PEIRCE-L Digest 1288-- February 7, 1998

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   From PEIRCE-L Forum, Jan 5, 1998, [name of author of message],
   "re: Peirce on Teleology"   

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Topics covered in this issue include:

  1) "grade/grades" quotes 3 of 4
	by Joseph Ransdell 
  2) "grade/grades" quotes   4 of 4
	by Joseph Ransdell 
  3) Re: "grade/grades" quotes
	by Thomas.Riese[…] (Thomas Riese)
  4) "gradation/gradations/gradum/gradus" quotes
	by Joseph Ransdell 


Date: Sat, 07 Feb 1998 12:38:54
From: Joseph Ransdell 
To: peirce-l[…]TTACS.TTU.EDU
Subject: "grade/grades" quotes 3 of 4
Message-ID: <[…]>

cont'd   3 of 4 of Peirce quotes on "grade"

============QUOTES FROM PEIRCE ON "grade"  3 of 4==========

Peirce: CP 5.192 
	192. In answer to the first of these objections, it is to be remarked that
it is only in deduction that there is no difference between a valid
argument and a strong one. An argument is valid if it possesses the sort of
strength that it professes and tends toward the establishment of the
conclusion in the way in which it pretends to do this. But the question of
its strength does not concern the comparison of the due effect of the
argument with its pretensions, but simply upon how great its due effect is.
An argument is none the less logical for being weak, provided it does not
pretend to a strength that it does not possess. It is, I suppose, in view
of this that the best modern logicians outside the English school never say
a word about fallacies. They assume that there is no such thing as an
argument illogical in itself. An argument is fallacious only so far as it
is mistakenly, though not illogically, inferred to have professed what it
did not perform. Perhaps it may be said that if all our reasonings conform
to the laws of logic, this is, at any rate, nothing but a proposition in
psychology which my principles ought to forbid my recognizing. But I do not
offer it as a principle of psychology only. For a principle of psychology
is a contingent truth, while this, as I contend, is a necessary truth.
Namely, if a fallacy involves nothing in its conclusion which was not in
its premisses, that is nothing that was not in any previous knowledge that
aided in suggesting it, then the forms of logic will invariably and
necessarily enable us logically to account for it as due to a mistake
arising from the use of a logical but weak argumentation. In most cases it
is due to an abduction. The conclusion of an abduction is problematic or
conjectural, but is not necessarily at the weakest **grade** of surmise,
and what we call assertoric judgments are, accurately, problematic
judgments of a high **grade** of hopefulness. There is therefore no
difficulty in maintaining that fallacies are merely due to mistakes which
are logically valid, though weak argumentations. If, however, a fallacy
contains something in the conclusion which was not in the premisses at all,
that is, was in no previous knowledge or none that influenced the result,
then again a mistake, due as before to weak inference, has been committed;
only in this case the mistake consists in taking that to be an inference
which, in respect to this new element, is not an inference, at all. That
part of the conclusion which inserts the wholly new element can be
separated from the rest with which it has no logical connection nor
appearance of logical connection. The first emergence of this new element
into consciousness must be regarded as a perceptive judgment. We are
irresistibly led to judge that we are conscious of it. But the connection
of this perception with other elements must be an ordinary logical
inference, subject to error like all inference.
Peirce: CP 5.203 
	203. The reason why it would be contrary to their principles to admit any
distance less than a measurable distance, is that their way of supporting
induction implies that they differ from the logicians of the second class,
in that these third class logicians admit that we can infer a proposition
implying an infinite multitude and therefore implying the reality of the
infinite multitude itself, while their mode of justifying induction would
exclude every infinite multitude except the lowest **grade**, that of the
multitude of all integer numbers. Because with reference to a greater
multitude than that, it would not be true that what did not occur in a
finite ordinal place in a series could not occur anywhere within the
infinite series -- which is the only reason they admit for the inductive
Peirce: CP 5.394 
 	394. The principles set forth in the first part of this essay  lead, at
once, to a method of reaching a clearness of thought of  higher **grade**
than the "distinctness" of the logicians. It was there noticed  that the
action of thought is excited by the irritation of doubt, and ceases when
belief is attained; so that the production of belief is the sole function
of thought. All these words, however, are too strong for my purpose. It is
as if I had described the phenomena as they appear under a mental
microscope. Doubt and Belief, as the words are commonly employed, relate to
religious or other grave discussions. But here I use them to designate the
starting of any question, no matter how small or how great, and the
resolution of it. If, for instance, in a horse-car, I pull out my purse and
find a five-cent nickel and five coppers, I decide, while my hand is going
to the purse, in which way I will pay my fare. To call such a question
Doubt, and my decision Belief, is certainly to use words very
disproportionate to the occasion. To speak of such a doubt as causing an
irritation which needs to be appeased, suggests a temper which is
uncomfortable to the verge of insanity. Yet, looking at the matter
minutely, it must be admitted that, if there is the least hesitation as to
whether I shall pay the five coppers or the nickel (as there will be sure
to be, unless I act from some previously contracted habit in the matter),
though irritation is too strong a word, yet I am excited to such small
mental activity as may be necessary to deciding how I shall act. Most
frequently doubts arise from some indecision, however momentary, in our
action. Sometimes it is not so. I have, for example, to wait in a
railway-station, and to pass the time I read the advertisements on the
walls. I compare the advantages of different trains and different routes
which I never expect to take, merely fancying myself to be in a state of
hesitancy, because I am bored with having nothing to trouble me. Feigned
hesitancy, whether feigned for mere amusement or with a lofty purpose,
plays a great part in the production of scientific inquiry. However the
doubt may originate, it stimulates the mind to an activity which may be
slight or energetic, calm or turbulent. Images pass rapidly through
consciousness, one incessantly melting into another, until at last, when
all is over -- it may be in a fraction of a second, in an hour, or after
long years -- we find ourselves decided as to how we should act under such
circumstances as those which occasioned our hesitation. In other words, we
have attained belief.
Peirce: CP 5.402 
	402. It appears, then, that the rule for attaining the third **grade** of
clearness of apprehension is as follows: Consider what effects, that  might
conceivably have practical bearings, we conceive the object of our
conception to have. Then, our conception of these effects is the whole of
our conception of the object.
Peirce: CP 5.405 
      405. Let us now approach the subject of logic, and consider a
conception which particularly concerns it, that of reality. Taking
clearness in the sense of familiarity, no idea could be clearer than this.
Every child uses it with perfect confidence, never dreaming that he does
not understand it. As for clearness in its second **grade**, however, it
would probably puzzle most men, even among those of a reflective turn of
mind, to give an abstract definition of the real. Yet such a definition may
perhaps be reached by considering the points of difference between reality
and its opposite, fiction. A figment is a product of somebody's
