How do we know things?

Imagine you know something—i.e., that $1+1=2$. Can you prove it? You could define addition as counting the first number from 0, and the second number from the first. You’ve probably seen a number line proof like that.

But can you prove that? After all, if you can’t prove it, you can’t say it’s always true.

In ZFC, we can prove addition of natural numbers. We use the axiom of infinity to define the natural numbers, then define the operation of addition with a recursive statement: $$a+0=a, a+S(b)=S(a+b)$$ where S is the function that increments a natural number. We’ve set up the base case and the general case for a proof by induction—we’re done. $$1+1=1+S(0)=S(1+0)=S(1)=2$$

Can you prove that the natural numbers exist? In Principia Mathematica, Bertrand Russell and Alfred Whitehead proved that $1+1=2$ using just logic. It took hundreds of pages, but it is possible.

But, can you prove logic works? If you can’t prove it, it may not be true. If you are not already attuned to such arguments, I hope to teach you about this infinite regress problem, the proposed solutions, and why the majority of people pick one in particular. Hint: it’s not skepticism.

The Trilemma, and the Skeptic Backdoor

The above example is an actual problem, with no good solution. Any statement must be justified, yet justificiations need justification as well. How do we resolve the truth of a statement?

1. We can let the justifications continue to infinity, I guess. That would be a regressive argument.
2. We can attempt to make a circular argument, where we support the justification with the proof.
3. We can simply assume that the justification is true, and refuse to prove it. This is a axiomatic or dogmatic argument.

None of those options sound great—this is most commonly called the Münchhausen trilemma. It proposes that we’re fundamentally limited in our ability to know, and we have to pick from a lose-lose-lose situation.

Some of these options are better than others. Regressive arguments are useless. Circular arguments are bad most of the time, but that could be my own bias and unfamiliarity with coherentism. Axiomatic arguments are the best we have—decide something is true, assume it to be so, and build everything on top of that. That’s how math works.

Skepticism is refusing to pick any option—we just can’t prove things.

A while ago, I found some common justifications Which is somewhat amusing, since we’re not supposed to be able to prove things. for skepticism—and their counter-arguments—in this article. The arguments deal a lot with the human mind and its weaknesses, and you’ve probably heard at least a couple of them before.

Popular Skepticism

The first I’ll mention:

We can’t say for certain that we aren’t brains in a jar, being fed a fake view of reality. A sufficiently advanced entity could have made our minds Or just yours, if you’re a solipsist. hallucinate every sensory input it’s ever received. Thus, we could percieve something as entirely true, and yet in reality it is entirely false.

It’s a fun idea to think about, but the premise is its own demise. If we are brains in a jar, we would never know we are brains in a jar. There would be no proof of it. We decide truth by what has been proven to be true—and if there’s no possible way to prove or disprove this statement, The term here is unfalsifiable. Russell’s teapot echoes this decently well. then it isn’t worth discussing arguments like this.

Sensory Skepticism

Our senses often fail us. After all, we are material beings trying to view a material world. How could it ever be possible for us to know anything—how can we know we were seeing the world objectively?

Often is not always. We may be deceived about the world sometimes, but that doesn’t mean that we can never observe objective reality.

What if it was always? In that case, we have:

Kantian Skepticism

The real world is inaccessible to humans. Our minds warp and bend reality such that what we view as objective truth is anything but. We could be viewing the world completely wrong!

It’s entirely true that we could be seeing the world completely wrong because of the way our minds work, but that is easy to counter. Let’s say that we want to know X, and we observe X to be false.

1. Design an experiment or machine to observe X.
2. The experiment / machine says X is true, or false.
3. Therefore, we know the objective value of X.

Think about electromagnetic waves: we would never think that such a thing existed And didn’t for millenia. because our bodies and minds don’t percieve them, but we’ve developed machines that show that they do exist.

Could our minds be deceiving us about the results? Sure—they do all the time through biases. If everyone were misled in the same way about the same results, isn’t that our objective reality? We can be wrong about something, but if there’s no way to know, this is sounding a lot like the first argument. Did you just think something like “I can use this argument to discredit your radio waves discussion above.”? Well, good for you—I can’t think of a counter right now.

Linguistic Skepticism

Our reliance on language is a crutch. It filters our perception of reality. The Ancient Greeks did not have a word for blue, leading Homer to call a sky the color of bronze, and a stormy sea the color of wine. English didn’t have a word for orange until oranges came around, so they described people with orange hair as “red-heads”.

It’s impossible to discuss an idea that you don’t have the words for. Reality could present itself to us, and we couldn’t describe it.

Imagine no one in the world has ever seen a cow before.

You have no words to describe a cow—no one does.

One day, you and a friend see a cow.

You think, “I have no clue what this thing is.”

Your friend asks, “Hey, what’s that thing over there?”

You turn to them and say, “I don’t know—let’s call it a poaoqnewr.”

And thus, humanity now knows about poaoqnewrs. There’s a reason we constantly borrow words from other languages to describe concepts that aren’t in our vocabulary. Language is adaptable.

Summary

Skepticism can be fun. I read through a fair bit of Celia Green’s The Human Evasion, and loved to think about how it’s possible that I could jump over my house. Basically, you’re basing your view about the future on facts from the past, but predictions are quite often wrong. It’s useful to remember our limitations as humans, physically and mentally.

That does not mean that skepticism is better than objectivism. Occam’s Razor says so, and even if the world we viewed wasn’t the objective reality, that world we perceive would be the objective reality. Skepticism at this low level is a statement of doubt about things that don’t matter if they’re doubted. If we actually have swapped the values of truth and false, what difference would that make? Electrical engineers have been working with swapped values for a hundred years just fine.

I will finish with a proof by G. E. Moore. Who I had never heard of before writing this section. All skeptical claims can be boiled down to this argument:

There is some possible skeptical situation (see above examples) S. There is some knowledge claim Q that is information about the world.

1. If you don’t know that S isn’t true, then you don’t know that Q is true.
2. You don’t know that S isn’t true.
3. Thus, you don’t know that Q is true.

Moore’s response:

Let Q be the fact that you have two hands.

1. If you don’t know that S isn’t true, then you don’t know that Q is true.
2. Here is one hand.
3. Here is another.
4. Q is true.
5. Thus, you know that S isn’t true.