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Writings of Charles S. Peirce: A Chronological Edition, Volume 8: 1890-1892

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Volume 8 of this landmark edition follows Peirce from May 1890 through July 1892—a period of turmoil as his career unraveled at the U.S. Coast and Geodetic Survey. The loss of his principal source of income meant the beginning of permanent penury and a lifelong struggle to find gainful employment. His key achievement during these years is his celebrated Monist metaphysical project, which consists of five classic articles on evolutionary cosmology. Also included are reviews and essays from The Nation in which Peirce critiques Paul Carus, William James, Auguste Comte, Cesare Lombroso, and Karl Pearson, and takes part in a famous dispute between Francis E. Abbot and Josiah Royce. Peirce's short philosophical essays, studies in non-Euclidean geometry and number theory, and his only known experiment in prose fiction complete his production during these years.

Peirce's 1883-1909 contributions to the Century Dictionary form the content of volume 7 which is forthcoming.

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1. Familiar Letters about the Art of Reasoning

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Familiar Letters about the

Art of Reasoning

15 May 1890

Houghton Library

Stagira, May 15, 1890.

My dear Barbara:

The University of Cracow once conferred upon a very good fellow a degree for having taught the philosophical faculty to play cards. I cannot tell you in what year this happened,—perhaps it was 1499. The graduate was Thomas Murner, of whose writings Lessing said that they illustrated all the qualities of the German language; and so they do if those qualities are energy, rudeness, indecency, and a wealth of words suited to unbridled satire and unmannered invective. The diploma of the university is given in his book called Chartiludium, one of the numerous illustrations to which is copied to form the title page of the second book of a renowned encyclopaedia, the Margarita Philosoph1 ica. Murner’s pack contained 51 cards. There were seven unequal suits; 3 hearts, 4 clubs (or acorns), 8 diamonds (or bells), 8 crowns, 7 scorpions, 8 fish, 6 crabs. The remaining seven cards were jokers, or unattached to suits; for such cards formed a feature of all old packs. The object of Murner’s cards was to teach the art of reasoning, and a very successful pedagogical instrument they no doubt proved.

 

2. Ribot’s Psychology of Attention

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Ribot’s

Psychology of Attention

19 June 1890

The Nation

The Psychology of Attention. By Théodule Ribot. Authorized translation. Chicago: The Open Court Publishing Company.

1890. 8vo, pp. 121.

Every educated man wants to know something of the new psychology. Those who have still to make acquaintance with it may well begin with Ribot’s little book on “attention,” which all who have made progress in the new science will certainly wish to read. It is the chef d’oeuvre of one of the best of those students who have at length erected psychology into a science.

Ribot regards the doctrine of attention as “the counterpart, the necessary complement, of the theory of association.” He means that attention is related to suggestion as inhibition to muscular contraction.

Physiologists, however, would scarcely rank inhibitibility with contractility as an elementary property of protoplasm. Besides, though suggestion by association may be likened to muscular action, how can the analogy be extended to the process of association itself, or the welding together of feelings? This welding seems to be the only law of mental action; and upon it suggestion and inhibition of suggestion alike depend. Attention is said by Ribot to modify reverie’s train of thought by inhibiting certain suggestions, and thereby diverting their energy to suggestions not inhibited. This makes the positive element of attention quite secondary. At the same time, we are told that the sole incitement to attention is interest. That is to say, a preconceived desire prepares us to seize promptly any occasion for satisfying it. A child’s cry, drowned in clatter of talk for others’ ears, attracts the mother’s attention because she is in some state of preparation for it. Ribot, however, does not remark that to say the mind acts in a prepared way is simply to say it acts from a formed association, such action not being inhibitory. If interest be the sole incitement to attention, it is that the energy spent

 

3. Six Lectures of Hints toward a Theory of the Universe

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Six Lectures of Hints toward a Theory of the Universe

Spring 1890

Houghton Library

Lecture I. Right reasoning in philosophy is only possible if grounded on a sound theory of logic.

Fruitful thinking and experimentation are only two branches of one process. They are essentially one. Thinking is experimentation; its results as startling, as inexplicable. Experimentation is thinking.

