What's Actually Possible? | The Unexamined “In Principle”
When "possible" is a placeholder for thought…
Recently, I was riffing with someone about whether “meaning” is well-defined. Let’s call him Pete.
Pete thought he would define meaning as “something is meaningful if it can be communicated.”
I rejoined, “Okay… well, what if you’re deaf or blind? What if you’re totally disabled in an iron lung, yet conscious… does that mean there’s no ‘meaning’ to your misery (or even ‘redness’) because you can’t communicate it?”
He then adjusted his statement and said, “Okay, fine. Something is ‘meaningful’ if (and only if) it’s capable of being communicated… in principle.”
Our conversation stopped there, but something bothered me about this usage of the phrase “in principle.” Generally, when most people (who aren’t philosophers) invoke the term “in principle,” it vexes me.
We speak about “in principle” as if we know what we’re anchoring it to, but I don’t think we do.
We’ll say, “In principle, if you could calculate it, you’d be able to determine your eye color from knowing the state of the wave function of the particles that comprise you.” Technically speaking, we don’t know if this is even remotely true! We have a tool that’s only been tested up to a few feet in front of you, and your friend will say, “In principle, it can have its extent to the next galaxy.” How do you know? On top of that, there are plenty of unsolved problems at the foundations of the field, not just at the far-emergent level. We don’t even know if assuming the truth of the Riemann Hypothesis leads to contradiction!
NOTE: Next week or so, I’ll be writing about why the standard argument for the nonexistence of lengths beneath the Planck length (“because probing it would create a black hole”) is faulty. In pursuing this line of reasoning, you’ll hear the phrase “in principle,” and this verbalism requires its own post (or two).
Mapping the Topography of What Could Be
Interestingly, there’s a field that studies “in principle” arguments explicitly, and it’s called modal philosophy. Modal philosophy concerns itself with notions of what is “possible,” the existence of “possible worlds,” as well as what is necessarily the case, etc. One of the problems is that there is no universal notion of “possible.” You have several qualifiers, such as “this is possible (in Lewisian semantics),” but then you can just argue whether David Lewis conceptualized possibility not just coherently but correctly.
Modal philosophy is what happens when philosophers discover they can just say “what if” and call it research.
Let’s delve into some detail…
You can state that something is possible “in principle” as long as it’s not somehow contradictory with the laws of physics, but then you can just ask, well, how do you know it’s not contradictory to the laws of physics?
For instance, “it’s ‘in principle’ possible to get from one side of the galaxy to the next in a microsecond (and back, without Earth aging by more than 2 microseconds)” would have been said a few centuries ago (if they knew about galaxies… but perhaps “in principle” they could have), however, we now “know” this to be not doable.
I say “know” in quotes because clearly there are manifold methods such as theoretically traversable wormholes that may be consistent with our current laws of physics which would allow you to do so. Furthermore, we have to put the proviso that the current laws are merely that… the “current” laws. Faster-than-light communication “in principle” is possible.
But notice what I did there. I just switched what I meant by “in principle!” This is the danger.
When you’re arguing with a non-philosopher, most are sloppy and won’t notice their different uses of this guileful phrase. “In principle” should have a subscript. Let me outline what I mean about subtle shifts in modalities with this dialogue from another (possible) world:
Dwayne Johnson: Dude… In principle we can calculate your very next thought from the exact micro-state of every particle in your body.
Roger Penrose: Quantum state measurement always disturbs the system; those micro-states can’t be read out intact.
Dwayne Johnson: That disturbance is only practical fam; in principle a non-invasive “weak” ensemble readout lets us infer the same data!
Roger Penrose: That’s “Sir” to you. And weak data give only statistics, not the single future history you promised.
Dwayne Johnson: Statistics suffice, yes; in principle Laplacean determinism means the ensemble narrows to one outcome given enough precision. Respec’.
Roger Penrose: But chaotic sensitivity amplifies the unavoidable error faster than you can refine it.
Dwayne Johnson: Yo chaos is classical bredgen; in principle a fully quantum description side-steps butterfly effects. And you didn’t even comment on how I used the word “suffice” correctly. That’s not easy.
Roger Penrose: Full quantum evolution yields branching but not certainty. Prediction of a definite choice is impossible.
Dwayne Johnson: Branches are just bookkeeping jabroni. In principle a post-selection onto our branch recovers the single answer.
