PEIRCE-L Digest 1287 -- 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) Re:  Re: Porphyry: On Aristotle's Categories/The New List (1)
	by JESJC[…]
  2) New List (paragraphs 2 and 3)
	by Thomas.Riese[…] (Thomas Riese)
  3) "grade/grades" quotes  1 of 4
	by Joseph Ransdell 
	by Joseph Ransdell 


Date: Sat, 7 Feb 1998 00:44:24 EST
From: JESJC[…]
To: peirce-l[…]
Subject: Re:  Re: Porphyry: On Aristotle's Categories/The New List (1)

In response to the question about the Aristotelian-Peirce connection, I must
confess I am by no means well versed in Peirce scholarship.  I just read the
New List for the first time for a class on Peirce at the University of South
Carolina, however, and I too was struck by the possibility of such a
connection and how and/or why Peirce thinks he is expanding upon, clarifying
or correcting the views of his predecessors.  
	To my knowledge, Aristotle never explicitly said that being had no content.
This idea is, it seems to me, indicative of Peirce's indebtedness to Kant, for
whom a hundred thalers in the mind has the same content as a hundred actual
ones.  Strictly speaking, for Kant existence is something that is tied to the
the unity of apperception and the a priori conditions of possible experience.
The copula is more of a grammatical mark - a sign, if you will - that suggests
such a synthesis.  Kant writes:  "if I investigate more precisely the relation
of the given modes of knowledge in any judgment, and distinguish it, as
belonging to the understanding, from the relation according to laws of the
reproductive imagination, which has only subjective validity, I find that a
judgment is nothing but the manner in which given modes of knowledge are
brought to the objective unity of apperception.  This is intended by the
copula 'is'. " (B:142)  Peirce seems to say something remarkably similar in
paragraph four (4).  "The unity to which the understanding reduces impressions
is the unity of the proposition.  This unity consists in the connection of the
predicate with the subject; and, therefore, that which is implied in the
copula, or the conception of being, is that which completes the work of
conceptions of reducing the manifold to unity."  He also says (in paragraph
seven (7)):  "The conception of being arises upon the formulation of a
proposition."  Does this mean that we only become aware of being, i.e. form a
conception of it, after becoming able to synthesize the manifold explicitly in
propositions?  Would this imply that being is a relational concept that is
formed through reflection on our capacity for synthesizing judgments and is ,
therefore, without content for this reason?  I am not sure how to answer this
from either Kant's or Peirce's perspective(s).  
	It is curious, though, that Peirce does treat substance in terms of
"firstness."  It is remarkably similar to both Aristotle's prime matter and
Kant's transcendental "x"/object.  The main difference with Aristotle would
seem to be that while Aristotle used prime matter as both a logical
construction as well as a metaphysical substrate, Peirce claims that he is
engaged in a logical analysis.  For me the really interestign question is how
Peirce thinks he is leaving Kant behind, assuming that the adjective "new" in
the title refers, at least in part, to the Critical philosophy.  Obviously,
paragraph one (1) seems to make such a link fairly explicit.

Andrew Jones-Cathcart


Date: Sat, 7 Feb 1998 11:12:53 +0100
From: Thomas.Riese[…] (Thomas Riese)
To: peirce-l[…]
Subject: New List (paragraphs 2 and 3)

One of the terms in the New List which always seemed to me curious is 
'gradation' which is introduced rather abruptly in the second 

"This theory gives rise to a conception of gradation among those 
conceptions which are universal."

I have no access to the electronic edition of the Collected Papers, 
but I think it might be interesting to search the CP for it 
('gradation' doesn't appear in the subject index of CP 1).

Perhaps it is helpful to have a historical perspective on the New 
List. I found in my notes a reference to a text passage which reminded 
me very much of the above curious sentence. It is from MS 693 (1904): 
"Reason's Conscience: A Practical Treatise on the Theory of Discovery; 
Wherein logic is conceived as Semeiotic". The MS consists of six 
notebooks which unfortunately have only partly been published in 
English. The most complete version in print is seemingly Helmut Pape's 
German translation in "Peirce, Semiotische Schriften, Band 2, 
pp.166-237, Suhrkamp Verlag Frankfurt a.M, 1990". There are larger 
fragments of the text in the 2nd volume of the "Historical 
Perspectives on Peirce's Logic of Science" and in vol IV of Carolyn 
Eisele's "New Elements of Mathematics" (pp.185-215). Unfortunately 
Carolyn Eisele leaves out just the passage that is here interesting. 
(It would have to be inserted in "Chapter II. The Sciences" on p. 188 
in the place of the ellipsis at the bottom of that page.)

I think much more of this text passage might be desirable for the 
value it has for better understanding  the New List. I here 
only give a  re-translation of a short passage from Pape's 
translation (p.179):

#        quote from: "Reason's Conscience" 
#   **Beware: very raw re-translation by ThR** 

Knowledge begins by being knowledge of single percepts, no matter 
whether the individuality of the percepts is absolute or whether they 
are merely fragments of the experience. From this the knowledge of 
single persons develops. It is certain that the individuality of 
persons is not perfect. It consists for the most part in the 
continuity or, to put it more exactly, in  the graduality of the 
change of habits, especially the class of habits which we call 
memory. But memory is extremely fragmentary. Let's take any man and 
call him James. He has in his recent past -- not to speak of his 
preceeding life -- forgotten more events than he remembers. So if a 
second man, let's call him John, would in a sort of hypnotic trance 
remember all that James has forgotten and nothing else, then John 
would be as identical with the James of the last week as the present 
James is. Exactly this of course never happens; but there are 
phenomena of double personality and obsession which show 
sufficiently, that the individuality of persons is not perfect, 
though we have the habit to believe this.

################ end of quote ###########################

This certainly would have to be discussed in a larger context of the 
text but the seeming rarity of the terms 'gradation' and 'graduality' 
in Peirce's writings and the content of the context seem to me to 
imply a strong connection to the ideas in the first few sentences and 
quite generally in the New List. What seems to me very remarkable is 
the fact that Peirce in the above text passage strongly connects 
graduality and continuity. 

