Changes

<p>Thus all the absolute conditions of multiplication are satisfied.</p>

<p>Thus all the absolute conditions of multiplication are satisfied.</p>

<p>The term "identical with ---" is a unity for this multiplication.  That is to say, if we denote "identical with ---" by !1! we have:</p>

<p>The term "identical with&nbsp;&mdash;&mdash;" is a unity for this multiplication.  That is to say, if we denote "identical with&nbsp;&mdash;&mdash;" by <math>\mathit{1}\!</math> we have:</p>

<p>whatever relative term <math>x\!</math> may be.  For what is a lover of something identical with anything, is the same as a lover of that thing.</p>

<p>'x'!1!  =  'x',</p>

<p>(Peirce, CP 3.68).</p>

 

<p>whatever relative term 'x' may be.  For what is a lover of something identical with anything, is the same as a lover of that thing.  (Peirce, CP 3.68).</p>

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Peirce in 1870 is five years down the road from the Peirce of 1865–1866 who lectured extensively on the role of sign relations in the logic of scientific inquiry, articulating their involvement in the three types of inference, and inventing the concept of "information" to explain what it is that signs convey in the process.  By this time, then, the semiotic or sign relational approach to logic is so implicit in his way of working that he does not always take the trouble to point out its distinctive features at each and every turn.  So let's take a moment to draw out a few of these characters.

Peirce in 1870 is five years down the road from the Peirce of 1865&ndash;1866 who lectured extensively on the role of sign relations in the logic of scientific inquiry, articulating their involvement in the three types of inference, and inventing the concept of "information" to explain what it is that signs convey in the process.  By this time, then, the semiotic or sign relational approach to logic is so implicit in his way of working that he does not always take the trouble to point out its distinctive features at each and every turn.  So let's take a moment to draw out a few of these characters.

[[Sign relation]]s, like any non-trivial brand of [[3-adic relation]]s, can become overwhelming to think about once the cardinality of the object, sign, and interpretant domains or the complexity of the relation itself ascends beyond the simplest examples.  Furthermore, most of the strategies that we would normally use to control the complexity, like neglecting one of the domains, in effect, projecting the 3-adic sign relation onto one of its 2-adic faces, or focusing on a single ordered triple of the form ‹&nbsp;''o'',&nbsp;''s'',&nbsp;''i''&nbsp;› at a time, can result in our receiving a distorted impression of the sign relation's true nature and structure.

[[Sign relation]]s, like any non-trivial brand of [[3-adic relation]]s, can become overwhelming to think about once the cardinality of the object, sign, and interpretant domains or the complexity of the relation itself ascends beyond the simplest examples.  Furthermore, most of the strategies that we would normally use to control the complexity, like neglecting one of the domains, in effect, projecting the 3-adic sign relation onto one of its 2-adic faces, or focusing on a single ordered triple of the form ‹&nbsp;''o'',&nbsp;''s'',&nbsp;''i''&nbsp;› at a time, can result in our receiving a distorted impression of the sign relation's true nature and structure.