Vol. II, p. 560 ¶ 1
” ” 2 §28
” ” 3 29
” 561 4 23.27
” ” 5 21
” ” 6 18
” ” 7 18
” 562 8 18 _bis._
” ” 9 21
” ” 10
” 563 11 12.21.22
” ” 12 19
” ” 13 19
” 564 14 3.12 _bis._ 22
” ” 15 8 _ter_, 16
” 565 16 21
” ” 17 3
” ” 18 3
” ” 19 13 note
” 566 20 14
” ” 21 13, 14
” ” 22 3.12.22
” ” 23 12
” ” 24 3.13.14
” 567 25 8
” ” 26 8
” ” 27 8.22
” ” 28 20.22
” ” 29 12
” 568 30 22
” ” 31 22 _bis_
” ” 32 22
” 569 33 22
” ” 34 22
” ” 35 8
” ” 36 29
” ” 37
” 570 38
” ” 39
” ” 40
” 571 41
” ” 42
” ” 43
” 572 44 23
” ” 45
” ” 46 5.23
” 573 47
” ” 48 7
” ” 49 7
” ” 50 7
” 574 51 7.25
” ” 52
” ” 53 25
” ” 54
” ” 55 25 _bis_
” 575 56 17
” ” 57 17 _bis_
” ” 58 17.25
” ” 59 17
” ” 60 17
” 576 61 7.17.25 _bis_
” ” 62 17.21
” ” 63 17
” 577 64 17 _bis_
” ” 65 26
” ” 66 25
” ” 67 25 _bis_
” 578 68 6.7
” ” 69 17
” 579 70 6
” ” 71 3
” 580 72 3
” ” 73 3
” ” 74 3
” ” 75 3
” 581 76 3
” ” 77 3.11
” ” 78
” ” 79 21
” 582 80
” ” 81 29
” ” 82 29
” ” 83 29
Vol. III, 68 84 5
” ” 85 27
” ” 86
” 69 87 12
” ” 88 5.15 _bis_
” ” 89
” ” 90
” ” 91 5
” ” 92 5
” 70 93 5
” ” 94 5
” ” 95 3
” ” 96 4.11
” 71 97
” ” 98
” ” 99
” ” 100
” 72 101
” ” 102 11
” ” 103 6
” ” 104
” ” 105
” 73 106 11
” ” 107 6
” ” 108 6
” ” 109 6
” ” 110 6
” ” 111 6
” 74 112 6
” ” 113 6.11
” ” 114 6
” ” 115 6
” 75 116 6.7
” ” 117 6
” 76 118
” ” 119 9
” ” 120 6.16
” ” 121 14
” ” 122 11
” 77 123 3
” ” 124 10
” ” 125 7
” 78 126 8
” ” 127 8
” ” 128 29
” 79 129
” ” 130
” ” 131
” ” 132
” ” 133 27
” ” 134
” 80 135
” ” 136
” ” 137 15
” ” 138 15
” ” 139 5.15
” 81 140 15
” ” 141 15
” ” 142 15.25
” ” 143 15.24
” ” 144 15 _bis_
” ” 145 15 _bis_
” ” 146 15 _bis_
” ” 147 15 _ter_
” 82 148 15
” ” 149 12.15
” ” 150 15 _bis._ 25
” 83 151 15.24
” ” 152 15.24
” ” 153 15.24
” ” 154 15.24
” ” 155 15.24
” 84 156 15 _bis_
” ” 157 15
” ” 158 15.24
” 85 159 15.24
” ” 160 15.24
” 86 161 15 _bis_
” ” 162 15
” ” 163 5.14
” ” 164 14
” 87 165 4.14
” ” 166 14
” ” 167 14
” ” 168 27
” ” 169 27
” 88 170 27
” ” 171 27
” ” 172 27
” ” 173
” ” 174
” 89 175 27
” ” 176 27 _bis_
” ” 177 27
” ” 178 27
” ” 179
” ” 180 30
” ” 181
” ” 182
” 90 183 30
” ” 184
” ” 185 27
” ” 186 27
” 91 187 27
” ” 188
” ” 189
” ” 190
” 92 191 4
” ” 192 27 _bis_
” ” 193 20.27 _bis_
” 93 194
” ” 195 8
” ” 196 8
” 94 197
” ” 198 6
” ” 199 30
” ” 200
” ” 201
” 95 202
” ” 203 20.29
” ” 204 29
” 96 205 20
” ” 206
” ” 207
§ 3. Dr. Carus’s philosophy is hard to understand. Some phrases which
he frequently uses lead the reader to imagine that he is listening to
an old-fashioned Königsberg Kantian. What, then, is our surprise when
we find (¶ 14) that he sneers at the Kantian, Sir William Hamilton
(whom he calls Mr. Hamilton) as having “no adequate conception of the
_a priori_.” In his “Ursache, Grund und Zweck” (1883), an admirably
clear and systematic exposition of much of his thought, he takes a
Schleiermacherian view of the _a priori_. He admits it to be founded in
the universal conditions of cognition; but he thinks it is among the
objective rather than the subjective conditions. This is an opinion
to which Hamilton is also at times inclined. It is a weak conception,
unless the whole distinction between the inward and the outward world be