I think this then means that the idea of continuity, which later 
became so prominent in Peirce's work, is already present in the 
second sentence of the New List -- at least in germ. There is an 
enormous continuity in his thought which here then even might nearly 
refute his own argument in the above text;-)

Of course, if we interpret the Kantian theme as the question what the 
relation between the objective and the subjective world is and whether 
and how there is an intermediate ground, then we should expect that 
the unity of the "Ich", personality, is much weaker than we might 
perhaps naively expect (I can only recommend Milton Erickson for 
further information;-)). Though: "weak" is here rather inappropriate a 
term. There is a much stronger unity than generally believed but not 
necessarily where we are accustomed to suspect it.

Furthermore I think it is not without interest that Peirce defines 
memory in terms of 'habit'. I can't resist the temptation to cite a 
passage from a text of the physicist Richard Feynman (Meaning and Use 
of Science, Address to the National Academy of Sciences, 1955): 
[urrgh, again my re-translation..]

"[...]We do not yet live in the age of science. Perhaps one of the 
reasons for this silence is that the notes of this music are not 
known. So you might find in a scientific paper the sentence: 'The 
content of radioactive phosphor in the brain of a rat is reduced to 
one half in two weeks.' But what does this sentence say? It says that 
the phosphor in the brain of a rat -- and in the same way in your and 
my brain -- is not any more the same as that two weeks ago. It says 
that the atoms in the brain are exchanged. Those that were there 
before are not anymore there. What then is our intellect? What are 
these consciousness capacitated atoms? Last year's snow! Nevertheless 
they are inhabited with a _memory_ of what happend in my intellect a 
year ago -- which has already renewed itself in the mean time. The 
insight that my so called Ego is only a pattern, a dance: _this_ is 
the true kernel of the discovery during which period of time the atoms 
of my brain are replaced by other atoms. The atoms get into my brain, 
dance their round dance and disappear again -- there are currently new 
atoms, but they dance, mindful of yesterday's round dance, the same 
dance again and again. [...]"

Maybe Peirce was still too conservative in his ideas?

I think if we want to have a more complete understanding of Peirce's 
concept of continuity we shouldn't neglect his early work. 
We can safely rely on the fact 
that he generally does what he says he does:-)

Thomas Riese.


Date: Sat, 07 Feb 1998 12:08:29
From: Joseph Ransdell 
To: peirce-l[…]TTACS.TTU.EDU
Subject: "grade/grades" quotes  1 of 4
Message-ID: <[…]>

I think Thomas Riese is right in stressing the possible importance of
Peirce's conception of grades, and I am posting all passages in the
Collected Papers which contain either "grade" or "grades" for those
interested in following up on this.  I have done nothing to improve on
result of the string search except to eliminate some clutter and to enclose
every occurrence of either "grade" or "grades" in flanking asterisks so
that one can easily go to the sentence in which the word is used.  This is
of coures a pure ascii version, with consequent loss in formatting.  Also,
I do not provide dates for the passages since there is no convenient way to
do that for a large batch like this, given the way dating is handled in the
electronic version.  

