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How and Why We Study Logic

April 27, 2023April 27, 2023 Brian KempleLeave a comment

Excerpted from the lectures given to the Lyceum Institute Trivium: Art of Logic Course.

“What more can be said about logic?” I am acutely aware, as I pen these words that I pen them not to be read (even if someone other than myself might and does indeed read them), but to be spoken; to be given in a lecture, that is—a lecture for the Lyceum Institute, a lecture belonging to a course, and a course belonging to a holistic study of all three arts constituting the Trivium. Though logic may be studied on its own, both as an art and as science, its greatest fruit comes when studied integrally with the other arts of the Trivium. This sentiment—or rather, the mixed sentiments of hope, humility, and no small amount of trepidation, since I am myself well aware of my woeful inadequacy as a teacher, especially of logic—this sentiment finds itself grounded by the well-wrought intellectual insights of far wiser men: men such as R.E. Houser, John Deely, and John Poinsot, all of whom I consider my own teachers in this most difficult of subjects. My failings, however, are not a reflection of their abilities: for I have learned logic through their printed works, rather than in-person instruction, and thus have not benefitted from direct correction.

The purpose of these lectures, indeed, is not to say anything new or novel about logic at all. That does not mean there is nothing new to be said about logic, only that I am not here intending to say it. Rather, these lectures aim—as is more broadly the goal of this course as a whole and of our first course of study of the Trivium in the Lyceum Institute—these lectures aim at displaying and explicating the art for a living audience. They form part of a multi-party dialogue: between myself, as the instructor, and you, as the audience; between us, as a class, and the texts, which we read; and between the shared knowledge we gain and the knowledge we yet seek. Between instructor and audience, there is formed a whole; between that whole, the class, and the texts, there is formed a second whole, that shared knowledge. But knowledge, always and invariably, prompts new questions, an inquiry beyond itself. These lectures are merely my own contribution… and rather a minor contribution, at that, in the grand scheme of this dialogue.

Our world—by which I mean not merely the physical environment of earth (though inclusive of it) but rather, more primarily, the specifically human environment of linguistically-perfused culture—suffers a problem of meaning. I have addressed this problem in many other places. We may redress this problem of meaning, however, only through language, and only if we conceive of language in the right way: not merely as an abstract system of arbitrarily-stipulated symbolic communications, ordered principally toward pragmatic ends and for the sake of manipulating that world to our ends (such manipulative bearing being one of, if not the, principal causes of our meaning problem), but rather as the way in which the true meaning of things comes to light in the first place. For developing a facility with language so-conceived, we must study all three arts of the Trivium. In the Art of Logic, in particular, we attend specifically to the illative relation, whereby we discover how language leads thinking through inference to truths not immediately evident—to truths obscured by malfeasant rhetoric or the will-to-power, to truths hidden by those who wish only to bend the world to their wills, instead of standing themselves humbly open to the real.

Sign up for the Lyceum Institute and join us in the study of Logic this Spring! Lectures begin 1 May 2023 and discussions on 8 May 2023. All members are welcome to take the Art of Logic course, at every level of enrollment.

Liberal Arts/Quotations/Tradition

John Deely on the “Practical Value” of Logic

April 20, 2023April 20, 2023 Brian KempleLeave a comment

Peirce rightly speaks of the practice of boasting of the utility of this or that science as a “nauseating custom” (1898a, alt. ver. : CP 1.667). This is because the practice in question almost invariably is indulged in for purposes quite unrelated to the true character of the science in question or to the advance of scientific inquiry as such. Nonetheless, there is a legitimate general sense in which all the sciences, logic and ethics included, may be said to have a practical value, inasmuch as, in the light of understanding gained from any given inquiry, application of that understanding may be made to meliorate some state of affairs or other. It is essential, however, to notice that this general “practical value” is a consequence of theoretical understanding, and not something separate from or independent of a properly scientific—that is to say, thematic and systematized—study of, for example, the symbolic structures of thought, on the one hand (in the case of logic) and action, its motives and consequences, on the other (in the case of ethics). No doubt our practice of discourse will be influenced by a study of logic, and, if the study is sound, improved. But to aim at this improvement directly and from the outset is a fundamental blunder. It is no wonder that many courses in “critical thinking” amount to little more than an elaborate spelling out of the steps to go through m choosing the best refrigerator to buy for your home, or a hopelessly superficial skill in identifying and labeling “fallacies”. For this reason, one of the most notable students of logic (Joseph 1916: 10) went so far as to recommend that we abandon speaking of logic as an art, in order to make plain what is in fact the case: that any properly human practical value of logic is in consequence of its theoretical study, and not an end that can be attained directly. In this sense, any scientific study has a “practical value”.

