Changes

If we analyze this in accord with the spreadsheet model of relational composition, the core of it is a particular way of composing a 3-adic ''giving'' relation <math>G \subseteq X \times Y \times Z</math> with a 2-adic ''training'' relation <math>T \subseteq Y \times Z</math> in such a way as to determine a certain 2-adic relation <math>(G \circ T) \subseteq X \times Z.</math>  Table&nbsp;13 schematizes the associated constraints on tuples.

If we analyze this in accord with the spreadsheet model of relational composition, the core of it is a particular way of composing a 3-adic ''giving'' relation <math>G \subseteq X \times Y \times Z</math> with a 2-adic ''training'' relation <math>T \subseteq Y \times Z</math> in such a way as to determine a certain 2-adic relation <math>(G \circ T) \subseteq X \times Z.</math>  Table&nbsp;13 schematizes the associated constraints on tuples.

{| align="center" cellspacing="6" width="90%"

| align="center" |

 

{| align="center" cellpadding="10" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center; width:60%"

Table 13.  Another Brand of Composition

|+ '''Table 13.  Another Brand of Composition'''

o---------o---------o---------o---------o

|-

|         #  !1!   |   !1!   |   !1!   |

| style="border-right:1px solid black; border-bottom:1px solid black; width:25%" | &nbsp;

o=========o=========o=========o=========o

| style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math>

|   G    #    X   |   Y   |   Z   |

| style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math>

o---------o---------o---------o---------o

| style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math>

|   T    #        |   Y   |   Z   |

|-

o---------o---------o---------o---------o

| style="border-right:1px solid black" | <math>G\!</math>

| G o T #    X   |         |   Z   |

| <math>X\!</math>

| <math>Y\!</math>

</pre>

| <math>Z\!</math>

|-

| style="border-right:1px solid black" | <math>T\!</math>

| &nbsp;

| <math>Y\!</math>

| <math>Z\!</math>

|-

| style="border-right:1px solid black" | <math>G \circ T</math>

| <math>X\!</math>

| &nbsp;

| <math>Z\!</math>

|}

|}

So we see that the notorious teridentity relation, which I have left equivocally denoted by the same symbol as the identity relation <math>\mathit{1},\!</math> is already implicit in Peirce's discussion at this point.

So we see that the notorious teridentity relation, which I have left equivocally denoted by the same symbol as the identity relation <math>\mathit{1},\!</math> is already implicit in Peirce's discussion at this point.