Amateur Logician Posts

I recently had the pleasure (and honor!) to have a short e-mail interview with Professor Gerard Casey. He has an excellent course on traditional logic at Liberty Classroom. I’ve gone through the course, benefited tremendously from it, and know you will too.

Dr. Gerard Casey is Professor Emeritus at University College Dublin. He received his primary degree from University College Cork, then went on to earn an MA and PhD from the University of Notre Dame. He also holds a Bachelor of Laws (LLB) from the University of London, a Master of Laws (LLM) from University College Dublin and a Doctor of Letters (DLitt) from the National University of Ireland. His books include Libertarian Anarchy, Freedom’s Progress?, ZAP, After #MeToo, and Hidden Agender.

Amateur Logician:
Dr. Casey, could you please tell us a bit about yourself and your interest in logic?

Gerard Casey:
Well, my discovery of philosophy at the age of sixteen coincided with my discovery of logic. I bought a copy of E. J. Lemmon’s Beginning Logic and spent the summer of 1967 teaching it to myself. Anyone who has ever read the Lemmon book will know that it’s not the most pedagogically friendly of texts, so I had many frustrating days that summer trying to come to grips with that book, especially as I didn’t have the assistance of a teacher, and the internet awaited invention.

When I went to Notre Dame for graduate studies in Philosophy, all graduate students were required to take a course in post-elementary logic. In that course, we had to come to grips with the more advanced ideas in metalogic: e.g. the Loewenheim-Skolem theorem, decidability, consistency and (in)completeness, advanced set theory, Cantor and infinity, etc.

When I took up my first teaching post at The Catholic University of America in D.C., in 1983 I taught logic for 3 years. When I returned to Ireland in 1986, it was to take up a position at University College Dublin in the Department of Logic and Psychology. I was given the responsibility for teaching an entire First Year course in Logic, which covered Aristotelian Logic, Propositional and Predicate Logic, Modal Logic, Philosophy of Logic and Metalogic. For the philosophy of logic, I discovered Susan Haack’s Philosophies of Logic and at the same time, I developed an interest in so-called deviant logics.

Dr. Casey, I enjoyed your logic course at Liberty Classroom tremendously. Your way of presenting things has influenced the site AmateurLogician.com. How did you design your logic course at Liberty Classroom and what makes it unique?

The essential elements in logic have been around ever since Aristotle codified them, but the presentation of the material is, or has been, often presented in a form that is unnecessarily complex. In my course, I try to focus on the basics and to do so in a way that makes it easy to remember and (relatively) simple to use. I have also (I think) added some constructive items not normally found in most treatments, such as the use of the rules of the syllogism to find a valid conclusion from given premises, or a premise that, if added to a single premise and putative conclusion, would give you a valid argument.

For the average person, what would you consider the most important thing to master in logic?

It may seem obvious to say this, but the core idea in logic is that of valid inference, the notion that if certain propositions are true, another proposition must also be true—not may be true, could be true, might be true, but must be true. After that, apart obviously from mastering the syllogism, grasping the relationship between propositions on the Square of Opposition is a great help to clarity of thought, that and being familiar with the other forms of immediate inference: conversion, contraposition and obversion.

What are some good books to get started in logic?

For more on Scholastic Logic, there is Raymond McCall’s Basic Logic if you’re lucky enough to find a copy second-hand, and similarly Andrew Bachhuber’s Introduction to Logic. For modern symbolic logic, there is no shortage of introductory texts, most of them, in my estimation, overloaded with material, but pretty much all of them adequate. My preference is for a minimal rather than a maximal account.

Didn’t you once collect neo-Scholastic textbooks? They sometimes get a bad rap, but there are some truly excellent texts: Peter Coffey’s logic book and ontology book, for example.

Yes, I used to have quite a collection of neo-Scholastic books but, once I retired, I had very little space for books in my house and had to reduce my collection drastically. Most of my neo-Scholastic books had to go, including my much-loved Klubertanz! I also had most of a series of such texts produced in the UK (can’t quite remember the name of the series) but that too had to depart.

Logic belongs both in the English Department and the Mathematics Department. Why do you think the education establishment has pushed away from teaching logic?

The English Department? I’ve never known an English Department to have courses in Logic! Philosophy Departments, yes; English Departments, ? Logic is still taught in Philosophy Departments, and is (or was) often a required course. I’m not sure it still is. In its more rarified aspects, logic has found a home in Mathematics Departments and, practically, in Departments of Computer Science (Logic Gates, e.g.).

Do you have a preference for Aristotelian-Scholastic logic versus the modern mathematical logic?

Yes. It is, in my judgement, more immediately relevant for practical use. But I have a preference for the modern presentation of sentential or propositional logic as I think it is more perspicuous.

Could you please summarize Henry Veatch’s arguments about the differences between these two logics?