reformed in the light of agapastic and synechistic ontology. For to deny
that the _a priori_ is subjective is to remove its essential character;
and to make it both subjective and objective (otherwise than in the sense
in which Kant himself makes it objective) is uncalled for, and is cut off
by Ockham’s razor. But when synechism has united the two worlds, this
view gains new life.
Another thing which has astonished me is Dr. Carus’s extravagant
laudation (¶ 17) of Venn’s highly enlightened and remarkably
bright-thinking, yet blundering little book, “The Logic of Chance.”[101]
This is the way he speaks of it: “This admirable work, we will make
bold to say, marks a new epoch in the study of logic.” He adds that it
“paves the way which Mr. Peirce has actually followed.” But the question
of the nature of probability had long before that publication engaged
the attention of some of the most powerful intellects in England; and
my opinion concerning it was fully made up before I saw the book. I do
not think I learned anything from that except a classification of the
philosophies of probability. However, after all his eulogy, Dr. Carus
only uses the book to quote from it Mill’s rewording of Kant’s definition
of causation, which he would better have quoted direct.
Let me say, not to Dr. Carus, but to the younger generation of readers,
that if they imagine that Hamilton, because he is antiquated, is not
worth reading, they are much mistaken. The Scotistic elements of his
philosophy, and his method in the notes on Reid are especially worthy of
attention. As for Mill, though his philosophy was not profound, it is,
at least in his “Examination of Hamilton,” admirably set forth. Whoever
wishes to appeal to the American philosophical mind needs to be quite
familiar with the writings of these two men.
Dr. Carus himself accepts all that I hold for erroneous in Kant’s
definition of causation as universal and necessary sequence. Mill
merely substitutes the exacter words _invariable_ for “universal,”
and _unconditional_ for “necessary.”[102] In giving his form of the
definition, Mill shows why it is not applicable to the sequence of day
and night, namely, that that is not necessary. Yet Dr. Carus writes (¶
18) of this very same sequence as if it came under Mill’s definition![103]
Again, why should he make it “the immortal merit of the great Scotchman”
(¶ 22), that is, of Hume, that he admitted the truth of Leibniz’s
principle?
The famed puzzle of causation is peculiarly understood by Dr. Carus.
The difficulties which the perusal of Hume suggested to the mind
of Kant,[104] were such as belonged to all categories, or general
conceptions of the understanding. The precritical Kant inherited a very
decided nominalism from Leibniz and Wolf; and the puzzle for him was
simply the usual difficulty that plagues nominalism when it finds itself
confronted with a reality which has an element of generality. Necessity
is, I need hardly say, but a particular variety of universality. But
Dr. Carus (¶ 24) passes over this, to dwell upon an entirely different
objection to causation, namely, that it seems to be a creation out of
nothing, and a miracle.
