Difficulty: What the heck
Consider the following argument:
“I will be a little late today; traffic is bad.”
Formulated more clearly, the argument looks like this:
Premise 1: Traffic is bad.
Conclusion: Therefore, I will be late.
That looks fine at first glance, but there is a missing premise that we would need to make explicit for the argument to deductively support the conclusion. In other words, the argument looks more like this:
Premise 1: Traffic is bad.
Premise 2: ?
Conclusion: Therefore, I will be late.
So what is the missing premise? People often guess things like, “I’m driving,” or “I’ll be stuck in traffic.” Those are reasonable guesses, but they are still not enough to make the argument deductively valid. To do that, we would need a hidden premise like this:
Premise 1: Traffic is bad.
Premise 2: If traffic is bad, I will be late.
Conclusion: Therefore, I will be late.
Now the argument has the form of modus ponens, perhaps the most basic rule in logic. Briefly, modus ponens is:
- P
- P
Q
- ∴ Q
where ‘P’ = ‘Traffic is bad’, ‘P Q’ = ‘If traffic is bad, I will be late’, and ‘∴ Q’ = ‘Therefore, I will be late.’
Without the second premise, the argument is deductively invalid.
Arguments like this one, containing at least one hidden premise or unstated conclusion, are called enthymemes.
Now, not all enthymemes are sneaky in a bad way. We leave premises unstated all the time because ordinary conversation would be unbearably tedious if we said every single thing out loud. Enthymemes become sneaky when the missing premise is exactly the part of the argument that is weakest, most controversial, or most in need of scrutiny.
That is why they matter so much.
If you fail to identify premise 2 (“If traffic is bad, I will be late”), then you have one fewer premise to target in the argument. You may find yourself trying to disprove premise 1 (“Traffic is bad”), which, if the traffic actually is bad, would make it much harder to criticize what is really going on.
But once we identify the hidden second premise, we begin to understand what to target: is premise 2 true? Is it really the case that if traffic is bad, then the speaker will necessarily be late?
Once we begin to question that previously hidden premise, we can come up with counterexamples. We can say: “If traffic is bad, you can still arrive on time.” Why? Because:
- you can take the metro
- you can work remotely
- you may already have built in extra travel time
- you may live close enough to walk
This is an easy example, but things start to get trickier once we get into advertisements and political arguments.
Consider this fictional advertisement that I made up just now:
Do you like being pampered? Do you want to be attractive, alluring, charming, sexy, whatever it is that floats your boat? Then you must apply our proprietary Bullshit Lotion.
First, let’s try to figure out what the argument is actually saying:
Premise 1: You like being pampered and you want to be attractive/alluring/charming/sexy/whatever.
Conclusion: Therefore, you must apply our proprietary Bullshit Lotion.
Once we do that, the missing second premise becomes obvious. The argument is really saying:
Premise 1: You like being pampered and you want to be attractive/alluring/charming/sexy/whatever.
Premise 2: If you like being pampered and you want to be attractive/alluring/charming/sexy/whatever, then you must apply our proprietary Bullshit Lotion.
Conclusion: Therefore, you must apply our proprietary Bullshit Lotion.
Now that we’ve identified the missing second premise, we can cast doubt on it.
Is it true that if you like being pampered and want to be attractive, etc., then you must apply the proprietary Bullshit Lotion? Perhaps not. Perhaps you can apply some other brand of lotion. Perhaps you do not need lotion at all. Or perhaps, if you want to be pampered and attractive, you can just go to a spa. You get the point.
Or take, for example, political enthymemes. Suppose that a politician says:
“My opponent wants to cut the military budget. So my opponent is weak on national security.”
What is the missing premise? And how might you cast doubt on that premise by providing plausible counterexamples?
I’ll leave that as a little exercise for you. But now you can see why enthymemes are so sneaky: what is doing the most argumentative work is often the very thing left unsaid.