imagination; it has such characters as his thought impresses upon it. That
those characters are independent of how you or I think is an external
reality. There are, however, phenomena within our own minds, dependent upon
our thought, which are at the same time real in the sense that we really
think them. But though their characters depend on how we think, they do not
depend on what we think those characters to be. Thus, a dream has a real
existence as a mental phenomenon, if somebody has really dreamt it; that he
dreamt so and so, does not depend on what anybody thinks was dreamt, but is
completely independent of all opinion on the subject. On the other hand,
considering, not the fact of dreaming, but the thing dreamt, it retains its
peculiarities by virtue of no other fact than that it was dreamt to possess
them. Thus we may define the real as that whose characters are independent
of what anybody may think them to be.
Peirce: CP 5.469 
	This illustration has much more pertinence to pragmatism than appears at
first sight; since my researches into the logic of relatives have shown
beyond all sane doubt that in one respect combinations of concepts exhibit
a remarkable analogy with chemical combinations; every concept having a
strict valency. (This must be taken to mean that of several forms of
expression that are logically equivalent, that one or ones whose analytical
accuracy is least open to question, owing to the introduction of the
relation of joint identity, follows the law of valency.) Thus, the
predicate "is blue" is univalent, the predicate "kills" is bivalent (for
the direct and indirect objects are, grammar aside, as much subjects as is
the subject nominative); the predicate "gives" is trivalent, since A gives
B to C, etc. Just as the valency of chemistry is an atomic character, so
indecomposable concepts may be bivalent or trivalent. Indeed, definitions
being scrupulously observed, it will be seen to be a truism to assert that
no compound of univalent and bivalent concepts alone can be trivalent,
although a compound of any concept with a trivalent concept can have at
pleasure, a valency higher or lower by one than that of the former concept.
Less obvious, yet demonstrable, is the fact that no indecomposable concept
has a higher valency. Among my papers are actual analyses of a number
greater than I care to state. They are mostly more complex than would be
supposed. Thus, the relation between the four bonds of an unsymmetrical
carbon atom consists of twenty-four triadic relations. Careful analysis
shows that to the three **grades** of valency of indecomposable concepts
correspond three classes of characters or predicates. Firstly come
"firstnesses," or positive internal characters of the subject in itself;
secondly come "secondnesses," or brute actions of one subject or substance
on another, regardless of law or of any third subject; thirdly comes
"thirdnesses," or the mental or quasi-mental influence of one subject on
another relatively to a third. Since the demonstration of this proposition
is too stiff for the infantile logic of our time (which is rapidly
awakening, however), I have preferred to state it problematically, as a
surmise to be verified by observation. The little that I have contributed
to pragmatism (or, for that matter, to any other department of philosophy),
has been entirely the fruit of this outgrowth from formal logic, and is
worth much more than the small sum total of the rest of my work, as time
will show.
Peirce: CP 5.477 
	477. Habits have **grades** of strength varying from complete dissociation
to inseparable association. These **grades** are mixtures of promptitude of
action, say excitability and other ingredients not calling for separate
examination here. The habit-change often consists in raising or lowering
the strength of a habit. Habits also differ in their endurance (which is
likewise a composite quality). But generally speaking, it may be said that
the effects of habit-change last until time or some more definite cause
produces new habit-changes. It naturally follows that repetitions of the
actions that produce the changes increase the changes. [It] is noticeable
that the iteration of the action is often said to be indispensible to the
formation of a habit; but a very moderate exercise of observation suffices
to refute this error. A single reading yesterday of a casual statement that
the "shtar chindis" means in Romany "four shillings," though it is unlikely
to receive any reinforcement beyond the recalling of it, at this moment, is
likely to produce the habit of thinking that "four" in the Gypsy tongue is
"shtar," that will last for months, if not for years, though I should never
call it to mind in the interval. To be sure, there has been some iteration
just now, while I dwelt on the matter long enough to write these sentences;
but I do not believe any reminiscence like this was needed to create the
habit; for such instances have been extremely numerous in acquiring
different languages. There are, of course, other means than repetition of
intensifying habit-changes. In particular, there is a peculiar kind of
effort, which may be likened to an imperative command addressed to the
future self. I suppose the psychologists would call it an act of
Peirce: CP 5.533 
	To return to self-control, which I can but slightly sketch, at this time,
of course there are inhibitions and co”rdinations that entirely escape
consciousness. There are, in the next place, modes of self-control which
seem quite instinctive. Next, there is a kind of self-control which results
from training. Next, a man can be his own training-master and thus control
his self-control. When this point is reached much or all the training may
be conducted in imagination. When a man trains himself, thus controlling
control, he must have some moral rule in view, however special and
irrational it may be. But next he may undertake to improve this rule; that
is, to exercise a control over his control of control. To do this he must
have in view something higher than an irrational rule. He must have some
sort of moral principle. This, in turn, may be controlled by reference to
an esthetic ideal of what is fine. There are certainly more **grades** than
I have enumerated. Perhaps their number is indefinite. The brutes are
certainly capable of more than one **grade** of control; but it seems to me
that our superiority to them is more due to our greater number of
**grades** of self-control than it is to our versatility.
Peirce: CP 5.534 
	Pragmaticist. To my thinking that faculty is itself a phenomenon of
self-control. For thinking is a kind of conduct, and is itself
controllable, as everybody knows. Now the intellectual control of thinking
takes place by thinking about thought. All thinking is by signs; and the
brutes use signs. But they perhaps rarely think of them as signs. To do so
is manifestly a second step in the use of language. Brutes use language,
and seem to exercise some little control over it. But they certainly do not
carry this control to anything like the same **grade** that we do. They do
not criticize their thought logically. One extremely important **grade** of
thinking about thought, which my logical analyses have shown to be one of
chief, if not the chief, explanation of the power of mathematical
reasoning, is a stock topic of ridicule among the wits. This operation is
performed when something, that one has thought about any subject, is itself
made a subject of thought. You remember how in the last IntermŠde to the
Malade Imaginaire, the doctor puts a question to the candidate for the
medical degree?

	Si mihi licentiam dat Dominus Praeses,
		Et tanti docti Doctores,
		Et assistantes illustres,
		TrŠs s‡avanti Bacheliero,
		Quem estimo et honoro,
	Domandabo causam et rationem quare
		Opium facit dormire.

To which the candidate replies,

		Mihi a docto Doctore
	Domandatur causam et rationem quare
		Opium facit dormire:
		A quoi respondeo,
		Quia est in eo
		Virtus dormitiva,
		Cujus est natura
		Sensus assoupire.

Whereupon the chorus bursts out,

	Bene, bene, bene, bene respondere,
		Dignus, dignus est entrare
		In nostro docto corpore.
		(Bene, bene respondere.)