I find myself equally at cross-purposes with him, when in ¶¶ 71-77, he
speaks of the prevalent views of logicians concerning _comprehension_.
This word, in logic, measures the amount of predicates or marks attached
to a conception; but Dr. Carus’s criticisms seem to be based upon the
idea that by comprehension is meant logical breadth, or the amount of
subjects to which the conception is applicable.
I am simply gravelled by his remarks (¶ 95) concerning sundry English
words.
No more do I know what to make of his praise (¶ 123) of the German
translation of a French phrase used in the theory of functions, meaning
_univocally determined_.
§ 4. One habit which goes far to obscure Dr. Carus’s meaning is that
whenever he finds his opinion at variance with a familiar saying, instead
of rejecting that formula, he retains it and changes the meaning. This is
calculated to throw the whole discussion into confusion. Thus, nothing is
more certain than that the so-called “law of identity,” or _A_ is _A_,
was intended to express the fact that every term is predicable of itself.
But Dr. Carus, simply because he finds that “meaningless and useless” (¶
96), thinks himself authorised to confuse the terminology of logic by
making this formula, _A_ = _A_, under the same old name, mean that things
to which the same name is applicable are for some purpose equivalent.
In like manner, he changes the meaning of the word _freedom_ (¶ 165),
so that the distinction between those who maintain and those who oppose
the freedom of the will may, in words, disappear. It seems scarcely
defensible for a thoroughgoing necessitarian, such as he is, to fly the
flag of Free Will.
He, also, changes the meaning of _spontaneity_ so far that, according to
him, “masses gravitate spontaneously” (¶ 191), and so pretends that his
doctrine does not suppress the spontaneity of nature!
§ 5. There are other questions of terminology in which I am unable to
agree with Dr. Carus. Thus, when I define necessitarianism as “the theory
that the will is subject to the general mechanical law of cause and
effect,” Dr. Carus (¶ 139) wishes to delete “mechanical.” But the result
would be to define a doctrine to which the advocates of free will would
generally subscribe, as readily as their opponents. In order properly to
limit the definition, it is quite requisite to exclude “free causation.”
By “mechanical” causation, I mean a causation entirely determinative,
like that of dynamics, but not necessarily operating upon matter.
Dr. Carus mentions (¶ 84) that there are several different ideas to
which the term necessity is applied. It seems to me that what lies at
the bottom of all of them is the experience of reaction against one’s
will. In the simplest form, this gives the sense of reality. Dr. Carus
himself admits (¶ 46) that reality involves the idea of inevitable fate.
Yet philosophical necessity is a special case of universality. But the
universality, or better, the generality, of a pure form involves no
necessity. It is only when the form is materialised that the distinction
between necessity and freedom makes itself plain. These ideas are,
therefore, as it seems to me, of a mixed nature. Dr. Carus (¶¶ 91-94)
insists that by the necessary, he wishes to be understood to mean in
all cases the _inevitable_. This is the idea of _fate_, and is not the
conception which determinists usually attach to the term necessity.
Yet he does not appear to be quite consistent. At one time (¶ 88), he
carefully distinguishes necessity from fate. At another time (¶ 163),
every element of compulsion is to be excluded from the conception of
necessity.
§ 6. One important key to Dr. Carus’s opinions is the recognition of the
fact that, like many other philosophers, he is a nominalist tinctured
with realistic opinions.
He says (¶ 103), that “there is no need of discussing the truism that,
properly speaking, there is no absolute sameness.” Now, upon the
nominalistic theory, there is not only no absolute or numerical identity,
but there are not even any real agreements or likenesses between
individuals; for likeness consists merely in the calling of several
individuals by one name, or (in some systems) in their exciting one idea.
On the other hand, upon the realistic theory, the fact that identity is
a relation of reason does not in the least prevent it from being real.
On that theory, it is real unless it is _false_ that anything is itself.
Thus, upon either theory, identity is just as real as similarity. But
Dr. Carus, being a nominalist leaning toward realism, is inclined to
make dynamical relations real, and second-intentional ones unreal. This
opinion, I think, is a transitional one.
