C. S. Peirce Manuscripts

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Logic Notebook 1867 March-Oct

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22r

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All U is the foresent U

All U is P

therefore

All [Dr?] U is P

No rather

The foresent U is U

The present U is P

therefore All U is P

Now we have why not then
All S is S S S' S" are taken as U
Some S is M therefore M is S or S' or S"
Some M is S S S' S" is P
therefore U is P

Why yes! This is it.

Induction consists in that very conversion which Aristotle says is necessary [Dr?] its validity.

The inference is _

2 that if - S S'S" occur only in consequence of being M

2' then All U has the common characters of S S' S"

Some S is M

Zen _ now to hypothesis * Fig 2

Last edit over 3 years ago by MarlowScribes
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18r

33

Whatever is a common character of many things devoted by M is likely to be a character of m.

That does not quite [fit ??] the [ferish ??] It does not contain the idea that the things must have been taken at random out of those devoted by M.

In what [point ??] of view shall we regard this necessity for a random selection? Suppose we look at the matter thus. Certain things have a certain character in common. It follows that these must be some genus of these things which have the character. We cannot take any genus lower [than ??] that which they are selected as belonging to. To take a higher one would involve a perfectly arbitrary [povfoition].

I am convinced that this is a very awkward way of taking hold of the matter.

Suppose we take it up another way for any subject or predicate we can substitute what?

Last edit over 4 years ago by agerdom

Logic Notebook 1865-7

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dicted not only by [I ??] but also or

"A class subordinate to A in extension is denoted by a symbol exclusive of B in extension"

but also by

"A class exclusive of A in [comprehension ??] is denoted by a symbol subordinate to B in [comprehension ??]."

Let a class [exclusive ??] of A in comprehension be called a reverse of A. And let a symbol subordinate of B in comprehension be called [some what ??] B.

Then we have

A All A is B I Some A is B W A reverse of A is B E No A is B O Some A is not B U A reverse of A is not B N All A is somewhat B Ω Some A is somewhat B A is contradicted by O ∝ Y I is contracted by E ∝ W W is contracted by I ∝ H H E is contracted by I ∝ H O is contracted by A

Last edit over 4 years ago by agerdom
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8r

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U H is contracted by W ∝ E Ω Y is contracted by A.

Proof of the above relations.

1. If we take A ∝ O both [informatively ??] it will of [appear ??] that both may be falsetrue if P has no [intension ??] [or ??] both false if S has no extension. But taking the five cases of extension that A has 2 and O the other three.

In the same way if we take A ∝ Y [informatively ??] both may be false if P has no intension & both true if S has no extension. But of the [5 relations ??] of intension A admits 2 and Y the other 3.

Dec 20

I find that a good deal of the above is wrong. [Propositions ??] have relations of Intension corresponding to [Subalternation && Contradiction ??] which are relations of Intension. 2 forms of [Propositions ??] are [contradictions ??] when taking any symbol as predicate [term ??] all [terms ??] are divisible into such which may be [put ??] as subject [term ??] one x of the other.

Corresponding to this will be a relation between two forms such that any symbol being taken as subject [term ??]

Last edit over 4 years ago by agerdom

Logic Notebook Directory

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C.S. PEIRCE'S LOGIC NOTEBOOK 5

109r in respect.... An 109v blank 110r argument.... 1898 June 14.... with Y. 110v blank 111r Questions.... another. 111v blank 112r Basic Formal Rules.... (in margin:) Replaced two pages on.... connections 112v The fact.... rules. (dated) 1898 June 15 113r Theorems / Notation .... (formulas) 113v blank 114r 1898 June 15 / Basic Formal Rules. . . . written 114v blank 115r Theorems./ Notation .... Q.E.D. 115v blank 116r XV If an.... ovals. 116v blank 117r XVII. Any evenly.... written. 117v (one graph with algebraic interpretation) 118r XX Any graph.... outside. 118v blank 119r XXIII. An evenly.... by XIV 119v 1903 June 9: Theorem XXVI may be extended as follows: (this a later note by CSP) ....(formulas) 120r XXV. A heavy.... (formulas) 120v (Two lines only) This is wrong.... It is correct. 121r Scholium This proof.... (formulas etc.) 121v blank 122r 1898 June 18. / The basic.... etc. 122v blank 123r XIV. A graph.... etc. 123v blank 124r XV. If any.... first. 124v blank 125r 1898 June 19. / The Dozen Basic Formal Rules.... indifferent. 125v (scribbling) V 126r 1898 June 20.... erased. 126v (in black at top) always.... (in blue) I. Any.... before (pencil notes at bottom) 127r 1898 Aug h .... be written 127v It is.... developed. 128r 1898 Aug h .... we now come to.... loved -— 128v blank 129r continued.... Turn over 129v (graphs and interpretation) 130r Continued.... (graphs etc.) 130v blank 131r No 5 Given.... (graphs etc.) 131v blank 132r 1898 Aug 5.... description 132v blank 133r But.... description 133v blank 134r ( graph) 134v blank 135r (graph, like that of 134r, but there are two cuts added to this one) 135v blank