The law of the development of fruitful conceptions, made out from the history of science. A genuine development.

The nature of assurance. Induction & Hypothesis.

Lecture II. The ideas of philosophy must be drawn from logic, as Kant draws his categories. For so far as anything intelligible and reasonable can be found in the universe, so far the process of nature and the process of thought are at one.

What are the fundamental conceptions of logic? First, Second,

Third. Explanation and illustrations.

Chance, Law, and Continuity must be the great elements in the explanation of the universe.

Lecture III. Critical survey of mental development in the last three centuries, and the ideas of today.

 

4. Sketch of a New Philosophy

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Sketch of a New Philosophy

Spring 1890

Houghton Library

DEVELOPMENT OF THE METHOD

1. It is not a historical fact that the best thinking has been done by words, or aural images. It has been performed by means of visual images and muscular imaginations. In reasoning of the best kind, an imaginary experiment is performed. The result is inwardly observed, and is as unexpected as that of a physical experiment. On the other hand, the success of outward experimentation depends on there being a reason in nature. Thus, reasoning and experimentation are essentially analogous.

2. According to what law are fruitful conceptions developed? Their

first germs present themselves in concrete and confused forms. The human mind, without being able to draw certain truth from its own depths, has nevertheless a natural bias toward true ideas of force and of human nature. It finds such ideas simple, easy, natural. Natural selection may be supposed to account for this to some extent. Yet the first origins of fruitful ideas can only be referred to chance. They promptly sink into oblivion if the mind is unprepared for them. If they meet allied ideas, a welding process takes place. This is the great law of association, the one law of intellectual development. It is very different from a mechanical law, in that it is only a gentle force. If ideas once together were rigidly associated, intellectual development would be frustrated.

 

5. [On Framing Philosophical Theories]

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[On Framing Philosophical Theories] late Spring 1890

Houghton Library

Three questions, at least, I think it must be admitted, ought to form the subject of studies preliminary to the formation of any philosophical st nd theory; namely, 1 , the purpose of the theory, 2 , the proper method of rd discovering it, 3 , the method of proving it to be true. I think, too, it can hardly be denied that it will be safer to consider these questions concerning the particular theory which is to be sought out, in the light of whatever we can ascertain regarding the functions, the discovery, and the establishment of sound theories in general. But these are questions of logic; and thus, no matter whether we ultimately decide to rest our philosophy upon logical principles as data, or upon psychological laws, or upon physical observations, or upon mystical experiences, or upon intuitions of first principles, or testimony, in any event these logical questions have to be considered first.

But if logic is thus to precede philosophy, will it not be unphilosophical logic? Perhaps logic is not in much need of philosophy. Mathematics, which is a species of logic, has never had the least need of philosophy in doing its work. Besides, even if logic should require subsequent remodelling in the light of philosophy, yet the unphilosophical logic with which we are obliged to set out will surely be better than no logic at all.

 

7. Review of Jevons’s Pure Logic

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Review of Jevons’s Pure Logic

3 July 1890

The Nation

Pure Logic, and Other Minor Works. By W. Stanley Jevons.

Edited by Robert Adamson and Harriet A. Jevons. Macmillan &

Co. 1890.

Though called Minor, these are scientifically Jevons’s most important writings. As when they first appeared, they impress us by their clearness of thought, but not with any great power. The first piece,

“Pure Logic,” followed by four years De Morgan’s Syllabus of Logic, a dynamically luminous and perfect presentation of an idea. In comparison with that, Jevons’s work seemed, and still seems, feeble enough. Its leading idea amounts to saying that existence can be asserted indirectly by denying the existence of something else. But among errors thick as autumn leaves in Vallambrosa, the tract contains a valuable suggestion, a certain modification of Boole’s use of the symbol ϩ in logic. This idea, directly suggested by De Morgan’s work, soon presented itself independently to half-a-dozen writers. But Jevons was first in the field, and the idea has come to stay. Mr. Venn is alone in his dissent.

