Types of Order and the System Σ

Types of Order and the System Σ

By: C.I. Lewis

It is a commonplace of current theory that mathematics and exact science in general is capable of being viewed quite apart from any concrete subject matter or any system of physical facts to which it may usefully be applied Geometry need not appeal to any intuition of spatial complexes or to a supposititious space form; it has no need to rely upon diagrams or make use of ‘constructions’. Arithmetic makes no necessary reference to the sensible character of collections of marbles or of areas. Dynamics does not require the dubious assumption that the ‘moving particles’ of which it treats are possible of experience or verifiable physical entities. The ‘points’ of geometry and kinematics, the ‘numbers’ of arithmetic, and so on are simply terms x’s, y’s, z’s, entities, anything,—and the question what concrete things may be successfully regarded as such x’s and y’s is a question of application of the science, not one which need be considered while the system itself is in process of development.

If considerations of usefulness and of application are important in determining what assumptions shall be made or what systems developed, still such pragmatic considerations are principles of selection amongst actual and possible systems, and not internal to the systems themselves.

An arithmetic, a geometry, a kinematics, is thus capable of being viewed simply as a complex of relations and operations (relations of relations) which obtain amongst entities the nature of which, apart from those properties which follow from the relations assumed, is wholly indifferent. Such a system may in fact admit of various interpretations and applications more or less useful, all of which satisfy the requirement that these relations and operations be valid. As Professor Royce is accustomed to put it: a system of science is a type of order, the distinguishing characteristics of which are the kind of relations—symmetrical or unsymmetrical, transitive or intransitive, etc.,—which obtain among its terms, and the relations of these relations, by means of which the terms are ‘ordered’ and the relations ‘transformed.’

The growing recognition of the advantages of so viewing systems of pure science is one of the prime motives for the present interest in symbolic logic, or logistic. For logistic is the science which treats of types of order. One may reach the particular type of order which it is desired to portray—the arithmetic or geometry—by further specification of that minimum order which must obtain among entities if they are to ‘belong together’ in a set or system—the order of logic. This can be done in a variety of ways, which may be roughly divided into two groups. These two methods are distinguished by the fact that in the one case the ‘numbers’ of arithmetic or ‘points’ of geometry are treated as (conceptual) complexes having a definite internal structure, while in the other the ‘numbers’ or ‘points’ are the simple and indifferent terms, the x’s and y’s of the system. The former mode of procedure is best illustrated by the investigations of Russell’s Principles of Mathematics and Principia Mathematica of Russell and Whitehead. The other method is exemplified by Dedekind’s Was sind und was sollen die Zahlen, by the Ausdehnungslehre of Grassmann, and by the paper of Mr. A.B. Kempe, “On the Relation between the Logical Theory of Classes and the Geometrical Theory of Points.” But this second method appears in its best and clearest form in the paper of Professor Royce on The Relation of the Principles of Logic to theFoundations of Geometry. Each of these procedures has its advantages and its difficulties. Of late, the first method has received a disproportionate share of attention. For this reason, if for no other, I deem it important to call attention to the second method in general and to Professor Royce’s paper—its notable exemplification—in particular.

Professor Royce generalizes upon certain relations previously pointed out by Kempe, in the paper mentioned above,—certain relations which are fundamental both for logic and for geometry. If ac · b represent a triadic relation in which a and c are the ‘even’ members and b is the ‘odd’ member, ac · b is capable of various significant interpretations. If a, b, and c represent areas, ac · b may be taken to symbolize the fact that b includes whatever area is common to a and c, and is itself included in that area which comprises what is either a or c (or both). The same relation may be expressed in symbolic logic as:

ac⥽b⥽(a +c); or; a̅bc̅ + ab̅c = 0.

This relation may be so assumed that it has the essential properties of serial order. Taking it in the form just given and presuming the familiar laws of the algebra of logic, if ac · b and ad · c, then also ad · b and bd · c. Hereupon we may translate ac · b by ‘b is between a and c,’ and the relation will then have the properties of the points, a, b, c, d, in that order. Further, if a be regarded as an origin with reference to which precedence is determined, ac · b may represent ‘b precedes c,’ and ad · c that ‘c precedes d.’ Since ac · b and ad · c together give ad · b, if ‘b precedes c’ and ‘c precedes d,’ then ‘b precedes d.’ Hence this relation has the essential transitivity of serial order, with the added precision that it retains reference to the origin from which ‘precedes’ is determined.

Professor Royce points out to his students that the last mentioned property of this relation makes possible an interpretation of it for logical classes in which it becomes more general than the inclusion relation of ordinary syllogistic reasoning. If there should be inhabitants of Mars whose logical sense coincided with our own—so that any conclusion which we regarded as valid would seem valid to them, and vice versa—but whose psychology was somewhat different from ours, these Martians might prefer to remark that “b is ‘between’ a and c,” rather than to note that “all a is b and all b is c.” These Martians might then carry on successfully all their reasoning in terms of this triadic ‘between’ relation. For ac · b meaning a̅bc̅ + ab̅c = 0 is a general relation which, in the special case where a is the “null” class contained in every class, becomes the familiar “b is included in c” or “all b is c.” By virtue of the transitivity pointed out above, 0c · b and 0d · b, which is the syllogism in Barbara, ‘If all b is c and all c is d, then all b is d.’ Hence these Martians would possess a mode of reasoning more comprehensive than our own and including our own as a special case.

The triadic relation of Kempe is, then, a very powerful one, and capable of representing the most fundamental relations not only in logic, but in all those departments of our systematic thinking where unsymmetrical transitive (serial) relations are important. In terms of these triads, Kempe states the properties of his ‘base system,’ from whose order the relations of logic and geometry both are to be derived. The ‘base system’ consists of an infinite number of homogeneous elements, each having an infinite number of equivalents. It is assumed that triads are disposed in this system according to the following laws.

1. If we have ab · p and cb · q, r exists such that we have aq · r and cp · r.

2. If we have ab · p and cp · r, q exists such that we have aq · r and cb · r.

3. If we have ab · c, and a = b, then c = a = b. 

4. If a = b, then we have ac · b and bc · a, whatever entity of the system c may be.

To these, Kempe adds a fifth postulate which he calls the ‘law of continuity’: “No entity is absent from the system which can consistently be present.” From these assumptions and various definitions in terms of the triadic relation, Kempe is able to derive the laws of the symbolic logic of classes and the most fundamental properties of geometrical sets of points.

