The Way of Logic

Description

⚘ Logic as a Liberal Art ☀ Christopher S. Morrissey

This book draws upon the latest research in semiotics in order to demonstrate the superiority of Aristotelian term logic over the symbolic logic currently dominant in the pedagogical paradigm of modern universities. In this book, traditional Aristotelian syllogistic is newly exhibited in light of semiotic distinctions that overcome its traditional limitations. This new presentation, which semiotically enhances Aristotelian term logic (ATL), reveals it to be a tool that is just as powerful as modern predicate logic (MPL). Even better, this semiotically enhanced Aristotelian term logic is much easier to understand than the dominant paradigm of symbolic logic. In light of postmodern intellectual consciousness, traditional Aristotelian term logic, newly enhanced from a semiotic standpoint as term functor logic (TFL), is thus shown to be far more consonant with human nature, and therefore more suited pedagogically to act as a beneficial art helping us to perfect the ability to think clearly. By showing the reader a self-reflective logic that is more in harmony with nature, this book removes the power of logic from the hands of a special elite, and it thereby gives logic back to all of humankind as a spiritual tool of wisdom for actually increasing human flourishing and true happiness. Although this book is written in English, many of its illustrations and examples and explanations draw upon the ancient Chinese wisdom of Laozi and Zhuangzi, and also a 21-page Chinese summary of the book's argument appears as an introduction to the book.

克里斯托弗·莫里西著的《逻辑之道(英文版)(精)/当代国际符号学名家文库》用详实的资料和严谨的论证，说明亚里士多德术语逻辑的内涵和特点。全书共八章，分别是“本质：术语的定义”，“存在：悖论方阵”，“同义律：直接推理”，“三段论：间接推理”，“逻辑谜题：省略三段论”，“推理规则以及推理规则图”等。

[DeepL transl.:] Christopher Morrissey's The Way of Logic (English Edition) (Fine)/The International Library of Contemporary Semiotics uses detailed information and rigorous argumentation to illustrate the connotations and characteristics of Aristotelian terminological logic. The book consists of eight chapters: "Essence: Definition of Terms", "Existence: Paradoxical Square", "Tautology: Direct Reasoning", "Trivium: Indirect Reasoning", and "Tractatus: Indirect Reasoning". Indirect Reasoning", "Logical Puzzles: Omitting Trigonometry", "Rules of Reasoning and Reasoning Rule Diagrams", etc.

Preface to the Series
总序
导读
Foreword
Preface
Introduction: Aristotelian Term Logic
Chapter 1
Essences--The Definition of Terms
Chapter 2
Existence--The Square of Opposition
Chapter 3
Equivalences--Immediate Inferences
Chapter 4
Syllogisms--Mediate Inference
Chapter 5
Puzzles--Enthymeines and Epichereimas
Chapter 6
Diagrams--Rules of Inference
Chapter 7
Proof--Quantification Theory
Chapter 8
Relations--The Method of Deduction
Conclusion
Appendix
References
Acknowledgments

Aristotelian logic from a semiotic perspective

cf. also:

Deely, John. 2018. Basics of semiotics. 8th, expanded edn. Nanjing: Nanjing Normal University Press.Google Scholar

Deely, John. 2018. Logic as a liberal art. Nanjing: Nanjing Normal University Press.Google Scholar

Morrissey, Christopher S. 2018. The way of logic. Nanjing: Nanjing Normal University Press.Google Scholar

“Term functor logic” (= “semiotically enhanced Aristotelian term logic”) seems to address the intrinsic constrictions of non-functor term logic.

In other words, it did need the said enhancement for its “traditional limitations” to be overcome. Otherwise, its claimed “superiority” would certainly appear to be a bit of a far-fetched claim.