Even in this burlesque instance, this operation of hypostatic abstraction
is not quite utterly futile. For it does say that there is some peculiarity
in the opium to which the sleep must be due; and this is not suggested in
merely saying that opium puts people to sleep. By the way, John Locke's
account  of a real function of this sort at Montpellier three years after
the play was first performed, with such tragic effect upon MoliŠre, shows
that there was more truth than caricature in the IntermŠde. In order to get
an inkling -- though a very slight one -- of the importance of this
operation in mathematics, it will suffice to remember that a collection is
an hypostatic abstraction, or ens rationis, that multitude is the
hypostatic abstraction derived from a predicate of a collection, and that a
cardinal number is an abstraction attached to a multitude. So an ordinal
number is an abstraction attached to a place, which in its turn is a
hypostatic abstraction from a relative character of a unit of a series,
itself an abstraction again. Now, Doctor Z, as well as I can make out, what
you mean by a concept is a predicate considered by itself, except for its
connection with the word or other symbol expressing it, and now regarded as
denotative of the concept. Such a concept is not merely prescissively
abstracted, but, as being made a subject of thought, is hypostatically
abstract. So understood, it is true that it is more removed from the
perceptual objects than is the Vorstellung, or composite of images. But for
all that, its intellectual purport is just the same. It is only the
grammatico-logical form that is transmuted.
Peirce: CP 5.416 Fn P1 p 279  
	^P1 It is necessary to say that "belief" is throughout used merely as the
name of the contrary to doubt, without regard to **grades** of certainty
nor to the nature of the proposition held for true, i.e., "believed."
Peirce: CP 6.116 
	116. In truth, of infinite collections there are but two **grades** of
magnitude, the endless and the innumerable. Just as a finite collection is
distinguished from an infinite one by the applicability to it of a special
mode of reasoning, the syllogism of transposed quantity, so, as I showed in
the paper last referred to, a numerable collection is distinguished from an
innumerable one by the applicability to it of a certain mode of reasoning,
the Fermatian inference, or, as it is sometimes improperly termed,
"mathematical induction."
Peirce: CP 6.119 
	119. Although there are but two **grades** of magnitudes of infinite
collections, yet when certain conditions are imposed upon the order in
which individuals are taken, distinctions of magnitude arise from that
cause. Thus, if a simply endless series be doubled by separating each unit
into two parts, the successive first parts and also the second parts being
taken in the same order as the units from which they are derived, this
double endless series will, so long as it is taken in that order, appear as
twice as large as the original series. In like manner the product of two
innumerable collections, that is, the collection of possible pairs composed
of one individual of each, if the order of continuity is to be maintained,
is, by virtue of that order, infinitely greater than either of the
component collections.
Peirce: CP 6.168 
	168. But further study of the subject has proved that this definition is
wrong. It involves a misunderstanding of Kant's definition which he himself
likewise fell into. Namely he defines a continuum as that all of whose
parts have parts of the same kind. He himself, and I after him, understood
that to mean infinite divisibility, which plainly is not what constitutes
continuity since the series of rational fractional values is infinitely
divisible but is not by anybody regarded as continuous. Kant's real
definition implies that a continuous line contains no points. Now if we are
to accept the common sense idea of continuity (after correcting its
vagueness and fixing it to mean something) we must either say that a
continuous line contains no points or we must say that the principle of
excluded middle does not hold of these points. The principle of excluded
middle only applies to an individual (for it is not true that "Any man is
wise" nor that "Any man is not wise"). But places, being mere possibles
without actual existence, are not individuals. Hence a point or indivisible
place really does not exist unless there actually be something there to
mark it, which, if there is, interrupts the continuity. I, therefore, think
that Kant's definition correctly defines the common sense idea, although
there are great difficulties with it. I certainly think that on any line
whatever, on the common sense idea, there is room for any multitude of
points however great. If so, the analytical continuity of the theory of
functions, which implies there is but a single point for each distance from
the origin, defined by a quantity expressible to indefinitely close
approximation by a decimal carried out to an indefinitely great number of
places, is certainly not the continuity of common sense, since the whole
multitude of such quantities is only the first abnumeral multitude, and
there is an infinite series of higher **grades**. On the whole, therefore,
I think we must say that continuity is the relation of the parts of an
unbroken space or time. The precise definition is still in doubt; but
Kant's definition, that a continuum is that of which every part has itself
parts of the same kind, seems to be correct. This must not be confounded
(as Kant himself confounded it) with infinite divisibility, but implies
that a line, for example, contains no points until the continuity is broken
by marking the points. In accordance with this it seems necessary to say
that a continuum, where it is continuous and unbroken, contains no definite
parts; that its parts are created in the act of defining them and the
precise definition of them breaks the continuity. In the calculus and
theory of functions it is assumed that between any two rational points (or
points at distances along the line expressed by rational fractions) there
are rational points and that further for every convergent series of such
fractions (such as 3.1, 3.14, 3.141, 3.1415, 3.14159, etc.) there is just
one limiting point; and such a collection of points is called continuous.
But this does not seem to be the common sense idea of continuity. It is
only a collection of independent points. Breaking grains of sand more and
more will only make the sand more broken. It will not weld the grains into
unbroken continuity.
Peirce: CP 6.173 
	173. It would, therefore, be most contrary to his own principle for the
synechist not to generalize from that which experience forces upon him,
especially since it is only so far as facts can be generalized that they
can be understood; and the very reality, in his way of looking at the
matter, is nothing else than the way in which facts must ultimately come to
be understood. There would be a contradiction here, if this ultimacy were
looked upon as something to be absolutely realized; but the synechist
cannot consistently so regard it. Synechism is not an ultimate and absolute
metaphysical doctrine; it is a regulative principle of logic, prescribing
what sort of hypothesis is fit to be entertained and examined. The
synechist, for example, would never be satisfied with the hypothesis that
matter is composed of atoms, all spherical and exactly alike. If this is
the only hypothesis that the mathematicians are as yet in condition to
handle, it may be supposed that it may have features of resemblance with
the truth. But neither the eternity of the atoms nor their precise
resemblance is, in the synechist's view, an element of the hypothesis that
is even admissible hypothetically. For that would be to attempt to explain
the phenomena by means of an absolute inexplicability. In like manner, it
is not a hypothesis fit to be entertained that any given law is absolutely
accurate. It is not, upon synechist principles, a question to be asked,
whether the three angles of a triangle amount precisely to two right
angles, but only whether the sum is greater or less. So the synechist will
not believe that some things are conscious and some unconscious, unless by
consciousness be meant a certain **grade** of feeling. He will rather ask
what are the circumstances which raise this **grade**; nor will he consider
that a chemical formula for protoplasm would be a sufficient answer. In
short, synechism amounts to the principle that inexplicabilities are not to
be considered as possible explanations; that whatever is supposed to be
ultimate is supposed to be inexplicable; that continuity is the absence of
ultimate parts in that which is divisible; and that the form under which
alone anything can be understood is the form of generality, which is the
same thing as continuity.
Peirce: CP 6.333 
     	333. There are two **grades** or constituents of Being: the Essence,
and the Existence. Each of these terms has an epistemological and
metaphysical force. I consider Existence first, and to begin with, in its
epistemological aspect. When a new image, optical, acoustical, or other,
appears in the mind, one subjects it to various tests in order to ascertain
whether it be of internal or of external provenance. These tests may be
distributed into three classes, according to their strength when they
testify to externality of origin (which I call being "affirmative") and
according to their strength when they testify to internality of origin
(which I call being "negative").
Peirce: CP 6.346 
	346. Blind existential being may possibly not occur at all; since we know
nothing with absolute certainty of existent things, and are especially in
the dark as to their modes of being, and above all know extremely little
about the ultimate parts of matter, beyond the fact that electricity,
itself a most mysterious sort of existent, is an ingredient of them. In the
book about God and religion upon which I have been at work for several
years, and hope to write, one of the questions which will come up for fair
consideration is whether either the monotheistic, absolute God or the
polytheistic, finite God of the pseudo-pragmatists could know the nature of
blind existence, as He must, if he had created it. It is an unexplored
passage in the mammoth cave of metaphysics; and various questions
concerning it suggest themselves. This much, however, seems clear about
such existence; namely, that there ought to be two **grades** of it; a
lower kind, approximating to the inner being of a simple quality, yet
existential, instead of being merely potential, consisting in the action of
the thing upon itself, a sort of embryonic self-consciousness; and a higher
**grade** consisting in the action of a thing upon all the other things of
the same universe, and measuring by its intensity its remoteness from each
of them. A whole universe of such existents can only have the lower, or
internal **grade** of existence.
Peirce: CP 6.371 
	Proximate possibility. It is very difficult to make out what is meant by
this; but the phrase is evidently modelled on potentia proxima, which is a
state of high preparedness for existence; so that proximate possibility
would be a high **grade** of possibility in a proposition amounting almost
to positive assertion.

