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Charles S. PeirceLogic, Considered as Semeiotic
An Overview of Charles Peirce's Philosophical Logic,Constructed
from Manuscript L75
Version 1
Analytical reconstruction by
Joseph RansdellDepartment of Philosophy
Texas Tech University Lubbock, TX 79409 USA
[email protected]
Version1ofMSL75isaspecialeditorialconstructiondesignedtobereadbydefaultasasinglelinearsequentialtext.Itisnotahypertextdocumentproperbutuseshypertextonlyasatoolformanagementofthetextforthepurposesofonscreenpresentation.
FortechnicalreasonstheMSistoolargetopresentasawholeonasingleweb"page"(i.e.asasinglecontinuousdocumentunit),andsoitispresentedhereintenconsecutiveparts.Itshouldbeunderstood,though,thatthesepartshavenosignificanceasregardsitsorganizationandmerelyreflecttheneedtobreakitintosmallerunitsfortechnicalreasonsonly.
Thedocumentisorganizedbysuccessivelynumberedmemoirsandsections.Theupanddownarrowheads
atthetopofeachmemoirorsectionmoveyou,respectively,tothebeginningofthepreviousandthefollowingmemoirsorsections,sothatyoucanjumpthroughthedocumentinasequentialorder,forwardorback,inthatwayifyouwish.
Thetitle,"Logic,ConsideredasSemeiotic,"iseditoriallysuppliedbutechoesPeircehimselfinrelatedcontexts.Peirce
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sometimesusedthespelling"semiotic"instead,andeitherspellingisjustified,givenhisvariableusage.SofarasIknow,Peirceneverspelleditas"semiotics".
PleasereadtheEditorialIntroductionifyouarenotalreadyfamiliarwiththisspecialreconstructionofthetextanditsrationale.
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BEGINNINGOFTHERECONSTRUCTEDTEXT
FinalVersionMSL75.345
Milford,Pa.,1902,July15
To the Executive Committee of the Carnegie Institution,
Gentlemen:
I have the honor respectfully to submit to you herein
anapplication for aid from the Carnegie Institution in
accomplishingcertain scientific work. The contents of the letter
are as follows:
1. Explanation of what work is proposed.
Appendix containing a fuller statement.
EDITORIAL NOTE: By the "Appendix" Peirce means the entirelist of
36 proposed "Memoirs," including his accompanyingdescriptions of
their contents: thus he is referring by this towhat we are treating
here as the body of the present work,which we have supplemented
extensively from the draftmaterial.
-
2. Considerations as to its Utility.
3. Estimate of the Labor it will involve.
4. Estimate of Other Expense involved.
5. Statement as to the Need of aid from the Carnegie
Institution.
6. Suggestion of a Plan by which aid might be extended.
7. Estimate of the Probability of Completion of the work,
etc.
8. Remarks as to the Probable Net Cost to the
CarnegieInstitution, in money and in efficiency.
9. Statement of my apprehension of the Basis of my claim
foraid.
Final Version MS L75.346349
SECTION 1
EXPLANATION OF WHAT THE PROPOSED WORK IS
Some personal narrative is here necessary. I imbibed from
myboyhood the spirit of positive science, and especially of
exactscience; and early became intensely curious concerning the
theoryof the methods of science; so that, shortly after my
graduation fromcollege in 1859, I determined to devote my life to
that study;although indeed it was less a resolve than an
overmastering passionwhich I had been for some years unable to hold
in check. It hasnever abated. In 1866, and more in 1867, I ventured
upon my firstoriginal contributions to the science of logic, and
have continued mystudies of this science ever since, with rare
interruptions of a fewmonths only each. Owing to my treating logic
as a science, like thephysical sciences in which I had been
trained, and making mystudies special, minute, exact, and checked
by experience, andowing to the fact that logic had seldom before
been so studied,discoveries poured in upon me in such a flood as to
be embarrassing.This has been one reason why I have hitherto
published but a fewfragments of outlying parts of |347| my work, or
slight sketches ofmore important parts. For logic differs from the
natural sciencesand, in some measure, even from mathematics, in
being moreessentially systematic. Consequently, if new discoveries
were madein the course of writing a paper, they would be apt to
call for aremodelling of it, a work for mature reconsideration.
Still, as far as Iremember, no definitive conclusion of importance
to which I have
-
ever been led has required retraction, such were the advantages
ofthe scientific methods of study. Modification in details and
changes(very sparse) of the relative importance of principles are
thegreatest alterations I have ever been led to make. Even those
havebeen due, not to the fault of the scientific method, but
chiefly to myadherence to early teachings. But what has, more than
that cause,prevented my publishing has been, first, that my desire
to teach hasnot been so strong as my desire to learn, and secondly,
that far fromthere having been any demand for papers by me, I have
alwaysfound no little difficulty in getting what I wrote printed;
and |348|when the favor was accorded, it was usually represented to
me thatfunds were sacrificed in doing so. My first papers, which
have sincebeen pronounced good work, were sent to almost every
logician inthe world, accompanied in many cases with letters; but
for tenyears thereafter I never could learn that a single
individual hadlooked into them. Since then, I have had little ardor
about printinganything. Now, however, being upon the threshold of
old age, Icould not feel that I had done my best to do that which I
was putinto the world to do, if I did not spend all my available
forces inputting upon record as many of my logical results as I
could.
Therefore, what I hereby solicit the aid of the
CarnegieInstitution to enable me to do is to draw up some three
dozenmemoirs, each complete in itself, yet the whole forming a
unitarysystem of logic in all its parts, which memoirs shall
present in aform quite convincing to a candid mind the results to
which I havefound that the scientific |349| method unequivocally
leads, addingin each case, rational explanations of how opposing
opinions havecome about; the whole putting logic, as far as my
studies of it havegone, upon the undeniable footing of a
science.
COMMENT to L75.349 by Ransdell (Rev. 7398)
From the beginning to the end of his career Peirce had ashis
goal the establishment of logic as a science, and"establish" should
be understood here in two senses: first, inthe sense of showing or
demonstrating some things about itwhich would make it rationally
plausible to regard it in thatway, and second, in the sense of
persuading others to thiseffect such that it actually came to be
publicly identified assuch, institutionalized appropriately in
universities, and soforth.
As regards the first aim, what needed to be shown wasboth that
its subjectmatter is essentially public, which isthe primarythough
not the onlysense of the dictum "allthought is in signs" that runs
like a leitmotiv throughoutPeirce's work, and that it can be
understood methodically, inthe manner of science generally.
"Methodically" does notmean "algorithmically": Peirce did not think
of scientific
-
method in terms of a mechanistic procedure of generating
orvalidating truths, but rather in terms of the exercise ofjudgment
in following complex cyclical and selfcorrectiveprocedures
involving hypothesis, deduction, and induction,the lastmentioned of
which he regarded in terms of testingrather than generating general
propositions.
To understand Peirce's logic and philosophy of science,though,
it is of the first importance to take due account of asecond sense
of "establish" which he, as a working scientisthimself, knew to be
at least as important as considerations ofthe sort just mentioned
above. For he also understood thatthe establishing of a science is
not a matter of an ingenioustour de force of demonstration by an
individual in a book orarticle, as philosophers are usually
inclined to conceive it, butmeans rather the actual establishing of
a shared practice ofinquiry by a community of inquirers with common
andoverlapping concerns. This second sense of "establishment"
isespecially relevant here; for Peirce regarded this applicationto
the Carnegie Institution as presenting the real possibility
ofestablishing logic, in a broad sense which includes what wenow
call "philosophy of science", as an institutionallyrecognized
scientific field on par with the hard sciences byappealing to his
own scientific peers in the hard sciences torecognize it as such by
supporting him in gathering andpresenting it systematically as
foundational work in the field.
Contrary to a continuing misconception, Peirce was not anunknown
figure in his time as regards academicians in generaland scientists
in particular, and had quite an impressivebacking for his
application by way of letters ofrecommendation from important
academicians, of whom agood many were in or connected in one way or
another withthe sciences, and the board of referees to whom he
wasappealing was a similarly prestigious board composed largelyof
people in the sciences. (Transcriptions of these letters
arecurrently being prepared and will be made available here atthe
Arisbe website in the near future.) The attempt,
thoughunsuccessful, was not quixotic: indeed, there is reason
tothink it would have been successful had it not been forextensive
clandestine activity aimed chiefly at discreditingPeirce's
character rather than his plan. This is discussed in alittle more
detail in the Editorial Introduction.
FromDraftAMSL75.2129
What I desire aid in doing is in bringing before the world
the
-
result of my researches into logic.
I began the study of logic in 1856, and it has been my
principaloccupation ever since. Twice, I have made determined
efforts todismiss the subject from my thoughts; but the bent of my
mind issuch that I did not succeed in doing so for more than a few
monthseach time. It was, however, not until 1861 that I ventured
upon anyserious original research; so that, subtracting
distractions, fortyyears' work is about what my results have cost
me.
