Changes

Now that is something that we can sink our teeth into, and trace the bigraph representation of the situation.  In order to do this, it will help to recall our first examination of the "tooth of" relation, and to adjust the picture that we sketched of it on that occasion.

Now that is something that we can sink our teeth into, and trace the bigraph representation of the situation.  In order to do this, it will help to recall our first examination of the "tooth of" relation, and to adjust the picture that we sketched of it on that occasion.

Transcribing Peirce's example, we may let m = "man" and ''t'' = "tooth of ---".  Then ''v''(''t'') = [''t''] = [''tm'']/[''m''], that is to say, in a universe of perfect human dentition, the number of the relative term "tooth of ---" is equal to the number of teeth of humans divided by the number of humans, that is, 32.

Transcribing Peirce's example:

 

| <math>\mathrm{m} = \text{man}\!</math>

| width="10%" | &nbsp;

| and

| <math>\mathit{t} = \text{tooth of}\,\underline{~~~~}.</math>

|-

|-

| Then

| <math>v(\mathit{t}) ~=~ [\mathit{t}] ~=~ \frac{[\mathit{t}\mathrm{m}]}{[\mathrm{m}]}.\!</math>

 

That is, in a universe of perfect human dentition, the number of the relative term <math>\text{tooth of}\,\underline{~~~~}</math> is equal to the number of teeth of humans divided by the number of humans, that is, <math>32.\!</math>

The 2-adic relative term ''t'' determines a 2-adic relation ''T''&nbsp;&sube;&nbsp;''U''&nbsp;&times;&nbsp;''V'', where U and V are two universes of discourse, possibly the same one, that hold among other things all of the teeth and all of the people that happen to be under discussion, respectively.  To make the case as simple as we can and still cover the point, let's say that there are just four people in our initial universe of discourse, and that just two of them are French.  The bigraphic composition below shows all of the pertinent facts of the case.

The 2-adic relative term ''t'' determines a 2-adic relation ''T''&nbsp;&sube;&nbsp;''U''&nbsp;&times;&nbsp;''V'', where U and V are two universes of discourse, possibly the same one, that hold among other things all of the teeth and all of the people that happen to be under discussion, respectively.  To make the case as simple as we can and still cover the point, let's say that there are just four people in our initial universe of discourse, and that just two of them are French.  The bigraphic composition below shows all of the pertinent facts of the case.