

11. Barry Stroud, "The Significance of Naturalized Epistemology," Midwest Studies in Philosophy, VI, ed. Peter A. French, Theodore E. Uehling, Jr., Howard K. Wettstein (Minneapolis: University of Minnesota Press, 1981), p. 464.

12. Cf. 6.168, where Peirce says he himself initially fell into Kant’s confusion of continuity with infinite divisibility.

13. I have discussed this point in "Peirce’s Verificationist Realism," Review of Metaphysics 32, no. I (1978):74-98.

14. I ignore here the question of motion, which requires identifying portions of space in a way that allows for change of relative position. Such identification must be given by scientific laws. I consider this question in my "Peirce’s Verificationist Realism."

15. Cf., e.g., the remarks on the nature of a person in 5.421 and the remarks in 6.338 beginning: ‘‘All thought is dialogic inform."

16. I have in mind passages like 5.496, in which the relations between metaphysics and epistemology are reassessed in the light of pragmatism.

17. A. N. Whitehead, Process and Reality (New York: Macmillan,

1929), p. vi.

18. Ibid., pp. 135 -- 36.

19. Robert Geroch, General Relativity from A to B (Chicago: University of Chicago Press, 1978), p. 11.

Response by Charles Hartshorne

Manley Thompson has chosen to deal with an extremely subtle aspect of Peirce’s philosophy. So far as I can judge, his account of Peirce’s view is essentially faithful to the evidence in Peirce’s writings. Peirce did make use of a rather unusual notion of individual identity as analogous to a continuous "line," a continuity, of reactions. Continuity here means, as Thompson says, "containing no definite parts," such as points. Now this is why I have trouble finding in Peirce’s doctrine definite terms for definite spatial or temporal relations. If individual X reacts now to a remembered past experience (as in what Peirce calls immediate memory), it is the individual now that reacts to the individual then. But with continuous change what is the now? A point-instant? Thompson’s discussion seems to limit "reaction" to transactions with simultaneous or contemporary entities; but Peirce as I read him allows memory (as in surprise) to instantiate secondness or reaction.

The lack of definite parts is the reason for Peirce’s denial that we ever, in a single definite experience, intuit or know a single other definite experience. Hence his rejection of the claim to immediate intuition. Always we are remembering an infinite series of remembering of remembering of . . . whatever we want to intuit, no matter how close to the present it is. And always, if we first intuit red and then yellow, we have, in any finite time, however short, gone through a continuum of intermediate hues. It is such contentions that seem to me to indicate an attachment to continuity. Thompson may be right, and I believe he is, that Peirce had other reasons or inclinations (including an influence of Kant) supporting his conclusion; but it is demonstrable from his own language in praise of the wonders of continuity that he did have this reason. So did his father, as the latter’s philosophical writings show.

It is hardly mere coincidence that Peirce not only had no encounter with quantum theory, with its emphasis on discontinuity, but that he did not want physics to develop any such theory. He tried to derive indications from his philosophy concerning suitable further developments in physics. This was to be one of the tests of the philosophy. Yet he never dreamed of anything like quantum physics. This is all the more remarkable in that it was the introduction of quanta which first caused physicists generally to take seriously the idea, so courageously defended by Peirce, of a tychistic or random aspect of the physical world. As Thompson says, Peirce had an argument favoring his synechism: since all things swim in continua, measurement is inevitably inexact, more or less indefinite or approximate, so that absolute determinism could never be observationally confirmed. I see a subtle error here. True, where continuity is in question, exact measurement is out of the question, whereas quanta can in theory be counted. However, the combination of quanta and continuity is, if possible, even more obviously recalcitrant to exact observation than either is alone. And the point is that laws, to be useful, must deal with possibilities as well as actualities, and the ultimate possibilities are, as Peirce rightly says, continuous. The wave functions of quantum theory illustrate this.

Consider light reflection. The amount of light going through a glass depends on the angle of incidence. The angle can presumably vary continuously. Alter the angle slightly, and more or fewer photons will be reflected in a given time; alter it sufficiently slightly, and it may not be enough to cause a single added or subtracted photon. What it will do is alter the probability of such an addition or subtraction. Consider the all-or-none law in neurology. Alteration in the forces at a synapse means either no change, or a fixed finite amount of change, beyond the synapse. Again, the law must be a probability law as to the number of discharges, each of fixed amount. Still again, an atom of uranium decays into an atom of lead -- when? No law prescribes the time for a single atom. But half of a large collection of such atoms will decay in a time fixed by the law. Probabilistic causality fits the case, not classical causality. Did Peirce realize this consequence of quanta? It favors his tychism at least as well as his synechistic view does.