Peirce: CP 1.257 
	257. We now come to consider groups one **grade** lower. Here is a point
where I must confess to have hesitated. Our branches of science are
distinguished by their different purposes; our classes by the fundamentally
different nature of their observations. Logic suggests that orders, to
which we next come, should be distinguished by the difference in the
intellectual part of the business of the sciences under them; so that among
the Physical Sciences, for example, we should have: first those which
investigate the laws common to all matter; second, those which study the
relations between different classes of physical objects; third, those whose
objects are the understanding of different individual objects; and it is
plain that a similar classification could be made in psychics. Still,
although this seems a priori plausible, a positive guarantee that this will
be a natural division is perhaps lacking. At any rate, no ground of
assurance is evident. It has occurred to me that we might distribute the
physical sciences into those which study objects predominantly under the
dominion of force and those predominantly under the influence of final
causality; giving physics and natural history. This separation would well
accord with the way in which the men naturally cluster. But for that very
reason, a suspicion is created that the point has not yet been reached
where that cleavage should be made. Before we come to groups of men
thoroughly understanding one another's work, we ought to consider groups of
which the one stands in the relation of teacher of principles to another;
just as, in a school, the relation of master and pupil makes a broader
natural division than that between different forms or classes. . . .
Peirce: CP 1.332 
    	332. The triad, feeling, volition, cognition, is usually regarded as a
purely psychological division. Long series of carefully planned
self-experiments, persistent and much varied, though only qualitative, have
left me little doubt, if any, that there are in those elements three quite
disparate modes of awareness. That is a psychological proposition; but that
which now concerns us is not psychological, particularly; namely the
differences between that of which we are aware in feeling, volition, and
cognition. Feeling is a quality, but so far as there is mere feeling, the
quality is not limited to any definite subject. We hear of a man whose mind
is jaundiced. That phrase well expresses feeling without reason. Feeling
also as such is unanalyzed. Volition is through and through dual. There is
the duality of agent and patient, of effort and resistance, of active
effort and inhibition, of acting on self and on external objects. Moreover,
there is active volition and passive volition, or inertia, the volition of
reform and the volition of conservatism. That shock which we experience
when anything particularly unexpected forces itself upon our recognition
(which has a cognitive utility as being a call for explanation of the
presentment), is simply the sense of the volitional inertia of expectation,
which strikes a blow like a water-hammer when it is checked; and the force
of this blow, if one could measure it, would be the measure of the energy
of the conservative volition that gets checked. Low **grades** of this
shock doubtless accompany all unexpected perceptions; and every perception
is more or less unexpected. Its lower **grades** are, as I opine, not
without experimental tests of the hypothesis, that sense of externality, of
the presence of a non-ego, which accompanies perception generally and helps
to distinguish it from dreaming. This is present in all sensation, meaning
by sensation the initiation of a state of feeling; -- for by feeling I mean
nothing but sensation minus the attribution of it to any particular
subject. In my use of words, when an ear-splitting, soul-bursting
locomotive whistle starts, there is a sensation, which ceases when the
screech has been going on for any considerable fraction of a minute; and at
the instant it stops there is a second sensation. Between them there is a
state of feeling.
Peirce: CP 1.353 
  	353. Perhaps it is not right to call these categories conceptions; they
are so intangible that they are rather tones or tints upon conceptions. In
my first attempt to deal with them, I made use of three **grades** of
separability of one idea from another. In the first place, two ideas may be
so little allied that one of them may be present to the consciousness in an
image which does not contain the other at all; in this way we can imagine
red without imagining blue, and vice versa; we can also imagine sound
without melody, but not melody without sound. I call this kind of
separation dissociation. In the second place, even in cases where two
conceptions cannot be separated in the imagination, we can often suppose
one without the other, that is we can imagine data from which we should be
led to believe in a state of things where one was separated from the other.
Thus, we can suppose uncolored space, though we cannot dissociate space
from color. I call this mode of separation prescission. In the third place,
even when one element cannot even be supposed without another, they may
ofttimes be distinguished from one another. Thus we can neither imagine nor
suppose a taller without a shorter, yet we can distinguish the taller from
the shorter. I call this mode of separation distinction. Now, the
categories cannot be dissociated in imagination from each other, nor from
other ideas. The category of first can be prescinded from second and third,
and second can be prescinded from third. But second cannot be prescinded
from first, nor third from second. The categories may, I believe, be
prescinded from any other one conception, but they cannot be prescinded
from some one and indeed many elements. You cannot suppose a first unless
that first be something definite and more or less definitely supposed.
Finally, though it is easy to distinguish the three categories from one
another, it is extremely difficult accurately and sharply to distinguish
each from other conceptions so as to hold it in its purity and yet in its
full meaning.
Peirce: CP 1.365 
	365. Thus, the whole book being nothing but a continual exemplification of
the triad of ideas, we need linger no longer upon this preliminary
exposition of them. There is, however, one feature of them upon which it is
quite indispensable to dwell. It is that there are two distinct **grades**
of Secondness and three **grades** of Thirdness. There is a close analogy
to this in geometry. Conic sections are either the curves usually so
called, or they are pairs of straight lines. A pair of straight lines is
called a degenerate conic. So plane cubic curves are either the genuine
curves of the third order, or they are conics paired with straight lines,
or they consist of three straight lines; so that there are the two orders
of degenerate cubics. Nearly in this same way, besides genuine Secondness,
there is a degenerate sort which does not exist as such, but is only so
conceived. The medieval logicians (following a hint of Aristotle)
distinguished between real relations and relations of reason. A real
relation subsists in virtue of a fact which would be totally impossible
were either of the related objects destroyed; while a relation of reason
subsists in virtue of two facts, one only of which would disappear on the
annihilation of either of the relates. Such are all resemblances: for any
two objects in nature resemble each other, and indeed in themselves just as
much as any other two; it is only with reference to our senses and needs
that one resemblance counts for more than another. Rumford and Franklin
resembled each other by virtue of being both Americans; but either would
have been just as much an American if the other had never lived. On the
other hand, the fact that Cain killed Abel cannot be stated as a mere
aggregate of two facts, one concerning Cain and the other concerning Abel.
Resemblances are not the only relations of reason, though they have that
character in an eminent degree. Contrasts and comparisons are of the same
sort. Resemblance is an identity of characters; and this is the same as to
say that the mind gathers the resembling ideas together into one
conception. Other relations of reason arise from ideas being connected by
the mind in other ways; they consist in the relation between two parts of
