"One of the most damaging and widespread social beliefs is the idea that most adults are incapable of learning new skills."
- Naval Ravikant
Congratulations to Joshua, who won a free year of my Introduction to Logic course in last week's one-year anniversary giveaway!
I created the Introduction to Logic course because I think greater logic literacy would be a net good for society.
But it isn't easy to capture those sweet mental gains that come from learning logic. Its benefits seem so abstract and general.
So here are four specific ways logic has helped me.
1. It helped me identify and learn the relation between premises and a conclusion.
If you stick with logic long enough, you will learn all kinds of ways that statements can support, or lack support for, a conclusion you want to defend.
When you argue for a particular point or claim--a conclusion--you typically give statements that are supposed to support that point or claim. In a formal deductive argument, the conclusion needs to follow necessarily from the supporting statements. In an inductive argument, the supporting statements provide some degree of support for what you want to argue, but it’s possible the conclusion could be false, despite whatever support that’s given. I see a white swan here, a white swan there, so I conclude all swans are white, but it’s possible there’s a black swan walking around somewhere.
2. It helped me identify the relation between word and world.
This was by the far the biggest benefit for me. How is language used to describe what the world is like in different, complex ways?
Learning the word-object relation is one of the fundamentals of logic. You start noticing that most nouns are supposed to refer to some particular object. We refer to blocks of time (”this morning”), social groups and objects (”the school”, “my company”), concepts (”AI”, “education”, “process”), physical things (”the 25 pound dumbbell”), etc. And then you ask what those things are like; what characteristics they have. That's where predicates come in.
Predicate logic in particular helps you pick out predicates within statements that attribute properties to objects. Something like “Ra” in predicate logic might be short for “The apple (a) is red (R).”
When you start learning formal rules and semantics for statements and arguments, you naturally start paying attention to how ordinary language is structured: whether the words someone uses actually refer to things out there, and whether particular claims and arguments follow those rules.
You also notice how often we talk about abstract and non-physical objects, and properties of those non-physical objects. We constantly refer to objects like numbers, things like the learning process, logic as a field of knowledge, and propositions, etc. Once you start noticing what people talk about, you start wondering what kind of object they have in mind, and it isn’t always obvious what that object is or what characteristics it has. Try paying attention to the things someone mentions and talks about the next time you read an article or see a post (even this one), and ask yourself whether it’s even possible to see that thing out in the world.
3. It helped me notice when sentences count things and quantify things.
When you graduate from propositional logic into quantified logic, you start to notice the ways language is used to quantify and count things. The two basic operators in quantified logic are ∀, which represents “all”, and ∃, which represents “at least one”. Simply understanding the quantification category in language helps you notice when someone makes a claim about a quantity of things.
One of the most obvious examples I notice is when someone makes a non-quantified statement about some particular people group, like “Republicans only care about the bottom line of rich companies”, or “Democrats are just looking to use immigration policy to destroy the country” or "Philosophers are socially awkward". Do they mean all? Some? How many? That kind of statement is called a generic, and generics tend to be not as clear because they don’t quantify at all.
4. It helped me better understand what's possible and what's necessary.
Learning the basic semantics of modal logic, where the logical language includes symbols that express possibility (⬦) and necessity (☐), helped me better understand what we might mean when we talk about what’s possible and what’s necessary.
Modal logic typically uses possible world semantics, where we imagine an infinite amount of possible worlds with infinite amounts of variation. It can get very technical, and there is a wide range of metaphysical assumptions one can make when talking about even the basic modal logic semantics. But for our purposes here, there’s a possible world where I have a different color shirt, and another one where I have a different eye color, and another one where I have an imperceptibly different shade of eye color, etc. For just about any variation you can think of, and infinitely more, there's a possible world for that. Fictional worlds like those in Star Wars or in The Lord of the Rings are kind of like possible worlds.
Modal logic gives you a framework and a structure to express claims that talk about statements that are possibly true but possibly false, or true in some worlds and false in others, in addition to necessary truths that can’t possibly be false (statements that are true in every possible world).
Here’s the through line for these four points: learning these specific, formally expressible aspects of language can give you helpful, guiding pathways that can steer you towards being more precise, more clear, and to have a better grasp of how much support you’re able to give for a claim or view you hold.
It can take a long time to grasp the basics of these logics, but I think it’s worth it.
Until next time.
Jared
This Week's Free Philosophy Resource:
Title: There is No Such Thing As a Purely Logical Argument
Author: Mette Høeg
Reading Level: Undergraduate
This is a summary of an article that just came out in the journal Think, arguing that all arguments have at least some aesthetic elements and narrative elements on top of whatever logic is used.
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