Directory talk:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives - Revision history

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2017-02-21T21:18:22Z

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Jon Awbrey: /* Commentary Note 8.1 */ remove rest of section for now

2015-12-04T19:26:20Z

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2015-12-04T19:24:15Z

Commentary Note 8.1: sub "." for ":" ???

Jon Awbrey: /* Commentary Note 8.1 */ Fix MathJax bug with extra blank after ":" ... By way of ''general terms'' in this discussion, we may begin with the following set: 

2015-12-04T19:20:05Z

Commentary Note 8.1: Fix MathJax bug with extra blank after ":" ... By way of ''general terms'' in this discussion, we may begin with the following set: 

Jon Awbrey at 19:14, 4 December 2015

2015-12-04T19:14:52Z

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← Older revision		Revision as of 21:24, 21 February 2017
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	==Mathematical Demonstration and the Doctrine of Individuals==		==Mathematical Demonstration and the Doctrine of Individuals==
−
−	~~===BLOG===~~
−
−	~~<pre>~~
−	~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~
−
−	~~BLOG -- Mathematical Demonstration and the Doctrine of Individuals~~
−
−	~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~
−
−	~~Post : Mathematical Demonstration & the Doctrine of Individuals : 1~~
−	~~http://inquiryintoinquiry.com/2015/02/22/mathematical-demonstration-the-doctrine-of-individuals-1/~~
−	~~Posted : February 22, 2015 at 11:40 am~~
−
−	~~Selection from C.S. Peirce, “Logic Of Relatives” (1870), CP 3.45–149~~
−
−	~~<blockquote>~~
−
−	92. Demonstration of the sort called mathematical is founded on suppositions of particular cases. The geometrician draws a figure; the algebraist assumes a letter to signify a single quantity fulfilling the required conditions. But while the mathematician supposes an individual case, his hypothesis is yet perfectly general, because he considers no characters of the individual case but those which must belong to every such case. The advantage of his procedure lies in the fact that the logical laws of individual terms are simpler than those which relate to general terms, because individuals are either identical or mutually exclusive, and cannot intersect or be subordinated to one another as classes can. Mathematical demonstration is not, therefore, more restricted to matters of intuition than any other kind of reasoning. Indeed, logical algebra conclusively proves that mathematics extends over the whole realm of formal logic; and any theory of cognition which cannot be adjusted to this fact must be abandoned. We may reap all the advantages which the mathematician is supposed to derive from intuition by simply making general suppositions of individual cases.
−
−	~~</blockquote>~~
−
−	~~References~~
−
−	~~• Peirce, C.S. (1870), “Description of a Notation for the Logic of Relatives,~~
−	~~Resulting from an Amplification of the Conceptions of Boole's Calculus of Logic”,~~
−	~~''Memoirs of the American Academy of Arts and Sciences'' 9, 317–378, 26 January 1870.~~
−	~~Reprinted, ''Collected Papers'' 3.45–149, ''Chronological Edition'' 2, 359–429.~~
−
−	~~Online~~
−	~~(1) ( http://www.jstor.org/stable/25058006 )~~
−	~~(2) ( https://archive.org/details/jstor-25058006 )~~
−	~~(3) ( http://books.google.com/books?id=fFnWmf5oLaoC ) .~~
−
−	~~• Peirce, C.S., ''Collected Papers of Charles Sanders Peirce'',~~
−	~~vols. 1–6, Charles Hartshorne and Paul Weiss (eds.),~~
−	~~vols. 7–8, Arthur W. Burks (ed.), Harvard University Press,~~
−	~~Cambridge, MA, 1931–1935, 1958.~~
−
−	~~• Peirce, C.S., ''Writings of Charles S. Peirce : A Chronological Edition'',~~
−	~~Peirce Edition Project (eds.), Indiana University Press,~~
−	~~Bloomington and Indianoplis, IN, 1981–.~~
−
−	~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~
−
−	~~Post : Mathematical Demonstration & the Doctrine of Individuals : 2~~
−	~~http://inquiryintoinquiry.com/2015/02/23/mathematical-demonstration-the-doctrine-of-individuals-2/~~
−	~~Date : February 23, 2015 at 11:30 am~~
−
−	~~Selection from C.S. Peirce, “Logic Of Relatives” (1870), CP 3.45–149~~
−
−	~~<quote>~~
−