But there are certain dubious features of Kempe’s procedure. As Professor Royce notes, the ‘law of continuity’ makes postulates 1 and 2 superfluous. And it renders entirely obscure what properties the system may have, beyond those derivable from the other postulates without this. For the negative form of the ‘law of continuity’ makes it impossible to assume the existence of an entity without first investigating all the properties of all the other entities and collections in the system, where some of these other entities and collections exist only at the instance of the ‘law of continuity’ itself. Consequently the existence of any entity or set, not explicitly demanded by the other postulates, can be assumed only at the risk of later inconsistency. Also, in spite of the fact that Kempe has assumed an infinity of elements in the base set, there are certain ambiguities and difficulties about the application of his principles to infinite collections.

In Professor Royce’s paper, we have no such ‘blanket assumptions’ as the ‘law of continuity,’ and the relations defined may be extended without difficulty to any finite or infinite set. We have here, in place of a ‘base system’ and triadic relations, the ‘system Σ’ and “O-collections.”

The system Σ consists of simple and homogenous elements. Collections of these may contain any finite or infinite number of elements; and any element may be repeated any number of times; so that x and x-repeated may be considered a collection, x, x-repeated, and y a collection, and so on. Greek letters will signify determinate collections in Σ. Collections in Σ are either O-collections or E-collections. O(——) signifies that (——) is an O-collection; E(——) that (——) is an E-collection, i.e., that it is not an O-collection. Assuming for the moment the principles of the algebra of logic, O(pqrs …) signifies that pqrs … + p̅q̅r̅s̅ … = 0. [Both the laws of the algebra of logic and the properties of O-collections which render them thus expressible are, of course, derived from the postulates and not assumed in the beginning.] It will be clear that the order of terms in any O-collection may be varied at will. ‘x is equivalent to y’ means that in very collection in which x or y occurs the other may be substituted for it and the collection in question still remain an O-collection.

If two elements in Σ, say p and q, are such that O(pq) is true, then p and q are said to be obverses, each of the other. Since it will follow from the postulates of the system that all the obverses of a given element are mutually equivalent, and that every element has at least one obverse, a ‘unique representative’ of the obverses of x may be chosen and symbolized by x̅. Pairs of obverses will turn out to have the properties of negatives in logic.

Any q such that O(βq) is true, is called a compliment of β.

Any r such that O(βq) and O(qr) are both true is called a resultant of β.

The postulates of the system Σ are as follows:

I. If O(α), then O(αγ), whatever collection γ may be.

II. If, whatever element bn of β be considered, O(δbn), and if O(β) is also true, then O(δ).

III. There exists at least one element in Σ.

IV. If an element x of Σ exists, then y exists such that x ≠ y.

V. Whatever pair (p, q) exists such that p ≠ q, r exists such that while both O(rp) and O(rq) are false, O(pqr) is true. 

VI. If w exists such that O(θw), then v also exists such that O(θv) and such, too, that whatever element tn of θ be considered O(vwtn).

From these assumptions the whole algebra of logic can be derived in such wise that the system Σ has the order of the totality of logical classes. To see this, we must first define the F-relation. If O(pqrs …) to any number of terms, we may represent the same fact by (F(p̅/qsr …), (Fp̅r̅/qs …), (r/Fp̅q̅s̅ …), etc., where the rule for transforming the O-collection into the corresponding F-collections is that we introduce a bar, separating any one or more elements of the O-collection from the remainder, and then replace each of the elements on one (either) side of the bar by its obverse. Since the order of terms in O-collections is indifferent, terms on the same side of the bar in any F-relation are independent of the particular order in which they are written. Also, it follows immediately from the definition of the relation that F(pq/r̅s̅) and F(p̅q̅/rs) are equivalent. Where the F-relation holds for three terms, it turns out to be identical with the triadic relation of Kempe, and the Kempean ac · b is thus a special case of the F-relation, namely F(b/ac), or F(ac/b), or F(a/bc̅), or F(a̅/b̅c), or F(b/ca), etc., all of which are equivalent. We may, then, define the “illative” relation,—“b is included in c” where b and c are classes, “b implies c” where b and c are propositions, “b precedes c,” where b and c are points or terms in one-dimensional array,—as the special case of any of the above F-relation in which a is the “zero element,” or “null class,” or “origin.” But these F-relations are equivalent, by definition, to O(ab̅c) and O(abc̅). Hence b⥽ac may be defined to mean O(ab̅c) and b⥽c to mean O(0b̅c). Thus in terms of the totally symmetrical O-relation, the unsymmetrical, transitive dyadic relation which characterizes both serial order and syllogistic reasoning can be defined.

As is well known, the entire algebra of logic may be derived from a class K, the idea of negation, and the illative relation, hence also in terms of the system Σ and O-collections. The ‘zero element’ or ‘null class’ is any arbitrarily chosen member with reference to which all illative relations are supposed to be specified. Such an element o itself bears the illative relation to any other, x, since F(ox/o), or O(oo̅x) holds for any element x. The element i, the “universe” of the algebra of logic, may then be defined as the negative or obverse of the o chosen. In the system Σ, o and i do not differ from any other pair of obverses, apart from the arbitrary choice of a reference element for illative relations. The logical product of two terms, x and y, is then definable as any P such that F(ox/P), F(oy/P), and F(xy/P). The logical sum of x and y is definable as any S such that F(ix/S), F(iy/S), and F(xy/S). P, so defined, will be such that P⥽x and P⥽y, while any w such that w⥽x and w⥽y will be also such that w⥽P. For S it will be true that x⥽S and y⥽S, and any v such that x⥽v and y⥽v is also such that S⥽v. S and P are, in fact, the “lower limit” and “upper limit,” with reference to the chosen zero element, of all the F-resultants of x and y, an F-resultant being any z such that F(xy/z). These definitions for the product and sum of two elements may be extended immediately to any number of elements, or any collection of β, if we replace x an y by “any element of β, however chosen.” The usual laws of the algebra of logic, connecting sums and products, terms and their negatives, and the elements o and i may then be verified for the system Σ. This order of logical entities is contained in Σ in an infinite variety of ways, since any pair of obverses may be arbitrarily chosen for i and o. F-relations and O-relations, not confined to dyads and triads, are capable of representing this order in a generalized form.

There is, moreover, a wealth of order in the system which the algebra of logic, even in terms of any polyadic relation, does not require. It is this difference which renders the system Σ capable of being viewed as a generalized space form.

