Mr. Peirce’s views would, upon the whole, offer no violent opposition to
my opinions if he would only consent to lop off the absolute-property
of his absolute chance. I would even swallow his Absolute if he would
promise to designate by that name some real quality of the world, or the
world itself as a whole, or something that is thinkable without making
one’s head swim.[129]
Every predication of absolute, changes a real and useful idea into its
caricature. To, say that a complicated calculation is “absolutely true,”
that is, true without stipulating the condition that the methods are
right, and that the execution is made without any mistake, is ridiculous;
and thus the phrase “in a Pickwickian sense” (which we gratefully borrow
from Mr. Peirce) would always form a drastic but adequate substitute
for the term absolute. “Absolutely true” is “true in a Pickwickian
sense” only. There are no absolute truths which are in this sense
unconditionally true. In the same way, “absolute chance” is different
from that real chance known to us in experience and instanced by the
throw of the dice. Absolute chance is “chance in a Pickwickian sense.”
Strange Mr. Peirce speaks of real chance when he means an imaginary
absolute chance. He apparently uses the word “real” in this connection
not to denote something that is a fact of experience but to express the
idea of its being perfect or complete. Thus we may speak of a “real”
perpetual motion, stating at the same time that it is neither real nor
realisable.
8. THE THEORY OF PROBABLE INFERENCE.
Mr. Peirce applies his theory of probable inference to everything; also
to those cases which are unequivocally determined. He granted in a
private conversation that 2 × 2 = 4 admits of no exception. But of other
purely formal statements which are in the same predicament, for instance,
that the sum of the angles of a triangle in a plane measures 180°, he
states as probable that they are either somewhat less or somewhat more
than 180°, adding, “that they are exactly that amount is what nobody
can ever be justified in concluding.” To determine the sum of the
angles of a plane triangle by measuring the parallaxes of stars rests
upon a fundamental misconception of the principles of formal sciences.
It would be consistent for Mr. Peirce to say, that 2 × 2 = 4 is true
only according to the definitions or axioms of arithmetic. But in order
to know whether 2 × 2 = 4 in reality, we ought to apply the theory of
probable inference. Until we had verified the statement 2 × 2 = 4 by
applying this formula to the farthest solar systems, we should not be
justified in concluding that it is exactly true. The theory of probable
inferences is supposed to help us out of this perplexity, “and within
another century our grandchildren will surely know whether the three
angles of a triangle are greater or less than 180°.”[130]
There is always danger in the application of abstract ratiocination; and
the theory of probable inference forms no exception to the rule. On the
contrary, it is especially liable to lead one astray. There is the case
of the doctor who said to his patient: “I am sure you will be cured, for
I had ninety-nine patients who died during the operation, and statistics
prove beyond doubt that one among a hundred will survive it. You are the
hundredth.”
The theory of probable inferences is often misapplied, but can it be
worse misapplied than by introducing it into the province of that which
is certain? There is no sense in applying the theory of probabilities to
what is certain. We may doubt whether the rays of light travel in exactly
straight lines, but we cannot doubt the straightness of lines in plane
geometry. We cannot doubt that all the radii in a circle are equal, or
that the sum of the angles of a Euclidean triangle are 180°.
9. ZWEIDEUTIG BESTIMMT.
Mr. Peirce very kindly informs me that the term _eindeutig bestimmt_ is a
translation of a French phrase. Very well, I do not deny it. I know very
well that the phrase has a long history, but I do not consider myself
bound to present the whole pedigree of every term I use.
Does Mr. Peirce perhaps suppose that the French phrase is the original?
If we have to go back to the original beginning at all, why does he not
tell us that the French _univoque_ is a translation from the mediæval
Latin _univoce_, which was coined and used by the schoolmen in opposition
to _æquivoce_. Neither the term _eindeutig_, as Mr. Peirce asserts,
nor its scholastic original _univoce_, is an exclusively mathematical
expression.
Although the term _eindeutig_ is a translation of the French _univoque_,
there is after all a great difference between the French term and the
German term, and I have a good reason to prefer the German expression.