 

8. Review of Carus’s Fundamental Problems

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Review of Carus’s

Fundamental Problems

7 August 1890

The Nation

Fundamental Problems: The Method of Philosophy as a Systematic Arrangement of Knowledge. By Dr. Paul Carus. Chicago:

The Open Court Publishing Company, 1889.

A book of newspaper articles on metaphysics, extracted from Chicago’s weekly journal of philosophy, the Open Court, seems to a New

Yorker something singular. But, granted that there is a public with aspirations to understand fundamental problems, the way in which Dr.

Carus treats them is not without skill. The questions touched upon are all those which a young person should have turned over in his mind before beginning the serious study of philosophy. The views adopted are, as nearly as possible, the average opinions of thoughtful men today

—good, ripe doctrines, some of them possibly a little passées, but of the fashionable complexion. They are stated with uncompromising vigor; the argumentation does not transcend the capacity of him who runs; and if there be here and there an inconsistency, it only renders the book more suggestive, and adapts it all the better to the need of the public.

 

9. Review of Muir’s The Theory of Determinants

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Review of Muir’s

The Theory of Determinants

28 August 1890

The Nation

The Theory of Determinants in the Historical Order of Its Development. Part I. “Determinants in General: Leibnitz (1693) to

Cayley (1841).” By Thomas Muir, M.A., LL.D., F.R.S.E. Macmillan & Co. 1890.

The only history of much interest is that of the human mind. Tales of great achievements are interesting, but belong to biography (which still remains in a prescientific stage) and do not make history, because they tell little of the general development of man and his creations. The history of mathematics, although it relates only to a narrow department of the soul’s activity, has some particularly attractive features. In the first place, the different steps are perfectly definite; neither writer nor reader need be in the least uncertain as to what are the things that have to be set forth and explained. Then, the record is, as compared with that of practical matters, nearly perfect. Some writings of the ancients are lost, some early matters of arithmetic and geometry lie hidden in the mists of time, but almost everything of any consequence to the modern development is in print. Besides, this history is a chronicle of uninterrupted success, a steady succession of triumphs of intelligence over primitive stupidity, little marred by passionate or brutal opposition.

 

10. Review of Fraser’s Locke

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Review of

Fraser’s Locke

25 September 1890

The Nation

Locke. By Alexander Campbell Fraser. [Philosophical Classics for English Readers.] Edinburgh: Wm. Blackwood & Sons; Philadelphia: J. B. Lippincott Co. 1890.

Mr. Galton’s researches have set us to asking of every distinguished personality, what were the traits of his family; although in respect, not to Mr. Galton’s eminent persons, but to the truly great—those men who, in their various directions of action, thought, and feeling, make such an impression of power that we cannot name from all history more than three hundred such—in respect to these men it has not been shown that talented families are more likely than dull families to produce them. The gifts of fortune, however, are of importance even to these. It is not true that they rise above other men as a man above a race of intelligent dogs. In the judgment of Palissy the potter (and what better witness could be asked?), the majority of geniuses are crushed under adverse circumstances. John Locke, whose biography by Berkeleyan

 

11. [Notes on the First Issue of the Monist]

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[Notes on the First Issue of the Monist]

23 October 1890

The Nation

—Many minds nowadays are turning towards high philosophy with expectations such as wide-awake men have not indulged during fifty years of Hamiltonianism, Millism, and Spencerianism; so that the establishment of a new philosophical quarterly which may prove a focus for all the agitation of thought that struggles today to illuminate the deepest problems with light from modern science, is an event worthy of particular notice. The first number of the Monist (Open Court

Publishing Company) opens with good promise, in articles by two

Americans, one Englishman, three Germans, two Frenchmen. Mr. A.

Binet, student of infusorial psychology, treats of the alleged physical immortality of some of these organisms. In the opening paper, Dr.