It follows from postulate V that if p ≠ q, then there is an element ‘between’ p and q. The postulate states: Whatever pair (p, q) exists such that p ≠ q, r also exists such that while both O(rp) and O(rq) are false, O(pqr) or F(pq/r̅) gives, by definition of the illative relation, r⥽qp and r̅⥽pq) or r is “between” p and q. And r̅ must be distinct from p and q both, for otherwise, it follows from the definition of obverses, one of the two O(r̅p) and O(r̅q) will be true. Hence postulate V may be restated in the form: For every pair of distinct elements, there exists an element, distinct from both, between them. It is at once obvious that if the elements be “points,” and p⥽oq mean that p is between o and q, postulate V requires that the order of points in Σ should be dense in every direction (with reference to every pair of points). It is further clear that if we take any pair of distinct points, o and z, and postulate t between o and t, v between t and z, and so on. Owing to the transitivity of the illative relation, we are thus required to postulate for every pair (o, z) an infinite number of elements in the order o⥽or⥽ot⥽ov⥽oz. Such an ordered collection is continuous. We have already seen that it is dense. It remains to see that it satisfies the requirement that every fundamental segment has a limit. Consider two sections from the collection, κ and λ, such that k is any element of κ, every element j such that j⥽ok belongs to κ, and every element l, such that for every element k of κ l⥽ok is false, belongs to λ. There is, then, an element, called S, such that for every element k in κ, k⥽oS, and if l is any element such that, for every element k of κ, k⥽ol, then S⥽ol. Such an element S is the ‘sum’ or ‘upper limit’ of κ, defined above. Hence every fundamental segment has a limit. Any collection thus characterized by a transitive unsymmetrical relation and continuous order deserves to be called a ‘line.’ Every pair of distinct elements in Σ determines such a line.

For every pair of distinct points, o and q, there exists p such that F(oq/p) and hence O(oqp̅). By the definition of the F-relation, if O(oqp̅), then F(o̅q̅/p). Hence if o and q determine a line, o … p … q, there exists also a line, o̅ … p̅ … q̅ or q̅ … p̅ … o̅, in which appear the obverses of all the elements in o … p … q. But it also follows from O(oqp̅) that F(op̅/q̅), or q⥽op̅. Thus if o … l … z be any line determined with reference to an “origin” o, the line containing the obverses of the elements of o … l … z may be determined by reference to the same origin. And if two elements of o … l … z, say m and n, are such that m⥽on, then n̅⥽om̅. If we further consider the order of elements in both lines, o … l … z, and z̅ … l̅ … o̅, with reference to the origin o and its obverse o̅, the two lines appear as a single line which passes from o to o̅ through l, and from o̅ back to o through l̅. Let m and n be any two elements of 0 … l … z such that F(on/m). We have m⥽on. Hence n̅⥽om̅. But if we have F(on/m), then also O(onm̅) and so F(o̅m/n). Hence n⥽mo̅. Thus any two elements, m and n, such that m is between o and n, are also such that n is between m and o̅. From the transitivity of the illative relation, m⥽oo̅. But if m⥽oo̅, then from the above m⥽oo. Thus we have the continuous line, o … m … n … o̅ … n̅ … m̅ … o, or o̅ … n̅ … m̅ … o … m … n … o̅, which has so far the character of the projective line with o as origin and o̅ the point at infinity. And if m, n, r, occur in that order in one ‘direction’ from the origin, then m̅, n̅, r̅, occur in that order in the ‘opposite direction’ from the origin.

Certain further characteristics of order in the system may be mentioned briefly. In general, lines such as those considered above may “intersect” any number of times. From the definition of obverses, O(aa̅) and O(cc̅) always hold. But by postulate I, if O(aa̅), then O(aa̅p), and hence F(aa̅/p), for any element p. Similarly, if O(cc̅), then F(cc̅/p). Thus collections consisting of the F-resultants of different pairs may have any number of elements in common. But in terms of such operations as were in question in the definitions of ‘sums’ and ‘products,’ sets of resultants may be determined such that they have one and only one element in common. Thus certain selected lines in the system intersect once and once only. There are any number of such sets.

In general, if any pair of elements in a set are obverses of one another, all the other elements of the set will be resultants of this pair, and their entire array will be “one-dimensional” so far as dimensionality may be attributed to such a collection. The problem of selecting sets suitable for any space form—any n-dimensional array—is the problem of selecting so that O-collections will be excluded. Such sets, containing no obverses, are the ‘flat collections’ of Kempe. As he pointed out, the excluded obverses will form an exactly similar set, so that ‘spaces’ come in pairs somewhat suggesting companion hemispheres. In terms of “flat collections,” one-dimensional, two-dimensional, n-dimensional arrays, may be specified in any number of ways.

Once the order of the system Σ is generated in terms of O-relations and F-relations, the determination of such more specialized types of order is a problem of selection only. In the words of Professor Royce, “Wherever a linear series is in question, wherever an origin of coordinates is employed, wherever ‘cause and effect,’ ‘ground and consequence,’ orientation in space or direction of tendency in time are in question, the dyadic asymmetrical relations involved are essentially the same as the relation here symbolized by p⥽yq. This expression, then, is due to certain of our best established practical instincts and to some of our best fixed intellectual habits. Yet it is not the only expression for the relations involved. It is in several respects inferior to the more direct expression in terms of O-relations….When, in fact, we attempt to describe the relations of the system Σ merely in terms of the antecedent-consequent relation, we not only limit ourselves to an arbitrary choice of origin, but miss the power to survey at a glance relations of more than a dyadic, or triadic character.”

With this hasty and fragmentary survey of the system Σ, we may turn to considerations of method. It was suggested in the introduction that the procedure here exemplified differs in notable ways from the method of such studies as those of Principia Mathematica. In that work, we are presented at the outset with a simple, though general, order—the order of elementary propositions so related to one another that one is the negative of another, two may be such that at least one of them is true, and so on. In terms of these fundamental relations, more special types of order—various branches of mathematics—are built up by progressive complication. In some respects this is the necessary character of deductive procedures in general; in other respects it is not. In particular, this method differs from that employed by Mr. Kempe and Professor Royce in that terms, as well as relations, of later sections are themselves complexes of the relations at first assumed. The complication thus made necessary can hardly be appreciated by those who would regard a number, for instance, as a simple entity. To illustrate: In Principia Mathematica, the “cardinal number” of x is the class of referents of the relation ‘similar to’ where x is the relatum. The ‘class of referents’ of any relation R is defined as α such that α is identical with x such that, for some y, x has the relation R to y. ‘Relatum’ is similarly defined. ‘m is identical with n’ means that, for any predicative function φ, φm implies φn. I do not pause upon ‘predicative function.’ α is ‘similar to’ β means that, for some one-to-one relation R, α is identical with the class of referents of R and β is identical with the class of relata of R. A ‘one-to-one’ relation is a relation S such that the class of referents of S is contained in i. ‘i’ is defined as α such that, for some x, α is identical with the x. ‘The x’ is my attempt to translate the untranslatable. The attempt to analyze ‘is contained in’ would require much more space than we can afford. But supposing the analysis complete, we discover that the ‘cardinal number of x’ is ——, where —— is the definition first given, with all the terms in it replaced by their definition, the terms in these replaced by their definition, and so on. All this complexity is internal to the terms of arithmetic. And only when this process is complete can any properties or relations of ‘the cardinal number of x’ be demonstrated. An advantage of this method is that the step from one order to another ‘based upon it’ is always such as to make clear the connection between the two. It preserves automatically the hierarchic arrangement of various departments of exact thinking. The process of developing this hierarchy is tedious and taxes our analytic powers, but there is always the prospect of assured success if we can perform the initial analysis involved in the definitions. But the disadvantages of this complexity can hardly be overemphasized. It is forbidding to those whose interests are simply ‘mathematical’ or ‘scientific’ in the ordinary sense. Such a work as Principia Mathematica runs great risk of being much referred to, little read, and less understood.

