Galileo's Ray of Light

I think I have a way of fixing philosophy

Longtime readers will know by now that I think math works, and science works, but philosophy, not so much. I think this is a huge problem, because I believe we really need philosophy. I also think I have the beginnings of a solution to the problem.

This may not seem exciting on first blush. Isn’t philosophy just a bunch of abstract questions that have no relevance for how many likes I’m getting on Instagram? But the current problems in philosophy actually have extremely practical consequences. For example, consider that:

A) America is riven by political disagreements that run more deeply than mere policy disputes. The bitter hatreds between factions arise from fundamental moral disagreements: A 2022 poll found 63% of Democrats see Republicans as immoral, while 72% of Republicans see Democrats as immoral, with these numbers increasing rapidly from previous years.¹ What really bothers me is that it isn’t even safe to be an independent anymore; failure to conspicuously support The Right Side means you are probably on The Wrong Side, and sorry if you’re just trying to do your job / fill your car with gas / pick crab apples from the side of the road, you’d better know the right answer to questions on whether global warming is going to destroy us all, whether the 2020 election was rigged, or how many genders there are.

B) Questions about whether Republicans or Democrats are right, or whether neither side is right and some other alternative is necessary, could be resolved if they were physical in nature. Experts would carry out the necessary experiments, discuss the problem among themselves, agree on a model, sand down the edges for the public, and explain what needed to be done in simplified but basically workable terms. Unfortunately, however, the problems are not physical, but philosophical. No experiments can be done. The idea of any philosophical problem being solved by “experts” begs the use of quote marks. Philosophers aren’t going convince anyone of anything, because there’s no effective methodology available for philosophers to figure things out. Where scientists have experiments, sophisticated mathematical tools, and reams of data, philosophers have the ability to cite one another in APA format.

As a result, philosophy is a discipline where All Things Are True. Multiple contradictory moral systems around, like Kantian Deontology, Bentham’s Utilitarianism, and even Aristotelian Virtue Ethics. Kant says it’s immoral to be a computer programmer, a doctor, or a baby; utilitarianism takes a moral intuition as its premise and violates moral intuitions for its conclusion; and Aristotelian Virtue Ethics was advanced by a guy whose style of reasoning lead to the conclusion that men have more teeth than women, which can be disproven by getting your cishet girlfriend to say “ahh” with you for a minute and a half. Virtue Ethics is over 2000 years old, and we still haven’t figured out how to demonstrate whether it’s right or not—we just see that whenever Aristotle used his philosophical tools to solve scientific problems, his results were a long string of failures.

“OK but that’s not fair to Aristotle,” you might say. “He really was brilliant, and laid the groundwork for many disciplines we regard as scientific today.” And it must be granted that Aristotle recorded an impressive number of observations, and drew more inferences from what he observed than most people who have ever lived. Back in the day, Aristotle wrote the book on basically everything.

From Wikipedia

Unfortunately most of those books have been eclipsed by modern understanding, when scientists were able to check what Aristotle said and showed it was generally not true. The bits of his writings people still refer to are largely confined to subjects where no one could ever check if he was right or not. And this is the point; if some guy is wrong about eels, and wrong about the sun, and wrong about teeth, are you going to trust him about moral excellence? If nobody teaches Aristotelian physics in school anymore because everyone knows it doesn’t work, and nobody repeats his biological claims anymore except for a laugh, what’s different about his ethical system? Is it that Aristotelian virtue ethics is just really great, or, might it rather be that philosophy just hasn’t been able to progress enough to shed any light on it?

I’m not going to challenge Aristotelian virtue ethics specifically here; instead I just want to point out that virtue ethicists who take Aristotle as an authority on morality are ignoring the way large swaths of Aristotle’s writings were also totally crazy and didn’t even remotely withstand what anybody would call the test of time. Elementalism, geocentrism, men having more teeth than women, the universe being eternal, eels not reproducing, whatever; for every discipline other than philosophy, Aristotle was basically an endless fountain of crazy ideas Muslims ardently preserved for the sake of confusing the living daylights out of Medieval Westerners, until Galileo came along.²

Also from Wikipedia.

Galileo wasn’t an ethicist, but he thought a lot about a couple of Aristotle’s big ideas—the geocentric notion of everything revolving around the Earth, and the elementalist notion that big rocks fall faster than little rocks. For those of you who aren’t that big on history, suffice it to say that Galileo observed moons orbiting Jupiter, which contradicted geocentrism; and Galileo dropped rocks of different sizes from the Leaning Tower of Pizza and found they fell at the same rate, which contradicted the idea that large rocks fall faster.

