of a current in which events float. But this is an illusion dispelled
by examination. Events cannot be submerged in time. Time cannot be
the vehicle of events. It is impossible to conceive time as existing
simultaneously with an event. It always follows it. What to Mr. Peirce
appears as a “flow,” arises from the foregoing. Take events, percepts,
or concepts, as a hypothetical series, _a_, _b_, _c_, _d_ ... and their
times as _a´_, _b´_, _c´_, _d´_ ... the first series contains the event
_per se_, or as happening; the “time when” is contained in the second
series, practically inseparable from the first, but the time when
necessarily follows—consequently if the first be _a_, the second must
be, at least _a_. But no concept or percept is abstract, except the
concept time itself, which, being unconnected, _seems_ anywhere, and,
like its fellow-abstract space, is spread out, to us, tri-dimensionally,
as past, present, and to come. And, as in space the position is simply
spectral,[74] a question of perspective or adjustment, so, in time, the
timal series is adjusted to the substantive idea. But this two-fold
spectral succession breeds by comparative intensity (which is another
complex series) the sense of a flow, where there is none, but only the
idea of a flowing, which is another matter. Thus, the so-called “veil
of the future” is no more a veil than it is a brickbat. It is simply
the indeterminateness of an unconnected adjective—as if one should say,
white—and the query arises, _What_ is it that is white? When the noun is
supplied you have something definite. Just so, when the future lapses
into the present.
Thus there is never anything without, at least, these three additions:
first, variety or difference; second, time; third, relation, spatial
or otherwise. These are all terms in a series, or set of concurrent
series. Nothing can be, practically, isolated, for everything runs in a
series. But this is a much broader theory of continuity than that which
Synechism affords.[75] All apparent perplexities vanish. The difficulty
no longer exists that to perceive a series we must hold it, as it were,
in solution. Since other than series nothing is. Hence the cosmos is
an illimitable series or complex of series. But inasmuch as the timal
element (as also the spatial) occurs through the series having time-term
and space-term resident within it, all difficulty in apprehending it as
a series vanishes. The impracticability, if any, would be in viewing any
term as isolated.
THE RESULT _RE_ TYCHISM.
What a flood of light does such a system shed indirectly upon Tychism,
since the controversy between the latter and determinism mainly hinges
upon the “must be,” the imperative, as it were, of the series! It has
been very ably pointed out by Dr. Carus in his article _re_ Mr. Peirce’s
“Onslaught on the Doctrine of Necessity” (_The Monist_, Vol. II, No.
4, pp. 573-4.) that the formula adopted by Mr. Peirce in his Tychism,
“chance is first, law is second, the tendency of habits is third,”
involves its author in the admission of a law in a system professing to
be, in its inception at all events, chanceful and _lawless_. Mr. Peirce’s
“Synechism” professes to be the law of mind. Parenthetically, however,
it may be remarked, that the distinction as to law, and lawlessness or
“chance,” narrows itself to the plane of one term more or less in a
series, or _even to less than that subordinate place_. For, although,
for convenience sake, and for facility of contrast, we have followed
Mr. Peirce’s figure of a series, to show more clearly also to what his
theory leads, it is nevertheless plain, that time and its accompanying
relations being placed on their proper level, that of integral percepts
and concepts, the figure of a series is simply a matter of convenience
of arrangement. Certainly as the “time when” is necessarily annexed to
every percept and concept the timal element may be said to follow, not
to precede, its fellow-term. Really, however, they may be said to be
simultaneous, since the timal refinements of finite, infinite, past,
present, and future are each of them contained in a percept of its own.
EXTERNALITY A SERIAL TERM.
But if the timal element be independent as a separate percept, the
spatial as another, and so on, it follows that, although the terms of the
series may, as it were, _run_, though we cannot conceive them separated,
or as, in practice, otherwise than as continuous in their flow, still,
theoretically, a series or complex of series it _is_, and a series may
be interrupted at any term. Thus externality itself being a spatial
relation, is but _one term more_, non-essential in theory, to the term
preceding. So that when the Neo-Kantians speak of the “constitution of
the objective” it ought to be added that it is not only the content
of the objective which is thus constituted by consciousness, but that
externality, all that goes to make up what is termed “out-sidedness,” is
constituted by consciousness also.