In contrast with such complexity, we have, by the method of Mr. Kempe and Professor Royce, an order completely generated at the start, and such that the various special orders contained in it may be arrived at simply by selection. Little or no complication within the terms is required. Involved as the structure of the system Σ may seem, it is, by comparison, a marvel of simplicity and compact neatness. With this method, there seems to be no assurance in advance that any hierarchic relations of different orders will be disclosed, but we shall certainly discover, and without difficulty, whatever analogies exist between various orders. Again, this method relies much more upon devices which may be not at all obvious. It may not tax severely the analytic powers, but it is certain to tax the ingenuity.

In another important respect, advantage seems to lie with this method. One would hardly care to invent a new geometry by the hierarchic procedure, or expect to discover one by its use. We have to know where we are going or we shall not get there by this road. By contrast, Professor Royce’s is the method of the path-finder. The prospect of the novel is here much greater. The system Σ may—probably does—contain new continents of order whose existence we do not even suspect. And some chance transformation may put us, suddenly and unexpectedly, in possession of such previously unexplored fields.

Which of the two methods will prove, in the end, more powerful, no one can say at present. The whole subject is too new and undeveloped. Certainly it is to be desired that the direct and exploratory method be increasingly made use of, and that the advantages of studying very general types of order, such as the system Σ, be better understood.

Reading Notes: June 6th, 2025

“[Every] idea is, after all, the experience of a self who is conscious. Even when, as students of the mere idea, we have neglected the self and taken no notice of it, yet all the time we have been dimly conscious of it as underlying all our feelings. In other words, we have realized that a perception, an imagination or an emotion does not exist independently, but that it is my perception, your imagination or his emotion. As James says: “Every ‘state’ or ‘thought’ is part of a personal consciousness….In this lecture room,…there are a multitude of thoughts, yours and mind….They are as little each-for-itself and reciprocally independent as they are all-belonging-together….My thought belongs with my other thoughts, and your thought with your other thoughts. The only states of consciousness that we naturally deal with are found in personal consciousnesses,…selves, concrete particular I’s and you’s.” This means that besides realizing my conscious experiences, or feelings, I am also conscious of my conscious self, as in a sense including, but not as identical with, the perceptions, the emotions or the thoughts of any given moment.” (Calkins, An Introduction to Psychology, 151)

“What, now, is this intimate consciousness of self which underlies and includes, though it does not consist in, the moment-by-moment ideas and experiences? What, in other words, do I mean by the ‘I’ which is conscious or has experiences?” (Calkins, An Introduction to Psychology, 151)

“The self underlying the conscious experiences…is not a single, lonely self, but a self related to a group of selves. Every self is, in other words, a social self, that is, a self in inextricable relation with many other selves, “a chain of linked thought, Of love and might to be divided not.” I, who read this paragraph, for instance, simply cannot be conscious of my own self except as related in the most varying ways to a vast number of other people.” (Calkins, An Introduction to Psychology, 152)

“Experiences may be contrasted as they refer to unparticularized selves, that is, to any or all selves, or as they refer to definite and particular selves. In perceiving, for instance, I am vaguely conscious that other people might see what I am seeing, but in hating I do not hate anybody in general, but some very special and definite person or persons.” (Calkins, An Introduction to Psychology, 154)

“The term ‘element’ is…almost always used of what we have called the structural elements, sensational, attributive, and relational.” (Calkins, An Introduction to Psychology, 151)

“A psychology which considers only psychic events or consciousnesses is, therefore a causal science; whereas psychology, in so far as it studies selves in their relations; does not treat its facts as causally related to each other, because, strictly speaking, only phenomena in time are causally connected, and selves are, to say the least, not primarily regarded as realities in time. Anybody may verify this by his introspection. One thinks of one’s body as beginning and ending at distinct moments; one thinks of one’s ideas and feelings as occurring yesterday or to-day—at a quarter of twelve or half-past three; but one does not primarily regard oneself as ‘in time,’ and one, therefore does not think of selves in causal relations to each other. They are related, of course, by virtue of the imperiousness, the demands, the acknowledgements, and the adoptions which make up, as we have seen, the very nature of a self; but these relations are not the causal ones which connect ideas.” (Calkins, An Introduction to Psychology, 154-155)

Materialism and the “First Breath” of Mentality (A Revised Version with Objections (to the Original Argument) and Replies)

According to Materialism, there was, at some point in time, an instant, M, whose “content” was the first-ever mental state; and this instant, M, was preceded in time by a compact series of non-mental instants (i.e., a compact series wherein each instant had a “content” that was exhaustively non-mental in character). How, then, does the Materialist go on to explain the “first breath” of mentality? He invokes an alluring word: “causality.” A reader sympathetic to the Materialist’s case might protest against such a brief statement of his position, so it would only be fair to let the Materialist interject and present his view in his own words:

Modern Materialism holds that mental states are nothing “over and above” physical states; mentality is but a delicate, rare, and ephemeral form of physicality. Old Materialism made an error that Modern Materialism has since corrected; it blundered by declaring a priori that (i) all physical states are non-mental in nature and that (ii) all mental states are non-physical in nature. Despite this supposed categorical difference between mental states (i.e., non-physical states) and physical states (i.e., non-mental states), Old Materialism went on to assert that every mental state located in the series of past, present, and future mental states is the causally-generated “effect,” or the epiphenomenal “by-product,” of a corresponding non-mental state located in the series of past, present, and future non-mental states. Thus, each mental state is causally dependent upon a particular non-mental state located in the total series of non-mental states. Although the total series of mental states was not itself conceived by these Old Materialists as being a “segment” of the total series of non-mental states, it was nevertheless made subordinate to it. While the thread of mental states lacked self-sufficiency, the chain of physical states (i.e., the totality of past, present, and future non-mental states—or the chain of non-mental states ordered in relations of “earlier than” and “later than”) constituted an independent series—resting on nothing other than itself. The Old Materialists recognized the difficulties in their position (e.g., the relationship between the two series), and failed to build an explanatory bridge that could intelligibly, and non-arbitrarily, unite “cause” with “effect.” Modern Materialism, by contrast, rejects the Old Materialist’s dogmatism and refuses to declare a priori that (i) every physical state is non-mental in nature, and that (ii) every mental state is non-physical in nature. Instead of maintaining that the thread of mental states is populated by non-physical, causally-generated “effects” or epiphenomenal “by-products” of an “independent” series that is exhausted by non-mental states, Modern Materialism, by contrast, holds that when a mental state occurs, this occurrence is identical to a particular physical state located in the total series of physical states. Thus, mental states are no longer viewed as “residual excrescences” that supervene upon the “shock of atoms” in the physical order; they are no longer granted a unique series of their own. On the contrary, mental states just are physical states. This is Modern Materialism.