The big lesson of course is that empirical methods are effective, Galileo used them to prove Aristotle was wrong, and this is why science wins out over old prescientific ideas based on dubious premises and handwavy arguments. It’s exciting if you’re young and still wrapping your head around the idea that it doesn’t matter that empiricism isn’t nearly as sophisticated as rationality—the messy process of guessing and checking has given us airplanes, computers, and atomic bombs, while constructing intricate arguments has mostly given us schisms between religious sects and abstruse questions about whether all of God’s attributes are compatible with one another.

But forget about that for a moment. I don’t want to just say, for the umpteenth time, that empiricism beats rationalism. By now, you all should know that. Instead, I want to say something else.

Galileo’s Ray of Light

People say Galileo was a scientist. A really good one. Wikipedia calls him an an Italian astronomer, physicist and engineer. Astronomy, physics, and engineering are all scientific disciplines. Everybody agrees Galileo dedicated his life to science, and discussions commonly include him alongside other scientific geniuses like Copernicus and Sir Isaac Newton.

Understandably, then, it took me a long time to realize Galileo wasn’t just a scientist.

What we remember best about Galileo is the way he solved problems and answered questions using the classical tools of mathematical modeling and experiment which are now synonymous with physics. But after thinking about the problems with philosophy for months now, I just realized that Galileo’s methods also gave a clue about how to move forward with philosophy, because Galieleo also did something very interesting to Aristotle’s ideas using reason alone:

If then we take two bodies whose natural speeds are different, it is clear that on uniting the two, the more rapid one will be partly retarded by the slower, and the slower will be somewhat hastened by the swifter… But if this is true, and if a large stone moves with a speed of, say, eight while a smaller moves with a speed of four, then when they are united, the system will move with a speed less than eight; but the two stones when tied together make a stone larger than that which before moved with a speed of eight. Hence the heavier body moves with less speed than the lighter…³

This isn’t science. This is philosophy! What Galileo the philosopher is saying is that a contradiction lurks in Aristotle’s formulation. A small rock and a large one individually may fall at different speeds, but what if we tie them together with some string of negligible weight? At first they’ll fall at their individual speeds, but then when the string pulls taut, the small rock should slow the faster one down. Yet, this means we have the entire system falling half the speed that it should. If the rocks were just stuck together to form a massive super-rock, we’d expect it to fall faster than either the small or big rock taken individually.

Try not to worry about units; this is Aristotelian physics, so mass is on the same footing as velocity (and we don’t talk about acceleration)

Yes, Galileo arrived at these ideas after years of careful investigation and experiment, coming up with ways of measuring time by the regular dripping of water, and ways of slowing gravity by rolling bronze balls down inclined planes. But what if he hadn’t been able to to do that? What if he’d been stuck under house arrest from the day he was born? What if they were really afraid he might attack his guards and escape, or kill himself, or invent some weird new heresy, and nobody let him have inclined planes, or pans with water, or bits of bronze? Couldn’t he have still pointed out the inherent contradiction in Aristotelian physics just by asking about what happens when we tie two rocks together?

The power of experimentation lies its ability to contradict an expectation. People often say, somewhat glibly, that science doesn’t prove anything, it only disproves things. But this disproof comes from contradiction. We consider a claim, make some prediction based on the claim, and then if the prediction doesn’t come true, that contradiction falsifies the claim.

Do we specifically have to use empiricism to find a contradiction with an idea? Well, Galileo didn’t have to do that. Fine, he would have been a heck of a lot less convincing without a bunch of experiments and observations. But he still had a contradiction, which either flatly disproved Aristotle’s idea by itself, or else, would have required some explanation about how Aristotle’s model didn’t really predict that two rocks tied together wouldn’t average their falling speeds (although frankly the only way I can see of avoiding the contradiction is to say that as soon as you tie the rocks together, however loosely, their falling speed instantly increases, and then you end up with Aristotelian physicists obsessed with definitions for knots).

As for whether Aristotle would have felt this was an argument he even needed to think about, that’s obviously very hard to say. But if I’m allowed to guess, I’m going to say Aristotle would have found Galileo’s argument convincing. Because alongside the flotsam and jetsam of ideas that piled up from Aristotle are quotations where he affirms what we know today as the principle of non-contradiction:

Evidently then such a principle is the most certain of all; which principle this is, let us proceed to say. It is, that the same attribute cannot at the same time belong and not belong to the same subject and in the same respect; we must presuppose, to guard against dialectical objections, any further qualifications which might be added. This, then, is the most certain of all principles…⁴

Modern philosophy often calls the principle of non-contradiction into question; it isn’t hard to find publications on dialetheism,⁵⁶ or logical systems like intuitionistic logic that allow for contradictions.⁷ I don’t know about you, but this is one of the things that simultaneously fascinates and annoys me about philosophy.