THE NOW-TIME.
“_The present is half past, and half to come_,” (p. 546) like the color
of a curved boundary line on a particolored surface; i. e. “betwixt
and between” the two. It is here that the theory of Synechism shows
its chief defect. Up to this stage we have been dealing with ideas,
feelings, _a_, _b_, _c_, _d_ ... successively passing through a point
of consciousness _e_. And the infinitesimal notation suits the required
process fairly well. It is complicated enough, but it is ingenious, and
at least plausible. Nothing up to this stage would lead us to suppose
that any additional element was to be imported into the _rationale_ which
Mr. Peirce presents. As we have seen, finite time would not serve his
purpose. By however minute a _finite_ interval have _a_, _b_, _c_ or _d_
passed the point _e_, all chance of their recovery is hopeless. Well, we
have recourse to infinitesimals, and find (to put it popularly, and not
in Mr. Peirce’s technical terms) that _a_ past the point of consciousness
by an infinitesimal interval heralds _b_. So that _e_ is simultaneously
confronted with the disappearing form of the first and the appearing
form of the second, and the same with _b_, and _c_, in turn, and so on.
Thus the present, in the sense of ideas successively passing through
consciousness, is half _a_ and half _b_, then half _b_ and half _c_, this
infinitesimal gradation ultimately ensuring the presence of the whole
series in the last “moment.”
But this will not avail with the concept time itself as distinguished
from timed succession. That these two are separate with Mr. Peirce it is
impossible to doubt. He says, e. g., “Time with its continuity logically
involves some other kind of continuity than its own,” (p. 547) and
speaks of “time and its flow,” and of “time as the universal form of
change.” And it is confusing, to say the least, when we are shifted
without warning from what is practically the perceptual to the conceptual
region. Granted the ideas, the feelings, or what not, “gliding almost
imperceptibly” (as did the late Mr. Bardell to another sphere) past the
central point of consciousness, yet not wholly past, only going, less
past than any assignable past date, granted this, the assertion is not
consequently warranted that time itself, the _present_, as time, not
as involving the succession of ideas, is “half past and half to come.”
The ideas, the feelings, of which Mr. Peirce writes, successively pass
through the stage of being thus half past and half to come, but that
is by no means the same thing as saying that the present is half past,
half to come, as Synechism avers. With our theory, as presented in the
foregoing pages there is indeed no such difficulty, but Mr. Peirce, on
the other hand, has elected to stand by infinitesimally measuring time,
as applied to ideas etc., as separate from conceptual time, and must take
the consequences of his decision. He says _the present, not the present
idea_.
Now, in the concept time as a whole, in its entire range, a definite
point may be selected—to the exclusion of other points—a point having
position but not extension, as _the present_. Is it, then,—the
present,—half past, half to come, as a timed idea is? Certainly not.
There is nothing of the flow of a series in it. Further, this selection
of the “now,” as a point, does not interfere with its permanence.
“Nowness” may persist. And the moment it partook, even infinitesimally,
of the character of the past or of the future, it would cease to be the
present. In the case of a series of ideas in time the difficulty is to
get them all in present solution, as it were, without detriment to their
evident continuity, but the definition of the present as a point in time
presents no such difficulty. The conditions are quite distinct. Yet
regarding this time point—the present—Mr. Peirce assures us that it is
“half past, half to come,” which is just that of which it is the precise
negation, if words are to have any meaning.
Again, Mr. Peirce’s _rationale_ shows, upon the face of it, that there
is (1) finitely divisible time and, (2) time divided infinitesimally,
for what finite time could not do, in that it had limitations,
the infinitesimal notation readily accomplishes. In its ulterior
consequences, this is somewhat unfortunate for Synechism, inasmuch as the
consciousness of ideas in continuity being confined to the infinitesimal
theory, where, it may be asked, is the place, in consciousness, for
the succession of finite intervals? Consciousness must be practically
doubled, so to speak, if it is to hold both of these together. This
is what comes of making one’s world-scheme hang upon a mathematical
subtlety—the subtlety in question partaking as a rule, more or less of
the nature of an escape from the difficulties of the vulgar notation, the
vulgar notation remains to be reckoned with, and both have to be credited
to consciousness. As an instance of this take the following from Mr.