Now, like any other physical state, the first-ever mental state (i.e., the “content” of the first-ever mental instant, M) would have been the effect of a preceding physical state, and this prior physical state would have been a non-mental state (i.e., the “content” of a non-mental instant)—but Modern Materialism assures us that there are no difficulties inherent in such a transition. By assimilating mental states into the physical order by way of “identity,” the Modern Materialist has advanced further than any of his predecessors: he has taken a step forward towards explaining the “first breath” of mentality.

Let’s examine the Materialist’s account in detail. The Materialist postulates two temporally-distinct instants: (i) a definite instant, M, whose “content” was the first-ever mental state, and (ii) a definite instant, Pn, whose “content” was a non-mental state that preceded the “content” of the first-ever mental instant in time. Let’s offer a brief sketch of the nature of the time-series by specifying some of its properties:

“A series is continuous when any term divides the whole series unambiguously into two mutually exclusive parts which between them comprise all the terms of the series, and when every term which so divides the series is itself a term of that series. From this second condition it obviously follows that a number of intermediate terms can always be inserted between any two terms whatever of a continuous series; no term of the series has a next term….The whole series of real numbers is continuous [because] every member of the number-series divides it into two classes, so that every number of one is less than every number of the other, and every number which thus divides the series is itself a term of the number-series....From the continuity of the series of real numbers it follows that any other series which corresponds point for point with the terms of the number series will be continuous. Now one such series is that of the [time series]. Every moment of time divides the whole series of moments into two mutually exclusive classes, the moments before itself and the moments which are not before itself. And whatever thus divides the time-series is itself a moment in that series.” (Taylor, Elements of Metaphysics, 171-172)

Thus, it follows from time’s continuity that no two instants in the time-series ever “touch.” When this fact and the Materialist’s proposed connection between the “content” of Pn and the “content” of M are brought into focus, we find that the “content” of Pn and the “content” of M cannot temporally overlap—i.e., the first-ever mental state (i.e., the “content” of instant M) and the non-mental state (i.e., the “content” of instant Pn) had to be not only not simultaneous with each other, but also had to be in a relation of “earlier than” and “later than” to each other. Indeed, if the “content” of Pn was simultaneous with the “content” of M, then we would have a contradiction on our hands: there would be a moment in time when there was mentality present in a world that, ex hypothesi, was exhausted by non-mentality. In light of this, we must ask the Materialist several questions:

Question (i): Was the “content” of Pn—rather than the “content” of any preceding non-mental instant—the “cause” of the “content” of M?

The Materialist’s theory requires that he answer question (i) in the affirmative. And so, in response to question (i), the Materialist declares the “content” of Pn—rather than the “content” of any preceding non-mental instant—to be the “cause” of the “content” of M.

Question (ii): What was it about the “content” of Pn that made it the non-mental state—rather than any preceding non-mental state—the “cause” of the “content” of M?

On pain of inconsistency, the Materialist must respond to question (ii) by asserting that the “content” of Pn was a non-mental state that possessed certain “special properties” (i.e., a set of characteristics absent from all prior non-mental states), and that its possession of these “special properties” made the “content” of Pn—rather than the “content” of any preceding non-mental instant—the “cause” of the “content” of M.

Question (iii): What were the “special properties” present in the “content” of Pn and absent from the “content” of all preceding non-mental instants, that made the “content” of Pn–rather than the “content” of any preceding non-mental instant—the “cause” of the “content” of M?

In reply to question (iii), the Materialist will likely posit a bunch of features that allegedly capture the essence or identity of these “special properties.” Let’s symbolize the identity of these “special properties” present in the “content” of Pn—but absent from all the “content” of all preceding non-mental instants—as C.

At first glance, all seems fine and well; however, there is a puzzle lurking beneath the surface: a puzzle involving (i) the continuous nature of the time-series, (ii) the Materialist’s identification of the “content” of Pn—rather than the “content” of any of the other non-mental instant—as being the possessor of the aforementioned “special properties,” and (iii) the Materialist’s identification of what these “special properties” actually are. Let’s explore this latent puzzle in the Materialist’s theory.

As we have noted above, the “content” of Pn (i.e., a state exhaustively non-mental in character) cannot be simultaneous with the “content” of M (i.e., a state that was not exhaustively non-mental in character)—on pain of contradiction. M must be “later than” Pn because, ex hypothesi, if the “content” of M was simultaneous with (or in any way overlapped with) the “content” of Pn, the time of the first-ever mental state would also be a time when the world was exhausted by solely non-mental states; and this, of course, is contradictory. Therefore, the “content” of Pn and the “content” of M are not simultaneous, but instead are in relations of “earlier than” and “later than” to each other. However, since the continuity of time implies that between any two instants in the time-series there is an intermediate instant, it follows that between Pn and M there was another instant, X, distinct from both Pn and M and whose “content” separates the “content” of Pn and the “content” of M in time. This prompts us to ask the Materialist more questions:

Question (iv): Is the “content” of X a non-mental state or a mental state?

The Materialist must answer question (iv) by declaring the “content” of X to be a non-mental state. Since he must hold that the “content” of X is a non-mental state, we can represent X as Pn+1. Now, if the Materialist asserted the “content” of X to be a mental state, then he would have fallen into inconsistency; indeed, he would have been mistaken about the “content” of M being the first-ever mental state because the “content” of X would have preceded the “content” of M in time.

However, if the Materialist answers question (iv) by declaring the “content” of Pn+1 (i.e., X) to be a non-mental state, then he either contradicts his answer to question (i) or his explanation becomes muddled in arbitrariness. Indeed, since the “content” of Pn+1 is “later than” the “content” of Pn in time, between the “content” of Pn—the supposed sufficient condition for the occurrence of the “content” of M—and the “content” of M, there would have been the occurrence of the purely non-mental “content” of Pn+1. However, if the identified “content” of the non-mental instant Pn was genuinely sufficient to produce the “content” of M, then the Materialist’s explanation stumbles into a difficulty.

