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Speaking of algebra, and having encountered already one example of an algebraic law, we might as well introduce the axioms of the ''primary algebra'', once again deriving their substance and their name from the works of [[Charles Sanders Peirce]] and [[George Spencer Brown]], respectively.

Speaking of algebra, and having encountered already one example of an algebraic law, we might as well introduce the axioms of the ''primary algebra'', once again deriving their substance and their name from the works of [[Charles Sanders Peirce]] and [[George Spencer Brown]], respectively.

<pre>

<br>

<p>[[Image:Logical_Graph_Figure_18.jpg|center]]</p>

|                                                          |

<p>[[Image:Logical_Graph_Figure_19.jpg|center]]</p>

<p><center><math>\mathrm{Figure~19}</math></center></p>

<br>

| Axiom J_1.      Insert <--- | ---> Delete                |

</pre>

 

<pre>

|                  \ /                 \ /                 |

| Axiom J_2.  Distribute <--- | ---> Collect                |

</pre>

The choice of axioms for any formal system is to some degree a matter of aesthetics, as it is commonly the case that many different selections of formal rules will serve as axioms to derive all the rest as theorems.  As it happens, the example of an algebraic law that we noticed first, ''a''( ) = ( ), as simple as it appears, proves to be provable as a theorem on the grounds of the foregoing axioms.

The choice of axioms for any formal system is to some degree a matter of aesthetics, as it is commonly the case that many different selections of formal rules will serve as axioms to derive all the rest as theorems.  As it happens, the example of an algebraic law that we noticed first, ''a''( ) = ( ), as simple as it appears, proves to be provable as a theorem on the grounds of the foregoing axioms.