The French term is nominalistic or even vocalistic, the German one
is realistic. _Univoque_ and _univocal_ mean that there is only one
name or one _vox_, while _eindeutig_ lays no stress on the name but
on the meaning of the name, denoting that which admits of but one
interpretation. This is a sufficient reason for me to prefer it, and it
ought to appeal to Mr. Peirce’s realistic mind.[131]
Mr. Peirce, maintaining that _eindeutig bestimmt_ is only a mathematical
term, adduces two equations, each one of which, taken singly, admits,
he says, of two possible determinations.[132] Mr. Peirce uses these
equations as an argument against my application of the term, adding,
sarcastically: “This shows how much that argument amounts to.” But his
example proves at best only that there are incomplete determinations;
some problems allow of several solutions. In a German township in which
blue hussars are garrisoned, children used to propose to another this
profound problem: “It lies under a plum-tree and is blue; what is it?”
If the child questioned argues, “It is a plum,” he is corrected “No, it
is a hussar.” But if he argues, “It is a hussar,” he is corrected, “No,
it is a plum.” So he has no chance of guessing right. The result of Mr.
Peirce’s first equation, which may be either 11·477 or 11·523, is like
the conundrum of the plum-tree: it amounts to the same, viz. to nothing,
and proves only that there are determinations which are _zweideutig
bestimmt_.
10. EXPLANATION.
The differences of method become very serious when we disagree on the
very meaning of “explanation” itself. How can two debaters accept or
reject one another’s arguments, if their ideas of explanation are
radically different?
Mr. Peirce’s definition of the term “explanation” appears to me very
unsatisfactory. He says (p. 57):
“I cannot admit that explanation is description of the fact
explained. It is true that in the setting forth of some
explanations it is convenient to restate the fact explained so
as to set it under another aspect, but even in these cases the
statement of other facts is essential. (!) In all cases it is
_other facts_, (!) usually hypothetical, which constitute the
explanation; (!) and the process of explaining is a process by
which from those other facts the fact to be explained is shown
to follow as a consequence by virtue of a general principle or
otherwise.”
“To explain a fact is to show that it is a necessary or
at least a probable result from another fact (!) known or
supposed.”
My definition of “explanation,” as a description in which the process
described is recognised as a transformation is sneered at. Says Mr.
Peirce (p. 558):
“A magician transforms a watch into a dove. Recognise it as
a transformation and the trick is explained, is it? This is
delightfully facile.”
Indeed, the magician’s trick is explained as soon as we know all the
changes that have taken place. Take the whole number of objects handled
by the magician, those which he shows and those which he conceals. Let
us observe how he hides the watch and how he produces the dove, and the
trick is explained. Is it not?
Explanation is, as the word suggests, a making plain, so that we can look
over the whole field before us, and leave nothing hidden from sight. This
whole field, the survey of which is needed for the recognition of the
transformation, is called the system of the explanation. After we have
seen how the changes take place, and after we have described in exact
formulas their modes of action, our desire for explanation is completely
satisfied.
The instances adduced by Mr. Peirce prove plainly that his objections
cannot be maintained. Every one of them is an instance of transformation
(with the exception of the emerald vest, which, however, is not stated
with sufficient completeness). Take, for instance, the following example
adduced by Mr. Peirce (p. 557):
“A ‘special process of nature,’ calling for explanation, is the
circumstance that the planet Mars, while moving in a general
way from west to east among the fixed stars, yet retrogrades a
part of the time, so as to describe loops in the heavens. The
explanation is, that Mars revolves in one approximate circle
and we in another.”
Can any one deny that this explanation is a description? We draw the
two orbits as correctly as possible for the required demonstration
and combine the points representing the earth with those representing
Mars at their successive positions. Considering the fact that we do
not perceive the motion of the earth, we have to construct a diagram
in which the directions of these lines are described as viewed from a
stationary point. This is a description of changes that take place. It is
a portrayal of the transpositions of two bodies, and the appearance which
the change of this relation presents to one of them.
