Cf: Charles Sanders Peirce, George Spencer Brown, and Me • 3 https://inquiryintoinquiry.com/2017/07/31/charles-sanders-peirce-george-spencer-brown-and-me-3/
All, Here's the next installment in my bio-graphical intro, with all the links repaired and the graphics upgraded. Re: Laws of Form https://groups.io/g/lawsofform/topic/c_s_peirce_spencer_brown/79916661 There are a number of “difficulties at the beginning” that arise here. I’ve been trying to get to the point where I can respond to James Bowery’s initial comments https://inquiryintoinquiry.com/2016/11/30/time-topology-differential-logic-6/#comment-33608 and also to questions about the relation between Spencer Brown’s imaginary logical values and the development of differential logic. The larger issue I see at this point has to do with the relationship between the “algebra” and the “arithmetic” of logical graphs. Peirce came right up to the threshold of discovering that relationship several times in his later work on existential graphs but never quite pushed it through to full realization. It was left to Spencer Brown to bring it to light. The relationship between Primary Arithmetic and Primary Algebra is discussed in the following article. Logical Graphs ( https://oeis.org/wiki/Logical_Graphs ) • Primary Arithmetic as Semiotic System https://oeis.org/wiki/Logical_Graphs#Primary_arithmetic_as_semiotic_system • Primary Algebra as Pattern Calculus https://oeis.org/wiki/Logical_Graphs#Primary_algebra_as_pattern_calculus The other issue has to do with my using a different J₁ than Spencer Brown. I believe I even called it J₁′ in the early days but eventually lost the prime as time went by. As far as I can remember, it initially had to do with negotiating between the systems of C.S. Peirce and Spencer Brown but I think I stuck with the variant because it sorts the types of change — modifying structure and moving variables — into different bins. Image Files =========== This Blog I₁ : https://inquiryintoinquiry.files.wordpress.com/2020/09/axiom-i1.jpg I₂ : https://inquiryintoinquiry.files.wordpress.com/2020/09/axiom-i2.jpg J₁ : https://inquiryintoinquiry.files.wordpress.com/2020/09/axiom-j1.jpg J₂ : https://inquiryintoinquiry.files.wordpress.com/2020/09/axiom-j2.jpg Oeis Wiki I₁ : https://oeis.org/wiki/File:Initial_I1.jpg I₂ : https://oeis.org/wiki/File:Initial_I2.jpg J₁ : https://oeis.org/wiki/File:Initial_J1.jpg J₂ : https://oeis.org/wiki/File:Initial_J2.jpg See also the discussions at the following locations. Logical Graphs • Formal Development https://inquiryintoinquiry.com/2008/09/19/logical-graphs-2/ Propositional Equation Reasoning Systems https://oeis.org/wiki/Propositional_Equation_Reasoning_Systems Regards, Jon
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