These results have never been published. It is true
thatfragmentary papers mostly upon relatively unimportant topics
haveappeared; but the whole forms a unitary system to such a
degreethat no part which seems to have any importance can be set
forthseparately in a manner to do it justice, either in respect to
itsmeaning or in respect to the evidences of it. I will explain how
thiscame to be the case. In May 1867 I presented |22| to the
Academyin Boston a paper of ten pages, or about 4000 words, upon a
NewList of Categories. It was the result of full two years' intense
andincessant application. It surprises me today that in so short a
time Icould produce a statement of that sort so nearly accurate,
especiallywhen I look back at my notebooks and find by what an
unnecessarilydifficult route I reached my goal. For this list of
categories differsfrom the lists of Aristotle, Kant, and Hegel in
attempting much morethan they. They merely took conceptions which
they found at hand,already worked out. Their labor was limited to
selecting theconceptions, slightly developing some of them,
arranging them, andin Hegel's case, separating one or two that had
been confused withothers. But what I undertook to do was to go back
to experience, inthe sense of whatever we find to have been forced
upon our minds,and by examining it to form clear conceptions of its
radicallydifferent classes of |23| elements, without relying upon
anyprevious philosophizing, at all. This was the most difficult
task I everventured to undertake. This list is fortunately very
short.Corresponding to Aristotle's Substance, there are two
conceptionswhich I call Being and Substance, but corresponding to
his nineAccidents I find only three, Quality, Reaction, Mediation.
Havingobtained this list of three kinds of elements of experience,
(forBeing and Substance are of a different nature,) the business
beforeme was the mixed one of making my apprehension of three
ideaswhich had never been accurately grasped as clear and plain
aspossible, and of tracing out all their modes of combination. This
last,at least, seemed to be a problem which could be worked out
bystraightforward patience. Such was the teaching of all the logic
Iknew, that of Aristotle, of the Greek commentators, of |24|
the11th century thinkers, of the great scholastic doctors, of
themodern French, English, and German logicians. Long after, when
Ihad developed the only effective methods of doing the one thingand
the other, that is, of rendering my apprehension clear and
offinding the forms of combination of the categories, I
ascertainedthat the latter was from the nature of things, not to be
compassed
-
by mere hard thinking, that it was necessary to wait for
thecompounds to make their appearance, and patiently to
analyzethem, until the list down to a certain point was complete.
But, notthen knowing this, after years of fruitless effort (I will
not say theywere wasted, since they gave me great training,) I said
to myself,this list of categories, specious as it is, must be a
delusion of which Imust disabuse myself. Thereupon, I spent five
years in diligently,yes, passionately, seeking facts which should
refute my list. Never inmy life have I been more thoroughly in
earnest |25| than I was inthat long struggle. It was in vain.
Everything that promised to refutethe list, when carefully examined
only confirmed it. The evidencebecame irresistible. Then that in
which I had failed must be feasible.
EDITORIAL NOTE: Peirce apparently means that he failed infinding
the forms of combinations of the categories. His pointseems to be
that these cannot be ascertained a priori. Thusin a draft version
of his comments on Memoir 5 he says:"These three categories are
compounded in a multitude ofways which can only be apprehended
through experience.They cannot be built up by an act of pure
thought. Some ofthese forms of composition have to be carefully
examined inorder to obtain distinct conceptions with which to build
atheory of logic."
But it never proved so; and at length I learned why it could
notprove so. To this solution I was guided by the very
categoriesthemselves. Then began the long work of collecting the
compoundsand analyzing them into the categories. This work is of
its natureabsolutely interminable. It involves a logical doctrine
which cannever be completed. But it was now worked up to the point
at whichthe general method of research could be made evident to
everymind.
But by that time, I had reached a mode of thought so remotefrom
that of the ordinary man, that I was unable to communicatewith him.
Another great labor was required in breaking a path bywhich to lead
him |26| from his position to my own. I had becomeentirely
unaccustomed to the use of ordinary language to expressmy own
logical ideas to myself. I was obliged to make a regular studyof
ordinary ideas and language, in order to convey any hint of myreal
meaning. I found that I had a difficult art to acquire. The
clearexpression of my thoughts is still most difficult to me. How
awkwardI am at it, this very statement will in some measure
show.
All this will explainnot distinctly, that would be
impossiblewithout going into details, yet in some vague way,how
impossibleit was that any fragment of the truth that it has been
granted to meto perceive should be adequately represented by
itself. Hence, it isthat I have been quite grotesquely
misrepresented. I have been
-
called a hedonist, I who from the beginning of my career to this
day,have not written one single piece of a general nature which did
notsufficiently show that I regard pleasure, not as most do, as a
smallsatisfaction, but as quite no rational satisfaction at all.
One Historyof Philosophy sets me down as a typical sceptic, though
Kant'scriticism was, so to say, my mother's |27| milk in
philosophy. I havebeen called a modern Hume, because Hume denied
causalityaltogether, and I, after calling attention to the fact
that all men setsome limits to causality, endeavored to define
these limits. BecauseI pointed out the insufficiency of existing
logical algebra, and haveused algebra as an aid in explaining the
logic of relations, it hasbeen assumed that I regarded logical
algebra as the whole, or chief,part of logic; although, in fact, I
have protested earnestly againstthe exaggerated importance attached
by many to this instrument oflogic. At almost the same moment, one
eminent philosopher wasreferring to me as a sort of Bchner, while
another was calling me apure Schellingian. I am supposed to be
opposed to Hegel at allpoints. Indeed, I do think that Hegel's
processes, if regarded asproofs, are quite the most absurd
reasonings that ever were or couldbe. But as to his main doctrines,
which were reached by him beforehe ever lit up his dialectical
procedure, I think there is a good dealof truth in them. |28| I
think that metaphysics, as it has beenhitherto, has mainly
consisted of pretty wellgrounded truthsenormously exaggerated, till
they become monstrous falsities; andHegel's opinion that they are
all onesided amounts to the samething. My main objection to Hegel
is that of all exaggerators he isthe most errant; and that he
carries onesidedness to its lastextreme. In my view, there are
seven conceivable types ofphilosophy. Three greatly exaggerate the
importance of some one ofmy three categories and more or less
underrate the others. Threemore somewhat overrate two and almost
utterly neglect the third.The seventh type does nearly equal
justice to all three. Hegelianismis one of the first three. But the
category which it exaggerates is theone most commonly overlooked;
and for that reason there is arelative wholesomeness in it. Vera
used to say that whileHegelianism was rejected, it had more or less
filtered into andpermeated all thought. Very well; dilute |29|
Hegelianism bydiminishing the importance it places upon mediation
and byrecognizing the due significance of the others, and you
havesomething like the truth.
From Draft B MS L75.39
That which I desire aid in doing is to bring before the world
theresults of my researches into logic.
I began this study in 1856; and it has been my
principaloccupation ever since. I cannot lay claim to the slightest
merit forthe constancy with which I have pursued it, since it has
been anuncontrollable impulse. On the contrary, it has been
necessary for
-
me at all times to exercise all my control over myself, for fear
thatmy mind might be affected by such unceasing application to
aparticular subject. When I have found myself in a solitary
situation,and there was not a daily round of duties to occupy me, I
have haddesperate struggles with my logic. It has kept me poor; but
myexperience is that there is only a small proportion of mankind
whoare able to make the earning or gaining of money their
leadingmotive. At any rate, I am sure that I am not one of that
class. I haveexperienced |4| extremely little encouragement. It was
more thanten years after I published my first papers that I became
aware inany way that anybody but myself and the printer had ever
lookedinto them. I have thus had every reason except one for
abandoningthe pursuit. Twice I have made determined efforts to do
so; but mybent was too strong.
Though I began the study as far back as 1856 and spent almostall
my time reading at that time the German philosophers andAristotle,
it was not until 1861 that I ventured upon any seriousoriginal
research, and not until 1866 that I was far enough advancedto offer
anything for publication. It is therefore the results of
aboutthirtyfive years work which I desire to present.
Merely fragments of the work have been published, andrelatively
unimportant parts, which moreover cannot be properlyunderstood when
standing alone. A striking |5| example of how I ammisunderstood is
that while one of the histories of philosophy setsme down as a
sceptic, a sort of Modern Hume, as I have been called,I note that
one of the greatest living philosophers ranks me as a
pureSchellingian. Both [of] those classifications cannot be true;
yet theyboth come from most competent and careful critics.
I shall be asked why I have published so little and in
[so]fragmentary a way. I answer,
1st, that I have had extreme difficulty in getting what I wrote
onlogic printed. My boxes are full of unprinted MSS on the subject
ascarefully written as anything I ever wrote. Only those things
couldbe printed which could pass as relating to some other subject,
andthen only if they were made so brief as to be almost
unintelligible,or else worked up so as to answer the purposes of
popularmagazines.|6|
2nd, that even so, I have not been able to learn that as many
ashalf a dozen persons have ever read any paper of mine, no
matterhow I had dressed it up.
3rd, that during all these years the vast volume of my results
hasbeen such that it has not been easy for me, with my aptitude for
thesubject, my personal interest in the discoveries, and my
incessantstudy of them, to hold them all in my head at once in an
orderlymanner; and the difficulty of the task of arranging them in
a lucidand convincing manner is such that several years of
exclusive
-
devotion to that task would be requisite for its
accomplishment.
4th, that up to within a few years [ago], new results
werecontinually coming in in such profusion as to leave me no
leisure toset forth old ones.