Last edit about 6 years ago by agerdom
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C. S. PEIRCE'S LOGIC NOTEBOOK 3

52r When we take relation.... (followed by formulas) 52v Nov. 9. / A.... (16 lines of formulas) 53r 1(a, b)= .... except zero \frac{=}{,} 53v Now if.... (formulas) 54r ∴ V, EV - O .... [1] 54v (9) Hence.... (formulas) 55r Nov. 10. / I think.... to some one 5. 55v Then.... else is. 56r Any term... (last line is numbered 19) 56v From.... might be written It 57r Mk have also.... (10 lines of formulas) 57v If.... anything not w 58r Let.... (formulas).... over 58v Let.... (followed by 18 lines of formulas) 59r (x + Ax)n = (1 +1.1)n x (fonmlaS) 59v Now if this is all right.... (formulas) 60r Now.... (formulas) 60v Nov. 11. / Then.... Fbr 61r However.... over 61v (first line numbered 1).... This hardly follows 62r so that.... for the present. 62v Nov 12. / If.... (formulas etc.) 63r In arithmetic.... But this is not so here 63v This.... not a 64r a, b = 0.... (formulas etc.) 64v 1 - x .... (formulas) 65r (formulas).... (next to last line: ) This n must be zero. 65v Nov. 15.... Caucasian 66r a - 1b .... (interpreted formulas in the logic of relatives) 66v Then if.... (formulas) 67r Every man.... (formulas) 67v blank 68r 1869 Oct. 6.... (formulas) 68v blank 69r Hence.... x, n = 0 69v blank 70r Oct 6. / Example.... are given 70v blank 71r let us.... when 71v blank 72r When A = 1 .... contradict it. 72v Oct 15 / If.... (formulas) 73r Eureka .... (formulas) 73v blank 74r 1880 Nov. 6.... moods etc. 71w blank 75r 0n Chapter II.... = V 75v blank 76r Then we have.... (formulas) 76v (One formula in middle of page) 77r In short.... is x. 77v Same thing.... (three lines only) 78r Then.... Cayley's proposal 78v blank 79r But if.... not -v. 79v blank

Last edit over 3 years ago by Jannyp

MS 611-15

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engaged upon a problem of a familiar kind. To fix my ideas I imagined the problem to be that of determining the atomic weight of tellurium.

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611

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MS 425 (1902) - Minute Logic - Chapter I

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{Upper left margin: "Logic 21"}

of logicality as often to reason ill, and unless he held the distinction between reasoning well and reasoning ill was that the former w̶a̶s is conducive to the knowledge of the t͟r͟u͟t͟h͟, and the latter not so, and that by the truth is meant something not dependent upon how we feel or think if [d?] be. Upon Sigwart's {Refers to Cristoph von Sigwart (1789-1844)} principle the distinction would be a mere distinction of taste, or the satisfaction of a subjective feeling. This harmonizes only two well with the practice of German university professors, whose r̶e̶a̶s̶o̶n̶i̶n̶g̶ opinions are mainly founded on subjective feeling and upon fashion. In the beginning of the next chapter we shall consider the argument by which Sigwart supports his opinion; and the reader will then be led clearly to understand how, without denying the existence of the ̶s̶e̶n̶s̶e̶ logical sense, ̶a̶n̶d̶ nor its intervention in all thought, I can maintain that it is extremely fallible

Last edit over 6 years ago by TommasoTempestini
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and that no appeal need or ought to be made to it in establishing the truths of logic. Judges by English standards and those which the present work aims to establish, Sigwart's teaching is calculated to undermine the vigor of reasoning, by a sort of phagedemic ulcera tion. So it would seem a priori; and a the impression made upon me by young reasoners who have been the most diligent students of Sigwart is that of debility and helplessness in thought. 2nd=. Since it must be nearly forty years since I read La Lagique of the Abbe Gratry, a writer of subtlety and exactitude of thought as weel as of elevation of reason, my account of his doctrine may not be accurate in its details. I insert it here because after feeling it seems natural to place proposed method of basing logical principles upon direct individual experience. Now since these principles are general, only a mystical expe

Margin: Logic 22 On Revolution

Last edit about 6 years ago by ebezjian
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