science – Philosophy without Bullshit

Is Philosophy Bullshit?

Difficulty: What the heck

Some philosophy is absolutely bullshit.

There is pseudo-profound nonsense. There is empty jargon. There is status-signaling dressed up as rigor. There are philosophers and graduate students who perform seriousness without being genuinely guided by the standards of inquiry they invoke. So if by “philosophy” you mean that sort of thing, then yes, philosophy can be bullshit.

But it does not follow that philosophy itself is bullshit any more than the existence of bad science shows that science itself is bullshit. The real question is whether philosophy, at its best, is a useless exercise in verbal fog—or whether it does something intellectually and practically significant.

My answer is: no, philosophy is not bullshit. At least, not when it is done properly.

To see why, we need to make one annoying but necessary move: we need to get clearer about what we mean by both “bullshit” and “philosophy.” Otherwise, people end up yelling past one another. One person means pseudo-profound academic fog. Another means logic, ethics, political theory, or the philosophy of language. One person means empty performance. Another means disciplined reflection on reasons, concepts, and arguments. Unless we sort that out, the question “Is philosophy bullshit?” is too muddy to answer well.

Now, trying to define philosophy in a perfectly neat way is hard, just as trying to define science in a perfectly neat way is hard. Science includes physics, chemistry, and biology, but also things like geology, medicine, neuroscience, and perhaps at least some of the social sciences. Philosophy is similarly sprawling. It includes logic, epistemology, ethics, metaphysics, political philosophy, philosophy of language, philosophy of mind, and much else besides. So instead of hunting for some magical one-sentence definition, it is more useful to ask: what does philosophy do when it is working properly?

At its best, philosophy clarifies concepts, tests reasons, exposes hidden assumptions, and asks what follows from what. It tries to distinguish what merely sounds plausible from what actually makes sense. It trains us not just to have opinions, but to examine them. And that, I think, is already enough to show why philosophy is not simply bullshit.

To answer whether philosophy is bullshit, then, we also need at least a rough grip on what bullshit is.

Let’s clear away a few common misconceptions.

Bullshit is not the same thing as lying.

Bullshit is not the same thing as falsehood.

On Harry Frankfurt’s account, bullshit is, roughly, a product of someone who is indifferent to the truth but pretends otherwise, misrepresenting herself as someone who cares. So a student who bullshits on an essay to reach a minimum word count may do so not by lying or writing what is false, but by not caring at all whether what she writes is true. She merely wants to appear as if she gives a shit so that she can get a decent score.

On my account, bullshit is, broadly put, the empty performance of norm-guided speech or conduct without being genuinely guided by the norms that make the practice intelligible. A few of the norms that make philosophy intelligible, for example, are clear argumentation, logical reasoning, and openness to criticism or objections. A philosopher who merely performs those norms while refusing to be genuinely guided by them is no longer engaged in serious inquiry. At that point, what we are seeing is not actual philosophy, but bullshit.

Now, what many people seem to mean when they say philosophy is bullshit is that philosophy is useless. But that opens another can of worms, because we would then have to clarify what “useless” means.

If by “useless” they mean that philosophy does not reliably lead to a high-paying job, then sure: philosophy is not a guaranteed path to wealth. But it would be a leap to say that because many philosophy majors do not become rich, philosophy is therefore bullshit. Poor career outcomes, even when they exist, do not show that a discipline is intellectually empty.

And even on practical grounds, philosophy is not obviously useless. Because philosophical inquiry emphasizes reading, writing, argumentation, and logical reasoning, philosophy majors tend to perform very well on standardized tests like the GRE and LSAT, and many go on to law school and careers in law, policy, business, and education. The ancient story of Thales of Miletus makes the same point in a more amusing way. According to Aristotle, Thales, annoyed at those who accused philosophers of being useless, used his intelligence to invest in the olive industry and made a fortune. “[Thales] proved,” Aristotle writes, “that philosophers can easily be wealthy if they wish, but this is not what they are interested in.”

So what are philosophers interested in?

They are interested in exercising their minds the way athletes exercise their bodies. They do this not to guarantee victory in every situation, but to build habits of discipline, responsiveness, and control that matter when things get difficult.