5th, that I have no natural gift of making myself understood,
andmy thoughts appear to me in a garb so |7| foreign from the
ordinaryways of thinking that it would be a difficult matter to
translate theminto the language used by readers.
6th, the chief reason remains unmentioned. In May 1867, as
theresult of two years of unceasing application, I published a
paper often pages which was either entirely mistaken or was one of
the mostimportant of philosophical generalizations. Several years
nextfollowing were largely occupied in tracing the matter out into
itsdevelopments. But here such difficulties were encountered
thatwere so great that, although my original result still seemed
evident,I began to think that some undiscovered error must lurk in
it andthat I was the victim of a selfdelusion. Almost persuaded
that thismust be so, for a considerable series of years I was
continuallyscheming to discover some downright refutation of my
theory. Butevery inquiry I made which promised |8| to lead to such
refutation,turned out in the end to afford only new evidence of its
truth.Finally, I discovered that the real reason of my difficulties
lay not inmy generalization, but in a view which had been accepted
by alllogicians without serious question. I now returned with
energy to myoriginal position which I adopted, with the utmost
advantage as asort of skeleton of my whole logical doctrine. It
brought great unityinto the whole subject, but at the same time
kept it far remote fromthe ordinary highway of men's thoughts.
Since that development, ithas been absolutely impossible to present
my views on almost anypart of logic separated from the whole.
7th, notwithstanding all I have said, without referring to
earlieressays, I have twice within my later years written a whole
bookupon logic. The first was offered to a publisher; but
notwithstandingthe recommendations of his readers, he declined it;
and I have beenvery glad he did. |9| The other was a very large
work, done withmuch care. However, when it was done, I found it to
be written toomuch from its own standpoint. It did not examine
opposed opinionswith sufficient sympathy and understanding; there
was an offensivetone throughout; it was unconvincing, and utterly
unworthy of thetheory which it had the honor to defend. I have
since thought muchand experimented much upon how the book should be
written. I cannow write a treatise which shall restrain every
assertion in it withinthe limits in which it shall be absolutely
convincing, which shallnotice everything of importance that has
been said on each topic,and shall meet every issue squarely and
fairly.
-
From Draft C MS L75.6064
What are the researches of which I speak?
They are the work of my life, that which I seem to have beenput
into the world to do. I was born in 1839, and brought up in
ascientific circle. I began to be initiated into the methods of
physicalscience before I was ten years old; and it has always been
methodswhich have chiefly interested me. By 1856, I was
alreadysystematically studying logic, in its broad sense, beginning
with theCritic of the Pure Reason. I continued my reading
diligently, passingto Hegel, Herbart, Aristotle, the scholastics,
Berkeley, Hume,Leibniz, etc. I first began serious original
research, parallel to myreading, about 1861, and began to publish
in 1866. From 1856 untilthis day my passion for the study of logic
has been so intense that noother motives could prevail, although
the amount of encouragementthat I have received has been so |61|
small that I have mostly beenin a desperate depression. Several
people have at one time andanother given me aid in pursuing my
studies. I can never forgetthem. In each case, there have been
solid results, as I shall show, inthe proper place. I have,
however, published very little, becausethere was no sort of
encouragement to do so. During the greaterpart of my life, the
chairs of logic at the universities have beenoccupied by men bred
in theological seminaries, devoid of any idealof progressive
science, penetrated with formalisms, examiningnothing with real
exactitude. This fact naturally brought along anentire situation
sufficient to discourage me from troubling a printerto set up what
no man would read. What little I could print had to bebrief and
fragmentary. I must select subjects concerning which whatI had to
say would be intelligible without previous studies.|62|
But my studies were continued almost without
interruption.Whatever distractions from my solitary position I
might seek, acertain amount of work upon my logic was a daily need.
Myperseverance was no merit, any more than my perseverance
inbreathing. The result has been that by this time I have built up
suchan elaborate system, that the task of undertaking to explain it
is oneof the utmost difficulty.
It is, however, now a good many years that I have had this
taskunder systematic study. Twice I have actually written treatises
onlogic. The first was rejected by the publisher, I am very happy
tosay. The second, a more ambitious performance, I myselfcondemned.
Finally, last year some friends offered to buy of me thecopyright
of a few sections of such a work; and I wrote several,amounting to
about 200,000 words in all, which if the funds had not|63| given
out, would have grown into the convincing book which Ishould
recognize as somewhat worthy of the great theory it wouldattempt to
expound.
What I desire is to divide my researches into a number of
heads,say from a score to two dozen in all, and to set forth my
-
investigations of each together with an exhaustive
criticalexamination of everything of importance that has been said
or couldbe said against my results. Each such paper would be
complete initself, except that it would suppose an acquaintance
with thosewhich had gone before. The different memoirs would range
from20,000 to 100,000 words each. Probably it would require, on
theaverage, some ten weeks to prepare each. During the last year
Ihave worked faster, it is true; but I hurried more than I ought
tohave done. If I lived to complete the plan, as there is every
reasonto expect that I |64| should under the enormous stimulus
whichassured aid would give my vitality, the whole when completed
wouldmake a large treatise on logic, somewhat the largest ever
given tothe world. It might be something like a million words. When
I speakof the number of words, I mean that it would when properly
printedoccupy as much space as that number of words of ordinary
matterset up solidly. A good deal of it would contain formulae,
diagrams,etc.
From Draft A MS L75.2933
But what would be the contents of my three ponderous volumesof
logic? I answer, in the first place, in reference to the
expectationswhich would be roused in uninstructed minds by the word
"logic,"that it would contain a theory of scientific reasoning and
also atheory of the reasoning of practical men about every day
affairs.These two would be shown to be governed by somewhat
differentprinciples, inasmuch as the practical reasoning is forced
to reachsome definite conclusion promptly, while science can wait a
centuryor five centuries, if need be, before coming to any
conclusion at all.Another cause which acts still more strongly to
differentiate themethodeutic of theoretical and practical reasoning
is that the lattercan be regulated by instinct |30| acting in its
natural way, while[the] theory of how one should reason depends
upon one's ultimatepurpose and is modified with every modification
of ethics. Theory isthus at a special disadvantage here; but
instinct within its properdomain is generally far keener, and
surer, and above all swifter,than any deduction from theory can be.
Besides, logical instinct has,at all events, to be employed in
applying the theory. On the otherhand, the ultimate purpose of pure
science, as such, is perfectlydefinite and simple; the theory of
purely scientific reasoning can beworked out with mathematical
certainty; and the application of thetheory does not require the
logical instinct to be strained beyond itsnatural function. On the
other hand, if we attempt to apply naturallogical instinct to
purely scientific questions of any difficulty, it notonly becomes
uncertain, but if it is heeded, the voice of instinctitself is that
objective considerations should be the decisiveones.|31|
The methodeutic utility of logic is still further limited by the
factthat the reasonings of pure mathematics are perfectly evident
and
-
have no need of any separate theory of logic to reinforce
them.Mathematics is its own logic.
Furthermore, the three normative sciences, esthetics, ethics,and
logic itself, although they do not come under that branch ofscience
called practical, that is, the arts, are nevertheless so
farpractical that instinct in its natural operation, is perfectly
adaptedto their reasonings after the subtle analyses of which these
sciencesthemselves take cognizance have prepared the premisses.
It follows that the only reasonings for which a science of logic
ismethodeutically useful are those of metaphysics, and the
specialtheoretical sciences, of the physical and the psychical
wing. Physicalscience has hitherto done well enough without any
appeal |32| to ascience of logic. But at this moment questions of a
logical naturehave arisen which nothing but a scientific logic are
likely to settle.Witness the controversy between those who are
about Poincare andthose who are about Boltzmann. Witness the still
more difficultquestion of the constitution of matter. To my
prevision physicsseems to be entering a period when such questions
will bemultiplied.
How much the psychical sciences have suffered from the lack ofan
exact logic can be understood from my memoir on the methods
ofresearch into history by means of documents.
In metaphysics the dependence is much stronger yet, but it is
ingreat part masked by the circumstance that metaphysics is
utterlydependent upon logic in a different way which the categories
ofKant and even those of Aristotle illustrate. Namely,
metaphysicsregards the universe as thinking, as representing, and
all the logicalrelations are repeated as meta|33|physical
relations. Metaphysics ishardly more than a corollary from logic.
Now metaphysics affectsphysics and the physical sciences most
intimately, even more than itdoes the psychical sciences.
Thus the methodeutic utility of the science of logic, although
itis beyond price, is pretty narrowly limited.
