Changes

<p>The asterisk I use exclusively to refer to the last correlate of the last relative of the algebraic term.</p>

<p>The asterisk I use exclusively to refer to the last correlate of the last relative of the algebraic term.</p>

<p>Now, considering the order of multiplication to be: — a term, a correlate of it, a correlate of that correlate, etc. — there is no violation of the associative principle.  The only violations of it in this mode of notation are that in thus passing from relative to correlate, we skip about among the factors in an irregular manner, and that we cannot substitute in such an expression as `g`'o'h a single letter for 'o'h.</p>

<p>Now, considering the order of multiplication to be: &mdash; a term, a correlate of it, a correlate of that correlate, etc. &mdash; there is no violation of the associative principle.  The only violations of it in this mode of notation are that in thus passing from relative to correlate, we skip about among the factors in an irregular manner, and that we cannot substitute in such an expression as <math>\mathfrak{g}\mathit{o}\mathrm{h}</math> a single letter for <math>\mathit{o}\mathrm{h}.\!</math></p>

<p>I would suggest that such a notation may be found useful in treating other cases of non-associative multiplication.  By comparing this with what was said above [in CP 3.55] concerning functional multiplication, it appears that multiplication by a conjugative term is functional, and that the letter denoting such a term is a symbol of operation.  I am therefore using two alphabets, the Greek and Kennerly, where only one was necessary.  But it is convenient to use both. (Peirce, CP 3.71–72).</p>

<p>I would suggest that such a notation may be found useful in treating other cases of non-associative multiplication.  By comparing this with what was said above [in CP 3.55] concerning functional multiplication, it appears that multiplication by a conjugative term is functional, and that the letter denoting such a term is a symbol of operation.  I am therefore using two alphabets, the Greek and Kennerly, where only one was necessary.  But it is convenient to use both.</p>

 

<p>(Peirce, CP 3.71&ndash;72).</p>

|}

|}

It is clear from our last excerpt that Peirce is already on the verge of a graphical syntax for the logic of relatives.  Indeed, it seems likely that he had already reached this point in his own thinking.

It is clear from our last excerpt that Peirce is already on the verge of a graphical syntax for the logic of relatives.  Indeed, it seems likely that he had already reached this point in his own thinking.