If the occurrence of the intervening non-mental “content” of Pn+1 between the “content” of Pn and the “content” of M matters causally to the occurrence of the “content” of M, this would contradict the sufficiency of the “content” of Pn—rendering the “content” of Pn insufficient to be the “cause” of the “content” of M. However, if the occurrence of the intervening non-mental “content” of Pn+1 between the “content” of Pn and the “content” of M does not matter causally to the occurrence of the “content” of M, then this makes the timing of the occurrence of the “content” of M arbitrary and inexplicable. Moreover, if the “content” of Pn was sufficient to be the “cause” of the “content” of M, this leads us to ask why the “content” of Pn+1—a “content” that, ex hypothesi, lacked the “special properties” necessary and sufficient for it to be the “cause” of the “content” of M—occurred between the “content” of Pn and the “content” of M.

In order to avoid introducing arbitrariness and inexplicability into his explanation of the “first breath” of mentality, the Materialist must revise his answer to question (i). He must now hold that the “content” of Pn+1—rather than the “content” of any preceding non-mental instant (e.g., Pn)—was the “cause” of the “content” of M.

Question (v): What was it about the “content” of Pn+1 that made it the non-mental state—rather than any preceding non-mental state (e.g., the “content” of Pn)—the “cause” of the “content” of M?

On pain of inconsistency, the Materialist must answer question (v) by asserting that the “content” of Pn+1 possessed certain “special properties” (i.e., a set of characteristics absent from the “content” of all prior non-mental instants), and that its possession of these “special properties” made the “content” of Pn+1—rather than the “content” of any preceding non-mental instant (e.g., Pn)—the “cause” of the “content” of M.

Question (vi): What were the “special properties” present in the “content” of Pn+1 and absent from the “content” of all preceding non-mental instants (e.g., the “content” of Pn), that made the “content” of Pn+1—rather than the “content” of any preceding non-mental instant (e.g., the “content” of Pn)—the “cause” of the “content” of M?

The Materialist is forced by his own hand to answer question (vi) by positing a bunch of features that allegedly capture the essence or identity of the “special properties” present in the “content” of Pn+1 (i.e., features present in the “content” of Pn+1 but absent from the “content” of all preceding non-mental instants) that made the “content” of Pn+1—rather than the “content” of any preceding non-mental instant (e.g., the “content” of Pn)—the “cause” of the “content” of M.

Now, the Materialist cannot, on pain of contradiction, supply us with the same list of “special properties” that he provided in his answer to question (iii). If, in response to question (vi), the Materialist simply regurgitated his answer to question (iii), then, ex hypothesi, the “special properties” of the “content” of Pn+1 would have been present in the “content” of an earlier non-mental instant (i.e., the “content” of Pn)—thereby contradicting the Materialist’s answer to question (v). Moreover, the Materialist cannot simply provide his answer to question (iii) in response to question (vi) because he himself has admitted, by implication, that the properties of the “content” of Pn were not of such a nature as to make the “content” of Pn the cause of the “content” of M. Let’s symbolize the Materialist’s revision of these “special properties” as C’.

However, another problem arises. In the same way the “content” of Pn had to be earlier in the time-series than the “content” of M, so too must the “content” of Pn+1 be earlier in the time-series than the “content” of M. If this were not so, and the “content” of Pn+1 was simultaneous with the “content” of M, there would be a moment in time when there was mentality present in a world that, ex hypothesi, was exhausted by non-mentality—and this, of course, is a contradiction. And, as we have seen, since the continuity of time implies that between any two instants in the time-series there is an intermediate instant, it follows that between Pn+1 and M, there was another instant, X’, distinct from both Pn+1 and M and whose “content” separated the “content” of Pn+1 and the “content” of M in time. This prompts us to ask the Materialist more questions:

Question (vii): Is the “content” of X’ a non-mental state or a mental state?

In answer to question (vii), the Materialist must, of course, respond by declaring the “content” of X’, to be a non-mental state. Since the “content” of X’ is a non-mental state, we can represent X’ as Pn+2.

Now, if the Materialist asserted the “content” of X’ to be a mental state, then he would have fallen into inconsistency; indeed, he would have been mistaken about the “content” of M being the first-ever mental state because the “content” of X’ would have preceded the “content” of M in time.

However, if the Materialist answers question (iv) by declaring the “content” of X’ to be a non-mental state, then he either contradicts his answers to questions (v) and (vi), or his explanation becomes muddled in arbitrariness. Indeed, since the “content” of Pn+2 is “later than” the “content” of Pn+1 in time, then between the “content” of Pn+1—the supposed sufficient condition for the occurrence of the “content” of M—and the “content” of M, there would have been the occurrence of a the purely non-mental “content” of Pn+2. However, if the identified “content” of the non-mental instant Pn+1 was genuinely sufficient to produce the “content” of M, then the Materialist’s explanation stumbles into a difficulty.

If the occurrence of the intervening non-mental “content” of Pn+2 between the “content” of Pn+1 and the “content” of M matters causally to the occurrence of the “content” of M, this would contradict the sufficiency of the “content” of Pn+1—rendering the “content” of Pn+1 insufficient to be the “cause” of the “content” of M. However, if the occurrence of the intervening non-mental “content” of Pn+2 between the “content” of Pn+1 and the “content” of M does not matter causally to the occurrence of the “content” of M, then this makes the timing of the occurrence of the “content” of M arbitrary and inexplicable. Moreover, if the “content” of Pn+1 was sufficient to be the “cause” of the “content” of M, this leads us to ask why the “content” of Pn+2—a “content” that, ex hypothesi, lacked the “special properties” necessary and sufficient for it to be the “cause” of the “content” of M—occurred between the “content” of Pn+1 and the “content” of M.

In order to avoid introducing arbitrariness and inexplicability into his explanation of the “first breath” of mentality, the Materialist must revise his answer to question (i). He must now hold that the “content” of Pn+2—rather than the “content” of any preceding non-mental instant (e.g., Pn+1)—was the “cause” of the “content” of M.