End of PART 1 of 10 of MS L75
Queries, comments, and suggestions toJoseph Ransdell Dept of
Philosophy
Texas Tech University, Lubbock Texas
[email protected]
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HomePagePeircePapersIntrotoL75L75Version2
FinalVersionMSL75.350357
MEMOIR 1
ON THE CLASSIFICATION OF THE THEORETIC SCIENCES OF RESEARCH
This will be a natural classification, not of possible sciences,
butof sciences as they exist today; not of sciences in the sense
of"systematized knowledge," but of branches of endeavor to
ascertaintruth. I shall not undertake to prove that there is no
other naturalclassification of the sciences than that which I give;
and this, beingmerely an introductory memoir, cannot have the same
convincingcharacter as the others. Every unitary classification has
a leadingidea or purpose, and is a natural classification in so far
as that samepurpose is determinative in the production of the
objects classified.The purpose of this classification is nearly the
same as that ofComte, namely, so to arrange a catalogue of the
sciences as toexhibit the most important of |351| the relations of
logicaldependence among them. In fact, my classification is simply
anattempt to improve upon that of Comte; first, by looking less
atwhat has been the course of scientific history, and more at what
itwould have been if the theoretically best methods had
beenpursued; second, by supplying the shocking omissions which
Comte'srage against nonsense led him to commit; and third, by
carryingdown the subdivision as far as my knowledge enables me to
do. Itwas necessary for me to determine what I should call one
science.For this purpose I have united under one science studies
such as thesame man, in the present state of science, might very
well pursue. Ihave been guided in determining this by noting how
scientistsassociate themselves into societies, and what
contributions arecommonly admitted into one journal, being on my
guard against thesurvival of traditions from bygone states of
science. A study to whichmen devote their lives, but not, in the
present stage of developmentof science, so numerously as to justify
exclusive societies andjournals for it, I call a variety of
science. That which forms thesubject of the narrowest societies and
journals, so that any studentof any part of it ought to be pretty
thoroughly informed about everypart, I call a species of science.
That branch of which the student ofany part is well qualified to
take up any other part, except that hemay not be sufficiently
acquainted with the facts in detail, I call a
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genus of science. If the only new training necessary to pass
from onepart to another is a mere matter of skill, the general
conceptionsremaining the same, I call the department a family of
science. Ifdifferent sorts of conceptions are dealt with in the
different familiesof a depart|353|ment, but the general type of
inquiry is the same, Icall it an order of science. If the types of
inquiry of the differentorders of a department are different, yet
these orders areconnected together so that students feel that they
are studying thesame great subject, I call the department a class
of science. If thereare different classes, so that different
students seem to live indifferent worlds, but yet there is one
general animating motive, Icall the department a branch of science.
Of course, there will besubbranches, subclasses, etc., down to
subvarieties; and evensometimes subsubdivisions. To illustrate, I
call pure science andapplied science different branches, and call
mathematics and thespecial sciences different classes; I say that
general physics, biology,and geology belong to different orders of
science. Astronomy andgeognosy are different families. Thermotics
and electrics aredifferent families. Optics and electrics |354| are
now differentgenera. Entomology and ichthyology are different
species of onegenus. The study of Kant and the study of Spinoza are
differentvarieties of one species.
Of course, the execution of this useful but ambitious design
can,in the first instance, notwithstanding all the labor on my part
thatseemed economically recommended, be but a sketch. It will
havefully attained all I hope for if it is respectable enough to
meritserious picking to pieces in its smaller and in its larger
divisions.Indeed, I may say of all these memoirs that what I most
desire is thattheir errors should be exposed, so long as they lead
to furtherscientific study of the subjects to which they relate.
The relation ofthis present memoir to those which follow it in the
series is that itgives, from a general survey of science, an idea
of the place of logicamong the sciences. I will here set down the
larger divisions of thescheme as well as I remember it (not having
the notes in mypossession). But it will be the discussion which
will form the chiefvalue of the memoir, not the |355| scheme
itself. Nearly a hundredschemes given hitherto will be
criticized.
A. Theoretical Science
I. Science of Research
i. Mathematics
ii. Philosophy, or Cenoscopy 1. Categorics [= phenomenology or
phaneroscopy] 2. Normative Science a. Esthetics b. Ethics c. Logic
[= semiotic] [philosophical grammar]
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[critical logic] [philosophical rhetoric] 3. Metaphysics
iii. Idioscopy, or Special Science 1. Psychognosy a. Nomological
or General Psychology b. Classificatory . Linguistics . Critics .
Ethnology |356| c. Descriptive . Biography . History . Archeology
2. Physiognosy a. Nomological or General Physics . Dynamics 1. Of
particles 2. Of aggregations . Elaterics and Thermotics . Optics
and Electrics b. Classificatory . Crystallography . Chemistry .
Biology c. Descriptive . Astronomy . Geognosy |357|
II. Science of Review, or Synthetic Philosophy (Humboldt's
Cosmos; Comte's Philosophie Positive)
B. Practical Science, or the Arts
EDITORIAL NOTE: Bracketed material in the above scheme
iseditorially supplied as a clarification. Josiah (Lee) Auspitz
hasobjected, though, that the simple identification of logic in
thebroad sense with semeiotic (also spelled "semiotic" by Peirce)is
not correct. His reasons for this are not clear to me and Ibelieve
the currently prevailing opinion is in agreement withmy own view
that they are supposed to be identical; but LeeAuspitz is a careful
and talented scholar and his dissent isworth taking special note
of. Perhaps he can be persuaded towrite up a critical note to that
effect which we can add to thepresent presentation by including it
through a hypertext link.This invitation applies to anyone else as
well who wants totake exception to any of my editorial
interpretation here orsimply wants to add something to it by way of
commentary for
-
further elucidation: write it up as a criticism or commentaryand
we will put a hypertext linkbutton for that note in thetext itself,
thus making it an addendum to the presentaccount.
FromDraftEMSL75.206207
This [classification] would be restricted to sciences as
theyactually exist, with some little provision of what is sure to
bebrought about soon. It would consider sciences, not as
"systematizedknowledge," but as organizations of research, as they
live today. Myclassification of the applied sciences, or arts, not
having been verysuccessful, I should probably not attempt to go
into that subject.Moreover, such studies as Humboldt's Cosmos, and
Comte'sPhilosophie Positive, although they are really studies of
science,would not fall within the scope of my classification, which
wouldthus be limited to the theoretical sciences. My classification
is quiteminute; but its leading divisions are: mathematics;
philosophy or, asBentham calls it, cenoscopic (i.e. based on
universal experience);and idioscopic, or special science. The last
falls into two parts,psychognosy (embracing psychology,
linguistics, ethnology, history,etc.) and physiognosy |207|
(embracing physics, chemistry, biology,astronomy, geognosy). I
divide philosophy into three parts, thecategories, normative
science (esthetics, ethics, and logic,) andmetaphysics. Geometry
and the science of time form a connectinglink between metaphysics
and idioscopy.
In constructing my classification, I have carefully studied
thereasons alleged for nearly a hundred other systems; so that
thecritical part of this memoir would be extremely laborious. Yet
as mypurpose is not to advance anything for which I cannot
produceconvincing proof, such criticism must be carefully and
respectfullyperformed throughout all the memoirs.
Final Version MS L75.357
MEMOIR 2
ON THE SIMPLEST MATHEMATICS
This is that mathematics which distinguishes only two
differentvalues, and is of great importance for logic.
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From Draft E MS L75.207
This is the system which has a scale of values of only
twodegrees. Since these may be identified (in an application of
thispure mathematical system) as the true and the false, this
systemcalls for somewhat elaborate study as a propaedeutic to
logic.
Final Version MS L75.357
MEMOIR 3
ANALYSIS OF THE CONCEPTIONS OF MATHEMATICS
Such are number, multitude, limit, infinity,
infinitesimals,continuity, dimension, imaginaries, multiple
algebra, measurement,etc. My former contributions, though very
fragmentary, haveattracted attention in Europe, although in respect
to priority justicehas not been done them. I bring the whole
together into one system,defend the method of infinitesimals
conclusively, and give manynew truths established by a new and
striking method.
From Draft E MS L75.208209
My work in this direction is already somewhat known,
althoughvery imperfectly. One of the learned academies of Europe
hascrowned a demonstration that my definition of a finite
multitudeagrees with Dedekind's definition of an infinite
multitude. It appearsto me that the one is hardly more than a
verbal modification of theother. I am usually represented as having
put forth my definition asa substitute for Dedekind's. In point of
fact, mine was published sixyears before his; and my paper contains
in very brief and crabbedform all the essentials of his beautiful
exposition (still more perfectas modified by Schrder). Many
animadversions have been made byeminent men upon my remark, in the
Century Dictionary, that themethod of infinitesimals is more
consonant with then (in 1883)recent studies of mathematical logic.
In this memoir, I should showprecisely how the calculus may be, to
the advantage of simplicity,based upon the doctrine of
infinitesimals. Many futile attempts havebeen made to define
continuity. In the sense in |209| the calculus,no difficulty
remains. But the whole of topical geometry remains in
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an exceedingly backward state and destitute of any method of
proofsimply because true continuity has not been
mathematicallydefined. By a careful analysis of the conception of a
collection, ofwhich no mathematical definition has been yet
published, I havesucceeded in giving a demonstration of an
important propositionwhich Cantor had missed, from which the
required definition of acontinuum results; and a foundation is
afforded for topicalgeometry, which branch of geometry really
embraces the whole ofgeometry. I have made several other advances
in defining theconceptions of mathematics which illuminate the
subject.
Final Version MS L75.357
MEMOIR 4
ANALYSIS OF THE METHODS OF MATHEMATICAL DEMONSTRATION
I shall be glad to place early in the series so unquestionable
anillustration of the great value of minute analysis as this memoir
willafford. The subjects of corollarial and theorematic reasoning,
of themethod of abstraction, of substantive possibility, |358| and
of themethod of topical geometry, of which I have hitherto
publishedmere hints, will here be fully elaborated.
