Why are physically impossible and logically impossible concepts considered separate in terms of probability?

Question

It is considered self contradictory to say that a triangular square exists. This is because it’s a ridiculous concept. It is contradictory inherently.

But why is postulating some hidden devil or angel or god controlling things in a hidden manner not considered equally ridiculous? How do we even know it’s meaningful, much less possible, for things to “magically” control things. Everything we’ve ever observed has been directly observable through the senses in one way or another.

Why do we even entertain ideas such as the brain being in a vat and not being certain that the world out there is actually real. Descartes said that we can’t be certain of anything except our own existence. But in order to not be certain of the world being real for example, wouldn’t one have to first acknowledge the mere possibility of it being a simulation? Since there’s no evidence that this is possible, why should we not be certain?

Answer 1

Brain in a vat, hidden demons etc. have one thing in common that the triangular square doesn't. They are unfalsifiable. Note that doesn't mean they are WRONG, just that they are impossible to prove in the negative. But that is also the property that makes them unusable or at least unhelpful for a theory that is derived from observation. If not observing them cannot disprove them, then a theory without them works as well in predicting the future. So our physical theories don't need them.

I say this despite being firmly theist. Let's take as an example angels. Assuming angels exist, people who angels have appeared to can confirm they exist, but people who had no angelic visitations have no chance at proving or disproving it. Assuming angels exist, and appear to people, you still gain nothing from including them in theories trying to predict anything. That would be like including actual people in some theory and trying to predict how they behave.

A triangular square is completely different, because we have a definition of a triangle, a definition of a sqaure, and we can prove they can't both be true at the same time for the same object. That is peak falsifiable.

Answer 2

Logically impossible and physically impossible are considered separate because they refer to different things.

Logically impossible events violate the laws of logic, i.e. it's contradictory.

A triangular square is logically impossible (if not simply impossible by definition), because to be triangular means to have 3 sides and to be square means to have 4 sides, and a shape cannot have both exactly 3 and exactly 4 sides at the same time.

Physically impossible events that violate the laws of physics. This isn't a particularly well-used term in a formal sense.

A person flying via unaided self-propulsion is physically impossible, because our understanding of the laws of physics would not allow for this.

A person flying in this way is not logically impossible, because there is no contradiction there.

Note: it is hypothetically possible that our understanding of physics is incorrect, so something we classify as physically impossible may, in fact, be possible. It's just extremely unlikely.

Anything that's logically impossible is also physically impossible, because the existence of a logical impossibility would violate the laws of physics.

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Brain-in-a-vat is a meta-physical claim that's neither logically nor physically impossible. It's not physically impossible because the laws of physics can work exactly as we know them to be, while being inside of the brain in the vat. The same applies to hidden beings controlling reality.

In the absence of sufficient evidence, these are, however, unnecessary assumptions and may lead to a contradictory worldview if applied consistently, as one may end up believing e.g. that magical fairies controls (all of) reality and that a demon controls reality. So these claims should be rejected on this basis.

Since there’s no evidence that this is possible, why should we not be certain?

There is no evidence that it's impossible. But even if there were, we still shouldn't be completely certain that it's impossible, because evidence, or our perception of evidence, can be flawed.

But we can be quite certain that it's impossible.

Why do we even entertain such ideas?

To understand the limits of our knowledge and to expand those limits by speculating about what lies beyond them.

A few hundred years ago, someone might've asked why we even entertain ideas such as "atoms" and "viruses" and whatnot, but if we didn't entertain such ideas, we may never have reached our current understanding of biology, chemistry and physics.

Although I think at this point in time, it's accepted that brain-in-a-vat and magical fairies and so forth are almost certainly not true, and no mechanisms exist that would allow us to investigate such claims.

These claims can also serve as points of comparison for the range of supernatural claims that people might actually believe to be true, to establish an epistemological basis for what we're justified to believe and what we should not believe.

Answer 3

Perhaps one way to resolve your puzzlement is to consider that humans are not Vulcans (that is, Spock-like). As a consequence, humans are susceptible to being irrational, superstitious, instinctive etc.

