deductive argument – Philosophy without Bullshit

What the Heck Is an Enthymeme? And Why Are They So Sneaky?

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 $\rightarrow$ Q
∴ Q

where ‘P’ = ‘Traffic is bad’, ‘P $\rightarrow$ 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.

The Experience Machine Part 1: What the Hell Is It and What Does It Aim to Show?

Difficulty: What the hell

In 1974, Robert Nozick offered, in his book Anarchy, State, and Utopia, a thought experiment, which he later revised in his book The Examined Life (1989). We will focus on this second version, which I’ve summarized:

You have access to a machine that could give you any experience(s) that you might desire. When plugged into this machine, you could experience writing a great poem, bringing about world peace, or loving someone and being loved in return, and you could feel “from the inside” the pleasures that these things bring. You could program this machine to give you experiences this week, this year, or for the rest of your life. If you should run out of ideas for pleasurable experiences, you could consult a library of suggestions taken from biographies and from novelists and psychologists. Would you want to be plugged into this machine for the rest of your life? If not, why not?

Further, Nozick stipulates that upon entering the machine, you will not remember having done so. You can optionally program uncertainty by using a randomizer built into the machine.

This thought experiment is Nozick’s attempt to refute the central argument for hedonism about well-being—that the goodness and badness of our lives, for ourselves, is wholly determined by the pains and pleasures we experience.

Simplified, Nozick’s argument can be formulated as a deductive argument:

Premise 1: If hedonism is true, then the vast majority of people would want to plug themselves into the experience machine.

Premise 2: It is not true that the vast majority of people would want to plug themselves into the experience machine.

Therefore, hedonism is false.

This argument is logically valid (it follows the form of modus tollens). The real question is whether Premise 1 is true.

Alternatively, we might reconstruct Nozick’s argument in a different, more controversial way:

Premise 1: The vast majority of reasonable people value reality in addition to pleasure.

Premise 2: If the vast majority of reasonable people value X, then X has intrinsic prudential value.

Conclusion 1: Therefore, reality has intrinsic prudential value.

Premise 3: If something besides pleasure has intrinsic prudential value, then hedonism is false.

Conclusion 2: Therefore, hedonism is false.

Here, “prudential” means “what is good for a person,” which corresponds to “well-being.” So something that has “intrinsic prudential value” is good for a person in itself, not merely as a means to something else.

Some quick examples:

Prudential values (good for you):

health
friendship
pleasure

Intrinsic values (good in themselves):

pleasure (for hedonists)
not money (since money is just useful for getting other things)

So something has intrinsic prudential value if it makes your life go better just by being part of it, not because it leads to something else.

The is-ought dichotomy

The deductive interpretation

The problem with this second interpretation is that it moves from what philosophers call an “is” to an “ought.” That is, just because something is the case doesn’t mean it ought to be the case.

For instance, it is the case that most people value money. That doesn’t allow us to conclude that people ought to value money.

This version of the argument assumes that what people happen to value determines what is genuinely valuable. That’s a controversial move, and without it, the argument doesn’t go through.

The abductive interpretation

So instead of interpreting Nozick’s argument as deductive, philosophers more charitably interpret it as abductive—an inference to the best explanation (IBE).

What the hell does that mean?

Say that you see smoke coming out of your car hood. You consider the following explanations:

You absent-mindedly left a cigarette in there.
Some part of the car is malfunctioning.
Criminals planted a stick of dynamite.

The best explanation is the simplest one: something is wrong with the car.

Applied to Nozick’s argument:

What’s the best explanation for the fact that many people care about reality, not just pleasurable experiences? One possible answer is that reality itself has intrinsic value.

This doesn’t prove that hedonism is false, but it gives us a reason to doubt it.

So there you have it: Nozick’s Experience Machine Thought Experiment (EMTE) in a nutshell. In future posts, I will present objections, counterarguments, and all that good philosophy shit. It gets complicated fast, so be prepared to move from “what the hell” to “what the fuck.”

What the Hell Is a Formal Fallacy? This Is Where Things Blur

Difficulty: What the hell

What the hell is a fallacy?

Philosophers draw a distinction between formal fallacies and informal fallacies.

Formal fallacies

Roughly, a formally fallacious argument is a deductively invalid argument where the form of the argument is wonky. Take, for example:

Premise 1: If I have COVID, then I display symptoms X.

Premise 2: I display symptoms X.

Conclusion: Therefore, I have COVID.

The form of this (bad) argument is:

C → D

D

Therefore C

Note that the conditional (if…then) is symbolized by an arrow going from left to right. That means C gets you D. But that doesn’t mean D always gets you C.

For instance, if it’s true that having COVID implies that I display symptoms X, I can’t conclude from the fact that I display symptoms X that I have COVID—because after all, I might have some other non-COVID lung problem that’s causing those symptoms.

And sure, it might also turn out that I do have COVID after all, but that possibility doesn’t make the argument any less fallacious. The problem is not that the conclusion happens to be false. The problem is that the form of the argument allows for a case where the premises are true and the conclusion is false. That is what makes it deductively bad. So:

fallacy ≠ false

formal fallacy = a deductive argument whose form does not guarantee the conclusion

Here’s another example:

Premise 1: If that’s a dog, then that’s a mammal.

Premise 2: That’s a mammal.

