The Good, the True and the Undefined

When you read a lot about philosophy and history of philosophy there are a few ideas you come across often enough that they start to feel like old friends. Or sometimes like old and slightly tiresome acquaintances you kind of wish would go away so you could meet more interesting people instead.

Sadly, many “classic” philosophical problems fall in this category. The good way to think about them is not so much as inviting answers but as revealing the nature and shortcomings of our thought patterns. The bad way is the opposite.

Just to pick something at random: object identity. The classic thought experiment The Ship of Theseus asks us what it means to say that something remains the same over time. The famous ship has a plank replaced, and we are asked if it’s still the same ship. Then another plank, and on and on until every single part is new. Is it still the same ship?

In a later version, an M. Night Shyamalan-moment is added and it’s revealed that every removed piece has been used to construct an identical, second ship somewhere else. Now which one is the original?

Let’s get a little weirder and go from a ship to a person. Donald Davidson devised a thought experiment called Swampman to ask what it means for a person to remain the same:

Suppose Davidson goes hiking in the swamp and is struck and killed by a lightning bolt. At the same time, nearby in the swamp another lightning bolt spontaneously rearranges a bunch of molecules such that, entirely by coincidence, they take on exactly the same form that Davidson’s body had at the moment of his untimely death.

This being, whom Davidson terms “Swampman,” has, of course, a brain which is structurally identical to that which Davidson had, and will thus, presumably, behave exactly as Davidson would have. He will walk out of the swamp, return to Davidson’s office at Berkeley, and write the same essays he would have written; he will interact like an amicable person with all of Davidson’s friends and family, and so forth.

Davidson nevertheless says that despite being identical, Swampman is not him and identity means something more than just physical form. Others, like Derek Parfit, argues that personal identity, like object identity, is incoherent in such situations and in fact incoherent altogether.

There are a number of clevernesses like this from the ancients greeks and those following in their footsteps, all designed to communicate the basic idea of philosophy: our ordinary intuitive ideas about things break down as soon as we start poking at them.

Socrates was a great poker. He went around asking people what beauty, truth and justice really was — if people used these words they should know what they mean, right? Whatever his interlocutors said, he would ask uncomfortable follow-up questions and come up with objections and counterexamples until they were forced to accept that they really didn’t know what they were talking about.

But it didn’t end there. Plato, using Socrates as his mouthpiece, did think that these questions had answers. They were just not obvious, and finding them would require some philosophy — that’s what he called his approach of figuring things out by thinking about them really hard.

In a very short and probably terrible summary (my education on this was brief, please don’t hit me, classicists[1]): Plato believed that concepts like truth, beauty and justice were the fundamental constituents of reality, but we could only perceive them as filtered by the imperfect, impure and temporary physical world — a world created by an entity called the Demiurge, obscuring the Pure Forms. He thought that by thinking, abstracting and generalizing, we could patch together what little we could perceive through the filter of the material world and get direct access to reality.

Why would he think that? It makes sense if you consider the greeks’ advances in mathematics. By observing a lot of round things and abstracting we can derive the pure “form of the circle”, and by observing kind-of-triangles in the world we can extract “the mathematical triangle”, free from any imperfections intermingling with mere matter brings. Shouldn’t that mean that if we observe a lot of imperfectly beautiful things, we could abstract away the irrelevant incidental features of physical objects and arrive at pure Beauty? By observing the just and the unjust and what separates them, should we not be able to isolate Justice? Our intuitions about truth, beauty, justice, etc. are in fact tools of perception, that allows us, however imperfectly, to apprehend the true nature of truth and goodness.

Nice thought, but it’s a disaster. Plato was the mind-projection fallacy personified.

It seems to me that philosophy has been too enamored with Plato’s mistaken ambitions for it’s own good, and clung for far too long to the idea that philosophical questions are supposed to have answers that can withstand any and all criticism.

Indeed, the history of philosophy can be described (partly) as an endless tug-o-war between some philosophers trying to find a correct and complete account of a slippery concept or question (the nature of objects and their properties, truth, good and evil, knowledge, possibility and necessity, existence, meaning, free will, beauty, blah blah, all the usual suspects), and other philosophers finding ways to break those accounts with cleverly constructed criticisms. The first set of philosophers would then be forced back to the drawing board. Rinse and repeat.