Peirce’s late article,[76] “Man’s Glassy Essence”—p. 15:
“In order that a sub-molecule of food may be thoroughly and
firmly assimilated into a broken molecule of protoplasm,
it is necessary not only that it should have precisely the
right chemical composition, but also that it should be at
precisely the right spot _at the right time_ and should be
moving in precisely the right direction with precisely the
right velocity. If all these conditions are not fulfilled, ...
it will be in special danger of being thrown out again” (The
italics are not in the original).
Now here is a “time when” which can be exactly specified in accordance
with the conditions. Certain results follow unless it is kept to.
This is what Mr. Peirce would doubtless consider as a timed physical
event, part and parcel of the regularity of matter, and yet an event
which, in its own time and way, goes to account for both feeling and
habit-taking—capable, therefore, of being stated in terms of finite
time, as happening at a given instant, and neither before nor after it.
But when this same molecule is, by virtue of keeping its appointment
punctually, safely installed in feeling protoplasm, the succession of
ideas, or feelings, of which, as subject, it is capable, obeys another
rule—a given _instant_ obtains no longer; it is the _moment_ which is
everything[77]—a moment half its predecessor, half its successor. Even
granted the function of the infinitesimal, this looks very much like a
reduction to absurdity. For, if the above mentioned timed coalescence
of the sub-molecule with the broken molecule were _also_ a matter of
subjective feeling, passed as process through a consciousness, the
conclusion follows that the juncture of the molecules happens at two
different times! There is no escape from this. Given the _instant_ in
the one case, the _moment_ in the other, these two cannot possibly be
the same point in time. The moment partakes, however insensibly, of the
preceding and succeeding stages, the instant does not. Hence they are not
the same but different times.
OTHERNESS.
The foregoing has a distinct bearing upon the question of “other selves”
of which Mr. Peirce writes as follows:
“The recognition by one person of another’s personality takes
place by means to some extent identical with the means by which
he is conscious of his own personality. The idea of the second
personality, which is as much as to say that second personality
itself, enters within the field of direct consciousness of
the first person, and is as immediately perceived as his ego,
though less strongly. At the same time, the opposition between
the two persons is perceived, so that the externality of the
second is recognised.” (“The Law of Mind,” p. 558.)
This is the scheme of “otherness” which, in the case of the Neo-Kantians,
particularly the French section, represented by M. Pillon, M. Renouvier,
and others, has proved such a snare. To these thinkers, (as indeed to
the late Prof. T. H. Green, of Oxford, though in a less degree,) the
so-called external world lies in “other” thinking subjects—in “foreign
centres of representations.” The free-trade doctrine has verily
penetrated to the philosophic region—the wholesale admission of foreign
wares to the detriment of home products. Why should I place the content
of that so-called external world, which, external or internal, is my
very own inalienably, in a centre of representation other than my own,
thus making my cognition of it rest entirely upon the “ejective” plane?
It is only when I discover, as I must sooner or later, that there is
nothing in the report of an “outsider” (or in any number of them) beyond
what I credit him or her with in my own consciousness; and that the
outsider is on the same plane as other objects, it is only then that
the mystification is cleared up. I do _not_ cognise, or recognise, the
external at second-hand. The “note” of otherness is simply another term
more or less in the cosmical series.
It is, however, not only with the familiar “other selves” of ordinary
life that we are confronted in Synechism. In the creed of animism
“Millions of spiritual creatures walk the earth,”
and Mr. Peirce speaks of “spiritual influences” (p. 559) as having at
least no hindrance presented to them by his doctrine. But he has some
other shadowy personalities at command, which, it must be confessed, are
well calculated to give us pause. “There should be something like[78]
personal consciousness in bodies of men who are in intimate and intensely
sympathetic communion.... None of us can fully realise which the minds
of corporations are.... But the law of mind clearly points to the
existence of such personalities.” It is probably true that the “minds of
corporations,” must ever present an insoluble riddle of perversity to the
suburban dweller, vexed with the mockery of paving and lighting. But we
need not linger over this speculation, for there are other shades behind.
