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| ===Commentary Note 8.4=== | | ===Commentary Note 8.4=== |
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− | <pre>
| + | To familiarize ourselves with the forms of calculation that are available in Peirce's notation, let us compute a few of the simplest products that we find at hand in the Othello case. |
− | To familiarize ourselves with the forms of calculation | |
− | that are available in Peirce's notation, let us compute | |
− | a few of the simplest products that we find at hand in | |
− | the Othello case. | |
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| Here are the absolute terms: | | Here are the absolute terms: |
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− | 1 = B +, C +, D +, E +, I +, J +, O | + | : 1 = B +, C +, D +, E +, I +, J +, O |
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− | b = O | + | : b = O |
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− | m = C +, I +, J +, O | + | : m = C +, I +, J +, O |
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− | w = B +, D +, E | + | : w = B +, D +, E |
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| Here are the 2-adic relative terms: | | Here are the 2-adic relative terms: |
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− | 'l' = B:C +, C:B +, D:O +, E:I +, I:E +, O:D | + | : 'l' = B:C +, C:B +, D:O +, E:I +, I:E +, O:D |
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− | 's' = C:O +, E:D +, I:O +, J:D +, J:O | + | : 's' = C:O +, E:D +, I:O +, J:D +, J:O |
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| Here are a few of the simplest products among these terms: | | Here are a few of the simplest products among these terms: |
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− | 'l'1 = "lover of anybody" | + | : 'l'1 = "lover of anybody" |
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− | = (B:C +, C:B +, D:O +, E:I +, I:E +, O:D)(B +, C +, D +, E +, I +, J +, O)
| + | :: = (B:C +, C:B +, D:O +, E:I +, I:E +, O:D)(B +, C +, D +, E +, I +, J +, O) |
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− | = B +, C +, D +, E +, I +, O
| + | :: = B +, C +, D +, E +, I +, O |
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− | = "anybody except J"
| + | :: = "anybody except J" |
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− | 'l'b = "lover of a black" | + | : 'l'b = "lover of a black" |
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− | = (B:C +, C:B +, D:O +, E:I +, I:E +, O:D)O
| + | :: = (B:C +, C:B +, D:O +, E:I +, I:E +, O:D)O |
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− | = D
| + | :: = D |
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− | 'l'm = "lover of a man" | + | : 'l'm = "lover of a man" |
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− | = (B:C +, C:B +, D:O +, E:I +, I:E +, O:D)(C +, I +, J +, O)
| + | :: = (B:C +, C:B +, D:O +, E:I +, I:E +, O:D)(C +, I +, J +, O) |
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− | = B +, D +, E
| + | :: = B +, D +, E |
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− | 'l'w = "lover of a woman" | + | : 'l'w = "lover of a woman" |
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− | = (B:C +, C:B +, D:O +, E:I +, I:E +, O:D)(B +, D +, E)
| + | :: = (B:C +, C:B +, D:O +, E:I +, I:E +, O:D)(B +, D +, E) |
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− | = C +, I +, O
| + | :: = C +, I +, O |
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− | 's'1 = "servant of anybody" | + | : 's'1 = "servant of anybody" |
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− | = (C:O +, E:D +, I:O +, J:D +, J:O)(B +, C +, D +, E +, I +, J +, O)
| + | :: = (C:O +, E:D +, I:O +, J:D +, J:O)(B +, C +, D +, E +, I +, J +, O) |
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− | = C +, E +, I +, J
| + | :: = C +, E +, I +, J |
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− | 's'b = "servant of a black" | + | : 's'b = "servant of a black" |
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− | = (C:O +, E:D +, I:O +, J:D +, J:O)O
| + | :: = (C:O +, E:D +, I:O +, J:D +, J:O)O |
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− | = C +, I +, J
| + | :: = C +, I +, J |
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− | 's'm = "servant of a man" | + | : 's'm = "servant of a man" |
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− | = (C:O +, E:D +, I:O +, J:D +, J:O)(C +, I +, J +, O)
| + | :: = (C:O +, E:D +, I:O +, J:D +, J:O)(C +, I +, J +, O) |
| | | |
− | = C +, I +, J
| + | :: = C +, I +, J |
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− | 's'w = "servant of a woman" | + | : 's'w = "servant of a woman" |
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− | = (C:O +, E:D +, I:O +, J:D +, J:O)(B +, D +, E)
| + | :: = (C:O +, E:D +, I:O +, J:D +, J:O)(B +, D +, E) |
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− | = E +, J
| + | :: = E +, J |
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− | 'ls' = "lover of a servant of ---" | + | : 'ls' = "lover of a servant of ---" |
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− | = (B:C +, C:B +, D:O +, E:I +, I:E +, O:D)(C:O +, E:D +, I:O +, J:D +, J:O)
| + | :: = (B:C +, C:B +, D:O +, E:I +, I:E +, O:D)(C:O +, E:D +, I:O +, J:D +, J:O) |
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− | = B:O +, E:O +, I:D
| + | :: = B:O +, E:O +, I:D |
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− | 'sl' = "servant of a lover of ---" | + | : 'sl' = "servant of a lover of ---" |
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− | = (C:O +, E:D +, I:O +, J:D +, J:O)(B:C +, C:B +, D:O +, E:I +, I:E +, O:D)
| + | :: = (C:O +, E:D +, I:O +, J:D +, J:O)(B:C +, C:B +, D:O +, E:I +, I:E +, O:D) |
| | | |
− | = C:D +, E:O +, I:D +, J:D +, J:O
| + | :: = C:D +, E:O +, I:D +, J:D +, J:O |
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− | Among other things, one observes that the | + | Among other things, one observes that the relative terms 'l' and 's' do not commute, that is to say, 'ls' is not equal to 'sl'. |
− | relative terms 'l' and 's' do not commute, | |
− | that is to say, 'ls' is not equal to 'sl'. | |
− | </pre>
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| ===Commentary Note 8.5=== | | ===Commentary Note 8.5=== |