=======end of 3 of 4 of Peirce quotes on "grade"==========

Joseph Ransdell - joseph.ransdell[…]  
Dept of Philosophy - 806  742-3158  (FAX 742-0730) 
Texas Tech University - Lubbock, Texas 79409   USA (Peirce website - beta)


Date: Sat, 07 Feb 1998 13:29:07
From: Joseph Ransdell 
To: peirce-l[…]TTACS.TTU.EDU
Subject: "grade/grades" quotes   4 of 4
Message-ID: <[…]>

cont'd:  quotes from Peirce on "grade"

========peirce quotes on 'grade' and 'grades'============

Peirce: CP 6.393 
	His sufficient reason is not an efficient cause, but a utility, or, in a
broad sense, a final cause. But a nominalist cannot admit that an immediate
final cause exists. Leibnitz, however, makes it true. For a realist, the
real is nothing but the immediate object of that which is true. But
Leibnitz has another notion of truth. Thus, in a letter to Arnauld (quoted
in Latta's accurate and convenient exposition, p. 61, note beginning p.
60), he says: "Always in every true affirmative proposition, whether
necessary or contingent, universal or singular, the notion of the predicate
is in some way comprehended in that of the subject, praedicatum inest
subiecto; otherwise I know not what truth is"; and in other passages he
shows that for him truth is a relation between notions. Yet, as a
nominalist, he could not hold that those notions immediately correspond to
anything real. Consequently, he does not say that there really is a
sufficient reason, but that anybody favorably situated would be able to
render a sufficient reason. There is nothing real that corresponds to it
immediately. Remotely, the purpose of God may correspond to it. Thus, the
world of reality and the world of truth are completely sundered; for the
former, Leibnitz is a pure individualistic nominalist; for the latter, on
the contrary, he is an intellectualist. When he says, for example, that
that which has no sufficient reason is "necessarily" non-existent, he uses
the adverb of logical not of metaphysical modality. He does not hold that
real things are either emanations or entelechies of anything corresponding
to a sufficient reason, but that is how the mind is affected. But when he
comes to the ultimate sufficient reason of contingent truths, which is God,
he ceases to draw the distinction between the world of thought and the
world of being; and this exception introduces difficulties into his system.
But Leibnitz confounds two things under his word "reason." The idea which
principally governs his doctrine is that a reason is an explanation of the
utility of that of which it is a reason; but he includes under the same
word any explanation of the logical necessity of the object, the why it
follows from a general law. Hence, in many cases, his sufficient reason
fulfills the function of an efficient cause. It would be quite possible to
quote passages from Leibnitz which conflict with this account of his
conception. In order that the reader should apprehend it as he did, it
would be requisite that his mind should be in the same unclear condition,
which is not possible after one has once attained a superior **grade** of
clearness. We can account for his implicit contradictions, but cannot
reproduce his apprehension of them when we once see them to be contradictions.
Peirce: CP 6.608 Fn P1 p 418  
	^P1 Indeed, to admit that reply is all but to admit the non-absolute
**grade** of necessity.
Peirce: CP 7.109 
	109. But some one will ask me, "Do you, then, really entertain any doubt
that twice two is four?" To this I must answer, "No, as well as I can
perceive, there is not the slightest real doubt of it in my mind." "But,"
he will say, "how can that be? You say it is not certain. Ought you not
then, to entertain a doubt of it; and if you feel that it ought to be
doubted, do you not, ipso facto, actually doubt it?" I reply: "Doubt is a
certain kind of feeling. It has not only **grades** of intensity, but also
varieties of quality. Now if I were able to modify my state of mind by a
sufficiently slight tincture of the right kind of doubt, I ought to do so.
But if I were to attempt really to feel any doubt at all, I should
certainly either feel none at all or else millions upon millions of times
too much. For I could not in the least recognize a tincture so small nor
even one that should be millions of times too great. If I were to devote my
whole life to the useless task of trying to make such slight distinctions
in my feelings, I could not come near to the requisite delicacy. My feeling
of doubt is one of the coarser of my sensations; and there would be no
practical use in making it more delicate than it is, for it is already so
far more delicate than that of almost all the persons with whom I converse,
that I often find an insuperable difficulty in making them comprehend the
slighter **grades** of my feeling, and there is no practical difference in
my conduct whether, say, 3/8 or 5/13 be the proper degree of doubt about a
matter not measurable. It would be a waste of time to adjust my feeling of
doubt more accurately, since it neither would have, nor ought to have, any
effect upon my scientific conduct. Instead of wasting effort on my feeling,
I devote my energies to learning more about the subjects concerning which I
have any considerable doubts, while very small doubts I neglect until I can
reduce the amount of my doubt concerning subjects of greater importance."
Peirce: CP 7.181 
	181. Now ancient history occupies a place among the psychical sciences
somewhat analogous to that of astronomy among the physical sciences. The
one is a description of what is distant in the world of mind, as the other
is a description of what is distant in the world of matter; and curiously
enough, or significantly enough, an ancient alliance exists between the two
sciences through chronology. Yet the amount of aid which physical astronomy
can derive from mathematics is quite moderate, notwithstanding the
mathematical perfection of nomological physics. Anybody can convince
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himself that the reasoning of physical astronomy is not of a demonstrative
kind by simply running over any text-book on the subject. But the science
of nomological psychics, -- psychology, as we call it, -- is still far too
backward to afford any distinguished aid to history; and consequently, the
demonstrative part of rightly reasoned history, exclusive of mere
chronology, must, for a long time, remain very small. History, however, is
as much more worthy than astronomy of being studied scientifically as mind
is more worthy of our attention than matter. The use we should desire to
make of ancient history is to learn from the study of it, and not to carry
our preconceived notions into it, until they can be put upon a much more
scientific basis than at present they can. Consequently, the staple of our
reasoning in ancient history should not be of the demonstrative kind, as it
is, as long as it remains, at best, an application of the mathematical
doctrine of chances. If somebody replies that in weighing arguments pro and
con critics make no use of the mathematical calculus of probabilities, the
rejoinder will be that their proceeding only differs from that by its
greater vagueness, and that a vague and inexact use of probabilities has no
logical advantage over a more critical employment of them. If it is said
that, as far as possible, the critics avoid likelihoods, and aim at
positive certainty, the answer will be that they endeavor to do this by the
employment of apodictic arguments, which only mark a still less exact
**grade** of the same kind of demonstrative reasoning. Fully to appreciate
the force of this argument one must have a well-matured comprehension of
the logic of science; but when it is fairly apprehended, it cannot but be
deemed quite conclusive.
Peirce: CP 7.231 
	231. A hypothesis having been adopted on probation, the process of testing
it will consist, not in examining the facts, in order to see how well they
accord with the hypothesis, but on the contrary in examining such of the
probable consequences of the hypothesis as would be capable of direct