one complex concept, or, as we may say, in the relation of a complex
concept to itself, in respect to two of its parts. This brings us to
consider a sort of degenerate Secondness that does not fulfill the
definition of a relation of reason. Identity is the relation that
everything bears to itself: Lucullus dines with Lucullus. Again, we speak
of allurements and motives in the language of forces, as though a man
suffered compulsion from within. So with the voice of conscience: and we
observe our own feelings by a reflective sense. An echo is my own voice
coming back to answer itself. So also, we speak of the abstract quality of
a thing as if it were some second thing that the first thing possesses. But
the relations of reason and these self-relations are alike in this, that
they arise from the mind setting one part of a notion into relation to
another. All degenerate seconds may be conveniently termed internal, in
contrast to external seconds, which are constituted by external fact, and
are true actions of one thing upon another.
Peirce: CP 1.529 
	529. I will just mention that among Firstnesses there is no distinction of
the genuine and the degenerate, while among Thirdnesses we find not only a
genuine but two distinct **grades** of degeneracy.
Peirce: CP 1.581 
	581. What I propose now to do is to pass in review every one of the
general classes of objects which anybody could suppose to be an ultimate
good, and to question consciousness, first, as to whether or not each of
these in turn could content us as the sole ultimate good independently of
any ulterior result, and if not, whether it can be considered to be in
itself a good at all, irrespective of its effects. I shall arrange my list
so as to commence with the most particular satisfactions and proceed step
by step to the most general. But since there are in each **grade** several
kinds of satisfactions, I shall begin in each **grade** of generality with
the most immediate and selfish and go on by steps to the most subservient.
Peirce: CP 2.605 
	More or less fixity in the object is requisite. Indeed, experience
supposes that its object reacts upon us with some strength, much or little,
so that it has a certain **grade** of reality or independence of our
cognitive exertion. All reasoning whatever has observation as its most
essential part. Whatever else there is in the act of reasoning is only
preparatory to observation, like the manipulation of a physical experiment.
Peirce: CP 2.667 
	667. But my purpose in doing so is to explain what probability, as I use
the word, consists in. Now it would be no explanation at all to say that it
consists in something being probable. So I must avoid using that word or
any synonym of it. If I were to use such an expression, you would very
properly turn upon me and say, "I either know what it is to be probable, in
your sense of the term, or I do not. If I don't, how can I be expected to
understand you until you have explained yourself; and if I do, what is the
use of the explanation?" But the fact [is] that the probability of the die
turning up a three or a six is not sure to produce any determination [of]
the run of the numbers thrown in any finite series of throws. It is only
when the series is endless that we can be sure that it will have a
particular character. Even when there is an endless series of throws, there
is no syllogistic certainty, no "mathematical" certainty (if you are more
familiar with this latter phrase)--that the die will not turn up a six
obstinately at every single throw. It might be that if in the course of the
endless series, some friends should borrow the die to make a pair for a
game of backgammon, there might be nothing unusual in the behavior of the
lent die, and yet when it was returned and our experimental series was
resumed where it had been interrupted, the die might return to turning up
nothing but six every time. I say it might, in the sense that it would not
violate the principle of contradiction if it did. It sanely would not,
however, unless a miracle were performed; and moreover if such miracle were
worked, I should say (since it is my use of the term "probability" that we
have supposed to be in question) that during this experimental series of
throws, the die took on an abnormal, a miraculous, habit. For I should
think that the performance of a certain line of behavior, throughout an
endless succession of occasions, without exception, very decidedly
constituted a habit. There may be some doubt about this, for owing to our
not being accustomed to reason in this way about successions of events
which are endless in the sequence and yet are completed in time, it is hard
for me quite to satisfy myself what I ought to say in such a case. But I
have reflected seriously on it, and though I am not perfectly sure of my
ground (and I am a cautious reasoner), yet I am more that what you would
understand by "pretty confident," that supposing one to be in a condition
to assert what would surely be the behavior, in any single determinate
respect, of any subject throughout an endless series of occasions of a
stated kind, he ipso facto knows a "would-be," or habit, of that subject.
It is very true, mind you, that no collection whatever of single acts,
though it were ever so many **grades** greater than a simple endless
series, can constitute a would-be, nor can the knowledge of single acts,
whatever their multitude, tell us for sure of a would-be. But there are two
remarks to be made; first, that in the case under consideration a person is
supposed to be in a condition to assert what surely would be the behavior
of the subject throughout the endless series of occasions--a knowledge
which cannot have been derived from reasoning from its behavior on the
single occasions; and second, that that which in our case renders it true,
as stated, that the person supposed "ipso facto knows a would-be of that
subject," is not the occurrence of the single acts, but the fact that the
person supposed "was in condition to assert what would surely be the
behavior of the subject throughout an endless series of occasions."
Peirce: CP 3.456 
	456. The third volume of Professor Schr"der's Exact Logic, which volume
bears separately the title I have chosen for this paper, is exciting some
interest even in this country. There are in America a few inquirers into
logic, sincere and diligent, who are not of the genus that buries its head
in the sand -- men who devote their thoughts to the study with a view to
learning something that they do not yet know, and not for the sake of
upholding orthodoxy, or any other foregone conclusion. For them this
article is written as a kind of popular exposition of the work that is now
being done in the field of logic. To them I desire to convey some idea of
what the new logic is, how two "algebras," that is, systems of
diagrammatical representation by means of letters and other characters,
more or less analogous to those of the algebra of arithmetic, have been
invented for the study of the logic of relatives, and how Schr"der uses one
of these (with some aid from the other and from other notations) to solve
some interesting problems of reasoning. I also wish to illustrate one other
of several important uses to which the new logic may be put. To this end I
must first clearly show what a relation is.
Peirce: CP 3.457 
	457. Now there are three **grades** of clearness in our apprehensions of
the meanings of words. The first consists in the connexion of the word with
familiar experience. In that sense, we all have a clear idea of what
reality is and what force is -- even those who talk so glibly of mental
force being correlated with the physical forces. The second **grade**
consists in the abstract definition, depending upon an analysis of just
what it is that makes the word applicable. An example of defective
apprehension in this **grade** is Professor Tait's holding (in an appendix
to the reprint of his Britannica article, Mechanics) that energy is
"objective" (meaning it is a substance), because it is permanent, or
"persistent." For independence of time does not of itself suffice to make a
substance; it is also requisite that the aggregant parts should always
preserve their identity, which is not the case in the transformations of
energy. The third **grade** of clearness consists in such a representation
of the idea that fruitful reasoning can be made to turn upon it, and that
