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| + | {{DISPLAYTITLE:Peirce's 1870 Logic Of Relatives}} |
| '''Author's Note.''' The text that follows is a collection of notes that will eventually be developed into a paper on [[Charles Sanders Peirce]]'s [[Logic of Relatives (1870)|1870 memoir on the logic of relative terms]]. [[User:Jon Awbrey|Jon Awbrey]] 06:06, 8 October 2007 (PDT) | | '''Author's Note.''' The text that follows is a collection of notes that will eventually be developed into a paper on [[Charles Sanders Peirce]]'s [[Logic of Relatives (1870)|1870 memoir on the logic of relative terms]]. [[User:Jon Awbrey|Jon Awbrey]] 06:06, 8 October 2007 (PDT) |
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| Giver of a Horse to a Lover of a Woman | | Giver of a Horse to a Lover of a Woman |
| </pre> | | </pre> |
| + | |
| + | ==Selection 8== |
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| <pre> | | <pre> |
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− | LOR. Note 8
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| | The Signs for Multiplication (cont.) | | | The Signs for Multiplication (cont.) |
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| |'Memoirs of the American Academy', Volume 9, pages 317-378, 26 January 1870, | | |'Memoirs of the American Academy', Volume 9, pages 317-378, 26 January 1870, |
| |'Collected Papers' (CP 3.45-149), 'Chronological Edition' (CE 2, 359-429). | | |'Collected Papers' (CP 3.45-149), 'Chronological Edition' (CE 2, 359-429). |
| + | </pre> |
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| + | ==Commentary Note 8.1== |
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− | LOR. Commentary Note 8.1
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| To my way of thinking, CP 3.73 is one of the most remarkable passages | | To my way of thinking, CP 3.73 is one of the most remarkable passages |
| in the history of logic. In this first pass over its deeper contents | | in the history of logic. In this first pass over its deeper contents |
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| w = B +, D +, E | | w = B +, D +, E |
| + | </pre> |
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| + | ==Commentary Note 8.2== |
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− | LOR. Commentary Note 8.2
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| I will continue with my commentary on CP 3.73, developing | | I will continue with my commentary on CP 3.73, developing |
| the Othello example as a way of illustrating its concepts. | | the Othello example as a way of illustrating its concepts. |
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| a winner over of Othello to Iago from Cassio, the elementary relative term | | a winner over of Othello to Iago from Cassio, the elementary relative term |
| "I:O:I:C" belongs to the relative term "winner over of --- to --- from ---". | | "I:O:I:C" belongs to the relative term "winner over of --- to --- from ---". |
| + | </pre> |
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| + | ==Commentary Note 8.3== |
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− | LOR. Commentary Note 8.3
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| Speaking very strictly, we need to be careful to | | Speaking very strictly, we need to be careful to |
| distinguish a "relation" from a "relative term". | | distinguish a "relation" from a "relative term". |
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| multiplication, or relational composition, will need | | multiplication, or relational composition, will need |
| to be adjusted accordingly. | | to be adjusted accordingly. |
| + | </pre> |
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| + | ==Commentary Note 8.4== |
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− | LOR. Commentary Note 8.4
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| To familiarize ourselves with the forms of calculation | | To familiarize ourselves with the forms of calculation |
| that are available in Peirce's notation, let us compute | | that are available in Peirce's notation, let us compute |
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| relative terms 'l' and 's' do not commute, | | relative terms 'l' and 's' do not commute, |
| that is to say, 'ls' is not equal to 'sl'. | | that is to say, 'ls' is not equal to 'sl'. |
| + | </pre> |
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| + | ==Commentary Note 8.5== |
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− | LOR. Commentary Note 8.5
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| Since multiplication by a 2-adic relative term | | Since multiplication by a 2-adic relative term |
| is a logical analogue of matrix multiplication | | is a logical analogue of matrix multiplication |
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| | 0 0 1 0 0 0 1 | | 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 1 | | | | 0 0 1 0 0 0 1 | | 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 1 | |
| | 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 | | | | 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 | |
| + | </pre> |
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| + | ==Commentary Note 8.6== |
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− | LOR. Commentary Note 8.6
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| The foregoing has hopefully filled in enough background that we | | The foregoing has hopefully filled in enough background that we |
| can begin to make sense of the more mysterious parts of CP 3.73. | | can begin to make sense of the more mysterious parts of CP 3.73. |
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| = D | | = D |
| + | </pre> |
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| + | ==Selection 9== |
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− | | + | <pre> |
− | LOR. Note 9
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| | The Signs for Multiplication (cont.) | | | The Signs for Multiplication (cont.) |
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