Conclusion: Therefore, that’s a dog.

The form here is identical to the (bad) argument about COVID. We have:

D → M

M

Therefore D

But this one is very obviously fallacious.

Again, it’s fallacious not because the conclusion happens to be false (it might very well turn out that the mammal is a dog), but because even if the premises are all true, you still can’t say for certain that the conclusion is true.

Informal fallacies

So where do informal fallacies come in?

Take something that is, in classical logic, both necessarily true and formally correct:

A = A

A

therefore A

And say that someone asks you this:

“Who is the current president of the United States?”

You respond with this argument:

John Adams is the current president of the United States. Why? Because John Adams is the current president of the United States.

That’s stupid—not because there’s anything wrong with the form of the argument, which is simply A, therefore A, but because the argument is rhetorically useless and question-begging. It gives the hearer no independent reason whatsoever to accept the claim.

So the John Adams argument is stupid due to something that logical form alone cannot capture, namely, some conversational, rhetorical, epistemic (knowledge), or other informal aspect of language itself.

Or take this example, taken from an old DirecTV commercial:

“When you pay too much for cable, you feel down. When you feel down, you stay in bed. When you stay in bed, they give your job to someone new. When they give your job to someone new, he has a lot to learn. When he has a lot to learn, mistakes are made. And when mistakes are made, you get body-slammed by a lowland gorilla. Don’t get body-slammed by a lowland gorilla. Get rid of cable, and upgrade to DirecTV.”

The chain part of the argument has a deductively valid form. It’s basically:

A → B

B → C

C → D

D → E

E → F

F → G

So:

A → G

Now, to get from there to “therefore don’t pay too much for cable,” you need at least one additional premise—something like this:

¬G

Therefore ¬A

And even if you generously grant the commercial that extra anti-gorilla premise, what’s still fallacious is not the logical form. The form is fine. What’s fallacious is the evidentiary stuff: the more links you have in a chain argument, the more evidence you need to justify each link. Is there enough evidence to say that “when mistakes are made, you’ll get body-slammed by a lowland gorilla”? No. And the same goes for several of the other links.

Where the line blurs

An interesting issue arises when we consider borderline cases of fallacies. Take this one:

Premise 1: Some dogs bark.

Premise 2: Guai Guai is a dog.

Conclusion: Guai Guai (probably) barks.

It’s unclear whether this is best treated as formally or informally fallacious.

The case for “formally fallacious”

If we ignore the word “probably” and interpret this as a deductive argument, the argument is deductively invalid because the form does not guarantee the conclusion.

You can illustrate that with a neat little Venn diagram like this one.

The red X in the overlap of the dog-circle and barker-circle stands for premise 1: some dogs bark.

But that X only tells you that at least one dog is in the barking region. It does not tell you which dog.

Premise 2 tells you that Guai Guai belongs somewhere inside the dog-circle. But it does not force Guai Guai into the overlap. Guai Guai could be in the barking part of the dog-circle, or in the non-barking part of the dog-circle.

That is the crux of the problem: even if the premises are true, the conclusion “Guai Guai barks” is still not guaranteed to be true.

If you’re not familiar with predicate logic, ignore the next few lines. But if you do know it, you’ll see the point immediately:

∃x(Dx ∧ Bx)

D(g)

Conclusion: B(g)

That inference is not deductively valid. The existential premise says that some dog barks. It does not say that this particular dog, namely Guai Guai, barks.

The case for “informally fallacious”

Now this is where things get messy. If we interpret the Guai Guai argument not as deductive (an argument that attempts to conclude that something is logically guaranteed to be true if the premises are all true) but as inductive (an argument that attempts to conclude that something is more likely true than not—in short, a probabilistic argument), then the defect seems to be evidentiary rather than purely formal.

Revisit the argument:

Premise 1: Some dogs bark.

Premise 2: Guai Guai is a dog.

Conclusion: Guai Guai probably barks.

If “some” turns out to mean “just one dog” (which it might, because “some” means at least one), then the conclusion that Guai Guai probably barks is supported by very weak evidence.

On the other hand, if “some” turns out to mean “99% of dogs” (which is also consistent with the word “some”), then that would be enough evidence to support the conclusion that Guai Guai probably barks.

This suggests that once we explicitly add the word “probably,” the argument is no longer best criticized as a deductive screw-up. Instead, the problem is that the evidence may be too weak to support the probabilistic conclusion. That makes the defect look informal rather than formal.

So what?

The problem with this borderline case is that intro-level logic teaching often makes the formal/informal divide sound cleaner than it really is.

Intro logic books often focus on a small handful of named formal fallacies, such as:

affirming the consequent (the COVID argument form)
denying the antecedent
undistributed middle

Possibly that’s because such fallacies are common, psychologically tempting, and canonically named.

But I don’t think fallacies have to be common or psychologically tempting to count as fallacies; they just have to be logically or linguistically defective. And that whole “canonically named” thing? That starts to smell a bit like dogma.

And even if broadening the term “formal fallacy” ends up making that category messier than philosophers would like, so what? If a counterexample makes the old definition unstable, that doesn’t show that the counterexample is bad. It might just show that philosophers’ understanding of the formal/informal divide is wonky and needs revision.

That’s my spiel for today. Keep thinking (and arguing).