The declaration (¶ 198) that “natural laws are simply a description
of nature as nature is,” and that “the facts of nature express the
character of nature,” are nominalistic. But in another place (¶¶
107-116), he says distinctly that uniformities are real.
He says (¶ 70), “Mr. Peirce attempts to explain natural laws as if they
were concrete and _single facts_.” This is eminently nominalistic. The
nominalist alone makes this sharp distinction between the abstract and
the concrete,[105] which must not be confounded with Hegel’s distinction
for which the same words are used. The nominalist alone falls into the
absurdity of talking of “single facts,” or _individual generals_. Yet
Dr. Carus says (¶ 68) that natural laws describe the facts of nature
_sub specie aeternitatis_. Now I understand Spinoza to be a realist.
In ¶117 he considers it “settled” “that there are samenesses.” This is
realistic. But in ¶ 120, he holds “the whole business of science to be to
systematise the samenesses of experience,” which is nominalistic.
§ 7. Dr. Carus seems to be in some doubt as to how far evolutionism ought
to be carried. In ¶¶ 48-51, he seems to side with my contention that it
should be thoroughgoing. In ¶116, he makes intellect an evolution from
feeling. Yet he is sometimes (¶ 125) “inclined” to say the world never
was a chaos; he sometimes (¶ 61) thinks it weak to suppose that real
chance begets order; and he sometimes (¶ 68) goes so far as to pronounce
eternity to be the _conditio sine qua non_ of natural law.
§ 8. Every reader of _The Monist_ knows that our good editor’s great word
is “formal law.” The clearest statement he has ever made of this doctrine
I find in the following two sentences (¶ 127):
“The _a priori_ systems of thought are ... constructions
raised out of the recognition of the formal, i. e. relational
samenesses that appear in experience. All possibilities of a
certain class of relations can be exhausted and formulated in
theorems.”[106]
This is perspicuous. For example, of pairs, we can easily show that
there are but two forms _A_:_A_ and _A_:_B_. This proposition,—theorem
if you will,—exhausts the possibilities. If we make believe there is no
danger of falling into error in mathematical reasoning,—and one danger,
though not, perhaps, a very serious one, _is_ eliminated,—then this
proposition is absolutely certain. But I will say, at once, that such a
proposition is not, in a proper sense, synthetic. It is a mere corollary
from the definition of a pair. Moreover, its application to experience,
or to possible experience, opens the door to probability, and shuts out
absolute necessity and certainty, _in toto_.
Concerning points like this, Dr. Carus, in company with the general
body of thinkers, is laboring under a great disadvantage from not
understanding the logic of relatives. It is a subject I have been
studying for a great many years, and I feel and know that I have an
important report that I ought to make upon it. This branch of logic is,
however, so abstruse, that I have never been able to find the leisure to
translate my conclusions into a form in which their significance would
be manifest even to a powerful thinker whose thoughts had not long been
turned in that direction. I shall succeed in doing so, whenever I can
find myself in a situation where I need think of nothing else for months,
and not before. That may not be for thirty years; but I believe it is the
intention of providence that it should be. Meantime, I will testify, and
the reader can take my testimony for what he thinks it is worth, that
all deductive reasoning, except that kind which is so childishly simple
that acute minds have doubted whether there was any reasoning there,—I
mean non-relative syllogism,—requires an act of choice; because from a
given premise, several conclusions,—in some cases an infinite number,—can
be drawn. Hence, Dr. Carus is altogether too hasty in his confidence
(¶¶ 195, 196) that general thinking machines “are not impossibilities.”
An act of original and arbitrary determination would be required; and
it seems almost evident that no machine could perform such an act
except within narrow limits, thought out beforehand and embodied in
its construction. Moreover, positive observation is called for in all
inference, even the simplest,—though in deduction it is only observation
of an object of imagination. Moreover, a peculiar act which may properly
be called _abstraction_[107] is usually required, consisting in seizing
evanescent elements of thought and holding them before the mind as
“substantive” objects, to borrow a phrase from William James. At the
same time, the process I am describing, that is, relative deduction, is
perfectly general and demonstrative, and depends upon the truth of the
assumed premises, and not, like inductive reasoning, upon the manner in
which those premises present themselves.