It may appear like the logic is sound but there are inconsistent uses of the term “in principle” being employed and you have to be extremely careful about this…
After you read this article, you’ll be able to notice that The Rock oscillates from technological feasibility to statistical inference, then to metaphysical determinism, and finally to logical post-selection. Each move evades the previous objection and does so without ever supplying the unattainable exact micro-state.
Prototype vs. Pipe Dream
There is:
The above triplet seems like a reasonable definition until you realize that the latter part isn’t even well-defined. What is meant by “ideal agent?” Is it “perfect materials?” Is it “unlimited cash?” What is meant by “perfect” material? What’s meant by “unlimited” cash? If you truly had unlimited cash, would your local bank not form a black hole?
When I was at the University of Toronto, my classmate would always tell me, “You know Curt, I could have invented Dropbox if I had enough time and resources.” Always the same story. “I could have done so-and-so, provided enough time and resources.” It’s this latter adjunct that is the hallmark of being possible in principle (technologically!).
Of course, you have to then say, “Well, what was preventing Joe on the street from doing so as well, given him enough time and resources?” Also, how much time? Which resources and how many? etc. But these questions are too in the weeds for someone imagining “in principle” arguments. They’d rather focus on the forest!
Personally, I don’t think these questions are too in the weeds. Analyzing the weeds will tell you whether the forest you fabricate is even feasible.
Standard Model, Standard Caveats
This means you assume the current laws of physics are fixed. You may believe this to be less controversial. However, the question that arises is exactly what you mean by the current laws. “Obviously, it’s the standard model and general relativity.”
This is correct, but what do you mean by “and…?” Do you mean we just take the conjunction? How do we do that? Do we analyze each situation by saying, “well, if it’s a gravity question, we’ll stay in the domain of general relativity. But if it’s a particle physics question, we’ll go to the standard model…” In other words, one analyzes a situation to see if it dominantly applies in one domain, and then it uses that domain exclusively.
What about when there are questions that require both? (e.g., black hole thermodynamics, early universe physics, etc.) Given we lack anything close to an agreed-upon manner of “and” for this duo, how do we know something is consistent with the laws or not?
Going back to my faster-than-light example, it is conceivable that somehow if spacetime emerges from something else which is “extra-spacetime” (a term I prefer to “pre-spacetime” since pre-implies temporality, whereas we’re attempting to undergird that temporality to begin with) then why not faster-than-light? What specifically is forbidden in that intersection, given we don’t know the goings-on there?
Of course, you can start with axiomatic quantum field theory and just enforce strict limits to your nomological possibility space, but axiomatic quantum field theory isn’t as successful as old-fashioned perturbative quantum field theory in terms of predictions that match data.
It’s like if a psychologist said, “Well, we tested it on undergrads, so obviously it applies to all sentient life…”
The Limits of the Knowable
A mathematical proof of some currently unknown theorem is, in principle, knowable if we were given that information. Most of the time when people use the phrase, “for all we know,” they’re referring to this. For instance, “For all we know, there is another mirror Earth somewhere with people debating all these questions except anytime they say ‘Curt’ they use the word ‘Oh Great and Wise Master Curt.’” This is the best Earth by the way. I approve of said mirror Earth.
The problem for me is that it’s unclear the relationship between this epistemological possibility space and the other possibility spaces, thus it’s smuggling in hidden assumptions of which both the speaker and the listener are unaware.
Perhaps the Universe is cruel and forbids “Oh Great and Wise Master Curt” at some level. This is the true problem of evil, .
This is nothing to say of what type of infinity is being used here. I don’t mean whether it’s countable or Aleph 1, but whether it’s “potential” (Aristotle) vs. “actual” (Cantor).
A “potential infinity” is one that is always finite but unbounded. It’s the one where you request more time on your homework because you keep growing gardens in Roblox. The amount of time you need is finite, but you can (hopefully) just ask for a week’s extension, continually. Or until GTA 6 comes out.
An “actual” infinity is one that is actually infinite! We don’t have a simple way of conveying it other than by invoking images of a deity outside this universe. Technically speaking, the Halting problem is solved if you were given an actual infinite amount of time (Hamkins–Lewis, 2000). Maybe other undecidable problems as well.
Mostly, when technological possibility refers to “an infinite amount of resources,” it means potential infinity.
Fitch’s Paradox of Knowability shines doubt on the coherence of “all truths are knowable (in principle)” by the way, but that’s a story for another Substack post.
Okay, the brief of it is that if you assume that for every truth p, it is possible in principle that p becomes known (formally, p → ◇Kp), then it logically follows that every truth is actually known (p→ Kp).
This is what happens when you let philosophers use math.
