List: Two significant reference volumes have recently been received and I await a third. Two of these volumes significantly illuminate the putative illations between propositional logic and model theory. (I did not check if these books are on Ben’s list or not.)
Truth and Assertibility, Nik Weaver, 2015. This well-written book is technical in nature and probably difficult for most lay readers. CSP’s logic are probably, in my opinion, Third order or Higher logic, depending on the taxonomy of the sin-signs. This book clearly and crisply separates First order from Second order logic, materially beneficial to peruse. One might say that this book is a fine example of Phaneroscopy of words, not merely old wine in new bottles. From Peirce to Skolem, Geraldine Brady, 2000. This book traces the historical developments of several logics and there intimately interconnected roots. Many arguments trace the propositions directly from CSP’s and Mitchell's early papers to the papers by Lowenheim and Skolem upon which rests mathematical model theory and intuitionistic logic. . Very interestingly, this book was nurtured by a former student of Saunders Mac Lane, one of the founders of Mathematical Category Theory. It answers, in detail, the questions concerning the propositional semi-lattices in relation to modern notions of identity (and hence the meanings of identifying signs (such as sin-signs.) (Looking backward in time and epistemic understanding, I recall a two-hour conversation with Professor Mac Lane about the turn of the Century. It was a turning point in my understanding of the mathematical foundations of natural philosophy.) Frankly, many a chuckle was generated as these texts de-fogged the illations between CSP’s text and the formal logic of the chemical sciences as it emergesd from Sir Rutherford’s numbers. Cheers Jerry
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