« […] Si l’esprit humain n’avait brisé ces entraves, il n’aurait pu en physique dépasser Aristote, ni Ptolémée en astronomie. » (Pierre Duhem)

Truly, this applies to logic too, which thankfully does not stop with Aristotelian logic, the “traditional limitations” of which do not permit to logically approach fields (including Trinitarian theology) governed by the extension of the notion of predicate into that of relation. This extension has notably given rise to the important notion of “arity” for each predicate conceived as the number of logical “terms” a given problem may be concerned with:

- Unary (e.g., Gen 1:7, וַיְהִי-כֵן),

- Binary (epitomized by Aristotle’s one size fits all ‘kitchen logic’ derived from descriptive language),

- Ternary (-> applicable especially to Catholic theology),

- Quaternary (-> applicable to the modal treatment of Creation, Gen 1:1-31, especially its subsumed structure found in Gen 1:1-2: שָּׁמַיִם ,אָרֶץ ,תְהוֹם, מָּיִם),...,

- n -ary.

Aristotelian logic captures only one use of the predicate relative to a logical subject identified with the grammatical subject... Like the Megarian logicians predating Aristotle and elaborating propositional and modal logics very similar to what has been expanded over the past 100 years or so, the Scholastics themselves laid out the ground for extending term logic, and in that especially anticipated the pivotal Fregean developments (which I touch on in the expanded and reworked French version of my The Scholastics’ Neglected Heritage: Thought and Denotation Before the Post-Aristotelian Development of Logic).

The primary merits of such developments, in themselves completely unrelated to “the pedagogical paradigm of modern universities,” consist in implementing a more general notion of the predicate to the extent of making it handle relations involving any number of individuals/terms/arguments. But there is much more, in post-Aristotelian logic, than the sole extension of the predicate (which is especially what Frege contributed, something that cannot be justly deemed inferior to ATL).

Why do you say Gen. 1:7 ("… Et factum est ita. ") is an example of unary logic?

Let me use a topography analogy, starting from the notion of a fold, noting it F. We see an opposition of the same to the same demarcated by F itself (two opposite spaces denoted by S): S and ¬ S. This is a good way of logically accounting for symmetry. Here, we have two values of truth, true (= S) or false (= ¬ S).

The specificity of unary logic, in the framework of this fold analogy, appears at the level of the fold itself. Because, on F , we find the case where there is neither S nor ¬ S. This case does not have any truth value that can support an opposite truth value.

The truth value here is unique , not binary. No judgement can be made. For, once posited, there can be no judgment of existence on existence (an axiomatic limit has been posited, which cannot be undone and suffers no discussion, since it is the given of all other givens). A proposition p which is ruled by unary logic will be indisputable, like topographical F , without which S and ¬ S do not exist. It will be indisputable/unquestionable because its truth value does not entail being equal to either 0 or 1.

T(p) = unique

An example in the Gospel of training the disciples in the use of unary logic is found in this exhortation of Our Lord (Matt 5:37):

Sit autem sermo vester, est, est: no, no.

In other words: in imitation of the Creator speaking reality into existence (Gen 1:7, 9, 11, 15, 24, 30), you must strive toward unary logic in the use of your own word.

Our thinking is almost entirely conditioned by what F , once it is established, conditions the appearance of, namely S (yes/1) and ¬ S (no/0). So much so that our “yes” is almost entirely conditioned by our “no,” and vice versa. Whereas our “yes,” modelled on וַיְהִי-כֵן, must become unquestionable, and so likewise our “no,” in imitation of the unquestionable divine Word axiomatically establishing reality (Psalm 32(33):9):

.כִּי הוּא אָמַר וַיֶּהִי; הוּא-צִוָּה וַיַּעֲמֹד

Quoniam ipse dixit, et facta sunt; ipse mandavit et creata sunt.

p. 005 (PDF p. 43), quotes from the recent printing of Deely's Logic as a Liberal Art on logic as "validation" (cf. "trueing"), which seems related to the Duhem-Quine thesis that invalid arguments can be fixed into valid ones.