−	93. In reference to the doctrine of individuals, two distinctions should be borne in mind. The logical atom, or term not capable of logical division, must be one of which every predicate may be universally affirmed or denied. For, let A be such a term. Then, if it is neither true that all A is X nor that no A is X, it must be true that some A is X and some A is not X; and therefore A may be divided into A that is X and A that is not X, which is contrary to its nature as a logical atom.
−
−	~~Such a term can be realized neither in thought nor in sense.~~
−
−	Not in sense, because our organs of sense are special — the eye, for example, not immediately informing us of taste, so that an image on the retina is indeterminate in respect to sweetness and non-sweetness. When I see a thing, I do not see that it is not sweet, nor do I see that it is sweet; and therefore what I see is capable of logical division into the sweet and the not sweet. It is customary to assume that visual images are absolutely determinate in respect to color, but even this may be doubted. I know no facts which prove that there is never the least vagueness in the immediate sensation.
−
−	In thought, an absolutely determinate term cannot be realized, because, not being given by sense, such a concept would have to be formed by synthesis, and there would be no end to the synthesis because there is no limit to the number of possible predicates.
−
−	A logical atom, then, like a point in space, would involve for its precise determination an endless process. We can only say, in a general way, that a term, however determinate, may be made more determinate still, but not that it can be made absolutely determinate. Such a term as “the second Philip of Macedon” is still capable of logical division — into Philip drunk and Philip sober, for example; but we call it individual because that which is denoted by it is in only one place at one time. It is a term not absolutely indivisible, but indivisible as long as we neglect differences of time and the differences which accompany them. Such differences we habitually disregard in the logical division of substances. In the division of relations, etc., we do not, of course, disregard these differences, but we disregard some others. There is nothing to prevent almost any sort of difference from being conventionally neglected in some discourse, and if “I” be a term which in consequence of such neglect becomes indivisible in that discourse, we have in that discourse,
−
−	~~[I] = 1.~~
−
−	This distinction between the absolutely indivisible and that which is one in number from a particular point of view is shadowed forth in the two words individual (?? ??????) and singular (?? ???? ???????); but as those who have used the word individual have not been aware that absolute individuality is merely ideal, it has come to be used in a more general sense.
−
−	~~</quote>~~
−
−	~~Note~~
−
−	~~Peirce explains his use of the square bracket notation at CP 3.65.~~
−
−	~~?http://inquiryintoinquiry.com/2014/01/29/peirces-1870-logic-of-relatives-%E2%80%A2-selection-2/~~
−
−	~~“I propose to denote the number of a logical term by enclosing the term in square brackets, thus, [t].”~~
−
−	~~The ''number'' of an absolute term, as in the case of I, is defined as the number of individuals it denotes.~~
−
−	~~References~~
−
−	~~• Peirce, C.S. (1870),~~
−	~~“Description of a Notation for the Logic of Relatives, Resulting from~~
−	~~an Amplification of the Conceptions of Boole's Calculus of Logic”,~~
−	~~''Memoirs of the American Academy of Arts and Sciences'' 9, 317–378,~~
−	~~26 January 1870. Reprinted in ''Collected Papers'' 3.45–149,~~
−	~~''Chronological Edition'' 2, 359–429.~~
−
−	~~Online~~
−	~~(1) ( http://www.jstor.org/stable/25058006 )~~
−	~~(2) ( https://archive.org/details/jstor-25058006 )~~
−	~~(3) ( http://books.google.com/books?id=fFnWmf5oLaoC ) .~~
−
−	~~• Peirce, C.S., ''Collected Papers of Charles Sanders Peirce'',~~
−	~~vols. 1–6, Charles Hartshorne and Paul Weiss (eds.),~~
−	~~vols. 7–8, Arthur W. Burks (ed.), Harvard University Press,~~
−	~~Cambridge, MA, 1931–1935, 1958.~~
−
−	~~• Peirce, C.S., ''Writings of Charles S. Peirce : A Chronological Edition'',~~
−	~~Peirce Edition Project (eds.), Indiana University Press, Bloomington and~~
−	~~Indianapolis, IN, 1981–.~~
−
−	~~Resources~~
−
−	~~• Peirce's 1870 Logic Of Relatives~~
−	~~http://intersci.ss.uci.edu/wiki/index.php/Peirce%27s_1870_Logic_Of_Relatives~~
−
−	~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~
−	~~</pre>~~