verification, especially those consequences which would be very unlikely or
surprising in case the hypothesis were not true. It is not easy to
enumerate the different kinds of consequences; but among them may be, that
the hypothesis would render the present existence of a monument probable,
or would result in giving a known monument a certain character; that if it
were true, certain ancient documents ought to contain some allusion to it;
that if it is misstated by some authority not considered in the selection
of the hypothesis, that misstatement would be likely to be of a certain
kind; that if the hypothesis is true, and an assertion or allusion found in
an ancient work is to be explained by the author's knowing it to be true,
he must have had certain other knowledge, etc. When the hypothesis has
sustained a testing as severe as the present state of our knowledge of the
particular branch of history to which it belongs renders imperative, it
will be admitted provisionally into the list of our present historical
results, subject of course to reconsideration along with all those other
results, when we are in a condition to insist upon a higher **grade** of
security. In order to make the difference between this method and that
usually pursued quite clear, I propose to give three illustrative examples.
I shall draw them from the history of philosophy, with which I am better
acquainted than I am with political history. I shall endeavor to make the
examples illustrative of different kinds of questions, and in departments
of history where various **grades** of probability can be insisted upon. I
shall, in each case, first show how the question would be treated in
accordance with the method of this paper; and then I shall show how some
one or more of the best critics actually have treated it. I shall not
notice the theories of those who carry higher criticism to its last
extravagances, but shall confine myself to those who are most esteemed for
their sobriety and thoroughness. It will be necessary to confine our
illustrations to some minor points, because these are the only ones which
can be discussed within moderate limits.
Peirce: CP 7.284 
	284. The meaning of this seems to be clear. That is, it possesses the
first **grade** of clearness of ideas, that of containing no element which
perfect familiarity does not enable us to use with entire confidence. But
that **grade** of clearness is not sufficient for precision of statement,
and logical security. For that purpose, we must say what we mean by
"gradually." In attempting to state this, it first occurs to us to say that
we mean by a gradual change of hue, such a change that in passing from one
exact hue to another we pass through all intermediate hues. There are two
reflections to be made upon this statement. First, it supposes that the
different hues are so related in our minds that we are able to say what
ones are, and what ones are not, intermediate between any given pair of
hues. That is to say, we must have a precise idea of what it means to say
that the hues are mentally arranged in a line. But if that be so, we need
not introduce the conception of a change in time; for that was only a
device to enable us to describe what we mean by a line of variations of
character. In truth, though the introduction of the idea of time gives
sensuous clearness to our idea, it contributes not in the least to logical
clearness. The second reflection which has to be made upon our attempt to
define gradual change of hue is that the hues form a circle, the so-called
color-circle; so that it is possible to pass from any one to any other by
going either way round the circle; and thus there is no particular hue that
we need pass through. To define a linear arrangement, the line being
permitted to return into itself, it is necessary to speak of four points on
the line.
Peirce: CP 7.397 
	397. The result of the study of the above formulae and of many others
(which I have never published, because no psychologist has paid the
slightest attention to those I have published) is that the contents of
immediate consciousness range all the way from feelings which an
indefinitely great effort is required to reduce to [a] given **grade** of
subjective intensity to feelings which an indefinitely great effort is
required to magnify to any given **grade** of subjective intensity. If we
assume, as a convenient scale of measurement, that the measure of
subjective intensity of an idea before such effort is applied to it is,
other things being equal, proportional to a base raised to a power
expressing the degree of effort required to lower its subjective intensity
to an assumed standard, then I find that no feelings affecting the mind
have the measures of their subjective intensities 0 or ì; but that they
approach indefinitely to those limits. Without any effort of attention at
all, certain feelings have sufficient subjective intensity to affect us in
certain ways, for instance, to cause us, in an off-hand answer, to reply
that we are affected by them. The subjective intensity of many a feeling is
sufficient for that without being sufficient to rouse us to decided
exertion. On the other hand, the subjective intensity of many a feeling,
though insufficient for that, is sufficient to affect our actions and color
our emotions strongly.
Peirce: CP 7.635 
	635. As for the subject of the perceptual judgment, as subject it is a
sign. But it belongs to a considerable class of mental signs of which
introspection can give hardly any account. It ought not to be expected that
it should do so, since the qualities of these signs as objects have no
relevancy to their significative character; for these signs merely play the
part of demonstrative and relative pronouns, like "that," or like the A, B,
C, of which a lawyer or a mathematician avails himself in making
complicated statements. In fact, the perceptual judgment which I have
translated into "that chair is yellow" would be more accurately represented
thus: " is yellow," a pointing index-finger taking the place of the
subject. On the whole, it is plain enough that the perceptual judgment is
not a copy, icon, or diagram of the percept, however rough. It may be
reckoned as a higher **grade** of the operation of perception.
Peirce: CP 7.655 
	655. One such deliverance is that any multitude of changes not too great
to be successive in any sense might take place in any lapse of time however
short. Now two things are demonstrable (although again I withhold the
demonstrations). One is that no multitude is so great as to prevent a
collection of objects of that multitude from being linearly arranged. The
other is that there is no maximum multitude. It follows, then, from the
deliverance just stated, that the possible mutually exclusive divisions of
any time, however short, exceed all multitude. In that case, time can not
only not have merely the pseudo-continuity of quantity, -- since the
multitude of quantities is well-known to be only the second of an endless
series of **grades** of infinite multitude, -- but it cannot be composed of
instants at all (as it might very well be and still enormously exceed the
differentiation of quantity) since the entire collection of such instants
would have a multitude.
Peirce: CP 8.19 
	19. Though this is the slightest possible sketch of the realism of Scotus,
and leaves a number of important points unnoticed, yet it is sufficient to
show the general manner of his thought and how subtle and difficult his
doctrine is. That about one and the same nature being in the **grade** of
singularity in existence, and in the **grade** of universality in the mind,
gave rise to an extensive doctrine concerning the various kinds of identity
and difference, called the doctrine of the formalitates; and this is the
point against which Ockam directed his attack.
Peirce: CP 8.176 
	176. A little book by Lady Victoria Welby has lately appeared, entitled
"What is Meaning." The book has sundry merits, among them that of showing
that there are three modes of meaning. But the best feature of it is that
it presses home the question "What is Meaning." A word has meaning for us