And I do not mean only intellectually difficult, though philosophy is certainly helpful for that. I also mean difficult in the more painful sense: your life turns to shit, and you are barely holding on.

In the 1960s, when U.S. naval officer James Stockdale was captured and tortured by North Vietnamese forces, he applied the Stoic philosophy he had learned at Stanford to remain sane. When Marcus Aurelius led the Roman Empire, he drew on the same philosophical tradition to maintain equanimity while confronting war, plague, and political burden.

So I am not saying that philosophy matters only in classrooms or journals. At one of the worst moments of my life, a philosopher once gave me a simple argument that helped keep me alive.

Sometimes, clear thinking is not an academic luxury. Sometimes, it is what makes life bearable. And often, it is what makes life worthwhile.

So, is philosophy bullshit?

Sometimes, yes—when it degenerates into pseudo-profound fog, empty performance, or jargon without guidance. But philosophy itself is not bullshit when it does what it is supposed to do: clarify, test, examine, and help us think more clearly about what matters.

Try it seriously, and that much should become obvious.

What the Actual Fuck Is the Soundness Theorem in Metalogic? (Explained to Myself like I’m a Dumbass): Part 1

Difficulty: What the actual fuck

Before you attempt to understand this article, make sure you first read my previous article, “What the Fuck Does “Proof” Even Mean? (And Why It Doesn’t Guarantee Truth).”

I’m going to attempt the impossible in this post: explain something that confused me and pissed me off so much in grad school that it became one of the (many) reasons I quit the program. But it’s been a decade since I left, and now that there’s no pressure to publish papers, meet deadlines, and pass the damn courses, it’s time to revisit this shit with a vengeance.

Metalogic — what in the actual fuck does that even mean?

We’ll lay down some foundational metalogic concepts first so we can tackle what’s called the soundness theorem in metalogic within what’s called the Hilbert system, not just as a vague example, but with as much precision as possible—while translating every piece of symbol garbage into normal human English.

The calculator analogy

Say you have a calculator.

2 + 2

and it spits out:

4

Cool. That’s just doing math.

That’s like doing a normal logic problem: you follow rules → you get an answer.

But metalogic asks something way more annoying:

“How do you know the calculator won’t randomly give you 5 or 10 or 17 one day?”

Not just for 2 + 2.

But for:

17 + 83
999 + 1
ANY numbers you plug in

So we’re not checking answers.

We’re checking whether the system itself ever screws up.

What we need to show

To prove the system is reliable, we need four things:

Premises
Axioms
Rule Case
Inductive Step

I’ll explain what the hell these things mean using analogies along the way.

(1) Starting assumptions (premises)

These are just things you’re told to start with.

Math analogy:

You get a math problem. It says assume that x = 5.

You don’t question the math problem and say shit like, “How do you know that x = 5? Can you prove it? No? Then shut the fuck up.”

Instead, you say, “Cool, let’s just say that x = 5 is true.”

Chess analogy:

Say that you’re playing a game of chess. You’re given a starting position: the white queen is on one square, the black queen is on another, the rooks are in the corners, and so on. You don’t say, “How do we know that’s where these pieces begin?” You just assume those positions are correct and move on.

Logic example:

Statement 1: If you eat Taco Bell, you’ll have diarrhea.

Statement 2: You eat Taco Bell.

…you don’t question whether these two statements are true. You assume they’re true for the sake of argument. If we want to add a few scary logic symbols, we write:

Γ = { Taco Bell, Taco Bell → diarrhea }

Translation (without the hieroglyphics)

Γ (the big scary Greek letter gamma) just means:

“the set of starting assumptions”

So this is just a fancy way of saying:

“Here are the things we’re starting with. This is like ‘assume x = 5’ in a math problem or a given starting position in a game of chess. Don’t question them (for now).”

Even simpler

Γ =

Taco Bell
If Taco Bell → diarrhea

That’s it.

No magic.

Important clarification (so nobody loses their mind)

We are NOT saying:

“Taco Bell is actually true in real life”

We are saying:

“Assume it’s true. Now let’s see what follows.”

One-line takeaway

Premises are just the starting point of the game—not guaranteed truth, just assumed truth.

(2) It starts with stuff that can’t be wrong (axioms)

Axioms are different from premises.

Premises are just assumptions you start with.

Axioms are patterns that come out true no matter what you plug into them.