it can be applied to the resolution of difficult practical problems.
Peirce: CP 3.458 
  	458. An essential part of speech, the Preposition, exists for the
purpose of expressing relations. Essential it is, in that no language can
exist without prepositions, either as separate words placed before or after
their objects, as case-declensions, as syntactical arrangements of words,
or some equivalent forms. Such words as "brother," "slayer," "at the time,"
"alongside," "not," "characteristic property" are relational words, or
relatives, in this sense, that each of them becomes a general name when
another general name is affixed to it as object. In the Indo-European
languages, in Greek, for example, the so-called genitive case (an inapt
phrase like most of the terminology of grammar) is, very roughly speaking,
the form most proper to the attached name. By such attachments, we get such
names as "brother of Napoleon," "slayer of giants," "{epi 'Ellissaiou}, at
the time of Elias," "{para all‚l"n}, alongside of each other," "not
guilty," "a characteristic property of gallium." Not is a relative because
it means "other than"; scarcely, though a relational word of highly complex
meaning, is not a relative. It has, however, to be treated in the logic of
relatives. Other relatives do not become general names until two or more
names have been thus affixed. Thus, "giver to the city" is just such a
relative as the preceding; for "giver to the city of a statue of himself"
is a complete general name (that is, there might be several such humble
admirers of themselves, though there be but one, as yet); but "giver"
requires two names to be attached to it, before it becomes a complete name.
The dative case is a somewhat usual form for the second object. The
archaic, instrumental, and locative cases were serviceable for third and
fourth objects.
Peirce: CP 3.464 
      464. Is relation anything more than a connexion between two things?
For example, can we not state that A gives B to C without using any other
relational phrase than that one thing is connected with another? Let us
try. We have the general idea of giving. Connected with it are the general
ideas of giver, gift, and "don‚e." We have also a particular transaction
connected with no general idea except through that of giving. We have a
first party connected with this transaction and also with the general idea
of giver. We have a second party connected with that transaction, and also
with the general idea of "don‚e." We have a subject connected with that
transaction and also with the general idea of gift. A is the only hecceity
directly connected with the first party; C is the only hecceity directly
connected with the second party, B is the only hecceity directly connected
with the subject. Does not this long statement amount to this, that A gives
B to C?
Peirce: CP 3.468 
    	468. Mr. A. B. Kempe has published in the Philosophical Transactions a
profound and masterly "Memoir on the Theory of Mathematical Form," which
treats of the representation of relationships by "Graphs," which is
Clifford's name for a diagram, consisting of spots and lines, in imitation
of the chemical diagrams showing the constitution of compounds. Mr. Kempe
seems to consider a relationship to be nothing but a complex of bare
connexions of pairs of objects, the opinion refuted in the last section.
Accordingly, while I have learned much from the study of his memoir, I am
obliged to modify what I have found there so much that it will not be
convenient to cite it; because long explanations of the relation of my
views to his would become necessary if I did so.
Peirce: CP 3.550 
	550. We thus not only answer the question proposed, and show that of two
unequal multitudes the multitude of ways of distributing the greater is the
greater; but we obtain the entire scale of collectional quantity, which we
find to consist of two equal parts (that is two parts whose multitudes of
**grades** are equal), the one finite, the other infinite. Corresponding to
the multitude of 0 on the finite scale is the abnumeral of 0 dignity, which
is the denumerable, on the infinite scale, etc.
Peirce: CP 4.107 
	107. The second, or middling, **grade** of multitude is that of
collections which have different attributes for different quantitative
collections; namely, for some such relations, every member of the class
superior to another member is next superior to some member, definitely
designatable, while for other quantitative relations it is not so. I
undertake to show that there is always some quantitative relation for which
(1) the class has a minimum but no maximum, (2) for which every member of
the class that is superior to another is next superior to some other, (3)
and for which the partial class consisting of any two members of the class
we are speaking of, together with all that are superior to one of these two
members but inferior to the other, is enumerable. Let us begin by thinking
of a member of this class, say a[x]. Then, considering a quantitative
relation in which every a superior to an a is next superior to an a, let us
think of that to which a[x] is next superior. Then, think of that to which
the last is next superior. Then consider a partial class to all of which
a[x] is superior, and the next inferior of each member of which is also
included under it, so that either there is a minimum, which is not superior
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to any member of the class, or else, if a[y] is any member of the class to
which a[x] is superior, and the a's at once inferior to a[x] and superior
to a[y] are enumerable, it follows that a[y] is a member of the partial
class. For if not, of all the a's superior to a[y] and inferior to a[x], a
part belongs to the partial class, and this part of an enumerable
collection, being itself (as such) enumerable, must have a minimum. But by
the definition of the partial class, whatever is next inferior to any
member of it also belongs to it. To this partial class, then, belongs every
a inferior to a[x], so long as between it and a[z], the collection of a's
is enumerable. We do not know that there is an a next superior to a[x]. But
we define a second partial class as containing the a next superior to a[x],
if there be any, and as containing nothing else, except that it contains
the a next superior to any a that it contains. Then, it will either contain
all the a's superior to a[x] up to some maximum, which need not be the
maximum of all the a's, but which has no a next superior to it, or, in the
absence of such a maximum, it will contain all the a's up to and beyond any
a superior to a[x], but such that the a's inferior to it and superior to
a[x] form an enumerable collection. The proof of this (so plain that it
hardly needs statement) is as follows: if this be not the case let a[z] be
an a superior to a[x] and such that the a's inferior to a[z] but superior
to a[x] form an enumerable multitude. Then, those of those which belong to
the second partial class, being part of an enumerable collection. are
themselves enumerable. Hence, they have a maximum, contrary to the
hypothesis. Taking the first and second partial classes together, I propose
to call such a series of a's a linear sequence. I will repeat its
Peirce: CP 4.115 
	115. The reasoning of Ricardo about rent is this. When competition is
unrestrained by combination, producers will carry production to the limit
at which it ceases to be profitable. Thus, a man will put fertilizers on
his land, until the point is reached where, were he to add the least bit
more, his little increased production would no more than just pay the
increased expense. Every piece of land will be treated in this way, and
every **grade** of land will be used down to the limit of the land upon
which the product can just barely pay.
Peirce: CP 4.121 
	But if b®n¯ when n is dinumerable gives a new **grade** of multitude, we
might expect that when n was innumerable, a still higher **grade** would be
Peirce: CP 4.121 
	Yet, on the other hand, looking at the matter from the point of view of
the original definitions given above, the three classes of multitude seem
to form a closed system. Still, nothing in those definitions prevents there
being many **grades** of multiplicity in the third class. I leave the
question open, while inclining to the belief that there are such
**grades**. Cantor's theory of manifolds appears to me to present certain
difficulties; but I think they may be removed.

