People love saying:
“Deductive arguments go from general to specific.”
“Inductive arguments go from specific to general.”
This is repeated so often that even professors say it.
Unfortunately, it’s wrong.
And if I hear one more person say that, I’m gonna have a fucking seizure.
First: what an argument actually is
An argument = a set of statements, a.k.a. premises, that lead to a conclusion.
So this is an argument:
Premise 1: If I hear one more person say “deductive arguments go from general to specific,” I’m gonna have a fucking seizure.
Premise 2: I hear one more person say “deductive arguments go from general to specific.”
Conclusion: Therefore, I’m gonna have a fucking seizure.
The form, or structure, of the argument is:
- H → S
- H
- Therefore, S
That logical move, by the way, is called modus ponens. It’s a valid and “duh” move, yes, but the Latin makes it sound deep, and it’s exactly the kind of structure all deductive logic is built on.
In logic, an argument is NOT defined as:
- yelling
- a claim (like “postmodern art is valuable, but postmodernism is not”–sounds deep, but that’s just a claim/statement)
- an opinion (including the ones everyone and their uncle feel entitled to express)
- disagreement
What deduction REALLY is
Deductive validity
Deduction means:
If the premises (of an argument) are true, then the conclusion must be true.
In other words:
The truth of the premises guarantee the truth of the conclusion.
So, if ‘H → S’ (premise 1) is true, and if H (premise 2) is true, then S (conclusion) must be true.
Specifically, that’s what we call a deductively valid argument.
Notice I kept on italicizing the word if. That’s because that’s super important–after all, one or more of these premises might not be true. For example, is premise 2 (“If I hear one more person say “deductive arguments go from general to specific,” I’m gonna have a fucking seizure”) true? No. So deductive validity doesn’t mean that the conclusion of your argument is true. It just means, again, that
if the premises are all true, then the conclusion must be true.
Deductive soundness
But what if you have a valid argument and its premises are all true? For example:
Premise 1: If I don’t have any money, I can’t pay the mortgage. (TRUE)
Premise 2: I don’t have any money. (TRUE)
Conclusion: I can’t pay the mortgage. (BOTH LOGICALLY AND IN REALITY GUARANTEED TO BE TRUE)
Then this deductive argument is what is called sound.
A word on that bullshit definition of “deduction”
Note that in neither the seizure example nor the mortgage example is anything “going from general to specific.” That’s because “going from general to specific” is simply not the correct definition of “deduction,” nor is it useful for a deeper understanding of how arguments work. But some teachers and professors will still use that definition no matter how many times I object. Whatever. Let’s move on.
What induction REALLY is
Inductive logic does not use labels like “valid” or “sound.” Instead, we use words like “weak,” strong,” and “apt.” This different terminology is important because, unlike deduction, induction is probabilistic.
Inductive weakness
Consider this argument:
Premise 1: Some dogs bark.
Premise 2: Guai Guai is a dog.
Conclusion: Guai Guai (probably) barks.
This is an inductively weak argument because of what the word “some” means.
“Some dogs” might be just 1% of dogs. “Some dogs” might even be just 0.01% of dogs. There simply isn’t enough reason for us to accept the conclusion that Guai Guai probably barks because, by definition, probably = roughly put, “more likely than not” or “high enough likelihood given the evidence.” And the word “some” is simply too weak to conclude that Guai Guai’s barking is probable.
Inductive strength
Now what about this one?
Premise 1: Most Martians like Dr. Seuss.
Premise 2: Zorp is a Martian.
Conclusion: Zorp (probably) likes Dr. Seuss.
This is an inductively strong argument. “Most Martians” doesn’t mean some exact math like 51%. It just means a strong majority—enough to make the conclusion actually likely. So that–and the fact that Zorp is a Martian–makes it probable that Zorp likes Dr. Seuss.
Inductive aptness
What happens when you have an argument that is inductively strong and all its premises are true? That’s when you have an inductively apt argument. Let’s go back to the dog argument and change it a little:
Premise 1: Most dogs bark.
Premise 2: Guai Guai is a dog.
Conclusion: Guai Guai (probably) barks.
This dog argument has a form that is identical to that of the Martian argument, so it is obviously inductively strong. But unlike the Martian argument, the dog argument has premises that are all true. Hence, it is inductively apt.
A word on that bullshit definition of “induction”
Note that none of these inductive arguments “go from specific to general.” That’s because, like the bullshit-y definition of deduction, the bullshit-y definition of induction is not very helpful for a deep understanding of how arguments work. And yet, textbooks teach that definition. Perhaps I will be having that fucking seizure after all.
Another type of argument: abduction
There’s at least one other type of argument–the abductive argument–that we can discuss. Abduction, or inference to the best explanation (IBE), aims to reach conclusions based on the best possible explanation. Ockham’s Razor–the principle that the best explanation is the simplest one that makes the least number of assumptions–is a case in point. For instance:
Suppose you walk into your living room and see that:
- The floor is wet
- Your dog is shaking water everywhere
- There’s a knocked-over bowl of water
You could come up with many explanations:
- A pipe burst
- Someone broke in and spilled water
- Your dog knocked over the bowl
But one explanation stands out as the best:
Your dog knocked over the bowl and made a mess.
That’s an abductive argument:
The floor is wet and the bowl is knocked over.
If the dog knocked over the bowl, that would explain all this shit.
Therefore, the dog probably knocked over the bowl.
Notice what’s happening here:
You’re choosing the explanation that best fits the evidence.
A brief note on abduction and probability
Abduction is often treated as probabilistic, even if people don’t always say it that way.
When you say “this is the best explanation,” what you usually mean is something like:
This explanation makes the observed evidence more likely than the alternatives.
That’s exactly the kind of reasoning philosophers like Elliot Sober analyze using probability. (Check out his book, Ockham’s Razors.)
So if someone tells you that abduction is “not probabilistic,” they’re either oversimplifying or just wrong.
Conclusion
If you forget most of what I just said, remember this one thing:
The difference between deductive and inductive arguments has nothing to do with “general vs. specific.” It has to do with certainty vs. probability.
That’s all for today. And keep thinking.
Philosophy without Bullshit 