From Draft B MS L75.19
[This memoir] will examine the nature of mathematicalreasoning.
Logic can pass no judgment upon such reasoning, becauseit is
evident, and as such, beyond all criticism. But logic is
interestedin studying how mathematical reasoning proceeds.
Mathematicalreasoning will be analyzed and important properties of
it broughtout which mathematicians themselves are not aware of.
From Draft E MS L75.209210
I have hitherto only published some slight hints of
mydiscoveries in regard to the logical processes used in
mathematics. Ifind that two different kinds of reasoning are used,
which I |210|distinguish as the corollarial and the theorematic.
This is a matterof extreme importance for the theory of cognition.
It remains
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unpublished. I also find that the most effective kind of
theorematicdemonstration always involves the long despised
operation ofabstraction, which has been a common topic of ridicule.
This is theoperation by which we transform the proposition that
"Opium putspeople to sleep" into the proposition that "Opium has a
soporificvirtue". Like every other logical transformation, it can
be applied ina futile manner. But I show that, without it, the
mathematicianwould be shut off from operations upon lines,
surfaces, differentials,functions, operationsand even from the
consideration of cardinalnumbers. I go on to define precisely what
it is that this operationeffects. I endeavor in this paper to
enumerate, classify, and definethe precise mode of effectiveness of
every method employed inmathematics.
From Draft C MS L75.90102
No science of logic is needed for mathematics beyond that
whichmathematics can itself supply, unless possibly it be in regard
tomathematical heuretic. But the examination of the methods
ofmathematical demonstration shed |91| extraordinary light
uponlogic, such as I, for my part, never dreamed of in advance,
althoughI ought to have guessed that there must be unexpected
treasureshidden in this quite unexplored ground. That the logic
ofmathematics belonged to the logic of relatives, and to the logic
oftriadic, not of dyadic relations, was indeed obvious in advance;
butbeyond that I had no idea of its nature. The first things I
found outwere that all mathematical reasoning is diagrammatic and
that allnecessary reasoning is mathematical reasoning, no matter
howsimple it may be. By diagrammatic reasoning, I mean
reasoningwhich constructs a diagram according to a precept
expressed ingeneral terms, performs experiments upon this diagram,
notes theirresults, assures itself that similar experiments
performed upon anydiagram constructed according to the same precept
would have|92| the same results, and expresses this in general
terms. This wasa discovery of no little importance, showing, as it
does, that allknowledge without exception comes from
observation.
At this point, I intend to insert a mention of my theory of
gradesof reality. The general notion is old, but in modern times it
has beenforgotten. I undertake to prove its truth, resting on the
principlethat a theory which is adapted to the prediction of
observationalfacts, and which does not lead to disappointment, is
ipso facto true.This principle is proved in No. 1. Then my proof of
grades of realityis inductive, and consists in often turning aside
in the course of thisseries of memoirs to show how this theory is
adapted to theexpression of facts. This might be mistaken for
repetitiousness; butin fact it is logically defensible, and it also
has the advantage ofleading the reader, step by step, to the
compre|93|hension of anidea which he would not be able to grasp at
once, and to theappreciation of an argument which he could not
digest at one time. I
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will not here undertake to explain what the theory is in
detail.Suffice it to say that since reality consists in this, that
a real thinghas whatever characters it has in its being and its
having them doesnot consist in its being represented to have them,
not even in itsrepresenting itself to have them, not even if the
character consistsin the thing's representing itself to represent
itself; since, I say, thatis the nature of reality, as all schools
of philosophy now admit, thereis no reason in the nature of reality
why it should not havegradations of several kinds; and in point of
fact, we find convincingevidences of such gradations. It is easy to
see that according to thisdefinition the square root of minus 1
possesses a certain grade of|94| reality, since all its characters
except only that of being thesquare root of minus one are what they
are whether you or I thinkso or not. So when Charles Dickens was
halfthrough one of hisnovels, he could no longer make his
characters do anything thatsome whim of a reader might suggest
without feeling that it wasfalse; and in point of fact the reader
sometimes feels that theconcluding parts of this or that novel of
Dickens is false. Even here,then, there is an extremely low grade
of reality. Everybody wouldadmit that the word might be applied in
such cases by an aptmetaphor; but I undertake to show that there is
a certain degree ofsober truth in it, and that it is important for
logic to recognize thatthe reality of the Great Pyramid, or of the
Atlantic Ocean, or of theSun itself, is nothing but a higher grade
of the same thing.
But to say that the reasoning of mathematics is |95|diagrammatic
is not to penetrate in the least degree into the
logicalpeculiarities of its procedure, because all necessary
reasoning isdiagrammatic.
My first real discovery about mathematical procedure was
thatthere are two kinds of necessary reasoning, which I call
thecorollarial and the theorematic, because the corollaries affixed
tothe propositions of Euclid are usually arguments of one kind,
whilethe more important theorems are of the other. The peculiarity
oftheorematic reasoning is that it considers something not implied
atall in the conceptions so far gained, which neither the
definition ofthe object of research nor anything yet known about
could ofthemselves suggest, although they give room for it. Euclid,
forexample, will add lines to |96| his diagram which are not at
allrequired or suggested by any previous proposition, and which
theconclusion that he reaches by this means says nothing about. I
showthat no considerable advance can be made in thought of any
kindwithout theorematic reasoning. When we come to consider
theheuretic part of mathematical procedure, the question how
suchsuggestions are obtained will be the central point of the
discussion.
Passing over smaller discoveries, the principal result of
mycloser studies of it has been the very great part which an
operationplays in it which throughout modern times has been taken
fornothing better than a proper butt of ridicule. It is the
operation ofabstraction, in the proper sense of the term, which,
for example,
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converts the |97| proposition "Opium puts people to sleep"
into"Opium has a dormitive virtue". This turns out to be so
essential tothe greater strides of mathematical demonstration that
it is properto divide all theorematic reasoning into the
nonabstractional andthe abstractional. I am able to prove that the
most practicallyimportant results of mathematics could not in any
way be attainedwithout this operation of abstraction. It is
therefore necessary forlogic to distinguish sharply between good
abstraction and badabstraction.
It was not until I had been giving a large part of my time
forseveral years to tracing out the ways in which
mathematicaldemonstration makes use of abstraction that I came
across a factwhich a mind which had not been scrutinizing the facts
so closely|98| might have seen long before, namely, that all
collections are ofthe nature of abstractions. When we pass from
saying, "Almost anyAmerican can speak English", to saying "The
American nation iscomposed of individuals of whom the greater part
speak English", weperform a special kind of abstraction. This can,
I know, signify littleto the person who is not acquainted with the
properties ofabstraction. It may, however, suggest to him that the
popularcontempt for "abstractions" does not aim very accurately at
its mark.
When I published a paper about number in 1882, I was
alreadylargely anticipated by Cantor, although I did not know it. I
howeveranticipated Dedekind by about six years. Dedekind's work,
althoughits form is admirable, has not influenced me. But ideas
which I havederived from Cantor are so mixed up with ideas of my
own that Icould not safely undertake to say exactly where the line
should be|99| drawn between what is Cantor's and what my own. From
mypoint of view, it is not of much consequence. Like Cantor and
unlikeDedekind, I begin with multitude, or as Cantor erroneously
calls it,cardinal number. But it would be equally correct,
perhapspreferable, to begin with ordinal number, as Dedekind does.
But Ipursue the method of considering multitude to the very end,
whileCantor switches off to ordinal number. For that reason, it is
difficultto make sure that my higher multitudes are the same as
his. But Ihave little doubt that they are. I prove that there is an
infiniteseries of infinite multitudes, apparently the same as
Cantor's alephs.I call the first the denumerable multitude, the
others theabnumerable multitudes, the first and least of which is
themultitude of all the irrational numbers of analysis. There is
nothinggreater than these but true continua, which are not
multitudes. Icannot see that Cantor has ever got the conception of
a truecontinuum, such that in any |100| lapse of time there is room
forany multitude of instants however great.
I show that every multitude is distinguished from all
greatermultitudes by there being a way of reasoning about
collections ofthat multitude which does not hold good for greater
multitudes.Consequently, there is an infinite series of forms of
reasoningconcerning the calculus which deals only with a collection
of
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numbers of the first abnumerable multitude which are
notapplicable to true continua. This, it would seem, was a
sufficientexplanation of the circumstance that mathematicians have
neverdiscovered any method of reasoning about topical geometry,
whichdeals with true continua. They have not really proved a
singleproposition in that branch of mathematics.
Cayley, while I was still a boy, proved that metrical
geometry,the geometry of the elements, is nothing but a special
|101|problem to projective geometry, or perspective. It is easy to
seethat projective geometry is nothing but a special problem of
topicalgeometry. On the other hand, since every relation can be
reducedto a relation of serial order, something similar to a scale
of valuesmay be applied to every kind of mathematics. Probably, if
theappropriate scale were found, it would afford the best
generalmethod for the treatment of any branch. We see, for example,
thepower of the barycentric calculus in projective geometry. It
isessentially the method of modern analytic geometry. Yet it
isevident that it is not altogether an appropriate scale. I can
alreadysee some of the characters of an appropriate scale of values
fortopical geometry.