==========END 1 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 12:15:37
From: Joseph Ransdell 
Message-ID: <[…]>

CONT'D  (2 OF 4)

===========PEIRCE QUOTES ON 'GRADE'  2 OF 4======================

Peirce: CP 4.181 
	181. I will now run over the different **grades** of multitude of discrete
collections, and point out the most remarkable properties of those multitudes.
Peirce: CP 4.181 
	The lowest **grade** of multitude is that of a collection which does not
exist, or the multitude of none. A collection of this multitude has obvious
logical peculiarities. Namely, nothing asserted of it can be false. For of
it alone contradictory assertions are true. It is a collection and it is
not a collection. Given the premisses that all the X's are black and that
all the X's are pure white, what is the conclusion? Simply that the
multitude of the X's is zero.
Peirce: CP 4.181 
	The multitude of ways of distributing nothing into two abodes is one. This
is the next **grade** of multitude. This again has certain logical
peculiarities. Namely, in order to prove that every individual of it
possesses one character, it suffices to prove that every individual of it
does not possess the negative of that character.
Peirce: CP 4.181 
	The multitude of ways of distributing a single individual into two houses
is two. This is the next **grade** of multitude. This again has certain
logical peculiarities which have been noted in Schr”der's Logik.
Peirce: CP 4.181 
	The multitude of combinations of two things is four, which is not the next
**grade** of multitude. The multitude of combinations of four things is 16.
The multitude of combinations of 16 things is 65,536. The multitude of
combinations of 65,536 things is large. It is written by 20,036 followed by
19,725 other figures. The multitude of combinations of that many things is
a number to write which would require over 600,000 thousand
trimillibicentioctagentiseptillions of figures on the so-called English
system of numeration. What the number itself would be called it would need
a multimillionaire to say. But I suppose the word trimillillillion might
mean a million to the trimillillionth power; and a trimillillion would be a
million to the three thousandth power. But the multitude considered is far
greater than a trimillillillion. It is safe to say that it far exceeds the
number of chemical atoms in the gallactic cluster. Yet this is one of the
early terms of a series which is confined entirely to finite collections
and never reaches the really interesting division of multitudes, which
comprises these that are infinite.
Peirce: CP 4.182 
	182. The finite collections, however, or, as I prefer to call them, the
enumerable collections, have several interesting properties. The first
thing to be considered is, how shall an enumerable multitude be defined? If
we say that it is a multitude which can be reached by starting at 0, the
lowest **grade** of multitude, and successively increasing it by one, we
shall express the right idea. The difficulty is that this is not a clear
and distinct statement. As long as we discuss the subject in ordinary
language, the defect of distinctness is not felt. But it is one of the
advantages of the algebra which is now used by all exact logicians, that
such a statement cannot be expressed in that logical algebra until we have
carefully thought out what it really means. An enumerable multitude is said
to be one which can be constructed from zero by "successive" additions of
unity. What does "successive," here, mean? Does it allow us to make
innumerable additions of unity? If so, we certainly should get beyond the
enumerable multitudes. But if we say that by "successive" additions we mean
an enumerable multitude of additions, we fall into a circulus in
definiendo. A little reflection will show that what we do mean is, that the
enumerable multitudes are those multitudes which are necessarily reached,
provided we start at zero, and provided that, any given multitude being
reached, we go on to reach another multitude next greater than that. The
only fault of this statement is, that it is logically inelegant. It sounds
as if there were some special significance in the "reaching," which by the
principles of logic there cannot be. For the enumerable multitudes are
defined as those which are necessarily so reached. Now the kind of
necessity to which this "necessarily" plainly refers is logical necessity.
But the perfect logical necessity of a result never depends upon the
material character of the predicate. If it is necessary for one predicate,
it is equally so for any other. Accordingly, what is meant is that the
enumerable multitudes are those multitudes every one of which possess any
character whatsoever which is, in the first place, possessed by zero and,
in the second place, if it is possessed by any multitude, M, whatsoever, is
likewise possessed by the multitude next greater than M. We, thus, find
that the definition of enumerable multitude is of this nature, that it
asserts that that famous mode of reasoning which was invented by Fermat
applies to the succession of those multitudes. The enumerable multitudes
are defined by a logical property of the whole collection of those multitudes.
Peirce: CP 4.189 
	Accordingly, there is but a single **grade** of denumerable multitude. So
it is to be noted as a defect in my nomenclature, which I unfortunately did
not remark when I first published it, that enumerable and denumerable,
which sound so much alike, denote, the one a whole category of **grades**
of multitude and the other a simple **grade** like, zero, or twenty-three.
Peirce: CP 4.212 
	212. It is one of the effects of the deplorable neglect by mathematicians
of the properties of primipostnumeral collections that we are in complete
ignorance of an arrangement of such a collection, which should be related
to its primal arrangement in any manner analogous to the relation of the
arrangement [of] the primal arrangement of the denumerable collection to
that indefinitely divident arrangement, which leads to a clear conception
of the next **grade** of multitude.
Peirce: CP 4.282 
	Demonstration. Let x be any quantity which is written on the sheet of
assertion with a vinculum under it, x§. We may confine ourselves to the
consideration of the case of the assertion x being true; for if it be not
true, it certainly cannot sustain a loss of truth, since, by the definition
of quantities, an assertion which has any other than the two **grades** of
truth does not enter into the algebra. Let us first suppose that x is a
proposition. Now every asserted proposition virtually asserts its own
truth. That is to say, it asserts a fact, which being assumed real, whoever
perceives that the proposition asserts that fact, has a perception which
can be formulated by saying that what the proposition asserts is true.
Therefore, if the vinculum is removed, nothing false is asserted by x,
assuming x to be true. The only difference is that x§ directly asserts what
x virtually asserts, and that x implies what x§ directly asserts. If, on
the other hand, x is not an assertion, still its being written upon a sheet
of assertions would make it assert itself to be an assertion; and whatever
asserts itself to be something asserts something. But, being a quantity of
this algebra, unless it is itself primarily an assertion, which would be
contrary to our present hypothesis, the only assertion it can be, by the
definition of quantities, is that a quantity of the algebra has some value.
But the only quantity of the algebra to which x could refer would be
itself. It must, therefore, assert that it has itself either the value v or
the value f. But, by I, it must assert something which implies the truth of
x§. Hence, x must assert that its value is v. But this is no more than is
asserted by x§; and therefore no falsity can be introduced by omitting the
Peirce: CP 4.337 
	337. All that it is necessary to insist upon here is that the only thing
that whole numbers can express is the relative place of objects in a
simple, discrete, linear series; and whole numbers are applicable to
enumerable multitudes and enumerable collections, only because it happens
that those multitudes have each its place in a simple, discrete, linear
series. It is true that Dr. Georg Cantor, the great founder and
Hauptf”rderer of the logico-mathematical doctrine of numbers, begins his
exposition with what he calls "cardinal numbers," but which ought properly
to be called multitudes. For cardinal numbers proper are nothing but the
vocables of a certain series of vocables that are used in the operation of
ascertaining the multitude of a collection, by counting, and thence are
applied as appellatives of collections to signify their multitudes.
Multitude itself, however, belongs to various different collections in
various different **grades**, where cardinal number has no application, at
all. Cantor, however, has partially shown, what is entirely true, that the
whole doctrine of multitude can be developed without any reference to
ordinal numbers. But in treating of ordinals we are obliged to say, in
substance, what their multitude is. Thus, when we look at the matter from a