When “What If” Defines What Is
Okay, now we’re getting somewhere.
When philosophers speak of “in principle” arguments, they most often mean this. This is what’s being referred to when philosophers speak of “possible-world semantics.”
For instance, this is the use of “in principle” from thought experiments like David Chalmers’ philosophical zombie (not an explanation for department faculty meetings. It’s a creature physically identical to a human but lacking consciousness. Actually maybe that does explain those meetings). It’s said to be “possible in principle” in that it’s metaphysically conceivable, even if not physically real.
Does the fact that you can conceive / imagine something mean it’s metaphysically possible? Why or why not? This is actually a large debate. You may think the answer is clearly “yes,” but Shoemaker contends that what we call “metaphysically possible, in principle” is nothing above just saying it’s “nomologically possible… just in another universe.” How the heck do you prove or disprove that?
You may think all of this is useless, but this is the basis of science itself. Our scientific method is influenced by the logical positivists, and (at least) one logical positivist, Schlick, said that a sentence has meaning only if there is some way to verify it by experience “in principle.”
What if the meaning of “in principle” is precisely what’s in question? Then does that entail the meaning of science or the scientific method as well?
Recall, we used to think you could “in principle” measure the electron’s momentum and position simultaneously to arbitrary accuracy, but Heisenberg found a rule in the algebra of operators that suggests otherwise… So then, suppose I was to say, “Well, in principle, it’s metaphysically possible for some other universe / world to exist where the electron’s position / momentum could be fully known.”
The problem is, we’re using the same word “electron” to refer to both cases: our current world where the uncertainty principle seems to rule, and this hypothetical one without such constraints. But is an electron that doesn’t operate by HUP actually an electron? The algebra of observables is so heavily intertwined with the actual definition of an electron (in this world) that if you change it so drastically, are we even referring to the same object, but just in a different world?
Is Logic the Ultimate Constraint?
Something is “in principle” possible if the statement isn’t contradictory, or if it doesn’t lead to a contradiction.
For instance, it’s “logically possible” in principle for pigs to fly (we can imagine no formal contradiction in that scenario).
The problem here is that this also needs to be qualified by which logical system one is using. There are more things in Heaven and Earth, Horatio, than are dreamt of in your classical logic. There’s also second-order logic, paraconsistent logic (which allows contradictions, by the way), and more. See this podcast with Graham Priest.
Furthermore, as was brought up to the great and late Anand Vaidya, I don’t see why you can’t have a hierarchy of possible worlds where logic is a strict subset. That is, no one knows if logic is what binds / grounds all forms of all possible universes. Most physicists I speak to believe so, but I don’t see why this has to be the case.
It’s conceivable that there is something “extra-logical” that can’t be formulated with words or rules or what have you, which is a superset of logical possibility.
The Nested Dolls of Possibility
The below is the containment:
You’ll notice that ◇_epist is missing and that’s because it’s tied to our knowing, thus it can shift between the layers as far as I can tell.
Laplace's Demon: The Original AI Hype That Didn't Pan Out
Look… it was common knowledge for a hundred years to think Laplace’s Demon (foolish name, it should be Laplace’s Intelligence, since that’s what Laplace himself called it, but that’s beside the point) was in principle possible technologically. Then we thought, “Okay, maybe we can’t build a device of Laplace, but it’s knowable in principle!” Then people like Jenann Ismael and John Norton came about and showed that not even that is true. For me, it’s not clear if it abides by logical possibility. Therefore, one needs to use “in principle” arguments with the utmost heedfulness before you look illogical… in principle, of course.
So what is the answer? Given we use “in principle” so frequently in formal and informal debates, what do we do? My answer is simple:
Stop using the phrase “in principle!”
Instead, be explicit (painfully so) about what you mean. Rather than say “in principle X could be done,” say “there exists a possible world consistent with the current laws of physics where X is done within a finite time.” I still object to “current laws,” but there’s so much less of an objection (and much less ambiguity!).
I want to hear from you in the Substack comment section below. I read each and every response.
—Curt Jaimungal
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Interesting read. It reminds me of yudowsky's objection to arguments of feasibility, where feasibility is contingent upon ignorance of the principles governing the system.
I've long felt that "in principle" was an intellectual sleight of hand that allowed the construction of arguments that were meant to seem definitive but we're actually more akin to hand waving.
I think it's legitimate as a technique for exploring "what if" scenarios but should never undergird any actual conclusion.
I thought your example of the electron made the point well. If it does not obey the rules by which we define an electron then whatever it is it's not an electron as we know it.