But science is essentially founded on the principle of non-contradiction, or at least a version of it, which says that the predictions generated by an idea should come true if that idea is correct. Whether the predictions absolutely have to come true is a matter for debate, but at the very least, science can usually say whether a claim is consistent with the available evidence or not. This is what science says: contradiction is bad, and consistency is good.

If we get rid of the principle of non-contradiction, and stop worrying about whether observations are consistent with our ideas, then who cares what any experiment says? There’s no point in even carrying out an experiment at all, if it can contradict our beliefs without forcing us to at least suspect there is a problem with those beliefs. If this had been everybody’s attitude, we wouldn’t all be here communicating using over the Internet. The fact you’re even reading this at all is good evidence that science works.

And if the principle of non-contradiction is how science works, then this suggests the existence of a powerful tool that really should work for philosophy as well: Even in the absence of emperical evidence, we can still have philosophical evidence against a position that contains, or entails, a contradiction. Thus:

A strategy to show a position is false is to show that the position contains, or entails, a contradiction.

I’m not (yet) guaranteeing that this is a means of proving a position is false. Right now I’m simply calling it a “strategy.” Just because the principle of non-contradiction worked for science doesn’t mean it will work for philosophy. Science has already found that rules you might think work everywhere—like, “time passes at the same rate everywhere,” or “things don’t teleport through barriers”—don’t work at relativistic speeds, or in the quantum world. So just because contradictions can’t exist in the physical world where science has been so successful doesn’t mean that they can’t exist in aesthetics, or ethics, or other weird abstract realms of philosophy. But if nothing else, seeing how science works gives us a path to follow philosophically as well. Let me be really, really clear here that I’m not saying the principle of non-contradiction must work in philosophy, but I am saying that, if it’s got an excellent track record so far, then it’s at least worth taking seriously.

Here’s an example of what this ray of light might be able to illuminate. I’ve complained before about people insisting that there is no way of talking about art being better or worse, and I came up with an argument that some art really is better or worse than other art. Unfortunately I did that by using a style of argumentation that left me feeling suspicious from the moment I finished it, because it still had the same general style of an argument by some random philosopher. But if the principle of non contradiction can be taken as a solid tool, then the discussion becomes quite easy:

Does Beauty Lie in the Eye of the Beholder?

Let’s say it does. In fact, let’s start with the strongest, clearest wording we can: Let’s say beauty only exists in the eye of the beholder. This is the classic position held by philosophers like David Hume: “Beauty is no quality in things themselves: It exists merely in the mind which contemplates them; and each mind perceives a different beauty.”⁸ So, where does this lead?

1. Beauty exists only in the eye of the beholder.

2. There are no aesthetic principles independent of an individual or culture. (This is just a more explicit wording of #1.)

3. All aesthetic principles necessarily depend on subjective perspective. (And this is a positive restatement of #2)

4. Point 3 is an aesthetic principle.

5. And point 3 is true independently of any individual or culture.

6. So point 3 is an aesthetic principle which is true independently of any individual or culture.

7. But point 2 allows no aesthetic principles which exist independently of the individual or culture.

8. There is a contradiction, so, our initial assumption from Point 1 must be false.

9. It is not true that beauty exists only in the eye of the beholder.

10. There are some aesthetic principles or laws which exist independent of any individual or culture.

This proof is obviously rather drawn out; it’s possible to arrive at the same conclusion in half the number of steps, but I wanted to be cautious and break down the argument as finely as I could to allay suspicion that I was skipping past any difficulties.

I also should clarify that this doesn’t mean beauty does exist outside of the eye of the beholder. Maybe beauty is nonsense; this would entail a single objective aesthetic principle that says “everything is equally beautiful,” or just “beauty doesn’t exist.” Likewise, there could be some subjective principles of beauty as well as some objective ones. All this proof says is that there are not only subjective principles regarding beauty.

There is, of course, a way to sneak a purely subjective account of beauty back in, by saying “1. Only two objective principles govern beauty, and 2. Aside from these two objective principles, further subjective aesthetic principles exist.” But this still leaves the subjectivist in a weak position, rhetorically. Not only does it become obvious that two is a very specific number (Not three? Not seven? There are a lot of whole numbers out there) but when we want to express it in words we have to say something like “beauty is mostly in the eye of the beholder” or “beauty is essentially subjective,” which is pretty great from my perspective, because it explicitly leaves open the idea that, pretty soon, you may find yourself arguing tooth and nail about two-and-only-two being your favorite number.