But, while any scientific study has practical value in an indirect sense, the practical value of logic, even if indirect, goes beyond that of the other special sciences, and precisely for this reason logic is commonly viewed not just as a “general education” requirement, but as a “core requirement”—that is to say, as one of the foundations of liberal arts education even from the days when science in our modern sense had not yet been established or envisioned as part of the curriculum of schooling at any level. In other words, uniquely in the case of the science of logic, we are quite justified in speaking of its utility or “practical value” for reasons that are related both to the nature of logic as a science and to the advance of logic as a scientific inquiry.

The exceptional extent of logic’s indirect practicality becomes apparent in Joseph’s spelling out (ibid: 11) of the threefold rationale for the practical value of logic. Of the three elements he identifies in this rationale, the first logic shares with any science, as we have taken note. The remaining two, however, distinguish logic’s foundational character as permeating the humanities and the sciences alike—that is to say, the whole of our discourse.

The first practical value of logic in general education, the one it shares with any exact science, is that it demands a careful, systematic and precise treatment of its own subject matter, which tends to produce a habit resulting from an appreciative understanding of the need and importance of carefulness in the study of any subject.

The second practical value of logic, however, lies in an effect which the study of a special science like chemistry, physics, or biology, is not equally calculated to produce. This effect is a better realization of what general forms are latent in the language we habitually use (especially where it is a question of our natural language, hut also in specialized and “artificial” circumstances of discourses which… inevitably interface with and influence the prejacent natural language, ensuring its continual evolution, in fact, and expansion into new scientific fields), through becoming familiar with the task of examining our reasonings precisely to see whether their form is conclusive in itself in its contrast with the factual content.

The third practical value of logic is likewise commensurate with our discourse in its totality, whether everyday or scientific, theoretically or practically oriented: logic requires us to deal directly with what knowing is, insofar as there are standards implicit in thought itself by which it is possible to separate knowledge from opinion and also to distinguish levels or grades of both, thereby making us more alive and sensitive to, as well as more careful about, shortcomings in our own opinions and those others try to persuade us of.

I think we need not go as far as Joseph recommended in abandoning all talk of logic as an art in order to appreciate the difference between logica docens and logica utens and to appreciate the essential dependency of the latter on the former as far as it concerns an educational context beyond the exercise of practical reason. It is true that the theoretical study of logic not only can be but, in recent years, has been entirely divorced from the context of actual discourse in common experience. But this need not he the case (nor is it wholly new), and may even be regarded, in many instances, as a pedagogical aberration. Nor does the late modern artificialization of the context of logical study change the fact that there are indirect consequences of logical study for everyday discourse when the foundations of such study are properly established (a project toward which this book is mainly aimed). These consequences are nonetheless real, and become direct from the side of the theoretical understanding once acquired. There is nothing wrong with pursuing the theoretical study in such a way as to facilitate that indirect consequence, that overflow, as it were, into practical reasonings, and much to recommend such a pursuit, however much late modernity chose to eschew it. Indeed, what has always distinguished logic as a liberal art from logic developed as a science in its own right, without any regard for its connections with daily discourse, is just this way of pursuing properly logical study.
John Deely 1985–2015: Logic as a Liberal Art, 12–15 (not to be confused with Houser’s Logic as a Liberal Art).

Sign up for the Lyceum Institute before May 8 and you can join us in our study of Logic! Open to all members. Enroll here.

Liberal Arts/News and Announcements

Trivium: The Art of Logic 2023

April 19, 2023April 20, 2023 Lyceum AssistantLeave a comment

On 1 May 2023, we will begin our second Trivium course of the year: The Art of Logic. Our first discussion session will take place on 8 May 2023 at 6:00pm ET. This course is open to all enrolled Lyceum Institute members; having taken Grammar is not a prerequisite. If you would like to sign-up and take this course, enroll here. You can find out more about our approach to studying logic here.