in so far as we are able to make use of it in communicating our knowledge
to others and in getting at the knowledge that these others seek to
communicate to us. That is the lowest **grade** of meaning. The meaning of
a word is more fully the sum total of all the conditional predictions which
the person who uses it intends to make himself responsible for or intends
to deny. That conscious or quasi-conscious intention in using the word is
the second **grade** of meaning. But besides the consequences to which the
person who accepts a word knowingly commits himself to, there is a vast
ocean of unforeseen consequences which the acceptance of the word is
destined to bring about, not merely consequences of knowing but perhaps
revolutions of society. One cannot tell what power there may be in a word
or a phrase to change the face of the world; and the sum of these
consequences makes up the third **grade** of meaning.
Peirce: CP 8.185 
	185. But it appears to me that all symptoms of disease, signs of weather,
etc., have no utterer. For I do not think we can properly say that God
utters any sign when He is the Creator of all things. But when [Lady Welby]
says, as she does, that this is connected with Volition, I at once note
that the volitional element of Interpretation is the Dynamical
Interpretant. In the Second Part of my Essay on Pragmatism, in The Popular
Science Monthly of 1877 Nov. and 1878 Jan., I made three **grades** of
clearness of Interpretation. The first was such familiarity as gave a
person familiarity with a sign and readiness in using it or interpreting
it. In his consciousness he seemed to himself to be quite at home with the
Sign. In short, it is Interpretation in Feeling. The second was Logical
Analysis = Lady Welby's Sense. The third,. . . Pragmatistic Analysis, would
seem to be a Dynamical Analysis, but [is] identified with the Final
Peirce: CP 8.199 
	199. The sort of science that is founded upon the common experience of all
men was recognized by Jeremy Bentham under the name of cenoscopy, in
opposition to idioscopy, which discovers new phenomena. But long before
Bentham's day the situation was sufficiently understood to set up a
movement in the more enlightened countries to supply the psychical sciences
with an analogous analytical foundation. The innumerable **grades** in the
distinctness of thought prevent us from assigning dates, but one may say
that the idea is struggling to the light in Locke's 'Essay' of 1689, and
that its development was the best fruit of the eighteenth century. It moved
in Italy, in France, and especially in Scotland. The analytical economics
of Adam Smith and of Ricardo were examples of it. The whole doctrine in its
totality is properly termed the Philosophy of Common Sense, of which
analytical mechanics and analytical economics are branches. That Pragmatism
of which so much has been said of late years is only an endeavor to give
the philosophy of common sense a more exact development, especially by
emphasizing the point that there is no intellectual value in mere feeling
per se, but that the whole function of thinking consists in the regulation
of conduct. All this it is most needful to comprehend in order to assign to
Wundt his proper rating in the history of philosophy.
Peirce: CP 8.213 
	213. It was in the desperate endeavor to make a beginning of penetrating
into that riddle that on May 14, 1867, after three years of almost insanely
concentrated thought, hardly interrupted even by sleep, I produced my one
contribution to philosophy in the "New List of Categories" in the
Proceedings of the American Academy of Arts and Sciences, Vol. VII, pp.
287-298. Tell your friend Julian that this is, if possible, even less
original than my maxim of pragmatism; and that I take pride in the entire
absence of originality in all that I have ever sought to bring to the
attention of logicians and metaphysicians. My three categories are nothing
but Hegel's three **grades** of thinking. I know very well that there are
other categories, those which Hegel calls by that name. But I never
succeeded in satisfying myself with any list of them. We may classify
objects according to their matter; as wooden things, iron things, silver
things, ivory things, etc. But classification according to structure is
generally more important. And it is the same with ideas. Much as I would
like to see Hegel's list of categories reformed, I hold that a
classification of the elements of thought and consciousness according to
their formal structure is more important. I believe in inventing new
philosophical words in order to avoid the ambiguities of the familiar
words. I use the word phaneron to mean all that is present to the mind in
any sense or in any way whatsoever, regardless of whether it be fact or
figment. I examine the phaneron and I endeavor to sort out its elements
according to the complexity of their structure. I thus reach my three
Peirce: CP 8.214 
  	214. Ever since I was paid that money by you and Mrs. Carus, I have been
engaged with all my energy, allowing only for such as I had to expend upon
my wife's health and upon getting this house habitable and in salable
condition, in trying to write an article or articles for you upon the
second **grade** of clearness, i.e., that which results from analytic
definition, and upon corrections to the errors and other faults of the
articles of mine that appeared in The Popular Science Monthly in 1877 and
1878, to which I should be glad if you would add a reprint of the article
of January, 1901, which requires no correction.
Peirce: CP 8.218 
	218. Then in regard to the second article, I ought to say that my three
**grades** of clearness are not, as I seemed then to think, such that
either the first or the second are superseded by the third, although we may
say that they are acquired, mostly, in the order of those numbers. I ought
to describe, if only in a paragraph, how to train oneself and one's
children in the first **grade** of clearness, so that, for example, one
will recognize a millimetre length when one meets with it, and so with
colors. I have done a great deal of work in training myself to this kind of
clearness. It would if put together amount to two or three years of
industry; and I should recommend systematic exercises of the sort to
everybody. Useful as that is, however, I don't hesitate to say that the
second **grade** of clearness is far more important, and all my writings of
late years illustrate that. Still, I continue to admit that the third
**grade** is the most important of all and a good example of it is William
James who is so phenomenally weak in the second **grade**, yet ever so high
above most men in the third. But there is no reason why all three should
not be symmetrically developed.
Peirce: CP 8.308 
	308. The other was your remark that the question is, is possibility a mode
of being. Good. Precisely so. As I remarked in the last Monist, my old
definition of the possible as that which we do not know not to be true (in
some state of information real or feigned) is an anacoluthon. The possible
is a positive universe, and the two negations happen to fit it, but that is
all. Of course, there is a general logical possible that is no more than I
defined it. But there is also a possible which [is] something else. I
reached this truth by studying the question of possible **grades** of
multitude, where I found myself arrested until I could form a whole logic
of possibility, -- a very difficult and laborious task. You would not have
reached it that way. You must have some short cut, which I am curious to
know more about.
Peirce: CP 8.320 
	320. I do not know whether or not you will approve of my particular way of
denying Necessitarianism. But as it is certain that the proposition that
every physical event is directly determined by dynamical non-telic
conditions and laws alone while every mental representation is directly
determined by logical and, as such, telic conditions and laws alone, does
not conflict with the proposition that physical events are determined by
mental representations and mental representations by physical events  (as
every student of G. Cantor will perceive); so on the other hand the