Mr. Peirce has neither the grace nor good-will to, understand my
proposition, that _explanation is always a tracing of form_. He says (p.
558):
“Forms may indulge in whatever eccentricities they please, in
the world of dreams, without responsibility.”
In the world of dreams, yes! But not in the world of reality. And even
the irresponsible eccentricities of dreams take place according to law.
Feeling that he mistakes my position, Mr. Peirce adds:
“Should Dr. Carus reply that I mistake his meaning, that it is
only ‘being in general’ (§ 66), that he holds unaccountable,
I reply that this is simply expressing scepticism as to the
possibility and need of philosophy.” (P. 558.)
Of course, I mean “being in general.” As to the scepticism imputed to me,
I answer, that any attempt at explaining how matter and energy, which I
take to be eternal, came into being, is a wrongly formulated problem.
Mr. Peirce might as well call me a sceptic, because I recognise that we
cannot square the circle. (Compare “Fundamental Problems,” 2d ed., pp.
283-285 and 291.)
Mr. Peirce’s gravest mistake is his belief that
“In all cases it is _other facts_ which constitute the
explanation.” (P. 557.)
The practical application of this mistake becomes fatal to his philosophy.
It is by no means necessary to pass beyond that system of facts which
contains the phenomenon to be explained. We must, as a matter of course,
keep completing the facts of a phenomenon until we have acquired a survey
of what we call the whole system of the facts, but we have never to
resort to other facts.
We are confronted every day with hundreds of facts of which we never
see the whole system to which they belong, but we readily supply these
deficiencies from the stock of our experience. We refer the unknown to
the known. The single case under observation is referred to something
with which we are familiar. Those systems of explanation which are known
to us serve as patterns for others that are only partially known, and we
fill out, with their assistance, the gaps of our observation.
The readiness and reliability of our explanation thus depends upon the
stock of knowledge we have. The more we know, the easier shall we conquer
the unknown; the more incomplete our knowledge is, the greater the number
of hypothetical facts that will have to be introduced; and this always
weakens the reliability of our explanations. Hypothetical facts should
be introduced only in cases of urgent necessity. However, if they are
admitted at all, they have to be thought of as parts of the system under
investigation, for they have been invented only because we are compelled
to assume that without them it would be incomplete.
Mr. Peirce adduces the following example to prove that “other facts” are
required in an explanation:
“It has been stated that a warm spring in Europe is usually
followed by a cool autumn, and the explanation has been offered
that so many more icebergs than usual are liberated during
a warm spring, that they subsequently lower sensibly the
temperature of Europe. I care little whether the fact and the
explanation are correct or no. The case illustrates, at any
rate, my point that an explanation is a special fact, supposed
or known, from which the fact to be explained follows as a
consequence.” (P. 557.)
When, as in this instance, we recognise that one fact is the necessary
result of another fact, we view them both as parts of one set or system
of facts in which a transformation is taking place, and, unless we
see the connection of the two facts as constituting one process of
transformation, we cannot say that the problem is explained. When we
observe changes which are the results of transformations taking place
beyond the horizon of our knowledge, we are, as a matter of course,
unable to give an explanation.
Mr. Peirce had perhaps in mind a special and more complex kind of
explanation, which we define as “comprehension.” He says (p. 557):
“The fact to be explained is shown to follow as a consequence,
by virtue of a general principle or otherwise.”
Take as an instance the law of gravitation. There are the facts of
falling stones and the motions of celestial bodies. Both sets of
facts are explained, according to Mr. Peirce, “by virtue of a general
principle,” i. e. gravitation, while we say, both sets of facts are
comprehended under a common formula. Mr. Peirce’s conception of
“explanation” rests on the antiquated view that gravitation is a
principle behind the gravitating masses which compels the stone to fall.
Gravitation, however, is not “another fact” foreign to the facts under
consideration. It is not a principle called in from the outside. On the
contrary, it is the essence and extract of the very facts that are to be
explained.