In brief, however: is there right reasoning concerning reasoning itself? Can we reason rightly about other things if we are misled as to the nature of reasoning itself? Of course we can; but incidentally, rather than properly, and in a manner not precisely under our own control. Without having successfully undergone training in logic, we are much more likely to go awry in the formation of our beliefs—holding things untrue or unfitting to reason, that is—than otherwise. Thus, even though it is quite difficult, Thomas Aquinas rightly says that we ought to begin our learning from logic:

And for this reason it is necessary in learning to begin from logic, not because it is easier than the other sciences—indeed, it has the greatest difficulty, since it concerns second intentions—but because the other sciences depend upon it, insofar as it teaches the mode of proceeding in all the other sciences.
c.1257-59: In de trin., q.6, a.1, p.2, ad.3: “Et hac ratione oportet in addiscendo a logica incipere, non quia ipsa sit facilior ceteris scientiis, habet enim maximam difficultatem, cum sit de secundo intellectis, sed quia alia scientiae ab ipsa dependent, in quantum ipsa docet modum procedendi in omnibus scientiis.”

In our course, we will concern ourselves not only with learning to analyze propositions and syllogisms of both categorical and hypothetical structure, to parse prose writing for its logical structure (and errors therein), and to illuminate the illative relation which ties together all our reasoning, but also situate logic both historically and as it fits within the broader tradition of the Trivium.

Again, this seminar is open to all Lyceum Institute members, at every level of enrollment. Our primary (required) textbook is R.E. Houser’s Logic as a Liberal Art.

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Philosophy/Quotations/Tradition

I.M. Bochenski on the Concept of Formal Logic

April 6, 2023April 6, 2023 Lyceum AssistantLeave a comment

Preliminary definition of the subject matter of the history of logic is hard to come by. For apart from ‘philosophy’ there is perhaps no name of a branch of knowledge that has been given so many meanings as ‘logic’. Sometimes the whole history of philosophy, and even knowledge in general, has been thus named, from metaphysics on the one hand, cf. Hegel, to aesthetics (‘logic of beauty’) on the other, with psychology, epistemology, mathematics etc. in between. With such a wide choice it is quite impossible to include in a history of logical problems all that has been termed ‘logic’ in the course of western thought. To do so would practically involve writing a general history of philosophy.

But it does not follow that the use of the name ‘logic’ must be quite arbitrary, for history provides several clues to guide a choice between its many meanings. This choice can be arrived at by the following stages.

1. First let us discard whatever most authors either expressly ascribe to some other discipline, or call ‘logic’ with the addition of an adjective, as for example epistemology, transcendental logic, ontology etc.

2. When we examine what remains, we find that there is one thinker who so distinctly marked out the basic problems of this residual domain that all later western inquirers trace their descent from him: Aristotle. Admittedly, in the course of centuries very many of these inquirers – among them even his principal pupil and successor Theophrastus – have altered Aristotelian positions and replaced them with others. But the essential problematic of their work was, so far as we know, in constant dependence in one way or another on that of Aristotle’s Organon. Consequently we shall denote as ‘logic’ primarily those problems which have developed from that problematic.

3. When we come to the post-Aristotelian history of logic, we can easily see that one part of the Organon has exercised the most decisive influence, namely the Prior Analytics. At some periods other parts too, such as the Topics or the Posterior Analytics, have indeed been keenly investigated and developed. But it is generally true of all periods marked by an active interest in the Organon that the problems mainly discussed are of the kind already to hand in the Prior Analytics. So the third step brings us to the point of describing as ‘logic’ in the stricture sense that kind of problematic presented in the Prior Analytics.

4. The Prior Analytics treats of the so-called syllogism, this being defined as a λογος in which if something is posited, something else necessarily follows. Moreover such λογοι are there treated as formulas which exhibit variables in place of words with constant meaning; an example is ‘B belongs to all A‘. The problem evidently, though not explicitly, presented by Aristotle in this epoch-making work, could be formulated as follows. What formulas of the prescribed type, when their variables are replaced by constants, yield conditional statements such that when the antecedent is accepted, the consequent must be admitted? Such formulas are called ‘logical sentences’. We shall accordingly treat sentences of this kind as a principal subject of logic.

5. Some logicians have limited themselves to the discovery, examination, and systematic ordering of logical theorems, e.g. many scholastic and mathematical logicians, as also Aristotle himself in the Prior Analytics. But logic so understood seems too narrowly conceived. For two kinds of problem naturally arise out of the theorems. First those about their nature – are they linguistic expressions, word-structures, psychical forms or functions, objective complexes? What does a logical law mean, what does a statement mean? These are problems which nowadays are dealt with in semiotics. Second, problems relevant to the question how logical laws can be correctly applied to practical scientific thought. These were dealt with by Aristotle himself, principally in the Posterior Analytics, and nowadays are the concern of general methodology. So semiotic and methodological problems are closely connected with logic; in practice they are always based on semiotics and completed in methodology. What remains over and above these two disciplines we shall call formal logic.