propositions that the laws of nature are not absolute and that important
physical events are due to human reasoning are far from proving that human
action is (in any important degree) free, except in the sense that a man is
a machine with automatic controls, one over another, for five or six
**grades**, at least. I, for my part, am very dubious as to man's having
more freedom than that, nor do I see what pragmatic meaning there is in
saying that he has more. The power of self-control is certainly not a power
over what one is doing at the very instant the operation of self-control is
commenced. It consists (to mention only the leading constituents) first, in
comparing one's past deeds with standards, second, in rational deliberation
concerning how one will act in the future, in itself a highly complicated
operation, third, in the formation of a resolve, fourth, in the creation,
on the basis of the resolve, of a strong determination, or modification of
habit. This operation of self-control is a process in which logical
sequence is converted into mechanical sequence or something of the sort.
How this happens, we are in my opinion as yet entirely ignorant. There is a
class of signs in which the logical sequence is at the same time a
mechanical sequence and very likely this fact enters into the explanation.
Peirce: CP 8.327 
    	327. But I wanted to write to you about signs, which in your opinion
and mine are matters of so much concern. More in mine, I think, than in
yours. For in mine, the highest **grade** of reality is only reached by
signs; that is by such ideas as those of Truth and Right and the rest. It
sounds paradoxical; but when I have devolved to you my whole theory of
signs, it will seem less so. I think that I will today explain the outlines
of my classification of signs.
Peirce: CP 8.331 
	331. I now come to Thirdness. To me, who have for forty years considered
the matter from every point of view that I could discover, the inadequacy
of Secondness to cover all that is in our minds is so evident that I scarce
know how to begin to persuade any person of it who is not already convinced
of it. Yet I see a great many thinkers who are trying to construct a system
without putting any thirdness into it. Among them are some of my best
friends who acknowledge themselves indebted to me for ideas but have never
learned the principal lesson. Very well. It is highly proper that
Secondness should be searched to its very bottom. Thus only can the
indispensableness and irreducibility of thirdness be made out, although for
him who has the mind to grasp it, it is sufficient to say that no branching
of a line can result from putting one line on the end of another. My friend
Schr”der fell in love with my algebra of dyadic relations. The few pages I
gave to it in my Note B in the 'Studies in Logic by Members of the Johns
Hopkins University' were proportionate to its importance. His book is
profound, but its profundity only makes it more clear that Secondness
cannot compass Thirdness. (He is careful to avoid ever saying that it can,
but he does go so far as to say that Secondness is the more important. So
it is, considering that Thirdness cannot be understood without Secondness.
But as to its application, it is so inferior to Thirdness as to be in that
aspect quite in a different world.) Even in the most degenerate form of
Thirdness, and thirdness has two **grades** of degeneracy, something may be
detected which is not mere secondness. If you take any ordinary triadic
relation, you will always find a mental element in it. Brute action is
secondness, any mentality involves thirdness. Analyze for instance the
relation involved in 'A gives B to C.' Now what is giving? It does not
consist [in] A's putting B away from him and C's subsequently taking B up.
It is not necessary that any material transfer should take place. It
consists in A's making C the possessor according to Law. There must be some
kind of law before there can be any kind of giving, -- be it but the law of
the strongest. But now suppose that giving did consist merely in A's laying
down the B which C subsequently picks up. That would be a degenerate form
of Thirdness in which the thirdness is externally appended. In A's putting
away B, there is no thirdness. In C's taking B, there is no thirdness. But
if you say that these two acts constitute a single operation by virtue of
the identity of the B, you transcend the mere brute fact, you introduce a
mental element . . . . The criticism which I make on [my] algebra of dyadic
relations, with which I am by no means in love, though I think it is a
pretty thing, is that the very triadic relations which it does not
recognize, it does itself employ. For every combination of relatives to
make a new relative is a triadic relation irreducible to dyadic relations.
Its inadequacy is shown in other ways, but in this way it is in a conflict
with itself if it be regarded, as I never did regard it, as sufficient for
the expression of all relations. My universal algebra of relations, with
the subjacent indices and ä and ã, is susceptible of being enlarged so as
to comprise everything; and so, still better, though not to ideal
perfection, is the system of existential graphs.
Peirce: CP 8.332 
	332. I have not sufficiently applied myself to the study of the degenerate
forms of Thirdness, though I think I see that it has two distinct
**grades** of degeneracy. In its genuine form, Thirdness is the triadic
relation existing between a sign, its object, and the interpreting thought,
itself a sign, considered as constituting the mode of being of a sign. A
sign mediates between the interpretant sign and its object. Taking sign in
its broadest sense, its interpretant is not necessarily a sign. Any concept
is a sign, of course. Ockham, Hobbes, and Leibniz have sufficiently said
that. But we may take a sign in so broad a sense that the interpretant of
it is not a thought, but an action or experience, or we may even so enlarge
the meaning of sign that its interpretant is a mere quality of feeling. A
Third is something which brings a First into relation to a Second. A sign
is a sort of Third. How shall we characterize it? Shall we say that a Sign
brings a Second, its Object, into cognitive relation to a Third? That a
Sign brings a Second into the same relation to a first in which it stands
itself to that First? If we insist on consciousness, we must say what we
mean by consciousness of an object. Shall we say we mean Feeling? Shall we
say we mean association, or Habit? These are, on the face of them,
psychological distinctions, which I am particular to avoid. What is the
essential difference between a sign that is communicated to a mind, and one
that is not so communicated? If the question were simply what we do mean by
a sign, it might soon be resolved. But that is not the point. We are in the
situation of a zo”logist who wants to know what ought to be the meaning of
"fish" in order to make fishes one of the great classes of vertebrates. It
appears to me that the essential function of a sign is to render
inefficient relations efficient, -- not to set them into action, but to
establish a habit or general rule whereby they will act on occasion.
According to the physical doctrine, nothing ever happens but the continued
rectilinear velocities with the accelerations that accompany different
relative positions of the particles. All other relations, of which we know
so many, are inefficient. Knowledge in some way renders them efficient; and
a sign is something by knowing which we know something more. With the
exception of knowledge, in the present instant, of the contents of
consciousness in that instant (the existence of which knowledge is open to
doubt) all our thought and knowledge is by signs. A sign therefore is an
object which is in relation to its object on the one hand and to an
interpretant on the other, in such a way as to bring the interpretant into
a relation to the object, corresponding to its own relation to the object.
I might say 'similar to its own' for a correspondence consists in a
similarity; but perhaps correspondence is narrower.