	===CP 3.92===		===CP 3.92===

← Older revision		Revision as of 15:35, 21 February 2017
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−	~~==Background Material==~~
−
−	~~===Propositions and Sentences===~~
−
−	* [http://intersci.ss.uci.edu/wiki/index.php/Inquiry_Driven_Systems_:_Part_2#2.2.3._Propositions_and_Sentences Inquiry Driven Systems • Propositions and Sentences]
−
−	It is convenient to transport the product and the sum operations of <math>\mathbb{B}</math> into the logical setting of <math>\underline\mathbb{B},</math> where they can be symbolized by signs of the same character. This yields the following definitions of a ''product'' and a ''sum'' in <math>\underline\mathbb{B}</math> and leads to the following forms of multiplication and addition tables.
−
−	The ''product'' <math>x \cdot y</math> of two values <math>x\!</math> and <math>y\!</math> in <math>\underline\mathbb{B}</math> is given by Table 9. As a dyadic operation on boolean values, that is, a function of the form <math>f : \underline\mathbb{B} \times \underline\mathbb{B} \to \underline\mathbb{B},</math> the product corresponds to the logical operation of ''conjunction'', written <math>{}^{\backprime\backprime} x \land y {}^{\prime\prime}</math> or <math>{}^{\backprime\backprime} x\!\And\!y {}^{\prime\prime}</math> and read as <math>{}^{\backprime\backprime} x ~\operatorname{and}~ y {}^{\prime\prime}.</math> In accord with common practice, the multiplication sign is frequently omitted from written expressions of the product.
−
−	~~<br>~~
−
−	~~{\| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:50%"~~
−	~~\|+ style="height:30px" \| <math>\text{Table 9.} ~~ \text{Product Operation for the Boolean Domain}\!</math>~~
−	~~\|- style="height:40px; background:ghostwhite"~~
−	~~\| <math>\cdot\!</math>~~
−	~~\| <math>\underline{0}</math>~~
−	~~\| <math>\underline{1}</math>~~
−	\|-
−	~~\| style="background:ghostwhite" \| <math>\underline{0}</math>~~
−	~~\| <math>\underline{0}</math>~~
−	~~\| <math>\underline{0}</math>~~
−	\|-
−	~~\| style="background:ghostwhite" \| <math>\underline{1}</math>~~
−	~~\| <math>\underline{0}</math>~~
−	~~\| <math>\underline{1}</math>~~
−	\|}
−
−	~~<br>~~
−
−	The ''sum'' <math>x + y\!</math> of two values <math>x\!</math> and <math>y\!</math> in <math>\underline\mathbb{B}</math> is given in Table 10. As a dyadic operation on boolean values, that is, a function of the form <math>f : \underline\mathbb{B} \times \underline\mathbb{B} \to \underline\mathbb{B},</math> the sum corresponds to the logical operation of ''exclusive disjunction'', usually read as <math>{}^{\backprime\backprime} x ~\text{or}~ y ~\text{but not both} {}^{\prime\prime}.\!</math> Depending on the context, other signs and readings that invoke this operation are: <math>{}^{\backprime\backprime} x \ne y {}^{\prime\prime}</math> or <math>{}^{\backprime\backprime} x \not\Leftrightarrow y {}^{\prime\prime},</math> read as <math>{}^{\backprime\backprime} x ~\text{is not equal to}~ y {}^{\prime\prime},</math> <math>{}^{\backprime\backprime} x ~\text{is not equivalent to}~ y {}^{\prime\prime},</math> or <math>{}^{\backprime\backprime} \text{exactly one of}~ x, y ~\text{is true} {}^{\prime\prime}.\!</math>