Principles which have not been derived either from the facts to be
explained, or from the additional facts which belong to their system, do
not and cannot explain the phenomena.
* * * * *
Comprehension is, as it were, an explanation of a higher degree. The
term means a grasping together, and it actually consists in viewing two
or several facts in such a way as to recognise their common features.
Comprehension is a reduction of our patterns of explanation; it unites
two or several of them in one formula.
For instance, it has been observed that certain objects float in water
while others sink to the bottom. The observations do not seem to agree,
they present two incoherent facts. When we find out that the weight of
a floating body is equal to the weight of water which it displaces,
we understand at once why bodies whose specific gravity is greater
than water sink while those of a lighter specific gravity float.
Comprehension, in this as in every other case, is the description of a
process which comprises all the facts that belong to a special class in
a common formula. The description must be applicable to all single cases
however different they may be.
This conception of comprehension has a great advantage over Mr. Peirce’s
view. While he has to bring in some “other fact” from the outside, we
need not introduce any foreign element. Comprehension, as we understand
it, can rise from the statement of particular facts to more and more
general formulations, until finally we arrive at universal laws. All
the laws thus formulated to satisfy our cravings for comprehension, are
found to belong to one great system of laws, and our scientists are
constantly engaged not only in widening the range of our experience by
new discoveries, but also in revising our statements of the uniformities
of nature and, where they appear to be in collision, in bringing them
into harmony.
This conception of comprehension is monistic, Mr. Peirce’s is dualistic.
We need not, in order to explain the facts of existence, go beyond them
into a supernatural realm. Mr. Peirce must go outside of the world
into non-existence when he attempts to understand the world by the
principles of his philosophy. It is very doubtful whether explanations,
the “essential” nature of which is to consist of “other facts usually
hypothetical,” will be satisfactory to anybody except himself.
Otherness makes any fact unfit to serve as a factor of an explanation and
indeed I cannot think of any instance, real or imaginary, in which the
explanatory facts, be they real or hypothetical, do not form parts of the
system under consideration.
There is only one instance to which Mr. Peirce’s method of explanation
has been applied, and I am under the impression that it has been invented
solely for this purpose. Mr. Peirce’s philosophy is too original to
be explained by the usual methods; it must have an original method of
its own. In order to explain “law” Mr. Peirce calls in “chance.” His
explanation must be an “other fact” and the only fact different from
law is not-law, lawlessness, or absolute chance. According to my idea
of explanation, law can never be explained by chance. According to Mr.
Peirce, it is the only possible thing that can be called in as that
“_other_ fact” which is supposed to be the essential constituent of an
explanation.
If Mr. Peirce’s method of explanation were sound, we should have to
explain order from chaos, possibility from impossibility, and sense from
nonsense.
II. MR. PEIRCE’S PHILOSOPHY.
Mr. Peirce’s constant references to scholastic philosophy remind me of
happy years long past when I was extremely interested in the theories
of such men as Thomas Aquinas, Duns Scotus, Occam, Abelard, Tauler,
and others. Together with my chum, now a sober Professor of physics at
a German University, I freely indulged in the construction of various
world-theories, which, alas! were quickly overthrown one after another by
the slightest puff of wind. I have not lost my interest in the schoolmen,
but it is considerably weakened.
Mr. Peirce’s repeated praise of scholastic realism and his condemnation
of any theory that he brands as nominalistic, seems to me like the method
of some of our politicians who, eager to revive toryism, should censure
all evils of the politics of to-day as whiggish. This comparison is not
exaggerated, for there are a few Hamiltonians who miss the refining
influence of an aristocratic class and regret that the historical
tradition of toryism has been so completely broken. I would not deny that
there is some truth in it, and there is some truth, too, in mediæval
realism, which has been neglected by the, first violently suppressed and
then triumphant, nominalism. But in reviving realism the Scotists should
be very careful to avoid a resurrection of its errors.