But the application of the logic of relatives shows that the propositions
of arithmetic, which Dr. Carus usually adduces as examples of formal law
(¶ 15), are, in fact, only corollaries from definitions. They are certain
only as applied to ideal constructions, and in such application, they are
merely analytical.
The truth is our ideas about the distinction between analytical and
synthetical judgments is much modified by the logic of relatives, and
by the logic of probable inference. An analytical proposition is a
definition or a proposition _deducible_ from definitions; a synthetical
proposition is a proposition not analytical. Deduction, or analytical
reasoning, is, as I have shown in my “Theory of Probable Reasoning,” a
reasoning in which the conclusion follows (necessarily, or probably) from
the state of things expressed in the premises, in contradistinction to
scientific, or synthetical, reasoning, which is a reasoning in which the
conclusion follows probably and approximately from the premises, owing to
the conditions under which the latter have been observed, or otherwise
ascertained. The two classes of reasoning present, besides, some other
contrasts that need not be insisted upon in this place. They also present
some significant resemblances. Deduction is really a matter of perception
and of experimentation, just as induction and hypothetic inference are;
only, the perception and experimentation are concerned with imaginary
objects instead of with real ones. The operations of perception and of
experimentation are subject to error, and therefore it is only in a
Pickwickian sense that mathematical reasoning can be said to be perfectly
certain. It is so, only under the condition that no error creeps into
it: yet, after all, it is susceptible of attaining a practical certainty.
So, for that matter, is scientific reasoning; but not so readily. Again,
mathematics brings to light results as truly occult[108] and unexpected
as those of chemistry; only they are results dependent upon the action
of reason in the depths of our own consciousness, instead of being
dependent, like those of chemistry, upon the action of Cosmical Reason,
or Law. Or, stating the matter under another aspect, analytical reasoning
depends upon associations of similarity, synthetical reasoning upon
associations of contiguity. The logic of relatives, which justifies these
assertions, shows accordingly that deductive reasoning is really quite
different from what it was supposed by Kant to be; and this explains how
it is that he and others have taken various mathematical propositions
to be synthetical which in their ideal sense, as propositions of pure
mathematics, are in truth only analytical.
Descending from things I can demonstrate to things of which various
facts, in the light of those demonstrations, fully persuade me, I
will say that in my opinion there are many synthetical propositions
which, if not _a priori_ in Dr. Carus’s sense, are, at least, innate
(notwithstanding his frequent denials of this, as in ¶ 15) though he
is quite right in saying that their abstract and distinct formulation
comes very late (¶ 126). But turn the facts as I will, I cannot see that
they afford the slightest reason for thinking that such propositions are
ever absolutely universal, exact, or necessary in their truth. On the
contrary, the principles of probable inference show this to be impossible.
Dr. Carus adduces the instance of a geometrical proposition, namely,
“that two congruent regular tetrahedrons, when put together, will form a
hexahedron.” (¶ 25.) This, he says, seems to be “a very wonderful thing”;
for why should not a larger tetrahedron be formed, just as two heaps of
flour make a large heap of flour? Yet, he continues, the probability
that the two tetrahedrons do always make a hexahedron is 1, “which
means certainty” (¶ 27). But as it happens, the proposition, in the
form stated is quite erroneous. What is true is this. If two tetrahedra
are so placed that one face of each is coincident with one face of the
other, while all the other faces are inclined to one another, and if of
the 8 faces, the 2 that are coincident are not counted, there remain to
be counted 8-2=6 faces. But there is nothing more wonderful about this
than that 8-2=6, which is an easy corollary from definitions. Very few
propositions in mathematics that appear “marvellous” will hold water; and
those few excite our astonishment only because the real complexity of the
conditions are masked in an intuitional presentation of them.