6. A complete history of the problems of logic must then have formal logic at its centre, but treat also of the development of problems of semiotics and methodology. Before all else it must put the question: what problems were in the past posited with reference to the formulation, assessment, and systematization of the laws of formal logic? Beyond that it must look for the sense in which these problems were understood by the various logicians of the past, and also attempt to answer the question of the application of these laws in scientific practice. We have now delimited our subject, and done so, as we think, in accordance with historical evidence.

But such a program has proved to be beyond accomplishment. Not only is our present knowledge of semiotic and methodological questions in the most important periods too fragmentary, but even where the material is sufficiently available, a thorough treatment would lead too far afield. Accordingly we have resolved to limit ourselves in the main to matters of purely formal logic, giving only incidental consideration to points from the other domains.

Thus the subject of this work is constituted by those problems which are relevant to the structure, interconnection and truth of sentences of formal logic (similar to the Aristotelian syllogism). Does it or does it not follow? And, why? How can one prove the validity of this or that sentence of formal logic? How define one or another logical constant, e.g. ‘or’, ‘and’, ‘if—then’, ‘every’ etc. Those are the questions of which the history will here be considered.
Ioseph Maria Bochenski, A History of Formal Logic

I.M. Bochenski’s History of Formal Logic presents a clear and systematic discussion of the major figures in the history of logic who have attended to problems in the above consideration, from antiquity to the early twentieth century, as well as a contrast between Western and Indian logic. We will use this text as a supplement in our upcoming Trivium: Art of Logic course (beginning May) which is available to all enrolled members.

Liberal Arts

Trivium: Logic

December 8, 2021December 8, 2021 Brian Kemple1 Comment

Logic as a Liberal Art – HFS Books — Houser: *Logic as a Liberal Art*
[Order – Amazon] [Order – CUA Press]

Beginning the week of January 10, all Lyceum Institute members will have access to a 13-week course in traditional Logic. Discussion sessions will be held twice per week: Mondays at 6:00-6:45pm and Thursdays at 11:45am-12:30pm (subject to change). Each week there will be an assigned reading, problem set, and brief lecture. Discussion sessions will cover both the reading and selected problems.

But why study traditional logic? Some will say it has been obsolesced by modern (symbolic) logic. Others will say that it is a frivolous activity used even less commonly in “real life” than algebra or calculus. Both are wrong: for though we do not break down our propositions and arguments into formal, syllogistic formulas, by a deep familiarity with their structure, their rules, and their application in natural language, we are able to recognize illogical arguments from others and to construct more logical arguments ourselves.

To quote our primary textbook, R.E. Houser’s logic as a Liberal Art:

The natural habitat of logic is the verbal and written language of ordinary human discourse, including the high-level verbal discourse that occurs in university courses. The man who invented this approach to logic was Aristotle, who wrote the first textbooks in logic in the fourth century B.C. The main reason why this approach is preferable for most people is that it avoids the two problems that have plagued the teaching of symbolic logic during its heyday and up to the present. First, the verbal approach is clearly preferable for those who have math phobia. The problems used in the verbal approach are set out in ordinary language, language that often contains clues that help us to understand the logic of verbal discourse. Such clues, of course, are missing from the mathematical symbols used in symbolic logic. Second, the verbal study of logic has the advantage of avoiding the problem of needing to translate back and forth between abstract logical symbols and the more concrete verbal symbols we call words. While mathematical symbols do on occasion help us see logical relations… by using ordinary or “natural” language to study logic we can avoid the large headache of translating from the language of symbols to ordinary language, and then back again. So we content ourselves with the smaller but real headaches involved in searching out the logic contained within verbal or natural language.
Houser 2020: Logic as a Liberal Art, xxviii.

This characterizes our approach to the Trivium as a whole at the Lyceum: striving to master language as a real and integral part of thinking. In our logic course, we will focus on affecting clarity in thought so as to better express it in words. I hope you will join us!

Learn more about Logic at the Lyceum

The Lyceum Institute offers courses in all three arts of the Trivium: Grammar, Logic, and Rhetoric. Together, they form a core of knowledge necessary to every educated human being.

Learn more about our approach at the links below.

trivium

Logic