My logical studies have already enabled me to prove
somepropositions which had arrested mathematicians of power. Yet
Idistinctly disclaim, for the present, all pretension to having
beenremarkably successful in dealing with the heuretic
|102|department of mathematics. My attention has been
concentratedupon the study of its procedure in demonstration, not
upon itsprocedure in discovering demonstrations. This must come
later; andit may very well be that I am not so near to a
thoroughunderstanding of it as I may hope.
I am quite sure that the value of what I have ascertained will
beacknowledged by mathematicians. I shall make one more effort
toincrease it, before writing this second memoir.
From Draft C MS L75.129132
I now pass to a rough statement of my results in regard to
theheuretic branch of mathematical thought. At the outset, I set up
formyself a sort of landmark by which to discern whether I was
makingany real progress or not. Cayley had shown, while I was, as a
boy,just beginning to understand such things, that metric geometry,
thegeometry of the Elements, is nothing but a special problem
inprojective geometry, or perspective, and it is easy to see
thatprojective geometry is nothing but a special problem in topical
geom
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HomePagePeircePapersIntrotoL75L75Version2
Final Version MS L75.358
MEMOIR 5
ON THE QUALITIES OF THE THREE CATEGORIES OF EXPERIENCE
An analysis and description of three irreducibly different
kindsof elements found in experience and even in the abstract world
ofpure mathematics. This memoir rests upon observation of
theexperience of every day and hour, this observation
beingsystematized by thought. It is proved, beyond doubt, that
there areno more than the three categories. The list was first
published byme in May 1867, but has since been repeatedly subjected
to theseverest criticism I could bring to bear upon it, with the
result ofmaking it far more evidently correct. The categories were
originallycalled "quality", "relation", and "representation". The
question ofnames and other terminology for them still somewhat
perplexes me.I am inclined to call them "flavor", "reaction", and
"mediation".
From Draft B MS L75.19
[This memoir] will show that all that is before the mind
asperceived, imagined, supposed, rejected, etc, has three kinds
ofelements and no more. These are the qualities of feeling,
reaction,and mediation. [EDITORIAL NOTE: Notice that elements of
the firstkind are qualities of feeling and not simply feelings.]
Great pains willbe taken to make these three conceptions perfectly
clear and vivid.
From Draft C MS L75.102108
My aim in this paper, upon which I have bestowed more laborthan
upon any other, beginning two years before my firstpublication on
the subject in May 1867, is far more ambitious thanthat of Kant, or
even that of Aristotle, or even the more extendedwork of Hegel. All
those philosophers contented themselves mainlywith arranging
conceptions which were already current. I, on thecontrary,
undertake to look directly |103| upon the universal
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phenomenon, that is, upon all that in any way appears, whether
asfact or as fiction; to pick out the different kinds of elements
which Idetect in it, aided by a special art developed for the
purpose; and toform clear conceptions of those kinds, of which I
find that there areonly three, aided by another special art
developed for thatpurpose.*
Editorial Note (by Ransdell):
Does anyone know what Peirce is referring to asregards these
special arts? If you have any ideas onthis let us know and we will
post it here as anannotation. You need not have the
"definitive"answer to this to post your comment here: the ideais
just to get some cooperative work done on thisand on other such
questions as might arise,proceeding at a leisurely pace and in the
manner ofa scholarly dialogue.
Let me know at [email protected] and I'llpost your response
here:
COMMENTS & RESPONSES:
(1) Bo Larsson: August 15, 1998
(2) Jeffrey Downard: June 19, 2007
In my present limited space, I cannot make myself clear,
stillless convincing. Yet I will give such hint as I can of the
three kinds ofelements. I might name them "qualities",
"occurrences", and"meanings". In order to get an idea of what I
mean by a "quality",imagine a being whose consciousness should be
nothing but theperfume of a damask rose, without any sense of
change, of duration,of self or anything else. Put yourself in that
being's shoes, and whatof the universal phenomenon remains is what
I call a "quality". Itmay be defined as that whose mode of |104|
being consists simplyin its being what it is. It is selfessence.
Suppose next that theconsciousness we have imagined should undergo
the simplestpossible experience; that, for example, the roseodor
shouldsuddenly change to violetodor. If it is to remain the
sameconsciousness, there must be a moment in which it is conscious
ofboth odors. It cannot in this moment be conscious of the flow
oftime; but the former roseodor will appear as its ego, as
itsconsciousness, while the new violetodor will at that moment be
itsnonego, the object of its consciousness. We have this sort
of
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consciousness whenever we experience an event. The old, whichhas
just come to an end, appears as an ego, with the new, which isjust
about to begin, over against it as a nonego instantly passinginto
the ego. The sense of actuality, of present fact, is
thusessentially a consciousness of duplicity, of opposition. When
wehave thus got the idea of an inner and an outer, we can
|105|review our experience and place ourselves back to a moment
whenboth the former and the latter states were nonegos, and thus
weget the idea of a force acting between outward objects. I do
notmean to say that historically we actually do so reflect;
probably not.But I mean that that would be a logical reflection.
Thus we mightlogically derive the notion of a thing, as something
whose mode ofbeing consists in a reaction against something else.
This is mysecond category. The occurrence is essentially present.
When it isnot present its peculiar mode of being is gone. There is
no timeconstituent in it; for the flow of time involves a very
differentelement. There is always a certain resistance to the
unexpected. Itis usually broken down so instantly that it can only
be detected incases in which peculiar circumstances cause its
continuance. Butthat the new experience always has to overcome a
resistance on thepart of the old is proved by the |106| fact that
we feel it to beirresistible. We feel its force. Now, there can be
no force wherethere is no resistance. The two are but reverse
aspects of the samephenomenon. This resistance is a counterforce.
Hence the sense ofactual fact is a sense of reacting efforts.
So far, we have left out of account the staple element of
theuniversal phenomenon. Since we have been considering things
astemporal, we may as well continue to take the same point of
view.The future grows into accomplished fact by a gradual
unrolling; thenew becomes gradually old. Its effects remain, but
they dwindle inimportance toward utter oblivion. According to
legitimate physicalpresumption, the evidence certainly now is
(although we may notthink it likely that it is quite true) that all
physical forces are atbottom conservative. Now conservative forces
necessarily producecyclical effects. It is true, that if two
particles are attractedprecisely inversely as the cube of their
|107| distance, or by anylaw equivalent to that, the one will move
in a spiral nearer to theother forever. This is an interesting
point; and I have never seen itstated with precision. Formulae
given on p. 878 of my father'sAnalytic Mechanics show that if P is
the rate of description of areaof the Boscovichian point moving
round a fixed attracting center,then if we use a system of
rectangular coordinates in which x shallbe equal to the square of
the reciprocal of the radius vector, and yequal to the square of
the velocity, then the straight line whoseequation is y = 4P2x will
determine the condition of the movingparticle reaching an apse;
that is, a maximum or minimum distance.Another curve, dependent on
the law of the variation of theattraction with the distance, will
determine how u2 will vary with 1/
2. If the attraction varies less rapidly than the inverse cube
of thedistance, this second curve will be |108| concave downwards;
if
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more rapidly, concave upwards. But if itever crosses the
straight line y = 4P2x thebody will have at that distance been at
amaximum or minimum distance. If it istangent to that straight
line, it maydescribe the circle at that distance. Whenit is below
the straight line its velocity willbe insufficient and the distance
willdiminish; so that x will increase.
From Draft C MS L75.134139
Although I cannot in my present limited space make myselfclear,
still less convincing, I will name the three elements which Ifind
and give some rough notion of the significations of the names.They
are called "qualities", "things", and "meanings". By a "quality"
ismeant a selfessence, or something which is what it is by and
initself alone. Such, for example, is any simple quality of
sensation.Mind, I am not speaking of the occurrence of that
sensation. What Imean can be understood by imagining a being whose
consciousnessshould consist, we will say, in the sense of the
perfume |135| of adamask rose, without any change, without any
sense of time,without attributing the smell to any object, without
any selfconsciousness. I do not say that one can realize that in
theimagination; but one can perceive that such a state of
consciousnessthere might be. One can even suppose, however
groundlessly, thatthe attar of roses has a consciousness which is
just that. Now takeaway the consciousness in which there is an
element of fact, ofaction, and in which there is an element of
representation, and thevery quality itself, which consists in its
own peculiar selfbeing, andyou have what I mean by the elements of
quality in the universalphenomena. The element that I call a
"thing" is more familiar; butthe logical analysis of it which is
given in the books is inaccurate,because it is colored by the
peculiar ways of thinking of the IndoEuropean languages. It is true
that there are proper |136| names inall languages; but common
substantives, such as ours are, definitelynot verbs, are certainly
not necessary in a language, and in myopinion they do not fully
exist in the majority of languages. In theShemitic languages, for
example, every common noun is regarded asa formation from a verb.
