This is a work-in-progress. I will be updating this often!
It’s my sincere hope that my website will be useful to you. Logic is a wonderful “science” to learn and, of course, to practice and apply.
Please take a look at my tutorial. It will give you the tools to master logic.
If you profit from it or enjoy it, please consider supporting my work.
— George Wick
The Amateur Logician Tutorial
Logic is a way to discipline our thinking.
Orderly and rigorously think, reason, and evaluate arguments with logic.
Learn Aristotelian-Scholastic logic first.
That’s my advice.
After, if you want, learn propositional logic.
Unless you’re only interested in mathematical argumentation, Aristotelian-Scholastic logic is better because it has a wider range of immediate applicability.
That’s partly because the Trivium has a focus on natural language, on the liberal arts. It’s easy to apply to arguments encountered in daily life, the media, politics, religion, or philosophy.
To be sure, it’s a contentious, debatable issue comparing the pros and cons of traditional logic to mathematical logic. Henry Veatch, an Aristotelian philosopher, argued that the two have different uses or aims. We cannot, therefore, rightly claim that the latter can “replace” the former. Nor can we rightly claim that the former is “out-of-date” compared to the latter.
With that said, mathematical logic is important and interesting. Propositional logic, for example, allows us to easily symbolize many complex propositions. There are times when it is better to use than traditional logic.
Logician E. J. Lemmon asks us to imagine, in his classic textbook Beginning Logic, how difficult it would be to put into words an algebraic expression like x^2 – y^2 = (x+y)(x-y).
There was a time when mathematicians didn’t yet have that symbolism.
The symbolism makes things so much nicer, clearer, and more concise!
Similarly, it makes sense to symbolize a complex argument. In “natural” language, an argument might be a paragraph long, though in mathematical logic it might only be a few short lines.
Even within the Aristotelian-Scholastic tradition, symbolization of arguments is found. Mathematical logic goes further in its ability to model (some) argumentative forms.
Introduction
Contemporary mathematical or symbolic logic is built on top of propositional logic. This foundational logic doesn’t concern itself with the terms in a proposition. That’s why a proposition like “all men are mortal” is represented with a single capitalized letter, such as P. Propositional logic doesn’t concern itself with the subject term or predicate term of a proposition. What matters is the “truth-functional” relationships between propositions.
Propositions can be combined to form new molecular propositions. A proposition’s truth depends upon the truth values of the possible sub-propositions that compose it. Molecular propositions are formed with connectives like the “not,” “and,” “or,” “if. . ., then,” and “if and only if.” We can represent the different possible truth values a proposition can take on through a so-called truth table.
Arguments can then be constructed with these propositions! Inferences include modus ponens, modus tollens, hypothetical syllogism, disjunctive syllogism, constructive dilemma, simplification, conjunction, and addition. Given workable premises, we can prove new propositions through such inferences, in addition to various properties of logical equivalence like De Morgan’s rule or the property of distribution.
Video Series
I am presently in the process of releasing a video series on (basic!) propositional logic and predicate logic based on the 1964 textbook First Course in Mathematical Logic by Patrick Suppes and Shirley Hill.
Propositional Logic Tutorial – a work in progress
1. Symbols & Translations
2. Basic Truth Tables
3. Complicated Translations
4. Introducing Rules of Inference
5. Equivalences (Replacement Rules)
6. Conditional & Indirect Proofs
References and Resources. . .
In the Trivium Logic Tutorial, I’ve referenced texts which cover propositional logic.
Take a look at A Concise Introduction to Logic by Patrick Hurley or Introduction to Logic by Irving Copi.
These texts are commonly used in college-level courses on introductory logic. As such, they cover not only propositional logic and predicate logic, but categorical logic, inductive logic, fallacies, and some informal logic.
Recently, I’ve picked up The Art of Reasoning by David Kelley and Debby Hutchins. It’s my present recommendation for those wanting an overview of basic contemporary logic. The content is similar to the Hurely and Copi textbooks.
So, it’s not limited to propositional logic. There’s much more in it.
E. J. Lemmon’s Beginning Logic is a classic text from the 1960s.
It’s a concise read with good exercises.
Metalogic is introduced. It’s a zero fluff textbook.
Unlike the textbooks so far mentioned, this is exclusively dedicated to mathematical logic. The first two chapters are on propositional logic and the last two chapters are on predicate logic. Excellent!
Introduction to Logic by Harry Gensler, while it focuses on contemporary logic, is more expansive in its coverage of mathematical logics. It deals with propositional logic, predicate logic, modal logic, deontic and imperative logic, and belief logic. I appreciate that it focuses on the task of translating ordinary English sentences into the symbolic languages of logic. Highly recommended!
A more advanced book to consider reading is Logic: The Laws of Truth by Nicholas J. J. Smith. It’s very thorough, and introduces metatheory or metalogic.
For the mathematically inclined, discrete math textbooks or math proof textbooks will cover a chapter on propositional and predicate logic.
Discrete Mathematics and Its Applications by Kenneth H. Rosen, for example, has six sections in the first chapter. Mathematical logic has become an important topic in computer science.
Similarly, the early chapters will cover logic in How to Prove It by Daniel Velleman. This book prepares the reader for advanced mathematics, which focuses on proof making.
A bunch of classic (and affordable!) books on mathematical logic are published by Dover. This includes the simple book First Course in Mathematical Logic by Patrick Suppes and Shirley Hill. Other books are far more advanced.
They cover topics including set theories, Peano axioms constructing arithmetic, Gödel’s incompleteness theorems, etc. Take a look at A Beginner’s Guide to Mathematical Logic by Raymond M. Smullyan, Mathematical Logic by Stephen Cole Kleene, An Introduction to Mathematical Logic by Richard E. Hodel, Introduction to Logic by Alfred Tarski, or one of the others.