Thompson mentions another argument that I consider fallacious -- that continuity allows for all possibilities, whereas discontinuity excludes some possibilities, so that we should initially approach reality with the completely open idea of continuity. But sheer continuity excludes an infinite variety of possible discontinuities and is thus the most exclusive view of all, unless discontinuity is simply impossible, inconceivable. Peirce himself in "The Logic of Continuity" seems to argue that it is primordial possibility that is continuous and that actualization consists in introducing some kind of discreteness, as when we draw a chalk line on a continuous blackboard.

I am puzzled by Thompson’s suggestion that Peirce can talk about definite experiences as sensations of reaction, whereas the continuity is in the reactions, not the sensations. Would Peirce’s argument against definite intuitions then not hold?

Thompson is right of course that synechism was put forth by Peirce as regulative, not constitutive. The arguments given were indeed for it as regulative, yet even as such the arguments seem misleading. The very idea of atomism, so immensefully fruitful in the history of science, was always a kind of departure from synechism, so far as I can see. I suspect the better regulative principle is to seek the right combination of continuous possibilities and discrete actualities. The wave-particle complementarity seems to indicate what this amounts to. "Wavicle" is perhaps a good term for the idea.

The important argument for synechism -- that merely discrete entities cannot intelligibly influence each other -- is not necessarily unambiguous in excluding all discreteness. We have here the question of internal relations. It is of first importance not to forget that Peirce is definitely and unambiguously committed both to external and to internal relations. His definition of firstness is one of the most precise definitions in the literature of the idea of external or nonconstitutive relation, and the definition of secondness is equally precise as definitive of internal or constitutive relations, except for the arbitrary limitation to dependence upon just one other entity. In my revision of the categories I remove this limitation. Events, as I construe Peirce (also Whitehead), depend on their predecessors; perhaps they depend also on their contemporaries (Peirce is less clear as to that), but not on their successors. Relations to the future are not to particular later events but to more or less general aspects of the future as expressed by probabilistic laws, laws tolerant of a tychistic aspect. Peirce suggests that things are where they act, but it does not follow that things act, or are, everywhere throughout space and time. We cannot act on our remote ancestors, and are not in their world at all, though they are in ours, which is why we can talk about them as they could not about us.

Peirce was an immense genius, but he was a physicist perched in a world with a physics about to change to the foundations. Thompson wrote in his book on Peirce that Peirce’s idea of existence calls for clarification in the direction of an Aristotelian or similar conception of individual substances. I agree that clarification is needed, but perhaps it should be in a less traditional direction, or, taking the Orient into account, in a more Buddhistic direction, into a clear doctrine of change as succession of acts of becoming, not instantaneous but unitary.

Peirce’s phrase "the logic of events’’ points forward to contemporary physics and Whitehead, as much as, if not more than, back to Aristotle or other pre-quantum thinkers. Note, too, that Peirce greatly admired Buddhism and made declarations that in some ways are the most nearly Buddhistic to be found in American philosophy before Whitehead. Here the influence of synechism was relatively helpful. We are, as Saint Paul had it, "members one of another."

A strong argument against unqualified synechism is given by Von Wright. Peirce himself somewhere says that an individual is determinate, conforming to the law of excluded middle as to predicates; but he also says, and by his tychism must say, that according to this definition there are no individuals, strictly speaking. Now Von Wright argues that continuous change makes it impossible to have any wholly definite actuality. In any time, however short, a subject will be first P and then not-P, with respect to some predicate or other. With continuous change, only in an instant could this contradiction or violation of excluded middle be avoided, but then in an instant nothing can happen. Time does not consist of instants. Would Peirce have accepted this? Whitehead had a somewhat different form of Zeno argument.

Peirce admired Aristotle as cordially as anyone ever has, calling him "by far the greatest intellect" in human history. I incline to call Peirce the greatest modern Aristotelian. But he wanted to go beyond Aristotle. In his theory of time as "objective modality," in some aspects of his theories of firstness, secondness, and thirdness and of his synechism, I think he did so. But perhaps one has to go further still away from Aristotle. Once when I was standing beside Bochensky and he heard me remark to a third person, "Reality consists of events," Bochensky said, "Aristotle says that. He didn’t dot all the i’s or cross all the t’s. . . ." I often think about this remark of Bochensky’s. Peirce dotted some of the i’s and crossed some of the t’s. But are there not more to be dotted or crossed?

Peirce’s idea of a continuum of reactions as defining individuality in a seemingly strict sense is troublesomely abstract, oversimplified. A human person seems to be only intermittently conscious, What is reacting when the person is in dreamless sleep? The body? But that is billions of cellular individuals, and far from an identical collection of them from moment to moment. Peirce was not unaware of the complexities of human personality. Consciousness, he wrote, is a sort of public spirit in the brain cells. The process theory of sequential societies of actualities, each of which is created and then persists thereafter as an objectified datum of prehension in later actualities, seems calculated to take the complexities into account more definitely and naturally than any talk about a rigorous continuity of action defining a single, identical, yet changing individual.