In doing so, the Materialist must also revise his answer to question (v) and question (vi). He must assert that the “content” of Pn+2 possessed certain “special properties” (i.e., a set of characteristics absent from the “content” of all prior non-mental instants) and that its possession of these “special properties” made the “content” of Pn+2—rather than the “content” of any preceding non-mental instant (e.g., the “content” of Pn or the “content” of Pn+1)—the “cause” of the “content” of M. However, this is possible only insofar as the Materialist specifies the “special properties” of the “content” of Pn+2. Just as before, the Materialist must list a set of features that allegedly capture the essence or identity of the “special properties” present in the “content” of Pn+2 (i.e., features present in the “content” of Pn+2 but absent from the “content” of all preceding non-mental instants) that made the “content” of Pn+2—rather than the “content” of any preceding non-mental instant (e.g., the “content” of Pn or the “content” of Pn+1)—the “cause” of the “content” of M. However, the Materialist cannot, on pain of contradiction, supply us with the same list of “special properties” that he provided in his original answer to question (vi). If the Materialist did so, then the “special properties” of the “content” of Pn+2 would have been present in the “content” of an earlier non-mental instant (i.e., the “content” of Pn+1); however, he himself has admitted, by implication, that the properties of the “content” of Pn+1 were not of such a nature as to make the “content” of Pn+1 the cause of the “content” of M. Ergo, the Materialist must supply us with a new set of properties that were allegedly present in the “content” of Pn+2, and made the “content” of Pn+2—rather than the “content” of any preceding non-mental instant—the “cause” of the “content” of M. Let’s symbolize the Materialist’s revision of these “special properties” as C’’.

However, the problem has only been aggravated. As we’ve seen before, the continuity of time implies that between any two instants in the time-series there is an intermediate instant; ergo, it follows that between Pn+2 and M there was another instant, X’’, distinct from both Pn+2 and M and whose “content” separates the “content” of Pn+2 and the “content” of M in time. This prompts us to ask the Materialist another question:

Question (viii): Is the “content” of X’’ a non-mental state or a mental state?

The Materialist must answer question (viii) by declaring the “content” of X’’ to be a non-mental state. Since the “content” of X’’ is non-mental, we can represent X’’ as Pn+3. And we know where this will lead us. The Materialist is trapped in a vicious regress; inconsistencies in the Materialist’s responses require that he continually revise his answers ad infinitum. He is unable to consistently identify the non-mental instant whose “content” allegedly gave birth to the “content” of the first-ever mental instant, M, and he is unable to consistently specify the identity of the alleged “special properties” present in the “content” of this non-mental instant that would have made it—rather than the “content” of any preceding non-mental instant—the cause of the “content” of the first-ever mental instant, M.

With every step the Materialist takes towards his first-ever mental state, he is forced to take one step back—he is forever barred from receiving his final reward. The Materialist fails to harmonize the “first breath” of mentality within an asphyxiatingly barren, non-mental world.

Objections to the Original Argument (with Replies)

Issue 1: “It is not clear to me why Pn must have a last instant. An event could occur over an open or half-open interval of time. If t is the time index of the first mental event, then Pn could be an event that occurs on [m, t) for any m < t. In this case there is neither overlap, nor intermediate causes.”

Reply to Issue 1: I have now revised the essay so that it makes a clearer distinction between positions in time and the “contents” that are isochronal to those positions in time. The “content” of an instant Pn is the state (i.e., the non-mental state) that obtains at Pn. By reframing the argument in terms of instants and their “contents,” rather than in terms of intervals and the boundaries of said intervals (e.g., their “first” and “last” instants, if they have a “first” or “last” instant), I think the revised argument avoids the objection that you bring up in “Issue 1.”

Issue 2: I also don't see why the existence of a moment in time between Pn and M implies that [the “content” of] Pn is not the cause of [the “content” of] M. If we identify special properties of [the “content” of] Pn that justify its being the cause of [the “content” of] M, it does not follow that every state between [the “content” of] Pn and [the “content” of] M also has those properties. It seems to me that you have introduced an additional assumption about the nature of causality, that one state can be the cause of another if and only if there is no state between them.

Reply to Issue 2: The second version of the argument does not depend on the assumption that a causal relation can only obtain between “temporally adjacent” “contents.” As mentioned above (in the second version of the argument), as soon as we acknowledge there being a purely non-mental instant (Pn+1) with its own distinct “content” (i.e., the “content” of Pn+1) intervening between the purely non-mental instant Pn and the first-ever mental instant M, we can reasonably ask whether we need to revise our list of “special properties” that we took to be responsible for the “coming into existence” of the “content” of M. For consider, if we assume that the “content” of Pn was the “cause” of the “content” of M, then we have a right to ask what “special properties” were present in the “content” of Pn and absent from the “content” of all preceding non-mental instants that made the “content” of Pn—rather than the “content” of any preceding non-mental instant—the “cause” of the “content” of M. However, our only reason for supposing the “content” of Pn to be the cause of the “content” of M was based upon our supposed identification of some properties of Pn as being the “special properties” responsible for its giving rise to the “content” of M. And, by implication, the “content” of Pn had these properties whereas and the “content” of all preceding non-mental instants lacked them. If it turns out that the “content” of Pn+1 intervenes between the “content” of Pn and the “content” of M, then our ordinary causal reasoning prompts us to reconsider if the properties of the “content” of Pn which we took to be the “special properties” were in fact the “special properties” responsible for giving rise to the “content” of M, or if we had instead only misidentified those properties as being the “special properties.”

Moreover, if we try and double down on our original assertion that those properties identified in the “content” of Pn were in fact the “special properties,” then we are left with no good reason for why the “content” of M didn’t occur before the “content” of Pn+1 occurred rather than after the “content” of Pn+1 occurred (i.e., why there was a “delay” even though the all the conditions were already present (only to vanish with the occurrence of the “content” of Pn+1)). However, if there was nothing about the intermediary “contents” (in addition to the “special properties” of the “content” of Pn) such that the occurrence of these intermediary “contents” were necessary for the occurrence of the “content” at time M, then we are left with a puzzle as to why the “content” of time M occurred earlier than some of the intermediary “contents” rather than before some of them. Moreover, this means that if the “content” of M could not occur unless the some of the intermediary “contents” occurred, then the occurrence of some of the intermediary “contents” were necessary to the occurrence of the “content” of M; yet if these were necessary to the occurrence of the “content” of M, then it would not be the case that the “content” of Pn was the necessary and sufficient condition for the occurrence of the “content” at M—thereby conflicting with the assumption that none of the intermediary “contents” mattered causally in the occurrence of the “content” of M. We can illustrate this by means of another argument:

Premise 1: Materialism posits that at some finite point, there occurred the first-ever mental state (i.e., the “content” of instant M), preceded solely by non-mental states.

Premise 2: Any causal explanation for the emergence of a first mental state (i.e., the “content” of instant M) from purely non-mental states (i.e., the “content” of non-mental instants) requires identifying specific non-mental conditions sufficient to produce mentality.

Premise 3: If an identified “content” of a non-mental instant Pn is asserted to be genuinely sufficient, then the occurrence of intervening purely non-mental “content” of instants Pn+1, Pn+2,… between Pn and M either:

(a) Contradicts the supposed sufficiency of the “content” of Pn, if those intermediates matter causally.

(b) Makes the timing of the occurrence of the “content” of M arbitrary and inexplicable, if those intermediates are causally irrelevant.