David Chalmers’s paper Why isn’t there more progress in philosophy? says that true progress in the scientific sense — the wholesale culling of bad ideas in favor of useful and productive ones — is rare. Instead philosophers defend their ideas, typically by making changes rendering them more complicated sophisticated.

Over many iterations this led to complex, overengineered philosophies bearing little relation to the common sense notions they ultimately descended from. Immanuel Kant justified morality by forbidding actions he claimed were logically self-contradictory and self-undermining, and therefore that being immoral was a way of being illogical. According to Peter Unger morality requires that we value the interests of people on the other side of the world as much as our own and our families’. A straightforward idea like “the greatest happiness for the greatest number” leads us straight into the repugnant conclusion. Robert Kane suggests in a 1996 book that free will is quantum events affecting electrons in the brain, and Harry Frankfurt conceives of that same freedom as a particular structure of meta-level desires about desires. Epiphenomenalism about consciousness, held by David Chalmers among others, means as far as I can tell that we are conscious, but it’s not our consciousness that causes us to say so. I mean… yeah[2].

You can find such argumentation-as-art interesting, elegant and convincing — not to mention fun — but these philosophies don’t have much in common with people’s everyday sense of morality or free will or consciousness and they don’t inspire much of “Yes! That’s what we were all thinking of! It all makes sense now! Good work, philosophers!” It seems unlikely that they ever will. Plato’s dream is dead and sometimes I feel we’re just putting more and more layers of makeup on the corpse.

When my oldest daughter started to talk, I wondered if some words would be difficult for her to wrap her head around. Words like “big” or “here” are tricky to pin down, how could she grasp the subtleties? “Here” can mean within arms reach, within earshot, in the same town, same country, continent or galaxy. Sometimes only a tiny area on my shoulder where I just got a mosquito bite and sometimes it’s not even a place but more like ”in this context”.

It can also be hard to know what “big” means. If I pick up two rocks, and I call one “big” and the other “small”, will she get confused if I put down the big one and pick up a tiny pebble, calling it “small” and the previously “small” rock “big”? It used to be small, now it’s big? Without changing? This is some crazy shit.

I shouldn’t have worried. It turns out toddlers deal just fine with the fuzziness, ambiguity and context-dependence of language. Philosophers sometimes don’t.

Nobody tries to find a rigorous defintion of ”here” or “big” because everyone understands that there isn’t one. There is no platonic “Form of the Big” imposing itself on matter, resulting in Big things. There is nothing behind the word we can “think ourselves towards”. It’s surface all the way down. That goes for other words too, including ones philosophers do like to fret over, like “true”, “free”,”possible”, ”real”, ”exist”, or ”knowledge”.

Don’t sweat it. They’re just words. A means of interpersonal communication embedded in specific situations and in need of local interpretation. We have no reason to expect them to have an abstracted, context-free, unambiguous meaning.

The Ship of Theseus shows that object identity fails when we try to use in a highly contrived hypothetical context deliberately designed to break it. Big whoop. Swampman and Parfit’s thought experiments show that personal identity becomes incoherent in weird situations that have never occurred. Whoop whoop. The Gettier problem demonstrates there are similar issues with our idea of knowledge, and I don’t even want to get into what people say about what “truth” means (here is a 15.000 word short summary to get you started).

Should we just not look into this stuff? [3] No, that’s not what I’m saying. I’m just saying you shouldn’t be too stubborn looking for things that aren’t there, and that there’s a limit to how far you should go to account for weird outliers. Plain dismissal is often a totally reasonable way to deal with noise or irrelevant edge cases (this article describes this attitude and its tensions with academic philosophy from a different angle).

Truth is, almost any account or definition can be “Gödeled” — broken by an example specifically engineered to break it. This article is good example of how the idea that there can exist necessary and sufficient conditions for defining something as “rape” (my apologies for bringing up an unpleasant concept unexpectedly, it’s just such a good article) gets completely destroyed. And some commenters respond with yes/no-answers to each case! That is NOT the point.

