The Brain, a User's Manual:
What Is Logic?
By Gabriel Blanchard
We finished hunting out fallacies; now what?
Having completed our reproach against the sophists, a new question naturally arises in the mind. There went a load of ways we shouldn’t think or argue, but how should we?
At this juncture, several self-appointed teachers will be clamoring for our attention. Some—the astrologers, the body language experts, the amateur phrenologists,* and those who just happen to have discovered the diet supplement that will turn our lives around—can be invited to leave us their contact info on a small pad, which we shall later throw out. A couple, however, are worth listening to. We must leave the expounder of the scientific method aside, at least for now; our focus is to be on the logician (whose discipline is part of the underpinnings of science itself).
Even as we prepare to do so, however, it is worth our time to pause, very briefly, over these words of Chesterton’s:
The real trouble with this world of ours is not that it is an unreasonable world, nor even that it is a reasonable one ... it is nearly reasonable, but not quite. Life is not an illogicality; yet it is a trap for logicians. It looks just a little more mathematical and regular than it is; its exactitude is obvious, but its inexactitude is hidden; its wildness lies in wait.
Learning logic cuts down the difficulty of every other subject, and it will lead us to a great deal of truth; but it can also lead us to mare’s nests. Logic, once mastered, will need to be complemented by something else.
However, that something else can wait until we have mastered logic. Now then.
Introducing Logic (Not the Musician; the Other Kind)
Logic technically comes in two varieties, inductive and deductive, but induction is more properly the domain of the scientist. Besides, when people say “logic” nowadays, they usually, if not entirely consciously, mean deduction. The relationship between logic and mathematics is also tricky to understand, let alone explain; we may therefore thank our stars we don’t have to do either. We also aren’t going to subject you to Boolean functions, or truth trees, or set theory, or Gentzen notation, or whatever abomination this is supposed to be:
φ ::= a1, a2, … | ¬φ | φ & ψ | φ ∨ ψ | φ → ψ | φ ↔ ψ
No. For the purposes of this User’s Manual, we’re going to concentrate just on a few elementary building blocks—in fact, we’ll only need three.
I. Predication
In plain English, predication basically means “saying things about stuff.” At first, this may not sound like a topic about which much that’s interesting or novel could be said; isn’t all speech “saying things about stuff”? The thing is, the truthful answer to that question is No. Lots of speech isn’t really about any specifiable stuff (or isn’t about the stuff it claims to be about), and plenty more speech fails to actually say things about its chosen stuff. Learning to predicate** properly begins with
(IA) definition.
We’ll need to learn how to define properly, because all argument and indeed all thought depend on the power to define. We may then go on to explore what kinds of predication we’re able to perform, also called
(IB) categories,
which Aristotle enumerated in his book, the aptly-named Categoriæ.
II. Term Logic
Speaking of whom, this type of logic is also called “Aristotelian logic.” This takes those predications we’ve learnt to do, and arranges them into recognizable kinds of statements, defined by two qualities: being either particular or universal, and either affirming or denying something about their chosen term. This is where we’ll learn about
(IIA) A, I, E, and O statements,
and how they are necessarily in various relationships to one another. Those relationships are in fact so regular, they can be mapped, on what’s called
(IIB) the Square of Opposition.
This will also be where we start to discuss how to string multiple predications together in sequences of A, I, E, and O statements, and to recognize when a sequence of statements can necessitate a further statement. In other words, we will be talking about
(IIC) syllogism, validity, and soundness.
III. Propositional Logic
After we’ve finished all that up, we shall move on to a kind of reasoning pioneered by the Stoics, generations after Aristotle. In particular, they dealt with two varieties of expression: “if-then” statements, or
(IIIA) conditionals and consequents;
and “or” statements, with or without an “either” in front—also known as
(IIIB) disjunctives.
And with that, we shall have a basic grasp of informal logic under our collective belt. See you next week.
*Though it is only justice to amateur phrenologists to admit, having a trained one is not really better.
**This word can be treacherous. As a noun, it’s pronounced prĕd-ĭ-kàt, and refers to the part of a sentence that isn’t the subject, but is instead what the speaker is saying about the subject. As a verb (which it is in the sentence we’re footnoting), it is instead pronounced prĕd-ĭ-kāt—nearly identical, but pay attention to that third vowel: it’s lax in the noun, long in the verb. “To predicate” is … well, what we just said above! Predicāting (verb sense) is constructing predicàtes (noun sense).
Educated at Rockbridge Academy and the University of Maryland, College Park, Gabriel Blanchard has a bachelor’s in Classics and works as CLT’s editor at large. He lives in Baltimore, MD.
If you enjoyed this piece, you might like our Great Conversation posts on judgment, technology, causality, and necessity, or our short biographies of Dante, de Pizan, and Camus as well. Thank you for reading the Journal and supporting CLT.
Published on 3rd October, 2024.