Veatch’s book, Two Logics, is really an essay in the Philosophy of Logic, an area of study in which Susan Haack’s Philosophies of Logic is a fascinating and challenging read. One way of characterising Veatch’s concerns would be to think of them as relating to the existential/essential implications of propositions.

Veatch believes that a universal affirmative proposition such as “All human beings are mammals”, if true, is necessarily true. In Aristotelian logic, this is an ‘A’ type proposition, and ‘A’ type propositions, if true, imply, by subalternation, the truth of the corresponding ‘I’ type propositions, in this case, ‘Some human beings are mammals’. So if “All human beings are mammals” is true, then “Some human beings are mammals” would have to be true as well.

Now, in symbolic logic, “All human beings are mammals” would be represented by (x)(Hx → Mx). In symbolic logic, from the truth tables for conditionals, a conditional is false only when its antecedent is true and its consequence false or, to make the relevant point here, a conditional is true whenever its antecedent is false! This means that in symbolic logic, if (x)(Hx →Mx) were to be true because Hx is false, it wouldn’t necessarily imply that there is in fact any human being that is a mammal!, i.e. (Ex)(Hx & Mx).

Now it could be argued that in concerning itself with existential matters, symbolic logic is engaged in a kind of category error, that the relationship between A-type and I-type propositions is an intensional matter that prescinds from the existential question altogether.

There are far too many issues to give an overall summary of all the relevant and insightful elements of Veatch’s book, but whether one agrees with him or not, completely or only in part, there can be no doubt that he is engaged in reflecting on some fundamental matters concerning the relationship of logic to the real world.

Can’t we both overstate and understate the importance of logic? While logic is often necessary, not sufficient, for us to arrive at true conclusions, we clearly need more than logic. And are there any major misconceptions people have about logic?

Yes, we can both overstate and understate the value of logic. Logic is necessary for rational discourse, but, as you suggest in your question, it is not sufficient. In addition to logic, we need rhetoric, understood in the classical sense as the art of finding the available means of persuasion. Logic is an island in a sea of rhetoric. In some ways, people need to learn logic more than ever. A knowledge of the more common fallacies, both formal and informal is helpful, is also useful.

All that said, logic is a formal codification of what is already present in our discourse and I believe it is impossible for our natural languages and any system of logic to be perfectly coincident.

Your more recent books include Hidden Agender, After #MeToo, and ZAP. What are some egregious examples of illogical thinking in today’s postmodern political culture?

The logical solecisms don’t change; just the material! Today’s postmodern culture abounds in non-sequiturs, begging the question, undistributed middles, and, most significantly, the revenge of the ad hominem! The idea that the truth or validity of what one says is inherently related to one’s race, sex or age is today the most popular form of the ad hominem.

Thank you so much, Dr. Casey!

I very much appreciate you spending some time with me and my readers.

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A Few After Thoughts:

In addition to Dr. Casey’s logic course, he has a two-part course on the history of political thought at Liberty Classroom. That was the impetus behind his massive book Freedom’s Progress?: A History of Political Thought. Though I’ve only read large scattered chunks of it, it’s extremely well-written. Dr. Casey is truly a gifted, erudite individual. The text can also be used as a self-defense weapon, given the size of the book!

For full disclosure, if you do sign up for Liberty Classroom through my link, I will earn some commission as an affiliate. I’m a student there and totally recommend it.

One thing I might have clarified better in the interview: I know logic is not taught in the English department, but I think it should be, at least in terms of “informal logic.” Consider writing an argumentative essay! It seems to me that, for example, in high school, students should ideally be learning some logic both in English and in mathematics.

Many readers likely haven’t heard of neo-Scholastic textbooks. These especially flourished during the time Pope Leo XIII wrote the 1879 encyclical Aeterni Patris calling for a revival of Thomistic philosophy and theology. I reference some of these texts as it pertains to logic here. These textbooks will help “ground” anyone in classical philosophy and traditional logic.

(For more on neo-Scholastic texts, here’s a blog post from the philosopher Edward Feser.)

I’ve also had a similar view, if I understand Dr. Casey correctly, on “existential import.” In this entry, I mention that in symbolic logic, why does the proposition “some unicorns are male” imply existence whereas “all unicorns are one-horned horses” does not imply existence? The former proposition can perfectly well be entertained without having it imply existence.

Mathematical logic has it that the conditional Φ → ψ is false only when Φ is true but ψ is false. It’s otherwise taken to be true. (To be sure, this seems puzzling! Though it preserves the consistency of mathematical logic, it leads to “paradoxes of material implication.”) I write about this, e.g., here and here.

In any case, there’s a lot of things we can explore here: Dr. Casey’s intellectual biography, what logic concerns, books on logic, immediate inference, fallacies, etc.

But I’m really grateful that Dr. Casey did this short interview. All of us can learn a lot from him. And, it is my hope, that more discover his work. Check out his X (Twitter) account.