Practically I am certain that my brain is not in a vat, that there is no hidden angel, devil or god, and that we do not live in a simulation. I would assign a probability of zero to all of those. However, the point is that there are some people who do believe in those things, notwithstanding the fact that they appear utter nonsense to me, and some (philosophers particularly) who like debate the possible existence of such things given that they cannot be disproved.

And therein lies the difference between physical and logical improbabilities. If you define certain axioms as true, you can prove that certain other statements are false, by which you mean incompatible with the axioms. You cannot prove all physical impossibilities in the same way. For example, you cannot prove by argument alone that there is not a giant pink rabbit in a cave on mars- and even if you examine all the caves on Mars, a devout adherent of the giant pink rabbit school might say that you have still not proved it, because the giant pink rabbit had seen you coming and hidden from you.

So in summary, there are certain classes of things that cannot be proven in a logically watertight way, and people being people, they will happily believe or discuss such things no matter how bonkers they might be.

Answer 4

Logic is essentially an entire universe of it's own that is based on a set of core ideas and interaction rules, called axioms, that are DECLARED TO BE TRUE BY DEFINITION. So it's essentially the big bang of the universe of logic, nothing before that, everything following from that and no means to investigate beyond that point.

So if the rules of that universe say that a triangle is a thing with exactly 3 angles, then a 4 angled thing is not a triangle. Simply because the rules of the universe say so. Though that doesn't mean that you couldn't imagine a different universe with a different set of rules that are logically consistent in which that might be possible. But that again would be a different universe with a different set of rules.

So while logic builds it bottom up, physics kinda has to build it top down. So we take for granted that there is 1 perceptible universe and in order to describe that we'd like to be able to build a logically consistent model for which we are looking for suitable axioms.

Which we then use to explain and predict the world and which we constantly update as data about it's performance comes in. So physically impossible can mean a lot of things from "we can't do it (yet)", "we can't imagine doing it", "it violates our current understanding of the world (logically impossible)", "we've never seen that happening" and many more.

But ultimately "impossible" is only what really actually doesn't happen. And that's "impossibly difficult" for us to prove. Because we are physically incapable of proving it. Like there's a lot of space that we haven't looked at, can't look at and therefore can't tell what's there. And not just the big is too big, also the small is too small.

Like think of how bacteria and viruses effect us but are practically invisible to us. How something as small as genes effect how we end up looking macroscopically. How small electrons are and how their flow is used to power large scale devices. Without high resolution microscopes and magnification through analogue processes all of that would be an effect without (a perceptible) cause and thus technically "magic".

Like if you had no idea of how it works then describing an infection as being possessed by demons and a doctor as being a high priest of an arcane religion performing rituals on the possessed is not actually that far off the truth if you think about it.

So in a weird sense it's some form of science. It's sometimes said that the difference between science and superstition is just better statistics. Like if you make up wild theories and only have 1-3 examples as proof that's a lot more sketchy than having thousands and more data points and thorough investigation of effects, but practically it's still developing hypotheses based on data and testing them by application.

So the general concept of having these wild ideas is not out of the ordinary and at times has been quite successful. However there's both a chance and a risk in the inherent ambiguity in this. Like if you describe bacteria as demons and have the definition of demons be up to individual fantasy, then uttering the same sentence can have vastly different meaning to different people. Which sparks creative solutions but is ultimately impractical so after a brainstorming period you'd set out to actually define terminology and codify ideas so that it once again approaches the attempt at a logic system.

Though in order to assign a probability to something you'd need to know the boundaries of your system. Like if you'd a dice with 6 faces, you'd know that the space of possible answers is limited to 1 of these 6 faces. However in the real world the possibility space is near endless and so possibility can only really be assigned with respect to the framework of a logic system. So it's not "the possibility of x is y" but rather "(under the assumption of x) the possibility of y would be z".

So TL;DR what you end up with is that things that are logically impossible being physically possible, because the logic system might have been build on insufficient data. Or the other way around something that is logically possible, being physically impossible, because while technically not forbidden we simply don't have the means to do it now or in the foreseeable future. Like visiting a planet out of the solar system. There's no logical axiom prohibiting us from doing that, but we have no physical means so far to build spaceships fast and safe enough for a human to cover that distance in a lifetime. So for now it's physically impossible.

Answer 5

Logically impossible events have absolutely zero probability.

Physically impossible events are theoretically possible, but with an extremely low probability.