The relation of logic to semiotics

Description

Semetsky's obituary of John Deely mentions that his essay won the Mouton D’or Award for Best Essay in the Field in the Calendar Year.

Partially, not wholly.

Logic as ars cogitandi ; and logic as “underlying”certain aspects of reality, in relationship to the thinking structure of the human intellect mirroring, through the use of names (of essences) and denotations (involving semiotics), the ars dialecticae divinis (the logical art of divine creation freely brought about through the Logos). We see this original mirroring taking place prior to Adam’s fall in Gen 2:19-20.

As ars cogitandi , 1) LOGIC is concerned with the conditions under which a particular statement is true, i.e. the conditions of its truth-value (which can be articulated through a variety of operators). It is given to the human intellect, as an echo of the divine Logos bringing about His creation, with its source operation, that of negation. I can develop this important idea about the logical primacy of the operation of negation another time (when time allows), as it is particularly crucial to understanding the origin and the true extent of logic (which is a signature and secret kiss of the divine Word upon the human intellect, Canticum canticorum , 1:1):

Osculetur me osculo oris sui…

Furthermore, as I remember pointing out in one of our previous discussions, Alan (prompted, if I recall correctly, by your question regarding “an exception to the law of non-contradiction”), original sin is tantamount to a logical error, of the nature of a violation of the law of non-contradiction. In the context of that conversation, I had written you the following (which I just retrieved w/out being able to exactly date it), already about the nature of logic:

Put another way: logic is actually what is most divine-like in us. Hence, the clarity of logic (which is so obscure for most of us, even for logicians), far from detracting from and devaluating the mystery, does truly “lead to the latter.”

Perhaps some thinkers may be tempted to imagine “an exception to the law of non-contradiction” (as, in effect, did Adam and his wife in the Garden) because they imagine its application to be limited to situations governed exclusively by two-valued logic: e.g. descriptive logic, (p ∨ q)∧¬(p ∧ q), and computerprogramming, (0, 1). However, the principle can be immersed in larger and no less rigorous logical situations involving n -ary terms (e.g. ternary and quaternary), which reinforce its function as opposed to weakening it, as could be shown in Trinitarian (ternary) theo-logy or in some natural application of n -valued logic. Not the place here though.

To make it brief this evening, I will simply and concisely add that 2) SEMIOTICS is concerned with the application of the conditions under which a particular statement is true to signs. It is not strictly the same as logic, but expresses the latter insofar as it applies “logic to all symbols” (cf. Peirce 1902, from the link you provided).

As for 3) SEMIOSIS, it is, as Peirce himself puts it, a relation of “three subjects” entailing a sort of ontological semantics, as it applies to the application of the conditions under which a particular statementis true, not only to signs, but to “signs” in relation to (precisely) their “objects” and their “interpretants.”

Logica sit ex Logos.

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You seem to be using "logic" in two senses: the

1. ars cogitandi
2. underlying order of reality.

¿Is this correct:

1. semiotics ("the pure theory of signs") = ars cogitandi
2. semiosis ("action of a sign") = logic (sense #2)

felix die VII infra octavam SS. Cordis Iesu

None of the 1 to 4 quoted lines actually equates, quiddatively speaking, semiotics to logic. The close relatedness of the two disciplines does not entail their confusion. Likewise, mathematics and logic are closely related, but are not the same. Attempting to equate the two has always failed. And this failure has far-reaching epistemological implications.

Nor can we reduce logic to its methods (e.g. deduction) or its rules (e.g. inference, which is an application of the method of deduction to derive propositions from propositions).

We cannot any more reduce logic to its more recently discovered association, for example in mathematical logic, especially with set theory, field (higher algebraic geometry) theory, and recursion theory. While it does apply to these domains (especially with the advent of computer science), logic is not a theory.

Logic is involved in both the rules of ordinary reasoning and of mathematical proof procedures. But its object reduces to neither. Certainly, it “treats of signs” (according to line 3 of the Peirce quote on logic you provided). However, its true object (which also touches on its nature) lies with the study of the conditions of the validity of a consequence… not merely with signs. The signs themselves, by virtue of what they are, show the underlying invisible “laws of signs” (according to line 3 of the Peirce quote on logic you provided), which logic definitely studies at some applied level. But its use of signs is not the same as what it (logic) consists of. For example, the use of mathematical signs and methods in mathematical logic does not mean that the object of logic is itself mathematical. Nor is its use of signs in “treating of signs” the same as saying that that the object of logic is itself semiotic. That is why, rather than “semiotics being another name for logic,” Boole (after Leibniz) refers to it, correctly so to my view, as the science of the “laws of thought”. The art of thinking being based on the proper application of these laws, I would say that it (more than semiotics) simply is another expression/name for what logic properly is. Ars cogitandi logica est!!!

That this art involves signs is not and never was in question. Rather, the claim was that “semiotics is not equipped to study the nature of logic itself,” in the sense that its object is different—the object of logic determining its specific nature, and the object of semiotics, its own specific nature.

Leibniz and Frege, in particular, aimed at the defense of logic so conceived, i.e. as the union of pura cogitandi (which is where the inception of logic lies) et lingua (which is where semiosis gives symbolic form or expression to invisible laws of thought irreducible to the former).

Foundationally speaking, per its nature, logic deals with truth in formalized languages. Formalized languages will rely on semiotics, understood as “the quasi-necessary, or formal, doctrine of signs” (according to line 4 of the Peirce quote on logic you provided). But these languages and the “doctrine of signs” they rely on in the process of signifying, expressing, and communicating (among embodied intellects) are not the same thing as the internal regulation of right-thinking logic ultimately consists of.

In other words, logic, the science dealing with demonstrating the veracity of propositions, is not reducible to the semantically arranged symbols of its communicated propositions. In a certain way, logical truth is immanent and thus invisible; whereas semiosis involves the visibility of signs, in logic and beyond.

For example, you may semiotically express that a proposition is a tautology. But the core purpose of logic (using, for instance, truth tables) is to demonstrate it, typically by means of some form of reductio ad absurdum , which is strictly based on thought, not on sign.

Μέσα και μέσα από το Λόγος, +.

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"What semiotics is not equipped to do is study the nature of logic itself." Really? Peirce, Kemple, and Deely seem to think semiotics is another name for logic.

Peirce on "logic":

1. …logic treats of the reference of symbols in general to their objects.
2. …Logic is the study of the laws of signs so far as these denote things – those laws of signs which determine what things they denote and what they do not…
3. Logic treats of signs. A sign is a third.
4. Logic , in its general sense, is , as I believe I have shown, only another name for semiotic (σημειωτική), the quasi-necessary, or formal, doctrine of signs.

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