================end of Peirce quotes  4 of 4==================

Joseph Ransdell - joseph.ransdell[…]  
Dept of Philosophy - 806  742-3158  (FAX 742-0730) 
Texas Tech University - Lubbock, Texas 79409   USA (Peirce website - beta)


Date: Sat, 7 Feb 1998 21:16:31 +0100
From: Thomas.Riese[…] (Thomas Riese)
To: peirce-l[…]
Subject: Re: "grade/grades" quotes

Dear Joe Ransdell,

thanks a lot for the interesting material! I think searching offers 
indeed interesting new possibilities for large text corpora -- well, 
perspectives again;-) It's of course not a substitute for a good 
"handcrafted" index, but it helps immensely to prepare one.
Anyway, the art of searching certainly is a part of the art of 
inquiry. And it is an art in itself.

That brings to my mind another possible idea to enhance the arisbe 
website: People at the University of Arizona have developed a search 
engine which can be incorporated into websites and allows visitors to 
search the site and I believe even linked sites. If I remember right, 
it is spelling error tolerant and has several other interesting 
features. It is available for free at

I don't know how much work it is to install it, but it seems that 
there are no special prerequisites what concerns the ISP server 
software etc. Perhaps you might want to have a look at it. Just an 
idea. If I can be a help, please let me know.

Thanks again,


Date: Sat, 07 Feb 1998 14:54:41
From: Joseph Ransdell 
To: peirce-l[…]TTACS.TTU.EDU
Subject: "gradation/gradations/gradum/gradus" quotes
Message-ID: <[…]>

We are right at the heart of Peirce in this, I believe.  Here are some more
Peirce quotes for the concept in question: this is the result of a string
search for 


Joe Ransdell

======Peirce quotes for 'gradation', etc.=================

Peirce: CP 1.8 
	8. Religious infallibilism, caught in the current of the times, shows
symptoms of declaring itself to be only practically speaking infallible;
and when it has thus once confessed itself subject to gradations, there
will remain over no relic of the good old tenth-century infallibilism,
except that of the infallible scientists, under which head I include, not
merely the kind of characters that manufacture scientific catechisms and
homilies, churches and creeds, and who are indeed "born missionaries," but
all those respectable and cultivated persons who, having acquired their
notions of science from reading, and not from research, have the idea that
"science" means knowledge, while the truth is, it is a misnomer applied to
the pursuit of those who are devoured by a desire to find things out....
Peirce: CP 1.546 
	546. This theory gives rise to a conception of gradation among those
conceptions which are universal. For one such conception may unite the
manifold of sense and yet another may be required to unite the conception
and the manifold to which it is applied; and so on.
Peirce: CP 4.659 
	Firstly. What, after all, are the cardinal numbers? What do they signify?
They signify the grades of multitude. Now a grade is a rank; it is an
ordinal idea. The English word grade which came in with the nineteenth
century, was evidently from Latin gradus, a stride, being the Latinized
form of the old English word gree, which the Scotch still use in the sense
of that which one strives to attain. It is the French gr‚. It is from an
Aryan root found in "greedy." See Fick's list of roots in the International
Dictionary, No. 49, [?û34]. There never was any idea of multitude attached
to this root. Some think the principal idea is desire; others, that it is
that of stepping out. It seems to me it is the idea of pushing on to the
attainment of what one hankers after. Thus, cardinal numbers are nothing
but a special class of ordinals. To say that a plural is five means that it
is of the fifth grade of multitude. It would be the sixth, if we were to
count none, or the foot of the staircase, as the first number; but we ought
in consistency to call it the "none-th" number. The ordinal "none-th" is a
desideration of gree, of thought that I have lately won. Just ponder the
utility of that view, my candid reader. Now Number is the mathematical
conception par excellence; and therefore the question is whether limiting
the grades we refer to in mathematics to grades of multitude advances and
aids mathematics to attain a higher grade of perfection or not. But this
answers itself. All that is essential to the mathematics of numbers is
succession and definite relations of succession, and that is just the idea
that ordinal number developes.
Peirce: CP 5.312 Fn P1 p 187  
	^P1 Eadem natura est, qu‘ in existentia per gradum singularitatis est
determinata, et in intellectu, hoc est ut habet relationem ad intellectum
ut cognitum ad cognoscens, est indeterminata. -- Quaest. Subtillissimae,
lib. 7, qu. 18.
Peirce: CP 7.283 
	283. Any one of those dimensions is such that the characters can pass
through the whole series of states in the course of time. It is easy to
imagine multitudes of variations so related to one another that one precise
character could not even in all time pass through them all by insensible
gradations. For example, colors differ from one another, not merely in hue,
but also in luminosity, and in chroma, or intensity of departure from grey.
Now, starting with a color of some precise hue, precise luminosity, and
precise chroma, if it is to change its hue gradually, for each precise hue
that it takes, it will have just one sole luminosity and one sole chroma;
so that, when it has gone through the whole cycle of hues, it will have had
for each of them but one single luminosity and but one single chroma.
Though it should pass through the cycle of hues times without end, it would
still not have begun to exhaust the possible luminosities and chromas for
each hue. The student may admit that it might be possible (and, in fact, it
might be shown to be possible) that if the color were so to jump from hue
to hue, from luminosity to luminosity, and from chroma to chroma, that
taking any two instants, no matter how near to one another, if during the
interval between them the variations should embrace the whole cycle of
hues, the whole range of luminosity, and the whole range of chroma, then
the color might in the course of time precisely assume for an instant every
special variety of color. But if the variation is to take place gradually,
then it is not possible that the color should in the course of time assume
every possible variation.

Joseph Ransdell - joseph.ransdell[…]  
Dept of Philosophy - 806  742-3158  (FAX 742-0730) 
Texas Tech University - Lubbock, Texas 79409   USA (Peirce website - beta)



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