The point is that the existence of edge cases and counterexamples doesn’t mean that concepts, maxims or principles are useless, don’t exist or are somehow invalid. There are people born with six fingers on each hand, that doesn’t invalidate “people have five fingers on each hand” as a rule. It just makes it less than infinitely true. A room contains some trace amounts of dirt no matter how well you clean it. It doesn’t mean it’s “dirty”. It’s just less than infinitely clean.

This is something we can deal with; it’s fine not to cover all cases if that saves us from tortured, overcomplicated philosophies sucking up valuable time and brainpower. Unless you think language is or can be a rigorous logical system operating by exactly the same rules as reality itself (it’s not and it can’t), why would we expect our pragmatic communication tools to work in situations they’ve never been exposed to? Humans can’t survive naked in Antarctica, on Venus or in a vacuum and this isn’t some inexplicable deficiency we ought to be able to cure with the right training regimen, supplement-rich diet or clever visualization exercises.

Think about mathematics. In mathematics some things are simply undefined, with no value or no answer. For example, if you have the formula y = 1/x and let x approach 0 by getting smaller and smaller, y grows infinitely large. So 1/0 is infinity? No, because if x is negative and approaches 0 from the other way, y instead drops towards negative infinity.


The relation y = 1/x simply does not have a value for y when x is 0. It is undefined; the system doesn’t cover it. This is how math works and we don’t need to develop new mathematics that can give 1/0 a value.

Some things are or should be undefined in philosophy as well, examples include ”Is the first or second ship the real Ship of Theseus?”, ”Is Swampman Davidson?” or the answers to moral dilemmas like “Should you push the fat man to stop the trolley?” and “Is it acceptable to torture a person to prevent a minor inconvenience for a large enough group of people?”[4]. The meaning of words and truth of statements can be included as well, if you want to be strict.

It might sound like I hate philosophy or look down on it. I don’t. I actually love philosophy, to the extent that I wrote a bachelor’s thesis[5] in it and have seriously considered pursuing a doctorate (except I also like making money). Here[6] I’m like the stereotypical Star Trek fan doing his favorite thing (complaining about Star Trek), full of disappointment fueled by intense caring and affection.

It might also sound like I think I’m bringing unique insights or new ideas[7]. I know I’m not; views like mine are common among philosophers and is similar to what’s called Quinean Naturalism after Willard van Orman Quine. Luke Muelhauser says this in an article on Less Wrong:

Yudkowsky once wrote, “If there’s any centralized repository of reductionist-grade naturalistic cognitive philosophy, I’ve never heard mention of it.”

When I read that I thought: What? That’s Quinean naturalism! That’s Kornblith and Stich and Bickle and the Churchlands and Thagard and Metzinger and Northoff! There are hundreds of philosophers who do that!

Great! We still have a problem — my experience is just like Yudkowsky’s. I’m not a philosopher but I’ve been interested in the subject ever since that first encounter with Sophie’s World many years ago; I’ve read a mix of pop-texts and more technical stuff for years, and from that list I recognize maybe the Churchlands and only know about Thomas Metzinger’s existence by accident (I bought one of his books on recommendation but still haven’t read it). Why have I not come across any of them in popularizations? Why are not these the philosophers the educated public knows?

Perhaps it’s because of the unfortunate conflation of Philosophy with the History of Philosophy.

If you try to study the first in a university, the second is what you’re likely to be taught. Starting with the greeks, we visit medieval scholasticism for a bit before moving on to Descartes, Hume, Locke, Kant and those guys. Then there are romantics, idealists and existentialists. Lots of Germans and French. Nietzsche, Heidegger and those guys. Lots of guys. The modern and postmodern eras and their world-shaking revelations are treated as an afterthought in most histories, the coda to the main story — when in fact the so-called main story is just the introduction, the overlong origin story of philosophy, the prelude, the charming-yet-clumsy early attempts.

I suspect the fact that we do it this way is partly responsible for the lack of progress in philosophy described by Chalmers. A philosophy education saddles you with all this conceptual baggage about the nature of truth, knowledge, language, meaning, rightness, goodness, objects and their properties[8] that you’re unlikely to unlearn once you catch up. Furthermore, those who fall in love with this baggage are the ones most likely to stay and perpetuate the discipline. And on and on we go.