Romanes defends against Wallace his segregation supplement to the

Darwinian theory, i.e., that the divergence of forms is aided by varieties becoming incapable of crossing, as, for instance, by blossoming at different seasons. Prof. Cope, who, if he sometimes abandons the English language for the jargon of biology, is always distinguished by a clear style, ever at his command in impersonal matters, gives an analysis of marriage, not particularly original, and introduces a slight apology for his former recommendation of temporary unions. Prof. Ernst Mach has an “anti-metaphysical” article characteristic of the class of ingenious psychologists, if not perhaps quite accurate thinkers, to which he belongs. Mr. Max Dessoir recounts exceedingly interesting things about magic mirrors considered as hypnotizing apparatus. Mr. W. M.

 

12. My Life

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My Life c. 1890

Houghton Library

An extraordinary thing happened to me at a tender age,—as I now reflect upon it, a truly marvellous thing, though in my youthful heedlessness, I overlooked the wonder of it and just cried at the pickle. This occurred 1839 September 10. At that time I commenced life in the function of a baby belonging to Sarah Hunt (Mills) Peirce and Benjamin Peirce, professor of mathematics in Harvard College, beginning to be famous. We lived in a house in Mason Street. This house belonged to Mr. Hastings, who afterward built an ugly house between Longfellow’s and the Todd’s.

I remember nothing before I could talk. I remember starting out to drive in a carryall and trying to say something about a canarybird; I remember sitting on the nursery floor playing with blocks in an aimless way and getting cramps in my fingers; and I remember an old negro woman who came to do scrubbing. I remember her because she frightened me and I dreamed about her. I remember a gentleman who came to see my mother,—probably William Story, who drew a sketch of her.

 

13. Note on Pythagorean Triangles

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14. Hints toward the Invention of a Scale-Table

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Hints toward the Invention of a Scale-Table c. 1890

Houghton Library

[Version 1]

§1. A system of logarithms is a system of numbers corresponding, one-to-one, to natural numbers in such a way that pairs of natural numbers which are in the same ratio to one another have logarithms which differ from one another by the same amount. Thus, since

10 : 15 ϭ 14 : 21 it follows that log 10 Ϫ log 15 ϭ log 14 Ϫ log 21.

Logarithms were invented by Napier, 1614.

§2. A logarithmic scale is a scale on which natural numbers are set down at distances from the origin measured by their logarithms. If we apply a piece of paper to such a scale and mark off the distance of 15 from 10 and measure this on from 14 we shall find 21; thus solving the proportion.

The logarithmic scale was invented by Edmund Gunter, 1624.

§3. All linear logarithmic scales are similar. Consequently, different systems of logarithms are only different scales of measurement along a logarithmic scale.

§4. Suppose I convert the edge of this sheet into a rude logarithmic scale, using the spaces between the lines as units of measurement. If I have no means at hand of subdividing them, except that of writing the numbers regularly, the proper subdivision of the scale may be treated in the use of it as a separate problem.

 

15. Logical Studies of the Theory of Numbers

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Logical Studies of the

Theory of Numbers c. 1890

Houghton Library & Max H. Fisch Papers

The object of the present investigation is to analyze carefully the logic of the theory of numbers. I especially desire to clear up the question of whether there can be fundamentally different ways of proving a theorem from given premises; and the law of reciprocity seems likely to be instructive in this respect. I also wish to know whether there is not a regular method of proof in the higher arithmetic, so that we can see in advance precisely how a given proposition is to be demonstrated.

I make use of my last notation for relatives. I write li to mean that two objects l and i are connected. These two objects generally pertain to different universes; thus, l may be a character and i a thing. But there is no reason why I should not, instead of li, write (l, i ), except that the first way is more compact. A line over an expression negatives it, so that ¯li means that l and i are disconnected. I also write li j to signify that l, i and j are connected; thus, l might be a mode of relation; and i and j two objects so related the one to the other.

 

16. Promptuarium of Analytical Geometry

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Promptuarium of Analytical

Geometry c. 1890

Houghton Library

Let P1 and P2 be any two points.