“If such a fact is capable of being made out anywhere it
should be in the Church.... Surely a personality ought to have
developed in that Church, in that ‘bride of Christ,’ as they
call it.” (“Man’s Glassy Essence,” pp. 21-22.)
A PERSONAL CREATOR.
Bearing our ecclesiastical divisions in mind, it is difficult to conceive
the unity of a “corporate personality” of this kind, but, to let that
pass, it may be remarked that, when any one begins to imagine that there
are others in the universe besides himself, he is not, as a rule, content
with two or three companions of his solitude. They come in battalions.
Thus, behind the other selves, corporate personalities and spiritual
influences of Synechism, there looms a transcendent personality. “A
genuine evolutionary philosophy,” we are told, “... is so far from being
antagonistic to the idea of a personal Creator, that it is really
inseparable from that idea.” And a philosophy of pseudo-evolutionism is
“hostile to all hopes of personal relations to God.” (“The Law of Mind,”
p. 557.)
Mr. Peirce thus assigns to his first cause a place in the _continuum_ of
ideas, and says that if there is a personal God we must have a direct
perception of that person and “indeed be in personal communication
with him.” The difficulty, he admits, is that if this be so, how is it
possible that the existence of this being should ever have been doubted
by anybody. And the only answer he can at present make is, that “facts
that stand before our face and eyes, and stare us in the face, are
far from being in all cases the ones most easily discerned. That,” he
adds, “has been remarked from time immemorial.” (“The Law of Mind,” pp.
558-559.)
One of the ablest of living philosophical writers, Professor Veitch,
of Glasgow University, puts it somewhat similarly, though with his own
realistic coloring, when he says:
“God, if at all, must rise above the line of finite regress; He
cannot be a cause in that; He cannot be a cause dependent on
another cause; He must be somewhere, or at some point, in the
line of an otherwise endless scientific regress, there, above
it, yet related to it, and in it; otherwise He is nothing for
us.” (“Knowing and Being,” p. 320.)
The parallelism is worth noting. Those views embody what has been the
contention of the present writer throughout this paper, _with this most
notable difference_: that no term of a series may thus transcend the
series, or be other than on a level with the other terms, being itself
only a term, a link, in the series itself. And with this falls forever
the idea of a cause uncaused.
Yet am _I_ not _in_ the series? For all that is in the series is
mine every percept, every concept; so that, “extravagant” as it may
appear, it is _I who am the series_. In other words, the ego is the
universe-synthesis, and the universe-synthesis the ego.
Is Mr. Peirce prepared to take the consequences of that which his
Synechism leads to?
G. M. MCCRIE.
FOOTNOTES:
[67] From τύχη, chance.
[68] _Tychism_ again comes to the front in the succeeding number of _The
Monist_, (Vol. III, No. 1,) in an article by Mr. Peirce, entitled “Man’s
Glassy Essence.”
[69] Dr. Carus, in his review of Mr. Peirce’s doctrines, (_The Monist_,
Vol. II, No. 4, p. 575,) notes this positivistic-constructionism.
[70] Cf. T. H. Green, _Prolegomena to Ethics_, Ch. II, p. 63.
[71] Nos. 258, 59, 61, August, 1892. _Miss Naden’s World-Scheme._
[72] In a note to this passage was appended a quotation from a pamphlet
by Dr. E. Cobham Brewer as a practical instance of the objective being,
on the antiquated subject-object plane, actually superseded. Suppose a
very remote star to become extinct, the “vibrations” would continue to
“travel” towards a spectator situated on our planet for years, it may
be for centuries. So that the spectator, ultimately, “sees” that which
does not even exist. Dr. Brewer’s comment, which cannot be considered any
contribution to a satisfactory _rationale_, is: “the objects, however,
must have existed, or no messenger could have been sent from their
courts.” Evidently, in this case, that which is sent is, at least, as
good as the sender—is, in fact, the self-same thing. Only, in that case,
what of the extinct object?
[73] Or to put it in another form, any one idea, and the timing of this
idea are really two ideas, although, as we shall see later, they may be
inseparable in practice.
[74] Cf., in this connection, the results of experiments by Cheselden,
as far back as 1727 on congenitally blind persons, couched for double
cataract.