−
−	~~<br>~~
−
−	~~{\| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:50%"~~
−	~~\|+ style="height:30px" \| <math>\text{Table 10.} ~~ \text{Sum Operation for the Boolean Domain}\!</math>~~
−	~~\|- style="height:40px; background:ghostwhite"~~
−	~~\| <math>+\!</math>~~
−	~~\| <math>\underline{0}</math>~~
−	~~\| <math>\underline{1}</math>~~
−	\|-
−	~~\| style="background:ghostwhite" \| <math>\underline{0}</math>~~
−	~~\| <math>\underline{0}</math>~~
−	~~\| <math>\underline{1}</math>~~
−	\|-
−	~~\| style="background:ghostwhite" \| <math>\underline{1}</math>~~
−	~~\| <math>\underline{1}</math>~~
−	~~\| <math>\underline{0}</math>~~
−	\|}
−
−	~~<br>~~
−
−	~~===Logical Implication===~~
−
−	* [http://intersci.ss.uci.edu/wiki/index.php/Logical_implication Logical Implication]
−
−	The concept of logical implication is associated with an operation on two logical values, typically the values of two propositions, that produces a value of ''false'' just in case the first operand is true and the second operand is false.
−
−	In the interpretation where <math>0 = \operatorname{false}</math> and <math>1 = \operatorname{true}</math>, the truth table associated with the statement <math>{}^{\backprime\backprime} p ~\text{implies}~ q {}^{\prime\prime},</math> symbolized as <math>{}^{\backprime\backprime} p \Rightarrow q {}^{\prime\prime},</math> appears below:
−
−	~~<br>~~
−
−	~~{\| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:45%"~~
−	~~\|+ style="height:30px" \| <math>\text{Logical Implication}\!</math>~~
−	~~\|- style="height:40px; background:#f0f0ff"~~
−	~~\| style="width:33%" \| <math>p\!</math>~~
−	~~\| style="width:33%" \| <math>q\!</math>~~
−	~~\| style="width:33%" \| <math>p \Rightarrow q\!</math>~~
−	\|-
−	~~\| <math>0\!</math> \|\| <math>0\!</math> \|\| <math>1\!</math>~~
−	\|-
−	~~\| <math>0\!</math> \|\| <math>1\!</math> \|\| <math>1\!</math>~~
−	\|-
−	~~\| <math>1\!</math> \|\| <math>0\!</math> \|\| <math>0\!</math>~~
−	\|-
−	~~\| <math>1\!</math> \|\| <math>1\!</math> \|\| <math>1\!</math>~~
−	\|}
−
−	~~<br>~~
−
−	~~===Work Area===~~
−
−	~~<br>~~
−
−	~~{\| align="center" cellspacing="6"~~
−	\|
−	~~<math>\begin{array}{\|c\|\|cc\|}~~
−	~~\hline~~
−	~~\texttt{=}\!\texttt{<} & 0 & 1 \\~~
−	~~\hline\hline~~
−	~~0 & 1 & 1 \\~~
−	~~1 & 0 & 1 \\~~
−	~~\hline~~
−	~~\end{array}\!</math>~~
−	\|}
−
−	~~<br>~~
−
−	~~{\| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:50%"~~
−	~~\|- style="height:40px; background:ghostwhite"~~
−	~~\| style="width:33%" \| <math>\texttt{=}\!\texttt{<}\!</math>~~
−	~~\| <math>0\!</math>~~
−	~~\| <math>1\!</math>~~
−	\|-
−	~~\| style="background:ghostwhite; width:33%" \| <math>0\!</math>~~
−	~~\| <math>1\!</math>~~
−	~~\| <math>1\!</math>~~
−	\|-
−	~~\| style="background:ghostwhite; width:33%" \| <math>1\!</math>~~
−	~~\| <math>0\!</math>~~
−	~~\| <math>1\!</math>~~
−	\|}
−
−	~~<br>~~
−
	==Commentary Work Area==		==Commentary Work Area==