1. DUNS SCOTUS AS A PHILOSOPHICAL PATRON SAINT.
Johannes Duns Scotus, a Franciscan, honored since his successful defense
of the Blessed Virgin’s Immaculate Conception by the title Doctor
Subtilis, and the very same man after whom, on account of the narrowness
of his later disciples during the time of the Reformation, a blockhead
is to-day called a dunce, was one of the most characteristic figures of
scholastic philosophy. He lived at the end of the thirteenth Century when
the authority of the philosophy of Thomas Aquinas who had died March 7th,
1274, was all but universally recognised. Scotus appeared as the most
powerful opponent of Thomas. Ingenious, original, bold, and buoyant in
his attacks he had a short but brilliant career and died comparatively
young at Cologne, in November, 1308.
While Thomas, surnamed Dr. Universalis, or Dr. Angelicus, is regarded by
his order, the Dominicans, as the greatest authority in philosophical
matters, Scotus succeeded in impressing his mode of thought upon the
Franciscans; yet Thomas is universally regarded in the Roman church and
also among Protestant theologians as the more orthodox Christian.
Almost all the ideas of Scotus were set forth in opposition to the views
of others and mainly of Thomas. Thomas was a determinist, Scotus an
outspoken indeterminist. Thomas says that man’s action is necessarily
determined by what he thinks is best. Scotus avers that man thinks in a
certain way because he wills in a certain way. Man’s ideas are fashioned
to suit his character. His motto is, “_voluntas superior est intellectu_”
and his idea of will is identified with the indetermined arbitrariness of
a perfect _liberum arbitrium_. According to Thomas, God commands us to do
the good because it is good. Scotus calls good that which God commands
simply because God commands it. The will of God, like the will of man is,
in Scotus’s opinion, undetermined, it is arbitrary. Thus God created the
world not because his will was determined by some motive, but because
it so pleased him; and Christ’s passion and death were not really an
atonement; they simply were accepted as such by God.
Without entering into this controversy of _anno olim_ we might say
that we side neither with Thomas nor with Scotus, but would modify the
statement of the former by the criticism of the latter. Thomas goes
too far when he says that whatever is recognised as the best will of
necessity be done. He overlooks the power of passions. Thomas’s statement
would be right, if every passion were regarded as a will which has its
own and independent but mistaken ideas about good. A soul whose passions
are more powerful than rational considerations will necessarily be
inclined to obey its irrational impulses. There is something in Scotus’s
criticism, but his view is no improvement. In speaking of will as
superior to the intellect, did he ever ask himself the question, What his
own will would be independent of his intellect? Further, when God is said
to command the good because it is good, Thomas separates in a logical
consideration two ideas which are identical. Scotus is right in defining
good as the will of God. From our standpoint we should say, the will of
God, viz., the moral order of the universe, is of a definite kind which
can be ascertained by experience. To speak of the will of God as good is
an anthropomorphic expression. Good is that which agrees with the will of
God; bad, that which opposes it. Suppose the moral order of the universe
were different, goodness and badness would change with it.
We have sketched the views of Scotus only to show the points of
contact between him and Mr. Peirce. Mr. Peirce is also an outspoken
indeterminist. He identifies feeling with chance, and his free will is a
_liberum arbitrium_. Mr. Peirce, like Scotus, also separates theology,
and, with it, religion, from philosophy.[133] Scotus ridicules those
who confound both, clearly indicating that he is aiming at Thomas, to
whose fervent faith their conciliation was a matter of momentous and all
important consequence. Scotus goes so far as to aver that something might
be true in philosophy which is wrong in theology (see Ed. “Wadding” Fol.
4, p. 848)—a statement that to an honest searcher for truth must almost
appear as frivolous.[134]
How much more imbued with true religiosity was his great namesake John
Scotus Erigena the venerable founder of scholasticism when saying: “_Non
est alia philosophia, i. e. sapientiae stadium, et alia religio_.”
2. MR. PEIRCE’S ORIGINAL THEORIES.
Mr. Peirce as a controversalist and critic is like Scotus, brilliant,
versatile, and powerful. But he is more; he is also constructive.