Just imagine if science education worked this way. ”You want to study chemistry? Sure, we have two years of study on the five classical elements, alchemy, caloric theory, phlogiston, vitalism, transubstantiation, essences and whatnot that you have to learn backwards and forwards, and then, when you’re ready, we’ll get to atoms and molecules — but that’s advanced stuff“. Would that make better chemists? Wiser in the end, maybe. But I doubt it’s a good way to perpetuate and further chemical knowledge effectively, especially if getting bogged down with studying and commenting on old approaches to chemistry was an accepted practice. What I don’t doubt is that it would severely screw up the general population’s scientific literacy.

A post on Meteuphoric asks why we should read old philosophy and settles uneasily on the answer that maybe philosophy isn’t about finding answers but about learning how to think like philosophers, and the best way to do that is to read old original texts to get inside the authors’ heads. Ok, but what if you want to make progress on important issues and not just cargo-cultishly imitate the ancients’ largely ineffectual habits? With all the knowledge available today we have a much better chance, and by nurturing the same philosophical impulse the greeks had we would create something different. Their philosophy is not ours.

Structuralism and poststructuralism reject a fixed, cross-contextual meaning of words, concepts and symbols, and the branch of philosophy following Wittgenstein, Quine etc. holds that a lot of classic philosophical problems are just the result of philosophers having unrealistic expectations about words[9]. While this doesn’t solve everything, it does represent a giant leap in figuring out what kind of answers to philosophical questions we can expect and should pursue.

Like physics and chemistry tells us what reality is made of and linguistics and semiotics tells us how concepts/words/symbols operate, cognitive science tells us how our apprehension and internal representation of the world works. Map, territory, and the relation between them — all the parts. Someone ought to step up and bring them all together.

We should consider these ideas the philosophical equivalence to atomic theory. Atoms, molecules and chemical reactions are the answers to our old questions about the nature of substances, what gives them their properties and how they can change etc. (even if we’re still filling in the details)[10]. These theories offered up a new paradigm in which to do chemistry that rendered all the old ways irrelevant, of interest to historians but not to chemists.

That makes two kinds of philosophy, before and after, old and new[11]. ”Old Philosophy”, where it is assumed that ordinary words had definite meanings and could be used in — and be the objects of — formal arguments, would be its own discipline. It would be mostly of historical interest, while ”New Philosophy” would be done within a combined poststructural-linguistic-and-scientific-reductionist-cognitivist paradigm[12].

A comment on the Meteuphoric post says:

Physics is about the territory. Philosophy is about the maps.

Perfectly put. And it tells us something about primacy. There are many different valid maps, focusing on different things, abstracting away different details, existing for different purposes. But it’s the relation to the territory that gives them value. Internal consistency, elegance, historical tradition or intuitiveness are nice, but they’re not what justifies the existence of maps.

It also tells us what philosophers need to study. Not just the history of philosophy but whatever it is you need to interpret, evaluate and understand maps well. That would be, 1) the territory (i.e physical sciences) and 2) lots of different maps (i.e the conceptual frameworks and vocabularies used in other fields).

• • •

I’m taking a big risk here, as classicists are known for their ferocity and upper-body strength.

No need to tell me I’m short-changing or misrepresenting these philosophers. I know. I’m just using them to make a point, and I think the examples do support that point.

Sure, look into questions and try to find good answers, by all means. But often the questions themselves use poorly defined words, which leads to silly things like arguing whether numbers, counterfactual worlds or macroscopic objects “exist”.

If there was such a thing as Moral Rightness out there lurking behind sensory reality, truly intractable moral dilemmas would not exist. Our moral intuitions would converge and settle on the right answer, much like more evidence eventually settles scientific controversies. This doesn’t happen.

My experience defending that thesis is a perfect example of what frustrates me. At one point my opponent said that I couldn’t assume materialism/naturalism in my paper and build on that, I had to justify it, philosophically. What I wanted to say was something like: “Are you freaking kidding me?! Arguing about the metaphysics of concepts and supernatural entities has been done to death, I’m trying to get somewhere here! Should I rather add more pages to my paper and retread a centuries-long argument I definitely won’t add anything of value to? If you don’t find materialism convincing based on the arguments that already exist, my attempts won’t make any difference. This is precisely the kind of pointless ritualistic games we don’t need.” What I did say was similar but more polite…

In this context: “In this context.”