Math analogy:

x = x.

No matter what number you plug in for x, it always comes out true. There is no situation where a thing is not equal to itself.

Chess analogy:

There are some things built into the chess system itself. One piece can’t occupy two squares at once. Two pieces can’t occupy the same square. If that happened, the game would already be broken before it even began.

Now here’s where my past self would start getting pissed off:

“Why the fuck are we allowed to just say this can’t be wrong? Aren’t we just assuming that?”

That sounds like what’s happening—but that’s not actually what’s going on. In logic and metalogic, it has something to do with a possible situation.

What the hell is a “possible situation”?

In logic, a “possible situation” does NOT mean:

some weird sci-fi universe
or “anything you can imagine”

It means something much more boring:

a way of assigning true or false to statements

That’s it.

That’s what truth tables are doing.

So we’re not assuming—it’s more like checking every possible truth assignment

Take a typical logical axiom:

“If A, then (if B, then A)”

Now we check ALL possible truth assignments:

A	B	B→A	A→(B→A)
T	T	T	T
T	F	T	T
F	T	F	T
F	F	T	T

This means:

If A = true and B = true, then A→(B→A) is true.
If A = true and B = false, A→(B→A) is still true.
If A = false and B = true, A→(B→A) is true yet again.
If A = false and B = false, A→(B→A) is true too.

We’ve exhausted all the possible situations, or all possible truth assignments. Whatever true/false shit you might assign A and B, A→(B→A) always comes out true.

In other words:

Does this thing EVER come out false?

No.

Not even once.

So we’ve proved that this is a legit axiom. That means we’ve proved that what we’re starting with can never spit out garbage.

Important clarification

You might say, “Hey, dumbass, what if I define a situation where A and ¬A are both true?”

For example:

A	¬A
T	T
F	F

Cool.

But then:

you’ve changed the rules of the game

You’re no longer doing classical logic.

And if you change the rules, then yes:

you have to redo the whole soundness proof for that new system

Final translation of “axiom”

Axioms aren’t trusted because we feel like it. They’re trusted because, given the system’s definition of truth, we can check every possible case—and they never come out false.

(3) The rules never mess things up (rule case)

Now we check the rules.

Math analogy:

Suppose you know:

2 + 2 = 4
4 + 4 = 8

Now you apply a rule:

“If a = b, then you can replace a with b”

So from:

2 + 2 = 4

you’re allowed to treat 4 as interchangeable with 2 + 2.

So (2 + 2) + 4 = 8.

This math rule never messes up.

Chess analogy:

Bishops move diagonally.

So if your bishop starts on a black square, it will always stay on black squares.

And if your bishop starts on a white square, it will always stay on white squares.

So the rule “bishops move diagonally” will never randomly make a bishop jump from a white square to a black square, or from a black square to a white square, or do some other crazy shit.

In logic, here’s the big rule:

Modus Ponens

A

If A → B

Therefore:

B

Concrete example

Metalogic is gay.

If metalogic is gay, Raymond’s ass is demolished.

Therefore:

Raymond’s ass is demolished.

Now here’s the important part

This isn’t about THAT specific sentence.

It’s about the form.

You can swap in anything:

Example 2

You eat Taco Bell.

If you eat Taco Bell, you’ll have diarrhea.

Therefore:

You’ll have diarrhea.

Example 3

I didn’t sleep.

If I didn’t sleep, I’m miserable.

Therefore:

I’m miserable.

Example 4

I make poop jokes.

If I make poop jokes, I’m childish.

Therefore:

I’m childish.

The key question

Is there ANY situation where:

A is true

“If A then B” is true

but B is false?

No.

There is no such situation.

Again, in intro to logic class, you can use a truth table to check this:

A	B	A → B
T	T	T
T	F	F
F	T	T
F	F	T

The only row where A is true and A → B is true is the first row. And in that row, B is true too.

Therefore:

This rule NEVER turns truth into bullshit.

(4) If every step is good, the whole thing is good (inductive step)

This is where grad school says:

“We proceed by induction”

and everyone (well, me, at least) dies inside.

Again, we’ll first use the math analogy.

Start with:

2 + 2 = 4
4 + 4 = 8
8 + 8 = 16

Notice something:

You’re always adding an even number to an even number.

And every time:

you get an even number

Now the key idea

If:

even + even = even (this NEVER fails)

Then:

no matter how many times you repeat this process, you’ll ALWAYS get an even number.

That’s the inductive step

You’re not checking:

just the first step
just the second step

You’re saying:

“This pattern keeps working forever.”

And how do we know it works forever? We know not because we’ve checked a bunch of numbers and got tired and said, “Fuck it, it works for all numbers for infinity.” It works because we get the form of the math. That is,

2a + 2b = 2(a + b)

Steel staircase analogy:

You’re building an infinite staircase. The first step you build is made of solid steel. It doesn’t collapse. The second step is built the exact same way. It doesn’t collapse. The third step is also built identically to the second. So it’s impossible for the entire staircase to collapse.

Why?

Not because you checked a few steps and said, “Cool, it works for all the steps.” It’s because the way each step is built is identical to the next.

Chess analogy:

If every move you make is legal, and every move is made according to the same rules, then the entire game stays legal. The board won’t suddenly sprout a third king or summon a UFO to suck away your pieces halfway through the game.

Translation

If every step in your reasoning is safe, then the final result is safe.

Conclusion

If your eyes glazed over, don’t worry. Just keep this in mind:

Every line in a logical proof is either:

a given assumption/premise (like x = 5)
an axiom (like If A, then (if B, then A))
the result of applying a rule (like modus ponens)

And induction is the method that lets us say:

if every step is safe, then the whole proof is safe

So if premises don’t start us with bullshit, axioms never spit out bullshit, and rules never turn truth into bullshit, then the whole logical system we’re checking is legit.

In other words:

If you can prove it (using the logical system you’re checking) (⊢), it’s true (⊨).

That’s all for today. In a future blog post, I’ll take you through the proof for the soundness theorem step by step, using the Hilbert system.

What the Hell Is an Argument? (And Why “Deductive = General to Specific” Is Bullshit)

Difficulty: What the hell

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.

What the Fuck Does “Proof” Even Mean? (And Why It Doesn’t Guarantee Truth)

Difficulty: What the fuck

This is the kind of weird shit logicians study in something called “metalogic.”

Briefly: Much confusion arises from the term “prove.” If I can prove something, doesn’t that just mean that that thing is true?

Not necessarily.

In logic (and analytic philosophy), “prove” has a different meaning from everyday usage. All it means here is: I can arrive at some conclusion if I follow the rules in a system.

Imagine that you’re playing a game called “Math for Morons.” The game is the aforementioned system, and the rules of that system include the following:

1+1 = 2
1 + 1 = 3

According to the rules of the “Math for Morons” system, you can then prove 2 = 3. But that doesn’t mean that it’s true that 2 = 3. The point being? Proof (according to the definition of “proof” in logic class) doesn’t guarantee truth.

And if you can prove something in the logical sense but still not arrive at the truth? That means the system is broken. Logicians call a broken system like this inconsistent.

Logicians even have a symbol for this kind of provability: ⊢ (the single turnstile).

But what if it’s the other way around? That is, something is true, but you can’t prove it.

This is what logicians call incompleteness.

Incompleteness:

does NOT mean “true but very hard to prove” (like the fact that my dad is an asshole—hard to prove, but not what logicians mean here)
means “true but you can’t prove it using the rules you have in your system/game” In other words: the truth is out there, but your system is too weak to reach it.

So imagine that in your “Math for Morons” system, there are no rules at all about even and odd numbers.

But it’s TRUE that

“2 is an even number.”

Then even though it’s true that 2 is even, you can’t prove it within the system, because the system simply doesn’t have the tools to express or derive that fact.

Logicians also have a different symbol for completeness: ⊨ (the double turnstile).

Roughly speaking, this doesn’t mean “you can prove it.”

It means:

“This has to be true, no matter how you interpret things.”

So metalogic asks a deeper question:

Do the things you can prove (⊢) line up with the things that are actually guaranteed to be true (⊨)?

Or are you just pushing symbols around and hoping for the best?

By the way, in standard (“classical”) logic, there’s a nice result:

If you can prove something using the rules (⊢), then it really is true in the relevant sense (⊨).

Logicians call this soundness.

But that’s another can of worms for another day.