Dr. Carus holds (¶ 15) that formal knowledge is absolutely universal,
exact, and necessary. In some cases, as where he says that, given the
number of dimensions of space, the entire geometry could be deduced (¶
35), the boasted infallibility will prove on examination to be downright
error. In all other cases, the propositions only relate to ideal
constructions, and their applicability to the real world is at the best
doubtful, and, as I think, false; while in their ideal purity, they are
not synthetical.
Thus, my good friend and antagonist holds that the combination of oxygen
and hydrogen to produce water is not “different in principle” from that
of the tetrahedra to produce a hexahedron (¶ 26). There is all the
difference between the ideal and the real; which to my Scotistic mind is
very important. But this is not the only passage in which he speaks as if
form were the principle of individuation.
§ 9. Dr. Carus’s position is even weaker than that of Kant, who makes
space, for example, a necessary form of thought (in a broad sense of that
term). But Dr. Carus appears to consider space as an absolute reality.
For he says (¶ 119) that “every single point of space has its special
and individual qualities.” Here again form is made the principle of
individuation; whence the queer phrase, “individual qualities.”
§ 10. Dr. Carus argues that whatever is unequivocally determinate is
necessary. (¶ 124.) Were the determination spoken of real dynamic
determination, this would be a mere truism. But the expression used,
_eindeutig bestimmt_, merely expresses a mathematical determination, and
therefore no real necessity ensues. The equation
(Transcriber’s Note: Italics have been removed from the
formulæ for readability.)
x² - 23x + 132¼ = 0
determines _x_ to be either 11·477 or 11·523. In this sense, _x_ has
necessarily one value or the other. The equation
x² - 12x + 6 = 0
determines _x_ to be either 11·477 or 0·523. Together, the two equations
uniquely determine _x_ to be 11·477. This shows how much that argument
amounts to.
§ 11. By “sameness,” Dr. Carus means equivalence for a given purpose. (¶¶
102, 106.) By the “idea of sameness,” he means (¶¶ 77, 96) the principle
that things having a common character are for some purpose equivalent.
This, he says, “has a solid basis in the facts of experience.” By a
“world of sameness” (¶ 113), he seems to mean one in which any two given
concrete things are in some respect equivalent. He argues (¶ 122) that
a “world of sameness is a world in which necessity rules.” I do not see
this. It seems to me so bald a _non sequitur_, that I cannot but suppose
the thought escapes my apprehension. If there were anything in the
argument, it would seem to be a marvellously expeditious way of settling
the whole dispute; and therefore it would have been worth the trouble of
stating, so as to bring it within the purview of minds like mine.
§ 12. My candid opponent sometimes endorses emphatically the Leibnizian
principle. “Necessitarianism must be founded on something other than
observation. Observation is _a posteriori_; it has reference to single
facts, to particulars; yet the doctrine of necessity ... is of universal
application. The doctrine of necessity ... is of an _a priori_ nature.”
(¶ 11.) “Millions of single experiences ... cannot establish a solid
belief in necessity.” (¶ 14.) “No amount of experience is sufficient to
constitute causation by a mere synthesis of sequences.” (¶ 22.) “Millions
of millions of cases” constitute “no proof” that a proposition “is always
so.” (¶ 29.)
Nevertheless, he holds that the law of “the conservation of matter and
energy” so conclusively proves necessary causation, that the obstinacy
of Hume, himself, could not have withstood the argument. (¶ 23.) One
wonders, then, what is supposed to prove this “law of the conservation of
matter and energy,” if no amount of experience can prove it.
But the _a priori_ itself can “be based on the firm ground of
experience.” (¶ 14.) In that case, it is not prior to experience, after
all! “The idea of necessity is based upon the conception of sameness,
and ... the existence of sameness is a fact of experience.” (¶ 87.)
If absolute necessity can be irrefragably demonstrated from the fact
that two things are alike, it is a pity Dr. Carus should not state
this demonstration in a form, that I, and men like me, can understand.
That would be more to the purpose than merely saying it can be proved.
Absolute chance is rejected as “involving a violation of laws well
established by _positive evidence_.” (¶ 149.)