Changes

===Commentary Note 11.24===

===Commentary Note 11.24===

And so we come to the end of the "number of" examples that we found on our agenda at this point in the text:

We come to the end of the "number of" examples that we found on our agenda at this point in the text:

'''NOF 4.5'''

'''NOF 4.5'''

|}

|}

There are problems with the printing of the text at this point.  Let us first recall the conventions that I am using in this transcription:  <math>\mathit{1}\!</math> for the italic 1 that signifies the 2-adic identity relation and <math>\mathfrak{1}</math> for the "antique figure one" that Peirce defines as <math>\mathit{1}_\infty = \text{something}.</math>

There are problems with the printing of the text at this point.  Let us first recall the conventions that I am using in this transcription, specifically, <math>\mathit{1}\!</math> for the italic 1 that signifies the 2-adic identity relation and <math>\mathfrak{1}</math> for the "antique figure one" that Peirce defines as <math>\mathit{1}_\infty = \text{something}.</math>

CP&nbsp;3 gives <math>[\mathit{1}] = \mathfrak{1},</math> which I cannot make any sense of.  CE&nbsp;2 gives the 1's in different styles of italics, but reading the equation as <math>[\mathit{1}] = 1,\!</math> makes the best sense if the "1" on the right hand side is read as the numeral "1" that denotes the natural number 1, and not as the absolute term "1" that denotes the universe of discourse.  Read this way, <math>[\mathit{1}]\!</math> is the average number of things related by the identity relation <math>\mathit{1}\!</math> to one individual, and so it makes sense that <math>[\mathit{1}] = 1 \in \mathbb{N},</math> where <math>\mathbb{N}</math> is the set of non-negative integers <math>\{ 0, 1, 2, \ldots \}.</math>

CP&nbsp;3 gives <math>[\mathit{1}] = \mathfrak{1},</math> which I cannot make any sense of.  CE&nbsp;2 gives the 1's in different styles of italics, but reading the equation as <math>[\mathit{1}] = 1,\!</math> makes the best sense if the "1" on the right hand side is read as the numeral "1" that denotes the natural number 1, and not as the absolute term "1" that denotes the universe of discourse.  Read this way, <math>[\mathit{1}]\!</math> is the average number of things related by the identity relation <math>\mathit{1}\!</math> to one individual, and so it makes sense that <math>[\mathit{1}] = 1 \in \mathbb{N},</math> where <math>\mathbb{N}</math> is the set of non-negative integers <math>\{ 0, 1, 2, \ldots \}.</math>

With respect to the 2-identity !1! in the syntactic domain ''S'' and the number 1 in the non-negative integers '''N'''&nbsp;&sub;&nbsp;'''R''', we have:

With respect to the relative term <math>^{\backprime\backprime} \mathit{1} ^{\prime\prime}</math> in the syntactic domain <math>S\!</math> and the number <math>1\!</math> in the non-negative integers <math>\mathbb{N} \subset \mathbb{R},</math> we have:

: ''v''!1! = [!1!] = 1.

| <math>v(\mathit{1}) ~=~ [\mathit{1}] ~=~ 1.</math>

And so the "number of" mapping ''v''&nbsp;:&nbsp;''S''&nbsp;&rarr;&nbsp;'''R''' has another one of the properties that would be required of an arrow ''S''&nbsp;&rarr;&nbsp;'''R'''.

And so the "number of" mapping <math>v : S \to \mathbb{R}</math> has another one of the properties that would be required of an arrow <math>S \to \mathbb{R}.</math>

The manner in which these arrows and qualified arrows help us to construct a suspension bridge that unifies logic, semiotics, statistics, stochastics, and information theory will be one of the main themes that I aim to elaborate throughout the rest of this inquiry.

The manner in which these arrows and qualified arrows help us to construct a suspension bridge that unifies logic, semiotics, statistics, stochastics, and information theory will be one of the main themes that I aim to elaborate throughout the rest of this inquiry.