← Older revision		Revision as of 14:48, 21 February 2017
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	<li>http://stderr.org/pipermail/inquiry/2009-April/003548.html</li>		<li>http://stderr.org/pipermail/inquiry/2009-April/003548.html</li>
	</ol>		</ol>
		+
		+	…

← Older revision		Revision as of 19:26, 4 December 2015
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	By way of ''general terms'' in this discussion, we may begin with the following set.		By way of ''general terms'' in this discussion, we may begin with the following set.
−
−	~~{\| align="center" cellspacing="6" width="90%"~~
−	\|
−	~~<math>\begin{array}{ccl}~~
−	~~^{\backprime\backprime}\mathrm{b}^{\prime\prime}~~
−	~~& = &~~
−	~~^{\backprime\backprime}\mathrm{black}^{\prime\prime}~~
−	~~\\[6pt]~~
−	~~^{\backprime\backprime}\mathrm{m}^{\prime\prime}~~
−	~~& = &~~
−	~~^{\backprime\backprime}\mathrm{man}^{\prime\prime}~~
−	~~\\[6pt]~~
−	~~^{\backprime\backprime}\mathrm{w}^{\prime\prime}~~
−	~~& = &~~
−	~~^{\backprime\backprime}\mathrm{woman}^{\prime\prime}~~
−	~~\end{array}</math>~~
−	\|}
−
−	~~The denotation of a general term may be given by means of an equation between terms:~~
−
−	~~{\| align="center" cellspacing="6" width="90%"~~
−	\|
−	~~<math>\begin{array}{*{15}{c}}~~
−	~~\mathrm{b}~~
−	~~& = & \mathrm{O}~~
−	~~\\[6pt]~~
−	~~\mathrm{m}~~
−	~~& = & \mathrm{C}~~
−	~~& +\!\!, & \mathrm{I}~~
−	~~& +\!\!, & \mathrm{J}~~
−	~~& +\!\!, & \mathrm{O}~~
−	~~\\[6pt]~~
−	~~\mathrm{w}~~
−	~~& = & \mathrm{B}~~
−	~~& +\!\!, & \mathrm{D}~~
−	~~& +\!\!, & \mathrm{E}~~
−	~~\end{array}</math>~~
−	\|}

	===Commentary Note 8.2===		===Commentary Note 8.2===

@@ Line 647: / Line 647: @@
 Each of these terms denotes in a singular fashion the corresponding individual in <math>X.\!</math>
-By way of ''general terms'' in this discussion, we may begin with the following set:&nbsp;
+By way of ''general terms'' in this discussion, we may begin with the following set.
 {| align="center" cellspacing="6" width="90%"

Directory talk:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives - Revision history

Jon Awbrey: /* Mathematical Demonstration and the Doctrine of Individuals */ delete blog-formatted pieces

Jon Awbrey: add part of article that was parsing okay last time

Jon Awbrey: cleanup

Jon Awbrey: update

Jon Awbrey: test

Jon Awbrey: remove text after problem point for now

Jon Awbrey: /* Commentary Note 8.1 */ remove rest of section for now

Jon Awbrey: /* Commentary Note 8.1 */ sub "." for ":" ???

Jon Awbrey: /* Commentary Note 8.1 */ Fix MathJax bug with extra blank after ":" ... By way of ''general terms'' in this discussion, we may begin with the following set:&nbsp;

Jon Awbrey at 19:14, 4 December 2015

Jon Awbrey: /* Commentary Note 8.1 */ Fix MathJax bug with extra blank after ":" ... By way of ''general terms'' in this discussion, we may begin with the following set: