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:

And so we come to the end of the "number of" examples

that we found on our agenda at this point in the text:

| It is to be observed that:

<p>It is to be observed that:</p>

: <p>[!1!] = `1`.</p>

Let us first recall the conventions that I am using in this transcription:

`1` for the "antique 1" that Peirce defines as !1!_oo = "something", and

!1! for the "bold 1" that signifies the ordinary 2-identity relation.

CP 3 gives [!1!] = `1`, which I cannot make any sense of.

<p>Boole was the first to show this connection between logic and probabilities.  He was restricted, however, to absolute terms. I do not remember having seen any extension of probability to relatives, except the ordinary theory of ''expectation''.</p>

CE 2 gives [!1!] = 1 , which makes sense on the reading

of "1" as denoting the natural number 1, and not as the

absolute term "1" that denotes the universe of discourse.

On this reading, [!1!] is the average number of things

related by the identity relation !1! to one individual,

the set or type of the natural numbers {0, 1, 2, ...}.

With respect to the 2-identity !1! in the syntactic domain S

<p>Our logical multiplication, then, satisfies the essential conditions of multiplication, has a unity, has a conception similar to that of admitted multiplications, and contains numerical multiplication as a case under it.</p>

and the number 1 in the non-negative integers N c R, we have:

'v'!1!  =  [!1!]  =  1.

<p>C.S. Peirce, CP 3.76</p>

And so the "number of" mapping 'v' : S -> R has another one

There appears to be a problem with the printing of the text at this point.  Let us first recall the conventions that I am using in this transcription:  `1` for the "antique 1" that Peirce defines as !1!_&infin; = "something", and !1! for the "bold 1" that signifies the ordinary 2-identity relation.

of the properties that would be required of an arrow S -> R.

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.

==Selection 12==

==Selection 12==