[75] Much more inclusive, also, than the Relational Theory of the
Neo-Kantians.
[76] _The Monist_, Vol. III, No. 1.
[77] Mr. Peirce uses the word “instant” to mean a point of time, and
“moment” to mean an infinitesimal duration.
[78] The phrase, “something like,” is significant, when we remember, (see
_ante_,) that with Mr. Peirce the excitants were “something like” the
excited feelings.
THE FOURTH DIMENSION.
MATHEMATICAL AND SPIRITUALISTIC.
INTRODUCTORY.
The tendency to generalise long ago led mathematicians to extend the
notion of three-dimensional space, which is the space of sensible
representation, and to define aggregates of points, or spaces, of more
than three dimensions, with the view of employing these definitions as
useful means of investigation. They had no idea of requiring people to
imagine four-dimensional things and worlds, and they were even still
less remote from requiring of them to believe in the real existence of
a four-dimensioned space. In the hands of mathematicians this extension
of the notion of space was a mere means devised for the discovery and
expression, by shorter and more convenient ways, of truths applicable to
common geometry and to algebra operating with more than three unknown
quantities. At this stage, however, the spiritualists came in, and coolly
took possession of this private property of the mathematicians. They
were in great perplexity as to where they should put the spirits of the
dead. To give them a place in the world accessible to our senses was not
exactly practicable. They were compelled, therefore, to look around after
some _terra incognita_, which should oppose to the spirit of research
inborn in humanity an insuperable barrier. The residence of the spirits
had to be a place inaccessible to our senses and full of mystery to the
mind. This property the four-dimensioned space of the mathematicians
possessed. With an intellectual perversity which science has no idea of,
these spiritualists boldly asserted, first, that the whole world was so
situated in a four-dimensioned space as a plane might be situated in
the space familiar to us, secondly, that the spirits of the dead lived
in such a four-dimensioned space, thirdly, that these spirits could
accordingly act upon the world and, consequently, upon the human beings
resident in it, exactly as we three-dimensioned creatures can produce
effects upon things that are two-dimensional; for example, such effects
as that produced when we shatter a lamina of ice, and so influence some
possibly existing two-dimensioned _ice_-world.
Since spiritualism, under the leadership of the Leipsic Professor
Zöllner, thus proclaimed the existence of a four-dimensioned space, this
notion, which the mathematicians are thoroughly master of,—for in all
their operations with it, though they have forsaken the path of actual
representability, they have never left that of the truth,—this notion
has also passed into the heads of lay persons who have used it as a
catchword, ordinarily without having any clear idea of what they or any
one else mean by it. To clear up such ideas and to correct the wrong
impressions of cultured people who have not a technical mathematical
training, is the purpose of the following pages. A similar elucidation
was aimed at in the tracts which Schlegel (Riemann, Berlin, 1888) and
Cranz (Virchow-Holtzendorff’s Sammlung, Nos. 112 and 113) have published
on the so-called fourth dimension. Both treatises possess indubitable
merits, but their methods of presentation are in many respects too
concise to give a lay mind any profound comprehension of the subject. The
author, accordingly, has been able to add to the reflections which these
excellent treatises offer, a great deal that appears to him necessary for
a thorough explanation in the minds of non-mathematicians of the notion
of the fourth dimension.
I.
THE CONCEPT OF DIMENSION.
Many text-books of stereometry begin with the words: “Every body has
three dimensions, length, breadth, and thickness.” If we should ask the
author of a book of this description to tell us the length, breadth, and
thickness of an apple, of a sponge, or of a cloud of tobacco smoke, he
would be somewhat perplexed and would probably say, that the definition
in question referred to something different. A cubical box, or some
similar structure, whose angles are all right angles and whose bounding
surfaces are consequently all rectangles is the only body of which it can
at all be unmistakably asserted that there are three principal directions
distinguishable in it, of which any one can be called the length, any
other the breadth, and any third the thickness. We thus see that the
notions of length, breadth, and thickness are not sufficiently clear and
universal to enable us to derive from them any idea of what is meant when
it is said that every body possesses three dimensions, or that the space
of the world is three-dimensional.