“Is logic totally useless?"

When I started, in the seventies to develop my first criticism in the scope of Formal Logic (FL) as a tool for philosophical analysis, I was not aware of Nietzsche's texts on logic (I would know them only in the nineties). But, curiously, I had already written texts where I said that my philosophy of logic was basically "Nietzschean" (a matter of instinct). Remember also that in the subtitle of The condemned Logic, A Lógica condenada (1987), a Nietzschean concept such as “extemporaneous” (unzeitgamässige) was already used. In fact, my criticisms formulated, in a more clearly and analytical way, the main idea of Nietzsche on logic: the basic and primitive disagreement between language (and the logical forms) and the world.

The most striking feature of introductions to logic is their monotony. The theory of elementary logic is presented as a consolidated doctrine, without any huge criticism against any aspect of its standard exposition. I do not mean (which would be factually false) that classical logic is not contested, expanded or waned, because that is precisely what makes “non-classical” logics. The thing is that all disputes, expansions or reductions make the “classical logic” inevitably a reference point (already in the proper name of “non-classic”). The classical logic should be well established so that all these “deviations” could be formulated.

All introductions to logic follow exactly the same pattern: initial chapters on the concept of “logic” and “argument”, clarification on “essential distinctions” (truth and validity, use and reference, etc), some notions of set theory, some information about the official history of logic, some presentation on the calculus of sentences and truth tables, the calculus of first-order predicates, one chapter on deduction and final chapters on the system of identity, meta-logic, and maybe something about non-classical systems or applications of logic in science or in common language. There are many exercises, sometimes with solutions (as the four Gospels, all different but all telling the same story).

I cannot study the “elementary logic” without continuously facing serious drawbacks in conception, notions that seem questionable, and wordings that I cannot agree with. I simply cannot advance beyond the first two or three pages. To explain this better, I list below some of the things that routinely are said about this subject, and whose questioning has constituted the structure of my philosophy of logic:

1. The idea that logic is quite general, not referring to any particular object; all objects, whatever their context or type of matter, would be affected by the laws of logic, because these are completely general and with the highest degree of formality. This becomes clear every time the books point out that the contents of the reasoning do not matter, that subjects can be any one, that a reasoning belonging to any theme should be submitted to the same laws of logic. It means that logic, in general, refers to an “object whatever”.

2. The idea that, in the application of logic to ordinary reasoning, it shall be considered that the logical instrument certainly has limits, but making some efforts to build paraphrases, the ordinary reasoning will “fit” more or less naturally within the forms of logic, and that its validity can be assessed by its methods. It is now a commonplace in which the logicians recognize the many analytical limitations of the formal apparatus provided by FL; there is no book that does not check for problems, disadvantages and limitations of logical analysis. I think, however, that they do not to correctly size the scope of these problems, and their importance to the relations of logic with philosophical analysis. (The problem, then, is not the observation of data, but to reflect on them).

3. The idea that all lexical connections (lawyer / professional, closed / open, single / married, etc.) should be outside the scope of the logic precisely because they are not generally or strictly “formal”, but connections based on “content” considerations. For FL, it is absolutely obvious that the inference passage of, say, “x is green” to “x is colored”, or “x is a lawyer” to “x has a profession”, etc, are not logical passages, because they are not formal, but dependent on the meaning of the terms used.

4. The idea that the elementary logic has a part purely sentential which operates with indecomposable units, and a quantificational part which operates an “internal analysis of sentences”. Whether one starts the exposition by the sentential part and then add the quantificational part, or present the first-order logic with the sentential part as a sub-part, in any case, it deals about two sectors of logic that must be exposed like structures completely stable and objective. (I speak here only of classical logic, not of advanced projects as “universal logic”. Anyway, the sentential / quantificational linkage is so strong that affects even many “divergent” logic: we have a modal sentential logic and a modal quantificational logic, sentential paraconsistent logic and quantificational paraconsistent logic, etc).

5. The idea that logic was created by Aristotle, took a “nap” for several centuries and was rediscovered by Frege in the nineteenth century, with nothing important in the centuries in between. (With remarkable expository curiosity, and proof of the mentioned monotony, I know almost no official history of the logic that does not refer to the famous Kant's statement that logic was born already finished in the Aristotle’s mind, as a tremendous misjudgment. I never saw, anywhere, no effort in trying to understand the meaning of the phrase of the great philosopher).

I see in this monotony one of the characteristic features of the professionalized academic philosophizing of the twentieth century. One philosophizes according to slogans of the community through standard expositions, without any reference to a critical view able to open other ways of understanding. The community of philosophers (and of logicians) took the place of authority and censorship, instead of the state or church, as still in the nineteenth century. When the monotonous uniformity is internalized by the community, the mechanisms of external censorship become unnecessary and create a false sense of intellectual freedom.