certain point of view, it seems that the doctrine of multitude is more
fundamental than that of ordinals, and that all whole numbers really
express multitudes. But this is a logical fallacy. That the concepts of
multitude and of ordinal place in a simple, discrete, linear series are
very intimately connected is true. The latter involves the consideration of
facts constituting the applicability of definite conceptions of multitude;
but it does not involve these conceptions themselves. Multitude, on the
other hand, is nothing but the place of a series in one or the other of two
simple, discrete, linear series, and it is impossible to define it at all
without the use of the ordinal conception itself.
Peirce: CP 4.639 
 	639. Denumeral is applied to a collection in one-to-one correspondence to
a collection in which every member is immediately followed by a single
other member, and in which but a single member does not, immediately or
mediately, follow any other. A collection is in one-to-one correspondence
to another, if, and only if, there is a relation, r, such that every member
of the first collection is r to some member of the second to which no other
member of the first is r, while to every member of the second some member
of the first is r, without being r to any other member of the second. The
positive integers form the most obviously denumeral system. So does the
system of all real integers, which, by the way, does not pass through
infinity, since infinity itself is not part of the system. So does a
Cantorian collection in which the endless series of all positive integers
is immediately followed by {”}[1], and this by {”}[1]+1, this by {”}[1]+2,
and so on endlessly, this endless series being immediately followed by
2{”}[1]. Upon this follow an endless series of endless series, all positive
integer coefficients of {”}[1] being exhausted, whereupon immediately
follows {”}[1]®2¯, and in due course x{”}[1]®2¯+y{”}[1]+z, where x, y, z,
are integers; and so on; in short, any system in which every member can be
described so as to distinguish it from every other by a finite number of
characters joined together in a finite number of ways, is a denumeral
system. For writing the positive whole numbers in any way, most
systematically thus:
Peirce: CP 4.654 
	654. In my eagerness to express myself, I have permitted myself to talk of
multitude without defining it. It is that respect in which discrete
collections of singulars of which one is greater than the other disagree.
It has two denumeral series of absolute **grades**, the one consisting of
all multitudes, that is, of all absolute **grades** of multitudes such that
the count of any collection of any such **grade** of multitude can be
completed, which multitudes are distinguished by the cardinal numbers
proper, that is, the finite cardinal numbers; these **grades** of
enumerable multitude running from 0 up endlessly, are followed by another
similar series of abnumerable multitudes, beginning with the multitude of
abnumerability zero, which is the multitude of a simply endless succession
of singulars; and each following multitude being the multitude of all the
possible collections that can be formed of the singulars of a collection of
the next lower multitude, so that this second and last series of multitudes
forms another simply endless series.
Peirce: CP 4.656 
	656. That multitude which is greater than any such multitude but is not
greater than any other multitude, is termed the denumeral multitude, which
in the higher, or second, series of multitudes corresponds to zero in the
lower, or first, series. After it follow one by one an endless series of
abnumerable multitudes. Yet so far as I know (I am not acquainted with the
work of Borel, of which I have only quite vaguely heard), it has never been
exactly proved that there are no multitudes between two successive
abnumerable multitudes, nor, which is more important, that there is no
multitude greater than all the abnumerable multitudes. Each abnumerable
multitude after the denumeral multitude is the multitude of all possible
collections whose singulars are members of a collection whose multitude is
the next lower abnumerable multitude, the denumeral multitude being
considered as the abnumerable multitude of **grade** Zero.
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
Peirce: CP 4.663 
	663. The fourth argument, much the most respectable of the list, certainly
shows that the device of considering numbers as multitudes gives very
pretty demonstrations of the values of products and powers of whole
numbers; but the first fault of the argument is that there are countless
parallel instances of devices giving charmingly clear intuitions of
mathematical truth, although nobody in his senses could say that the
imported considerations were essentially involved in the subjects to which
the theorems relate. Thus, a number of difficult evaluations of integrals
can be obtained most delightfully by considering those integrals as the
values of probabilities and then applying common sense, or some simple
reasoning, to answering the question of probability. Yet who would say that
the idea of probability was essentially involved in the idea of an abstract
integral? The proper inference is the converse of that; I mean that the
idea of the integral is essentially involved in the idea of the problem in
probabilities. Just so, in the instances adduced; what they evidently prove
is that the abstract ideas of multiplication and of involution are
involved, the one in the more concrete idea of a collection whose units are
collections, and the other in the concreter idea of the different ways of
distributing the members of one collection into connection with the several
units of another collection. I admit, with all my heart, the
instructiveness of these remarks and to the fact that they shed a brilliant
illumination upon the essential nature of the arithmetical and algebraical
results. Indeed, they are so rich in their curiosity and their eye-opening
virtues, that I will not spoil their effect by tagging any discussion of
them upon this already exorbitant paper. I will only say that if on another
occasion I ring up the curtain upon what they have to show, it will be seen
that one of their first lessons is that numbers may stand for **grades** of
any kind and not exclusively for **grades** of multitude. You will observe
that, for example, in the iconization of involution, it was not members of
a multitude that were put into the different parts of another multitude,
but members of a collection which are attached to different singulars of a
collection. Now while numbers may on occasion be, or represent, multitudes,
they can never be collections, since collections are not **grades** of any
kind, but are single things. It may be reckoned a second fault of that
fourth argument that it quite overlooks the necessity of proving the
exclusive limitation of numbers to a single variety of **grades**; and a
third fault of it is that it baldly asserts, with not so much as an
imitation-reason, that it is impossible to obtain a clear conception of
multiplication without appeal to cardinals. That is a gage that I am
obliged to take up. Let me first call attention to the fact that an object
of pure mathematical thought does not possess this or that definite
sensible quality, but is distinguished from other such objects by the form
of relation involved in its structure. It must further be noticed that
there are different kinds of multiplication, especially the "internal" and
the "external"; and besides that, there are different allowable ways of
using the term, so that what at one time would be called multiplication, at
another time would not be multiplication. I have to define what could with
propriety be called multiplication with the proper strictness and proper
looseness. Above all, extreme care will be needed to avoid vicious circles
and phrases that seem to have a meaning but really have none. For example,
I shall have to mention addition in defining multiplication, and,
consequently must begin by defining that. Now if I were to say that
addition consists in simply putting two quantities together, that would
sound as if it meant something; yet I do not clearly see what it would or
well could mean; for if anybody were to ask me what kind of "putting
together" I meant, why, what I should find myself meaning is simply the
adding of them together. So since addition is of course adding, my
statement might just as well be omitted, and no meaning would be lost with
the omission.
Peirce: CP 4.677 
	677. I guess that a good many people, among whom many mathematicians must
be included, to judge by their often writing Ä, 1, 2, 3, ...... ì, ... have
a notion that nothing but a limitation attached to human powers prevents a
finite collection receiving successive finite increments until it becomes
denumeral; though I do not suppose that any modern mathematician would
deliberately say that the positive integers strictly run up to the
denumeral. It is not because of an human imperfection that we cannot add
units to a collection until it becomes denumeral, but it is because the
supposition involves a contradiction in itself, and therefore cannot be