Even if no such verb exists, it would seemthat the Shemites cannot
think of a noun except as a part of a verb;for they give it a form
as if it were of that nature. Indeed, there areIndoEuropean
languages in which the idea of the common noun isnot completely
hardened. For it is plain that with nouns, full nounsalone, one
could not frame a sentence which should satisfy the mindas
completely expressed. Now the majority of languages aredestitute of
any substantive verb "is". In ancient Egyptian, a pronoun"that"
usually takes its place. In Greek there is little or no feelingthat
a sentence without a verb is elliptical. |137| It is,
therefore,
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impossible that in those languages the common noun should
bethought as a mere name, as we think it. In Ancient Egyptian,
itseems that the pictorial way of thinking, so prominent in
thehieroglyphics, was more influential in their thought than it is
withus. The word "man" would then be replaced by what we can
nearestexpress as "something is a man", the word "animal" by
"something isan animal". Hence to express the idea that "man is an
animal", thepronoun "that" would naturally be more appropriate than
"is". Theywould think "Something is a man that something is an
animal". It isour idea of a common noun as a name which has caused
thelogicians to regard a thing as something selfsubsistent. There
is noroom for doubt that that is the way the idea arose. A proper
name isalways the name of something more or less familiar to both
theutterer of the sentence in which it occurs |138| and the
personwhom he addresses. For otherwise the sentence would have
nomeaning. If I inform you that the first king of England was
Arthur,and you had never before heard of Arthur, still my
description ofhim as the first king of England gives you some
acquaintance withhim before I use the word "Arthur". If I say
"Arthur was the first kingof England" I am using a faulty
inversion. But a common noun doesnot suppose any such familiarity.
The sentence "Flyingfishes arecommon in the gulf stream" is
sufficiently intelligible to a personwho never heard of a
flyingfish. That the idea of a thing or, as thelogicians say, a
substantia, not only does not consist in selfsubsistence, which
really describes a quality, but is downrightrepugnant to it, is
seen by trying to imagine a universe in whichnothing should exist
but a single atom. It has been shown above thatit is quite possible
to conceive of a universe in which there |139|should be absolutely
nothing but a roseodor, without time, space,or anything else. But
to suppose that nothing existed but a singleatom would be absurd.
Suppose it should exist and not exist everyother day: what
difference would there be between the odd andeven days? The
difference between an actually existing magnet anda phantasm of a
magnet is that one actually pulls and the other doesnot. Actuality,
or existence, consists in reaction. When I call aphenomenon a
thing, I mean that it is an object, a something actingob, or over
against me.
From Draft C MS L75.140142
I will name these elements here, although I cannot stop
toexplain what the names mean. They are simple qualities,
subjectsof force, and mind. Mind, in particular, is a very
differentconception from that which is current. It is nearly the
HegelianBegriff. There are three points of view from which these
elementshave to be studied before they can be clearly apprehended.
Theseare the points of view of qualities, of subjects, and of
minds. Fromthe point of view of quality, they appear respectively
as quality,|141| reaction, and mediation. From the point of view of
subjectsthey appear as quales, relates, and representations. This
is [the]
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point of view most familiar to ordinary thought, and will appear
theclearest to a beginner in the subject. Remembering that by
"theuniversal phenomenon" I mean everything which has got into
themind in any way whatever, including every fiction and false
notion,anyone can without difficulty see that there is an idea of a
thing asit is in itself with certain qualities, however occult,
which do notconsist in its actual relation to anything else. In the
next place,things are related to one another in pairs. That is,
they are atdistances from one another, attract or repel one
another, etc. In thethird place, finally, there are things which
represent other things tosome purposing mind; that is, they act as
substitutes for those otherthings for some purpose; that is, again,
they render the objectrepresented available for the |142| purpose.
Thus, to take anexample where, at first sight, one does not
perceive any element ofrepresentation, A gives B a present, C. As a
consequence of that act,B comes into direct relation with C, and A
has no more to do withthe matter. But as long as A's act of gift is
in process ofperformance, this act consists in giving B a
consciousness of having apower over C. It is a particular kind of
representation to B of theobject C. In [the] third place, from the
point of view of mind, thethree categories appear as feeling or
immediate consciousness, asthe sense of fact, and as conception or
mind strictly.
These three categories are compounded in a multitude of
wayswhich can only be apprehended through experience. They cannot
bebuilt up by an act of pure thought. Some of these forms
ofcomposition have to be carefully examined in order to
obtaindistinct conceptions with which to build a theory of
logic.
EDITORIAL NOTE: Here is a tabulation of the nomenclature forthe
three categories which Peirce uses in the different versionsof this
memoir above:
quality relation representation
flavor reaction mediation
qualities of feeling reaction mediation
qualities occurrences meanings
qualities things meanings
simple qualities subjects offorce mind
quality reaction mediation
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quales relates representation
feeling or immediateconsciousness
sense offact
conception or mindstrictly
FinalVersionMSL75.358
MEMOIR 6
ON THE CATEGORIES IN THEIR REACTIONAL ASPECTS
[Peirce said nothing under this heading in any extant version of
MSL75.]
FinalVersionMSL75.359
MEMOIR 7
OF THE CATEGORIES IN THEIR MEDIATE ASPECTS
These two memoirs [i.e. Memoirs 6 and 7] develop and renderclear
a considerable number of conceptions of which I shall makeconstant
use in the remaining memoirs, and which are of constantuse in all
parts of philosophy and even in mathematics.
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FinalVersionMSL75.359
MEMOIR 8
EXAMINATIONS OF HISTORICAL LISTS OF CATEGORIES
My list differs from those of Aristotle, Kant, and Hegel in
thatthey never really went back to examining the phenomenon to
seewhat was to be observed there; and I do not except
Hegel'sPhnomenologie from this criticism. They simply took
currentconceptions and arranged them. Mine has been a more
fundamentaland more laborious undertaking since I have worked up
from thepercepts to the highest notions. I examine those systems as
well assome others.
FinalVersionMSL75.359361
MEMOIR 9
ON THE BEARING OF ESTHETICS AND ETHICS UPON LOGIC
I begin by explaining the nature of the normative sciences.
Theyhave often been mistaken for practical |360| sciences, or arts.
Ishow that they are at the opposite pole of the sphere of
science,and are so closely allied to mathematics that it would be a
muchsmaller error to say that, like mathematics, they were
simplyoccupied in deducing the consequences of initial hypotheses.
Theirpeculiar dualism, which appears in the distinctions of the
beautifuland the ugly, right and wrong, truth and falsity, and
which is onecause of their being mistaken for arts, is really due
to their being onthe border between mathematics and positive
science; and to this,together with their great abstractness, is due
their applicability toso many subjects, which also helps to cause
their being taken forarts. Having analyzed the nature of the
precise problems of thethree, and given some considerations
generally overlooked, I showthat ethics depends essentially upon
esthetics and logic upon ethics.The latter dependence I had shown
less fully in 1869. (Journal ofSpeculative Philosophy, Vol. II, pp.
297 et seq.) But the methods ofreasoning by which the truths of
logic are established must bemathematical, such reasoning alone
|361| being evidentindependently of any logical doctrine.
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From Draft E MS L75.161162
[This memoir] will explain the nature of a normative science
andshow that, so far from such science approximating to
practicalscience, or art, it is, on the contrary, its extreme
abstractness,closely approaching the nature of pure mathematics,
surpassing inabstractness all other positive science, or science of
fact (whichpure mathematics is not), which imparts to it its
peculiar dualism(fine and ugly, good and bad, true and false), and
at the same timemakes it more nearly applicable to every subject
than any othersuch science except mathematics and categorics. The
preciseproblems of the three normative sciences are made clear in
fourstages or degrees of clearness. In what manner the truths
ofesthetics are to be discovered [is its] main proposition.
Ethicsdepends upon esthetics; we cannot know how we are
deliberatelyprepared to aim to behave until we know what we
deliberatelyadmire. The two leading doctrines of ethics. Logic in
its turnessentially depends upon ethics (as I showed, in a general
andvaguer way in 1869, |162| Journal of Speculative Philosophy,
II,207208), but its methods of reasoning must be mathematical,
suchreasoning being evident and therefore not requiring the support
ofany logical doctrine. Preliminary sketch of the three great
doctrinesof logic.
From Draft D MS L75.231233
I here show the peculiar character of a normative
science;namely, that while it is a purely theoretical science, and
notessentially practical, it nevertheless pronounces some things to
begood and others bad. Esthetics does so within the realm of
thecategory of feeling, ethics in the realm of action, and logic in
therealm of thought. As far back as 1869, I proved clearly that it
isimpossible for a man to be logical unless he adopts certain
highmoral aims. The argument is extremely |232| simple: All
positivereasoning depends upon probability. All probability depends
uponthe supposition that there is a "long run." But a long run is
anendless course of experience. Now even if there be a future
life,every man's course of experience with which his reasoning has
to docomes to a speedy end. Therefore, if his purposes are purely
selfishhe cannot be logical. That argument is open to some
apparentobjection; but the subsequent careful analysis of it has
only shownthat the argument has even more force than was supposed.
Otherconsiderations have also appeared which make the dependence
ofwhat we ought to think upon what we aim at still more close.
Logicis, therefore, more or less dependent upon ethics. Ethics, in
itsturn, or the question what we are deliberately prepared to aim
at,depends in a similar way upon esthetics, or what it is that we
woulddeliberately pronounce to be kalon k'agathon. Indirectly,
therefore,logic even depends upon esthetics. For |233|this reason,
with thehelp of the categories, I commence with an attempt at
outline
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analyses of the problems of esthetics and of ethics.