But is Contradiction Always Fatal to a Claim?

The ten-step argument above is just one example of a way in which the principle of non-contradiction would allow incremental progress to be made in philosophy. The trouble is that we don’t know how strongly we can rely on my conclusion without knowing how big of a deal contradiction is. If you can wriggle out of the argument at Point 8 on the grounds that contradictions are allowed, then the whole argument is a waste of time.

What we might hope is that contradiction is absolutely not allowed ever, under any circumstances, because then we could use contradiction as a fully reliable tool to reject any self-contradictory premise with 100% confidence.

We might get greedy, and imagine the case where we could also rely on logical inference with complete confidence. Then if an idea leads logically to some conclusion down the line that contradicts the original idea, or even if two conclusions drawn from the initial premise contradict one another, then we can reject the premise with total, complete, 100% confidence. That’s what I tried to do just now with subjective morality: the premise leads logically to a structure of ideas that contains a contradiction.

The problem here is that even if logic always works, I could have been misusing it. But this is a possibility that doesn’t bother me. In principle, we could investigate what the chance of my making some error might be, by asking about what is the error chance per inference? 0.1%? 1%? 2%? Unlike philosophy, mathematics already works, and it’s trivial to calculate the chance my entire argument falls down as a function of the error chance per inference: It’s just 1-(1-rate)^9, so 0.9%, 8.6%, or 17%, respectively. I’ll stress these issues don’t seem to matter much in science; “Model X makes Y prediction” usually works well enough that the only thing anyone cares about is whether Y is consistent with the evidence or not.

What really matters is whether the general form of that argument is effective. Ultimately it all comes down to a question of whether the principle of non-contradiction must always apply in philosophy? And, how would we even answer that without using the principle of non-contradiction in the first place?

All I want to say about that (right now) is that the innumerable successes of science over hundreds of years are clearly in line with Aristotle’s insistence that something can’t be both true and false in the same sense at the same time. Aristotle also tried to use other forms of argumentation—mostly, he tried to draw questionable inferences from bizarre assumptions—yet through Galileo, the principle of non-contradiction became a ray of light illuminating the path forward.

So why hesitate? Why not simply embrace the principle of non-contradiction and move forward with confidence?

You may think me over-timid, but the reason for my hesitation is memory—or memories—of strange things I have encountered lurking in the metaphysical abyss. We already have hints of dialetheias, tetralemmas, unprovable principles, absurdities, and insoluble paradoxes guarding the way forward. These monsters may be terrible enough, but metaphysics is poorly charted territory, and who can say what aberrations lie in wait for us beyond the ordered realms of mathematics and empirical science? I haven’t found anyone else who has been able to actually vanquish these creatures. My only weapons so far are logical inference and the principle of non-contradiction, and can either one really be relied upon by anyone who strays too far from the safe and familiar realms of scientific empiricism?

(I think they can. However, I also think I have more thinking to do.)

1. Nadeem, R., & Nadeem, R. (2024b, April 14). As partisan hostility grows, signs of frustration with the Two-Party system. Pew Research Center. https://www.pewresearch.org/politics/2022/08/09/as-partisan-hostility-grows-signs-of-frustration-with-the-two-party-system/

2. Yes, this is a simplification, for more reasons than one.

3. Galilei, G. (1914). Dialogues concerning two new sciences (Henry Crew & Alfonso de Salvio, Trans.). http://files.libertyfund.org/files/753/Galileo_0416_EBk_v6.0.pdf

4. Aristotle. (2013). Metaphysics: Book IV. (W.D. Ross, Trans.). Roman Roads Media. http://classics.mit.edu/Aristotle/nicomachaen.2.ii.html (Original work published 350 B.C.)

5. Boccardi, E., & PErElda, F. (2020). What it is like to be a Dialetheia. The Ontology of True Contradictions. Eternity & Contradiction Journal of Fundamental Ontology, 2(2), 116-162.

6. Eldridge-Smith, P., & Joaquin, J. J. (2024). Can a dialetheist stay regular?. Journal of Applied Non-Classical Logics, 1-20.

7. Van Dalen, D. (2017). Intuitionistic logic. The Blackwell guide to philosophical logic, 224-257.

8. Hume, D (1777). Essay XXIII, Of the Standard of Taste. In D Hume, Essays, Moral, Political, and Literary, Part 1. https://davidhume.org/texts/empl1/st