rendered definite in all respects. For the denumeral is and by definition
that which cannot be reached by successive additions of unity. Nothing,
however, prevents an endless series being followed by some definite unit as
its limit; and this is what Cantor means, and expressly says he means, by
his {”}. It is not produced by additions of unity but it is the first
ordinal number after having passed through an endless series. There is no
contradiction in the idea of passing through an endless series; for it is
only endless in the sense of being incapable of production by successive
additions of unity, just as Achilles can easily overtake the tortoise
although he can never do so by repeatedly going only part way to where the
tortoise will be the instant Achilles gets there. So we can and often do
reach the w term of a series, though not by merely passing through all
previous terms. Yet while reaching the denumeral does not consist in
passing from one number to the number exceeding that by 1, though this be
done to any extent; nevertheless because the series of finite numbers is
endless, it follows that to pass all finite numbers is to pass beyond them
all, and in doing that to attain the denumeral. There are in Cantor's
exposition of his ordinal numbers several points like that which will give
the unmathematical student difficulty, not because he lacks intelligence,
but because he thinks so exactly as to see the difficulties, while not
being sufficiently acquainted with the subtleties of mathematics he is
unable to solve them, while many mathematicians, especially of the
pre-Weierstrassian school have their ideas hazy on these points, although
they may be perfectly clear for all mathematical purposes. There is
certainly no really sound objection to anything in Cantor's system of
ordinals until the second abnumerable ordinals are reached; and even then
in my opinion my modification of his law of progression removes any
possible error that there may there be. But my article is already so long
that I must cut that short. Suffice it to say that there is certainly a
possible series of ordinals of the first abnumerable multitude, while the
entire multitude of all possible multitudes is only denumeral. On that
point there is no possible doubt for a competent judge. It follows that the
cardinal numbers, even in the extended sense in which Cantor employs the
term, to denote any multitudes whatever, cannot be so rich in relations and
therefore must belong to a lower [order] than that of ordinals, which are
merely exact **grades**, regardless of what sort of states they are
**grades** of; and hence the restriction of number to cardinals involves a
serious lopping off of the highest part of mathematics. Indeed it is not
necessary to consider Cantor's ordinals to reach that conclusion, since the
multitude of all possible irrational values, say between 0 and 1, is
abnumerable and therefore can in no way be reduced to cardinals, of which
the entire multitude is infinitely less.
Peirce: CP 5.3 
	3. This maxim was first proposed by C.S. Peirce in the Popular Science
Monthly for January, 1878 (xii. 287); and he explained how it was to be
applied to the doctrine of reality. The writer was led to the maxim by
reflection upon Kant's Critic of the Pure Reason. Substantially the same
way of dealing with ontology seems to have been practised by the Stoics.
The writer subsequently saw that the principle might easily be misapplied,
so as to sweep away the whole doctrine of incommensurables, and, in fact,
the whole Weierstrassian way of regarding the calculus. In 1896 William
James published his Will to Believe, and later  his Philosophical
Conceptions and Practical Results, which pushed this method to such
extremes as must tend to give us pause. The doctrine appears to assume that
the end of man is action -- a stoical axiom which, to the present writer at
the age of sixty, does not recommend itself so forcibly as it did at
thirty. If it be admitted, on the contrary, that action wants an end, and
that that end must be something of a general description, then the spirit
of the maxim itself, which is that we must look to the upshot of our
concepts in order rightly to apprehend them, would direct us towards
something different from practical facts, namely, to general ideas, as the
true interpreters of our thought. Nevertheless, the maxim has approved
itself to the writer, after many years of trial, as of great utility in
leading to a relatively high **grade** of clearness of thought. He would
venture to suggest that it should always be put into practice with
conscientious thoroughness, but that, when that has been done, and not
before, a still higher **grade** of clearness of thought can be attained by
remembering that the only ultimate good which the practical facts to which
it directs attention can subserve is to further the development of concrete
reasonableness ; so that the meaning of the concept does not lie in any
individual reactions at all, but in the manner in which those reactions
contribute to that development. Indeed, in the article of 1878, above
referred to, the writer practised better than he preached; for he applied
the stoical maxim most unstoically, in such a sense as to insist upon the
reality of the objects of general ideas in their generality.
Peirce: CP 5.132 
	This suggestion must go for what it may be worth, which I dare say may be
very little. If it be correct, it will follow that there is no such thing
as positive esthetic badness; and since by goodness we chiefly in this
discussion mean merely the absence of badness, or faultlessness, there will
be no such thing as esthetic goodness. All there will be will be various
esthetic qualities; that is, simple qualities of totalities not capable of
full embodiment in the parts, which qualities may be more decided and
strong in one case than in another. But the very reduction of the intensity
may be an esthetic quality; nay, it will be so; and I am seriously inclined
to doubt there being any distinction of pure esthetic betterness and
worseness. My notion would be that there are innumerable varieties of
esthetic quality, but no purely esthetic **grade** of excellence.
Peirce: CP 5.142 
	142. As to logical goodness, or truth, the statements in the books are
faulty; and it is highly important for our inquiry that they should be
corrected. The books distinguish between logical truth, which some of them
rightly confine to arguments that do not promise more than they perform,
and material truth which belongs to propositions, being that which veracity
aims to be; and this is conceived to be a higher **grade** of truth than
mere logical truth. I would correct this conception as follows. In the
first place, all our knowledge rests upon perceptual judgments. These are
necessarily veracious in greater or less degree according to the effort
made, but there is no meaning in saying that they have any other truth than
veracity, since a perceptual judgment can never be repeated. At most we can
say of a perceptual judgment that its relation to other perceptual
judgments is such as to permit a simple theory of the facts. Thus I may
judge that I see a clean white surface. But a moment later I may question
whether the surface really was clean, and may look again more sharply. If
this second more veracious judgment still asserts that I see a clean
surface, the theory of the facts will be simpler than if, at my second
look, I discern that the surface is soiled. Still, even in this last case,
I have no right to say that my first percept was that of a soiled surface.
I absolutely have no testimony concerning it, except my perceptual
judgment, and although that was careless and had no high degree of
veracity, still I have to accept the only evidence in my possession. Now
consider any other judgment I may make. That is a conclusion of inferences
ultimately based on perceptual judgments, and since these are indisputable,
all the truth which my judgment can have must consist in the logical
correctness of those inferences. Or I may argue the matter in another way.
To say that a proposition is false is not veracious unless the speaker has
found out that it is false. Confining ourselves, therefore, to veracious
propositions, to say that a proposition is false and that it has been found
to be false are equivalent, in the sense of being necessarily either both
true or both false. Consequently, to say that a proposition is perhaps
false is the same as to say that it will perhaps be found out to be false.
Hence to deny one of these is to deny the other. To say that a proposition
is certainly true means simply that it never can be found out to be false,
or in other words, that it is derived by logically correct arguments from
veracious perceptual judgments. Consequently, the only difference between
material truth and the logical correctness of argumentation is that the
latter refers to a single line of argument and the former to all the
arguments which could have a given proposition or its denial as their

=================END 2 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)



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