Peirce himself says that a person is an idea. I recall Whitehead independently saying to Raphael Demos, "There’s the Demos idea" and going on to explain how this was the "identifying characteristic" which made the society called Demos the same from moment to moment. There are indications that Peirce was to some extent, in Matthew Arnold’s words, "between two worlds, one dead and the other powerless to be born." So were countless other people at the time. Only in some ways, as in his logic, his tychism and probabilism, was Peirce well into the new world.

I agree with Thompson that Peirce is not a systematic writer. He has materials for a system, clues to one, but it never quite crystallizes. He even had a theory to justify this. He forces one to make one’s own system. In some ways I find Peirce more helpful than Whitehead, for instance, in the Peircean theory about the primordial continuum of possible qualities out of which anything so definite as blue (or a certain quality of emotion) is an emergent, not an eternal object.

One of the subtleties of the question of continuity is that, even if one accepts the theory of discrete actualities, the limitations of our powers of introspection (which is really, as Ryle says and Whitehead implies, a form of memory) prevent us from clearly identifying definite intuitions of or by single experiences. Rather the discreteness is blurred for our awareness, as Whitehead admits. There is reason to think we come close to single experiences in noting the number of successive musical notes we can be aware of in a second. So, although for practical purposes our lack of intuitive certainties is much as Peirce says, theoretically we can say what we mean by definite relations and definite terms, and this seems an advantage.

Permit me to summarize my view about Peirce on continuity and individuality. When Peirce discusses individuals, he is writing about what for me are sequential societies of actualities, not single actualities. About these societies I, with Whitehead and the Buddhists, would accept much of what Peirce says about individuals. Their relations to our knowledge and to each other are very much as Peirce says. The disagreement concerns rather their relations to their own momentary states, also the details of the mind-body distinctions involved.

Individuals or societies are not wholly definite; their identifying traits are partly conventional or arbitrary (When did I first become myself? When will I cease to be myself?). Societies are not "simply located" in space but are partly internal to one another. Also the distinction between a person’s experiences and the person’s bodily states is extremely complex and subtle. The body is a vast society of societies; the mind or psyche is a single, personally ordered society whose primary immediate data are indistinctly intuited momentary actualities forming the bodily societies.

My criticism of Peirce’s synechism concerns primarily his assertion that actual becoming is continuous and that, in a finite time, we have an infinity of experiences, each infinitesimally short, temporally.

My accusation that Peirce made a definite mistake in arguing that the initial assumption of inquiry must be that actuality is continuous, since otherwise one would be ruling out possibilities, may be put as follows. A continuum is indeed an infinity of possibilities, but none of these possibilities is realizable except in an actualized discontinuity. An actualized continuity is an impossibility, and this impossibility is all that the assumption of discreteness rules out. It does so on the ground that, just as continuity is the order among possibilities, so discontinuity is the order among actualities. Any particular discontinuity rules out all the other possible ones in a given case. Hence no particular discontinuity should be assumed a priori. That there must in every actual case be some discontinuity or other, rules out no particular discontinuity, and hence no possibility. Peirce’s argument is invalid.

That individuals are not wholly external to one another (not simply located in space) is acceptable, but only in terms of a real discontinuity of momentary actualities. Only past actualities are internal to a present actuality. However, an actuality in my personal series may be internal to a later actuality in yours, and vice versa. In this way we are internal to each other, react to each other. Peirce has not reached the final level of analysis. Nor had Kant reached it.

Do I not react continuously? If "I" refers to me as conscious individual, then in dreamless sleep what is my reaction? I see none. Common-sense individuals are not ultimate terms of analysis. The Buddhists saw that so well.

Peirce’s own doctrine that dichotomies are crude tools of analysis may be cited here. Besides universals and changing individuals there are actual entities which are created but do not change. Also a human person or metazoan animal is not merely a single individual but many individuals on various levels.

I do not recall "instantaneous reactions" as Peirce’s doctrine. For me an actual entity reacts or has secondness to its predecessors in a finite portion of time, and this action is a creation, not a change. The finiteness is not an internal trait of the entity but measures it in relation to other actual entities and their time of becoming. In the fraction of a second it takes a single actual entity on the human level to become, a multiplicity of briefer entities can become on subhuman levels. But in this we are deep in difficult problems of physics and biophysics, also in the problem of relating quantum theory and relativity theory, a problem about which no one seems completely happy.

I congratulate those who arranged these meetings upon their including a real expert on the philosopher whose writings were one of the big things in my life. I have never regretted time spent reading Peirce. It was a huge piece of luck to be given as a task an occupation which was an education and a delight throughout. That it was so much a delight as it was, especially in the latter part of the job, was partly because of a second piece of luck, Paul Weiss’s turning up to help with a substantial part of what, as a one-man job, would have been excessively difficult and have taken up too large a portion of the career of one as eager to do his own writing as I (or as Weiss) was.

My cordial thanks to Manley Thompson.