I think there is something true in the idea that FL moved away from philosophy, even if I do not agree in the arguments and observations of traditionalist philosophers when they talk about this subject. My point of departure, in my own formulating of questions of logic, is the search for a logical theory - semi-formal or informal - that is of primary interest to the philosopher, as conceived in PHILOSOPHY, that is, for anyone interested in thinking and reflecting along a continuum of possibilities, where the logical analysis is one of the poles. If what matters is the logical-analytical study of reasoning as those the philosopher makes, the central concern of the logical theory could not be the “full generality” or the “formality of the highest level”, but the generality and formality that are appropriate to the study of those pieces of reasoning.

Taking all this into consideration, my presentation of logic could be summarized in the following five items:

1. Against the over-generality.

I believe that the statement 1 is false. In the choice of “logical terms” (connectives, quantifiers, etc.), there is, at the same time, a choice of one type of object in which logic is concerned. The specific type of object that FL studies is, for example, an object not affected by temporality, causality and by the real processes, a type of object fully sensitive to operations such as commutation, contraposition, etc. But not all objects in the world are of this type. Why that “object whatever”, independently of the different thematic areas, should be, for example, a timeless object? I would say, however, that if temporality lacks, this proves that the logic is not dealing with the “object whatever” whatever, but with a very peculiar type of object (almost all the objects in the world are affected by temporality).

2. Against adequacy.

I believe that the counterexamples and difficulties that logicians often find in the implementation of FL schemes to ordinary reasoning and philosophical discourse have greater importance than the logicians are willing to accept, in its power to undermine the usual presentation of logic (if this pretend to be analytical and with philosophical interest). The paraphrases “reduce’", sometimes brutally, the variety of forms of objects to pre-determined logical schemes. The devices which logicians make use to obtain the “fit” and the relative arbitrariness of paraphrases, full of crucial decisions about the most “successful” translation, show that FL is much more inadequate than the usual belief, and that should be drawn from the consequences of it. It is therefore not only insisting on the inadequacies, already well visualized, nor analyzing single issues of inadequacy, but situating the criticism based on these observations in a wide and radical range of reflection.

3. Against the exclusion of lexical forms.

If what first matters is the ordinary reasoning as philosophers do, nothing more typical than the connections between lexical pieces of language in a broad sense (not just the “analytical” connections studied in literature, but connections that are at the interface between dictionaries and encyclopedias, lexical connections of various types). If FL targets a type of “generality” leaving entirely aside by principle, as is usually done, the lexical connections as “materials”, it will have set aside one of the most interesting features of the ordinary reasoning. The introduction of formal studies on lexical connections may have to change substantially the entire presentation of logic, diluting the very concept of “classical logic” as understood today. It is false that the lexical connections are purely material: linguists and my collaborator Olavo L.D.S. Filho in the written work of joint authorship Lexical Inferences and interpretation of networks of predicates (Inferências Lexicais e Interpretação de redes de predicados), showed that lexical connections may be regarded as formal in the light of further analysis to those offered by FL: analysis working with networks of lexical pieces, searching for formalizable structures. This point is the strict counterpart of item 1: since usual logical forms of FL are not as “formal” and “general” as they claim, the lexical connections are not as material and “extra-logical” as commonly assumed.

4. Against the fixed referential of "classical logic"

Therefore, the construction of logical theory, if our primary concern is philosophical, could start from the lexical connections. The connection of at least two predicates could be considered as the act of inauguration of logic: the inter-sentential connections and quantification may come later. If the connection between “x is green” and “x is colored” is formally established, the connections between these two sentences (“x is green and x is colored”, “x is green or x is colored”, “if x is green, then x is colored”, etc.) and generalizations about their content ( “For all x, if x is green, then x is colored”, “There is an x such that it is green and colored”, etc.) may be derived from those primitive predicate connections. On the other hand, if this connection does not exist, the sentences and quantifications will not occur. The idea is that the usual logical connections (sentential and quantificational) can be considered as derivatives if we suspend the ban to consider lexical connections as material or non-formal.

5. Against the official history of logic.

Last but not least: throughout the history of philosophy, there were many philosophers who had intuitions about the interaction between form and content within the construction of the logical theory; they presented criticisms to the so-called “full generality” of logical structures, with considerations about how the contents could be formally studied. Hegel, Dewey and Husserl are, for example, three modern philosophers, who constructed logical theories in this direction and were completely excluded from the official history of logic. Many other philosophers (notably, Descartes, Locke and Kant), during the “dark period” which is usually considered (monotonously and without criticism) as one in which “there was nothing valuable in logical terms”, had critical ideas against the unilateral formality of the usual logic (in its scholastic or modern Aristotelian form) and constructive insights about other ways to present logic. Obviously, this suggests a history of logic quite different from what we have today.

In my book from 87, The Condemned Logic, A Lógica Condenada, developments of all these topics can be found. Later, I continued presenting my ideas in other geographical areas of discussion. These ideas were presented in France and in Mexico with receptivity and interest. The most important texts on these issues, in addition to the recent articles are “Is Logic really topically neutral and completely general?” (“Es realmente la lógica tópicamente neutra y completamente general?”) and“Predicative networks and lexical inferences (An alternative to formal logic in the analysis of natural languages” (“Redes predicativas e inferências lexicais (Uma alternativa à lógica formal na análise de línguas naturais)”, are the books 10 and 13 also mentioned in COMPLETE WORKS.

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