Sometimes I feel like I’m dangerously close to being the person Existential Comics mocks with the line:

Up next: A 20-year-old freshman philosophy student has solved philosophy. He claims that morality is just relative, and we should just, like, use science for everything else. The philosophical community is shocked that such an obvious answer has eluded them for 3000 years.

Cute, but I’m kind of tempted to bite the bullet and say that the student has a bit of a point. While there is tremendous value in philosophy, a lot of it does seem to be game-playing. And that professional philosophers wouldn’t agree with a dismissal of their field isn’t actually much of a counterargument — it’s a community of people obviously selected for not holding that view (just like theologians are selected for believing that God exists etc.). There is a difference between being arrogant enough to think you can do someone’s job better than them and simply disagreeing that what they do is worth doing.

When we reify simplifying map-concepts like “objects” and “properties” we become vulnerable to nonsense like Goodman’s Paradox.

Such as thinking that the logical relationships between words in an argument tells us something reliable about the real-world relationships between what the words are meant to represent.

This is in my view the single greatest scientific achievement of them all — finding a neat, coherent explanation for so much of our everyday experience.

Splitting philosophy wouldn’t be unprecedented. The division between analytic and continental philosophy exists, as does in many countries a divide between practical (ethics, politics) and theoretical (metaphysics, logic, language) philosophy.

I think the idea that philosophy should be more fundamental than science and therefore justify the methods of science has done a great deal of damage. Philosophy is based on intuition and intuition is not reliable; it’s heavily biased towards believing that the fundamental building blocks of reality are the same as the fundamental building blocks of our mental lives. As far as I know, every human culture has developed something like a religion — the idea that reality runs on intention, ideas and ”meaning”, and not mechanistic laws.

However, science is an amazing success story and intuitive thinking isn’t, so it seems more apt that science should explain our intuitive thinking than vice versa. Philosophy needs a foundation and despite centuries of attempts, none that holds has been found. We can’t even justify induction, for chrissakes…

Building conceptual frameworks on top of the physical universe as revealed by science (rather than trying to build a foundation in the middle of nothing, on dubious abstractions like “pure reason” or “pure experience”) seems the obviously most fruitful approach to me. Nothing can justify itself, so something has to be taken for granted, and I think scientific materialism is the best candidate we have.

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7 thoughts on “The Good, the True and the Undefined

  1. > The relation y = 1/x simply does not have a value for y when x is 0. It is undefined; the system doesn’t cover it. This is how math works and we don’t need to develop new mathematics that can give 1/0 a value.

    Once upon a time sqrt(-1) was undefined. Once upon a time 1-1 was undefined. I agree with your overall point, but, math is a domain where new branches (of undeniable utility) are developed *all the time* by a refusal to accept “undefined” as an answer. This makes it a bad example for making this particular point.

    Liked by 1 person

    1. Fair point. But I don’t mean that metaphor to be quite as broad. I just mean that the function 1/x in particular isn’t defined on the whole real line, and similarly object identity doesn’t need to be defined over all possible cases. It’s more of an example illustration than an argument.


  2. Some things are or should be undefined in philosophy as well, examples include ”Is the first or second ship the real Ship of Theseus?”, ”Is Swampman Davidson?” or the answers to moral dilemmas like “Should you push the fat man to stop the trolley?”.

    To the extent that such examples are contrived and designed to be “godelian”
    counterexamples, I agree. But, for instance, in ethics, a lot of such counterexamples seem like situations that could conceivably arise in real life – or at least situations that are ethically analogous. It seems unsatisfying to potentially be in a real life situation with my hand on a metaphorical trolley lever, and having to be like – “I guess I’ll flip a coin…”

    Liked by 1 person

    1. I don’t think there’s a way to make them satisfying, I guess. Yes, you can create these scenarios to get at contradictions in our moral intuitions, but that’s all you can do, imo. There’s no “solution”, no clever argument that can really solve the issue. And I don’t see a reason to expect there to be.


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