Premise 4: Both horns—causal contradiction or explanatory arbitrariness—are unacceptable to a coherent causal account. But if the Materialist cannot provide a coherent causal account, then he cannot adequately explain the causal origin of the first-ever mental state from purely non-mental states.

Conclusion: Therefore, the Materialist cannot adequately explain the causal origin of the first-ever mental state from purely non-mental states.

Issue 3: I also think it is possible for Pn and M to share a boundary point t. You argue that this is impossible because it would imply that, at time t, the world contained mental properties (because M is a mental event), but also was exhausted up to and including time t by non-mental events (because Pn is non-mental and contains t). But it does not necessarily follow that because an event has a property that each moment comprising the event has that property. For example, a physical object can have the property of being liquid, and be exhaustively comprised of subatomic particles, yet none of the subatomic particles are liquid. So too the materialist can coherently claim that the instants of time comprising a mental event do not have the property of mentality, but their agglomeration does have that property.

Reply to Issue 3: This objection does not apply to the revised version of the argument. This new version is framed in argument in terms of instants and their “contents,” rather than in terms of intervals and the boundaries of said intervals (e.g., their “first” and “last” instants, if they have a “first” or “last” instant).

Issue 4: I also think, perhaps most importantly, that the materialist simply does not have to agree that there is a first mental event. Because mentality is not metaphysically fundamental in the materialist theory, they don't even need to specify clear boundaries on the concept of “mental,” which could function rather like the notion of a species of animal, where there is a gradient of descent with no clear first member.

Reply to Issue 4: It seems that by denying that there was a “first-ever mental event” you either wade into some form of panpsychism (wherein there was never an instant whose “content” was solely “non-mental” (i.e., that “mentality” featured in the “content” of every past instant in some degree)), or you end up shifting the problem by introducing some form of “proto-mental continuum” (which, ultimately, seems to slip into some form of panpsychism again). Either way, the Materialist cannot give up the position that there was a point in time where the universe was solely non-mental—and it is precisely this position that generates the puzzle.

Inconsistencies in Keith Frankish’s Case Against Panpsychism (Part I)

I’m not a Panpsychist, or, rather, I’m not a Panpsychist in any contemporary sense of the term. Nevertheless, Panpsychism has a rich and rigorous history. It deserves to be taken very seriously. With that being said, I stumbled across an article written by the Illusionist philosopher, Keith Frankish—an article that criticizes Panpsychism severely. I wanted to come to Panpsychism’s defense. I also wanted to examine several inconsistencies in Frankish’s own arguments against Panpsychism.    

“Panpsychism’s popularity stems from the fact that it promises to solve two deep problems simultaneously. The first is the famous “hard problem” of consciousness. How does the brain produce conscious experience? How can neurons firing give rise to experiences of color, sound, taste, pain and so on? In principle, scientists could map my brain processes in complete detail but, it seems, they could never detect my experiences themselves—the way colors look, pain feels and so on: the phenomenal properties of the brain states involved. Somehow, it seems, brain processes acquire a subjective aspect, which is invisible to science. How can we possibly explain this?” (Frankish, Why Panpsychism is Probably Wrong, 1)

Keith Frankish insists that colors, sounds, tastes, and pains are real, and that our experiences of colors, sounds, tastes, and pains are also real (he simply qualifies this by saying that we mischaracterize our experiences (or objects of those experiences) as having properties which they don’t actually instantiate but only “seem” to). If we take the above passage at face value, then Frankish seems to be suggesting that my experience of a color, sound, taste, or pain is the way in which the color, sound, taste, or pain looks, sounds, tastes, or feels to me. Or, to simplify, “my-experience-of-a-color” is “the-way-in-which-the-color-looks-to-me,” “my-experience-of-a-pain” is “the-way-in-which-the-pain-feels-to-me,” and so on. 

Frankish goes on to say that the ways in which colors, sounds, tastes, and pains look, sound, taste, and feel to me are “phenomenal properties.” For example, he says, “the way colors look, pain feels and so on: the phenomenal properties of the brain states involved,” (Why Panpsychism is Probably Wrong) “It seems obvious that phenomenal properties, such as the feel of pain,” (Panpsychism and the Depsychologization of Consciousness), etc. To Frankish, “phenomenal properties…seem completely inaccessible to science. They are wholly subjective features, which simply do not show up on the scientific radar.” (Panpsychism and the Depsychologization of Consciousness). Now, if “phenomenal properties” were real, and were instantiated in the world, then what would these “wholly subjective features” be properties of? Frankish states that these “phenomenal properties” (if they were indeed instantiated in the world) appear to be properties of the brain states involved in our experiences of colors, sounds, tastes, pains, and so on (Why Panpsychism is Probably Wrong).

Confusion ensues. If “my-experience-of-a-color” is just “the-way-in-which-the-color-looks-to-me,” and “the-way-in-which-the-color-looks-to-me” is a “phenomenal property,” then we are faced with several inconsistencies.

(I) Frankish denies that “phenomenal properties” are “real” and instantiated in the world. Since Frankish holds that “my-experience-of-a-color” is just “the-way-in-which-the-color-looks-to-me” (cf. “my experiences themselves—the way colors look, pain feels and so on...” (Why Panpsychism is Probably Wrong)), and that “the-way-in-which-the-color-looks-to-me” are “phenomenal properties” (cf. “the way colors look, pain feels and so on: the phenomenal properties…” (Why Panpsychism is Probably Wrong)), it follows that Frankish is committed to the unreality of my experiences of colors, sounds, tastes, and pains. However, this conflicts with his insistence that “our lives are filled with conscious experiences—episodes of seeing, hearing, smelling, tasting, feeling, and of having bodily sensations of various kinds” and that these experiences are indeed real (Cf. The Demystification of Consciousness). 

(II) Furthermore, Frankish, being an Identity Theorist, is committed to the view that “my-experience-of-a-color” is identical to a process in my brain. However, Frankish asserts that “phenomenal properties” (if they were instantiated in the world) would be properties of the brain states involved in our experiences of colors, sounds, tastes, pains, and so on. (cf. “the way colors look, pain feels and so on: the phenomenal properties of the brain states involved.” (Why Panpsychism is Probably Wrong)) This is a manifest contradiction. Let me illustrate this. If “my-experience-of-a-color” is identical to “the-way-in-which-the-color-looks-to-me,” and “the-way-in-which-the-color-looks-to-me” is a “phenomenal property,” then it cannot be the case that the “phenomenal property” is a property of the brain processes involved in “my-experience-of-a-color.” Indeed, “my-experience-of-a-color” is ex hypothesi identical to that very brain process. A property (“phenomenal” or “non-phenomenal”) of the brain process cannot be identical to the brain process of which it is a property—an adjective cannot have itself as its own substantive!