Changes

{| align="center" cellspacing="6" width="90%" <!--QUOTE-->

{| align="center" cellspacing="6" width="90%" <!--QUOTE-->

|

|

<p>I propose to assign to all logical terms, numbers;  to an absolute term, the number of individuals it denotes;  to a relative term, the average number of things so related to one individual.<p>

<p>I propose to assign to all logical terms, numbers;  to an absolute term, the number of individuals it denotes;  to a relative term, the average number of things so related to one individual. Thus in a universe of perfect men (''men''), the number of "tooth of" would be 32. The number of a relative with two correlates would be the average number of things so related to a pair of individuals;  and so on for relatives of higher numbers of correlates. I propose to denote the number of a logical term by enclosing the term in square brackets, thus, <math>[t].\!</math></p>

 

<p>Thus in a universe of perfect men (''men''), the number of "tooth of" would be 32.</p>

 

<p>The number of a relative with two correlates would be the average number of things so related to a pair of individuals;  and so on for relatives of higher numbers of correlates.</p>

 

<p>I propose to denote the number of a logical term by enclosing the term in square brackets, thus <math>[t].\!</math></p>

<p>(Peirce, CP 3.65).</p>

<p>(Peirce, CP 3.65).</p>

|}

|}

We may formalize the role of the "number of" function by assigning it a local habitation and a name ''v''&nbsp;:&nbsp;''S''&nbsp;&rarr;&nbsp;'''R''', where ''S'' is a suitable set of signs, called the ''syntactic domain'', that is ample enough to hold all of the terms that we might wish to number in a given discussion, and where '''R''' is the real number domain.

We may formalize the role of the "number of" function by assigning it a name and a type as <math>v : S \to \mathbb{R},</math> where <math>S\!</math> is a suitable set of signs, a so-called ''syntactic domain'', that is ample enough to hold all of the terms that we might wish to number in a given discussion, and where <math>\mathbb{R}</math> is the real number domain.

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, 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.