EDITORIAL NOTE: The Greek phrase "kalon k'agathon",
theconventional but uninformative translation of which is"beautiful
and good", combines the idea of that which excitesor calls forth
admiration and fascination and that towardwhich something is
directed in its movement or change.
End of PART 3 of 10 of MS L75
Queries, comments, and suggestions toJoseph Ransdell Dept of
Philosophy
Texas Tech University, Lubbock Texas
[email protected]
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FinalVersionMSL75.361362
MEMOIR 10
ON THE PRESUPPOSITIONS OF LOGIC
I here show that much that is generally set down as
presupposedin logic is neither needed nor warranted. The true
presuppositionsof logic are merely hopes and as such, when we
consider theirconsequences collectively, we cannot condemn
scepticism as to howfar they may be borne out by facts. But when we
come down tospecific cases, these hopes are so completely justified
that thesmallest conflict with them suffices to condemn the
doctrine thatinvolves that conflict. This is one of the places
where logic comes incontact with ethics. I examine the matter of
these hopes, showingthat they are, among other things which I
enumerate, that any givenquestion is susceptible of a true answer,
and that this answer isdiscoverable, that being and being
represented are different, thatthere is a reality, and that the
real world is governed by ideas.Doubt and everyday belief are
analyzed; and the differencebetween the latter and scientific
acceptance is shown. Otherdoctrines are examined.
From Draft B MS L75.18
[This discussion concerns] what it is that the sincere student
oflogic must certainly already believe beyond all doubt. He
mustbelieve, or at least hope, that there is such a thing as The
Truth, atleast with reference to some questions. He must therefore
thinkthat there is some reality which is independently of its
beingrepresented to be. He must therefore think that there is an
externalworld, however intimately it may be connected with himself,
or hewith it. He must agree that things happen, and that there is
somesuch thing as compulsion, or at least as force. He must agree
thatthere is such a thing as the influence of abstract ideas, such
as TheTruth, upon hard facts. That it is really true, and no
meremetaphor, that The Truth is a great power. All these things it
will be
-
shown that the student of logic, if he is sincerely such, does
believe.
From Draft D MS L75.230231
Most logicians, if not all, hold that there are
certain"presuppositions," or postulates, which logic must assume to
betrue; but they differ much as to what these presuppositions are,
andeven as to their forming a definite list or code. I find that
mostlogicians have outrageously exaggerated these presuppositions,
butthat there nevertheless are certain beliefs which a man must
holdfirmly or at least hope are true; otherwise there would be no
sensein his studying logic. These I endeavor to catalogue and
define. It isobvious that precision in this matter is quite
indispensable. Myposition here seems to be secured by the fact that
all thedifferences between me and other logicians consist in my
holdingpropositions not to be presupposed which they hold are so.
Now ifthey say that these things are presupposed by everybody, I
opposeto that the fact that I do not presuppose them. If they say
theyought to be presupposed, in the first place, they cannot
saydefinitely how, and in the second place, I offer a proof which,
if notdemonstrative, is very strong, that there can be no
argumentestablishing such an ought.
From Draft C MS L75.110118
Logicians generally, and especially the Germans, hold that
themere fact of reasoning, or endeavoring to reason, commits us to
thecategorical assertion of a considerable body of doctrine. But
Iundertake to show that in this instance, as in innumerable
others,those philosophical minds who have had no training in a
progressiveand living science exaggerate enormously, if not
infinitely, theconclusions which they are really entitled to draw.
In this number, Ipropose to examine with care, first, in what sense
anything is"presupposed" in merely entering upon an inquiry, and
just what itis; and secondly, whether there is anything additional
which aperson is committed to by the act of inquiring into logic,
and if so,what it is, and how he is committed to it. I undertake to
show beyond the possibility of any attentivereader's doubt, that
the bulk of the propositions which the logicianssay we are bound to
affirm, we are really, at most, only bound inconsistency to hope
for or expect, and that instead of our beingbound to assert
universal propositions, we merely hope that certainquite narrowly
personal propositions may be true. At the same time,among the
propositions that are said to be "presupposed," there aresome
which, though the reasoner may not be bound to adhere to
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them, it is quite clear that he does hold them to be evident
orundoubted facts. I further undertake to show that operations
ofwhich we are unconscious are beyond our direct control, and that
itis idle to ask whether an operation over which we have no
controlhas been properly performed or not. For example, I open my
eyesand look; and I thereupon say "There seems to be a bay horse".
Thisis a proposition. A percept is not a proposition. But the
propositionis supposed truly to represent the seeming of the
percept. It is, as Ihold, quite idle to inquire whether this is
correct or not. It isconceivable that it should not be correct; but
the operation offorming that perceptual judgment from the percept
being utterlybeyond our control, at present, it must go
unquestioned. It is out ofour power to doubt it. It appears
evidently. Propositions which wecannot doubt have to be accepted
without criticism. Genuinecriticism of them is impossible. It is
true that we believe that amongthe propositions which seem evident
to us there are some that arefalse and that we shall ultimately
discover to be false. That is a goodreason for not hastily
pronouncing that a proposition is indubitableby us today. Still,
until we can contrive to doubt a proposition noreal inquiry into
its truth can take place.
Having put these principles into a clear light, and examined
allother possible objections to them, it will behoove me to admit
thatthey are not free from the defect common to almost all
propositionsin philosophy, that of being more or less vague and
open tounwarrantable exaggeration. To be able to doubt a
proposition, if itmeans to doubt it this instant, can include only
actual doubt. If thetime be extended changes of mind may take
place. Doubt may alsobe so slight that it is not decidedly
recognizable. It is easy to findpropositions of which we cannot
positively say whether they can bedoubted or not. Nevertheless, I
undertake to show that theprinciples are sufficiently definite for
the purposes of logic.
I next undertake something like an enumeration of theindubitable
propositions. I shall not affirm that my enumeration iscomplete,
but shall only mention those which must be taken accountof in
logic. Nor shall I name all the individual propositions; for
theywill be different for different persons and even for the same
personat different times. But I shall enumerate categories of them.
Thesewill be enumerated in the form of propositions which are
notthemselves indubitable in advance of the proofs of them which
Ishall adduce. Nor can these proofs be apodictic. They will
leaveroom for hypothetical doubts; but I do not think they will
leave anyreally possible doubt in the reader's mind.
I have not decided upon the order of my enumeration; nor will
Ibe positive that upon reconsideration I may not slightly alter
mypresent statement. But the propositions which I shall show to
bebeyond criticism will be pretty nearly as follows.
I will first mention judgments descriptive of one's own state
of
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thought. These will include perceptual judgments, that
is,judgments as to the character of present percepts, such as "The
skyis blue". They will also include judgments as to the meanings
whichthe person making the judgment himself attaches to words
andother signs. Thus, if I say to myself "There seems to be a
horse",then, that being true in the sense I attach to the word
"horse", I amquite sure that there is an animal. For I am quite
sure that by ahorse I mean a kind of animal. It is true that I am
sometimes indoubt exactly what I do mean. Precisely where shall I
draw the linebetween "many persons" and "not many persons"?
Moreover, I mayblunder about my meaning. I may declare that in
saying the sky isblue I therein imply that it is not orangecolored,
although, in fact,when I said the sky was blue I was not referring
at all to thepossibility of its being orange colored. But I shall
show thatnevertheless all judgments concerning one's own thought
are in theonly reasonable sense of the words beyond criticism.
The proposition here laid down, that all judgments concerningthe
contents of our own thought are beyond criticism, is not
itselfbeyond criticism. It is a matter to be argued out; and some
logiciansvirtually deny it. Their doctrine is that it is only the
first impressionsof sense or other immediate consciousness that are
to be acceptedwithout criticism. But I deny both branches of this
opinion, and holdthat the first impressions of sense and all
immediate consciousnessare of the most dubious character, while
certain propositions whosepsychological genesis may be traced are
nevertheless quiteindubitable. I will undertake to put this beyond
all real doubt.
Another class of propositions beyond criticism results from
theapplication of one indubitable judgment to another. For example,
ifI say that a judgment is false, I am referring to something out
ofthought. For what I mean is that the proposition refers to a
subjectand misrepresents it, which it could not do if it referred
only to thecontents of thought. Consequently, the following
proposition is notconfined to the thought of the person who judges
it: "There is such athing as a false proposition." Now two things
are indubitable; first,that to say that that proposition, if it
were enunciated, would befalse would imply that that proposition
was not enunciated, andsecond, the perceptual judgment that one
hears that propositionenunciated. Consequently, the proposition is
beyond criticism; andthis is an important result. It will be
observed that I do not deny thatits being beyond criticism is
itself a proposition requiring carefulexamination. Various
objections might be made to it. For example,it may be said that
Hegel does not admit it, so that it cannot be soincapable of doubt.
I reply that it might be doubted if we overlookedwhat we actually
perceive, as Hegel does. But if he would open hiseyes to the fact
that his own opinion is denied, it would at oncebecome impossible
for him to retain that opinion.
Another class of judgments exempt from criticism refers
toobjects of the mind's own creations.
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From Draft C MS L75.6590
{65} German logicians generally maintain that the
mereincipiescence of reasonin