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| ===Commentary Note 11.1=== | | ===Commentary Note 11.1=== |
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− | <pre>
| + | We have reached in our reading of Peirce's text a suitable place to pause — actually, it is more like to run as fast as we can along a parallel track — where I can due quietus make of a few IOU's that I've used to pave my way. |
− | We have reached in our reading of Peirce's text a suitable place to pause -- | |
− | actually, it is more like to run as fast as we can along a parallel track -- | |
− | where I can due quietus make of a few IOU's that I've used to pave my way. | |
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− | The more pressing debts that come to mind are concerned with the matter | + | The more pressing debts that come to mind are concerned with the matter of Peirce's "number of" function, that maps a term t into a number [t], and with my justification for calling a certain style of illustration by the name of the "hypergraph" picture of relational composition. As it happens, there is a thematic relation between these topics, and so I can make my way forward by addressing them together. |
− | of Peirce's "number of" function, that maps a term t into a number [t], | |
− | and with my justification for calling a certain style of illustration | |
− | by the name of the "hypergraph" picture of relational composition. | |
− | As it happens, there is a thematic relation between these topics, | |
− | and so I can make my way forward by addressing them together. | |
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− | At this point we have two good pictures of how to compute the | + | At this point we have two good pictures of how to compute the relational compositions of arbitrary 2-adic relations, namely, the bigraph and the matrix representations, each of which has its differential advantages in different types of situations. |
− | relational compositions of arbitrary 2-adic relations, namely, | |
− | the bigraph and the matrix representations, each of which has | |
− | its differential advantages in different types of situations. | |
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− | But we do not have a comparable picture of how to compute the | + | But we do not have a comparable picture of how to compute the richer variety of relational compositions that involve 3-adic or any higher adicity relations. As a matter of fact, we run into a non-trivial classification problem simply to enumerate the different types of compositions that arise in these cases. |
− | richer variety of relational compositions that involve 3-adic | |
− | or any higher adicity relations. As a matter of fact, we run | |
− | into a non-trivial classification problem simply to enumerate | |
− | the different types of compositions that arise in these cases. | |
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− | Therefore, let us inaugurate a systematic study of relational composition, | + | Therefore, let us inaugurate a systematic study of relational composition, general enough to explicate the "generative potency" of Peirce's 1870 LOR. |
− | general enough to explicate the "generative potency" of Peirce's 1870 LOR. | |
− | </pre>
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| ===Commentary Note 11.2=== | | ===Commentary Note 11.2=== |