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| | | |
| <p>The comma here after 'l' should not be considered as altering at all the meaning of 'l', but as only a subjacent sign, serving to alter the arrangement of the correlates. (Peirce, CP 3.73).</p> | | <p>The comma here after 'l' should not be considered as altering at all the meaning of 'l', but as only a subjacent sign, serving to alter the arrangement of the correlates. (Peirce, CP 3.73).</p> |
− | </blocquote> | + | </blockquote> |
| | | |
| Just to plant our feet on a more solid stage, let's apply this idea to the Othello example. | | Just to plant our feet on a more solid stage, let's apply this idea to the Othello example. |
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| And next we derive the following results: | | And next we derive the following results: |
| | | |
− | {| cellpadding="4" | + | :{| cellpadding="4" |
| | 'l', | | | 'l', |
| | = | | | = |
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| |} | | |} |
| | | |
− | <pre>
| |
| Now what are we to make of that? | | Now what are we to make of that? |
| | | |
− | If we operate in accordance with Peirce's example of `g`'o'h | + | If we operate in accordance with Peirce's example of `g`'o'h as the "giver of a horse to an owner of that horse", then we may assume that the associative law and the distributive law are by default in force, allowing us to derive this equation: |
− | as the "giver of a horse to an owner of that horse", then we | |
− | may assume that the associative law and the distributive law | |
− | are by default in force, allowing us to derive this equation: | |
| | | |
− | 'l','s'w = 'l','s'(B +, D +, E) | + | :{| cellpadding="4" |
| + | | 'l','s'w |
| + | | = |
| + | | 'l','s'(B +, D +, E) |
| + | |- |
| + | | |
| + | | = |
| + | | 'l','s'B +, 'l','s'D +, 'l','s'E |
| + | |} |
| | | |
− | = 'l','s'B +, 'l','s'D +, 'l','s'E
| + | Evidently what Peirce means by the associative principle, as it applies to this type of product, is that a product of elementary relatives having the form (R:S:T)(S:T)(T) is equal to R but that no other form of product yields a non-null result. Scanning the implied terms of the triple product tells us that only the following case is non-null: J = (J:J:D)(J:D)(D). It follows that: |
| | | |
− | Evidently what Peirce means by the associative principle,
| + | :{| cellpadding="4" |
− | as it applies to this type of product, is that a product
| + | | 'l','s'w |
− | of elementary relatives having the form (R:S:T)(S:T)(T)
| + | | = |
− | is equal to R but that no other form of product yields
| + | | "lover and servant of a woman" |
− | a non-null result. Scanning the implied terms of the
| + | |- |
− | triple product tells us that only the following case
| + | | |
− | is non-null: J = (J:J:D)(J:D)(D). It follows that:
| + | | = |
− | | + | | "lover that is a servant of a woman" |
− | 'l','s'w = "lover and servant of a woman" | + | |- |
− | | + | | |
− | = "lover that is a servant of a woman"
| + | | = |
− | | + | | "lover of a woman that is a servant of that woman" |
− | = "lover of a woman that is a servant of that woman"
| + | |- |
− | | + | | |
− | = J
| + | | = |
| + | | J |
| + | |} |
| | | |
| And so what Peirce says makes sense in this case. | | And so what Peirce says makes sense in this case. |
− | </pre>
| |
| | | |
| ===Commentary Note 10.6=== | | ===Commentary Note 10.6=== |