P1

P2

Now consider this expression l P1 ϩ (1 Ϫ l ) P2 where l is a number. P1 and P2 are not numbers, and therefore the binomial cannot be understood exactly as in ordinary algebra; but we are to seek some meaning for it which shall be somewhat analogous to that of algebra. If l ϭ 0, it becomes

0 P1 ϩ 1 P 2 and this we may take as equal to P2, making 0 P1 ϭ 0 and 1 P2 ϭ P2.

Then if l ϭ 1, the expression will become equal to P1. When l has any other value, we may assume that the expression denotes some other point, and as l varies continuously we may assume that this point moves continuously. As l passes through the whole series of real values, the point will describe a line; and the simplest assumption to make is that this line is straight. That we will assume; but at present we make no further assumption as to the position of the point on the line when l has values other than 0 and 1. We may write l P1 ϩ (1 Ϫ l ) P2 ϭ P3.

 

17. Boolian Algebra

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Boolian Algebra c. 1890

Houghton Library

The algebra of logic was invented by the celebrated English mathematician, George Boole, and has subsequently been improved by the labors of a number of writers in England, France, Germany, and America. The deficiency of pronouns in English, as in every other tongue, begins to be felt as soon as there is occasion to discourse of the relations of more than two objects, and forces the lawyer of today in speaking of parties, as it did Euclid of old in treating of the relative situations of many points, to designate them as A, B, C, etc. This device is already a long stride toward an algebraical notation. Two other kinds of signs, however, must be introduced at once. The first embraces the parentheses and brackets which are the punctuation marks of algebra. The imperfection of the ordinary system of punctuation is notorious; and it is too stale a joke to fill up the corner of a newspaper to show a phrase may be ambiguous when written from which the pause of speech would exclude all uncertainty. In our algebraical notation, we simply enclose an expression within a parenthesis to show that it is to be taken together as a unit. We thus easily distinguish the “black (lady’s veil),” from the

 

18. Boolian Algebra. First Lection

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Boolian Algebra. First Lection c. 1890

Houghton Library

§1. INTRODUCTORY

The algebra of logic (which must be reckoned among man’s precious possessions for that it illuminates the tangled paths of thought) was given to the world in 1842; and George Boole is the name, an honoured one upon other accounts in the mathematical world, of the mortal upon whom this inspiration descended. Although there had been some previous attempts in the same direction, Boole’s idea by no means grew from what other men had conceived, but, as truly as any mental product may, sprang from the brain of genius, motherless. You shall be told, before we leave this subject, precisely what Boole’s original algebra was; it has, however, been improved and extended by the labors of other logicians, not in England alone, but also in France, in

Germany, and in our own borders; and it is to one of the modified systems which have so been produced that I shall first introduce you, and shall for the most part adhere. The whole apparatus of this algebra is somewhat extensive. You must not suppose that you are getting it all in the first, the second, or the third lection. But the subject-matter shall be so arranged that you may from the outset make some use of the notation described, and even apply it to the solution of problems.

 

19. Notes on the Question on the Existence of anExternal World

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Notes on the Question of the

Existence of an External World c. 1890

Houghton Library

1. The idealistic argument turns upon the assumption that certain things are absolutely “present,” namely what we have in mind at the moment, and that nothing else can be immediately, that is, otherwise than inferentially known. When this is once granted, the idealist has no difficulty in showing that that external existence which we cannot know immediately we cannot know, at all. Some of the arguments used for this purpose are of little value, because they only go to show that our knowledge of an external world is fallible; now there is a world of difference between fallible knowledge and no knowledge. However, I think it would have to be admitted as a matter of logic that if we have no immediate perception of a non-ego, we can have no reason to admit the supposition of an existence so contrary to all experience as that would in that case be.

But what evidence is there that we can immediately know only what is “present” to the mind? The idealists generally treat this as self-evident; but, as Clifford jestingly says, “it is evident” is a phrase which only means “we do not know how to prove.” The proposition that we can immediately perceive only what is present seems to me parallel to that other vulgar prejudice that “a thing cannot act where it is not.” An opinion which can only defend itself by such a sounding phrase is pretty sure to be wrong. That a thing cannot act where it is not, is plainly an induction from ordinary experience which shows no forces except such as act through the resistance of materials, with the exception of gravity which, owing to its being the same for all bodies, does not appear in ordinary experience like a force. But further experience shows that attractions and repulsions are the universal types of forces.

 

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