12,080
edits
Changes
MyWikiBiz, Author Your Legacy — Friday September 27, 2024
Jump to navigationJump to searchDirectory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
Revision as of 15:58, 10 October 2007
, 15:58, 10 October 2007segmenting
|'Memoirs of the American Academy', Volume 9, pages 317-378, 26 January 1870,
|'Memoirs of the American Academy', Volume 9, pages 317-378, 26 January 1870,
|'Collected Papers' (CP 3.45-149), 'Chronological Edition' (CE 2, 359-429).
|'Collected Papers' (CP 3.45-149), 'Chronological Edition' (CE 2, 359-429).
</pre>
==Commentary Note 9.1==
<pre>
Let us backtrack a few years, and consider how Boole explained his
Let us backtrack a few years, and consider how Boole explained his
twin conceptions of "selective operations" and "selective symbols".
twin conceptions of "selective operations" and "selective symbols".
| Reprinted, Dover, New York, NY, 1958.
| Reprinted, Dover, New York, NY, 1958.
| Originally published, Macmillan, 1854.
| Originally published, Macmillan, 1854.
</pre>
==Commentary Note 9.2==
<pre>
In setting up his discussion of selective operations and
In setting up his discussion of selective operations and
their corresponding selective symbols, Boole writes this:
their corresponding selective symbols, Boole writes this:
| Reprinted, Dover, New York, NY, 1958.
| Reprinted, Dover, New York, NY, 1958.
| Originally published, Macmillan, 1854.
| Originally published, Macmillan, 1854.
</pre>
==Commentary Note 9.3==
<pre>
In algebra, an "idempotent element" x is one that obeys the
In algebra, an "idempotent element" x is one that obeys the
"idempotent law", that is, it satisfies the equation xx = x.
"idempotent law", that is, it satisfies the equation xx = x.
operations. It will also link up with the statements that Peirce makes
operations. It will also link up with the statements that Peirce makes
about his adicity-augmenting comma operation.
about his adicity-augmenting comma operation.
</pre>
==Commentary Note 9.4==
<pre>
Boole rationalized the properties of what we now dub "boolean multiplication",
Boole rationalized the properties of what we now dub "boolean multiplication",
roughly equivalent to logical conjunction, in terms of the laws that apply to
roughly equivalent to logical conjunction, in terms of the laws that apply to
representations that we discovered to provide us with such able
representations that we discovered to provide us with such able
assists to the intuition in so many of our previous adventures.
assists to the intuition in so many of our previous adventures.
</pre>
==Commentary Note 9.5==
<pre>
Peirce's comma operation, in its application to an absolute term,
Peirce's comma operation, in its application to an absolute term,
is tantamount to the representation of that term's denotation as
is tantamount to the representation of that term's denotation as
u o o o o o o o
u o o o o o o o
B C D E I J O
B C D E I J O
</pre>
==Commentary Note 9.6==
<pre>
Just to be doggedly persistent about it all, here is what
Just to be doggedly persistent about it all, here is what
ought to be a sufficient sample of products involving the
ought to be a sufficient sample of products involving the
| 0 0 0 0 0 0 0 | | 1 | | 0 |
| 0 0 0 0 0 0 0 | | 1 | | 0 |
| 0 0 0 0 0 0 1 | | 1 | | 1 |
| 0 0 0 0 0 0 1 | | 1 | | 1 |
</pre>
==Commentary Note 9.7==
<pre>
From this point forward we may think of idempotents, selectives,
From this point forward we may think of idempotents, selectives,
and zero-one diagonal matrices as being roughly equivalent notions.
and zero-one diagonal matrices as being roughly equivalent notions.
But now I must return to the anchorage of Peirce's text,
But now I must return to the anchorage of Peirce's text,
and hopefully get a chance to revisit this topic later.
and hopefully get a chance to revisit this topic later.
</pre>
==Selection 10==
<pre>
| The Signs for Multiplication (cont.)
| The Signs for Multiplication (cont.)
|
|
