Physical possibility vs Metaphysical possibility vs Logical possibility

We start with three kinds of possibility: Physical, metaphysical, and logical.

Alex Malpass says he's not sure what the difference is between metaphysical and physical possibility. https://www.youtube.com/watch?v=tsErbEt9MOQ - 52 minutes

I have been frustrated by this same question. When I hear someone describe something as metaphysically impossible, it just sounds like it's physically or logically impossible to me. As Alex Malpass gestures toward in the interview, we might put it like this:

Do the laws of logic exist? Yes. That which is logically impossible is that which violates the laws of logic.
 
Do the laws of nature exist? Yes. That which is physically impossible is that which violates the laws of nature.
 
Do the laws of metaphysics exist? Uh... no? What would those be? (You might think of principles like causal finitism or the principle of sufficient reason as being (alleged) metaphysical laws. But I'm not sure.)

I have found what I think is the first place I've heard of the distinction: William Lane Craig's 2016 Question of the Week #463. https://www.reasonablefaith.org/writings/question-answer/struggling-with-the-ontological-argument

Here Craig shares what Plantinga calls 'narrow logical possibility' versus 'broad logical possibility'. The idea seems to be that contradictions are explicitly in the form of A & ~A, but there are some things which are impossible and yet not explicitly contradictory. We might say they are implicitly contradictory, but not explicitly so. But this would mean metaphysical impossibility = implicit logical impossibility. So this would reduce metaphysical possibility to logical possibility.

Plantinga gives the example of a Prime Minister made out of prime numbers. This doesn't involve an explicit contradiction (you're not saying it's a Prime Minister that is not a Prime Minister), but it does involve an implicit one (prime numbers, which cannot materially constitute anything, do materially constitute a Prime Minister; or, that-which-cannot-be-made-out-of-numbers is made out of numbers).

(Maybe: numerical properties are immaterially causal, because they play a causal role in the bringing about of contingent immaterial objects, namely our thoughts about them. But numerical properties cannot play any kind of material causal role, because they are immaterial. Except substance dualists say that our thoughts, though immaterial, do play a material causal role, as they have effects on our bodies.)

I take it then that Craig would say that square circles and married bachelors are implicit contradictions, and therefore metaphysically impossible. Because square circles and married bachelors are so clearly contradictory, it's easy to take them as logically impossible. But you still have to tease out the contradiction: a square circle is an object-with-no-angles with angles (or an object-with-angles without angles). A married bachelor is a man-who-is-not-married who is married.

So that's one option: reduce metaphysical possibility to logical possibility by defining the former as implicit logical possibility and the latter as explicit logical possibility.

In the interview, Wes Morriston gestures toward the idea that metaphysical possibility has to do with the possibility that the laws of nature could have been different. So 'metaphysically possible' means something like "Physically possible according to a counterfactual set of laws of nature".

But Malpass responds, suggesting something roughly along the following:

Something is logically possible if it's consistent. So as long as there's a set of the laws of nature that are consistent, then we have a logically possible set of laws.

But if 'metaphysically impossible' means "possible according to an impossible set of laws of nature", then 'metaphysically impossible' means "possible according to a logically impossible set of laws of nature". But if something is possible only in a logically impossible scenario, then it's logically impossible. So metaphysical impossibility again reduces to logical impossibility.

So we can get down to just two kinds of possibility: physical and logical. But can we reduce things farther? Maybe.

Because of the problem of contingency, I suspect we need a necessary foundation of the universe. This will entail necessary laws of nature (this is debatable; I'm going with Graham Oppy who chooses the 'necessity' explanation in the face of contingency, fine-tuning, and the uncanny applicability of mathematics). 

The argument from contingency is a logical argument, so if it succeeds, then it will be logically necessary that there is this foundation. This will then logically entail the laws of nature (again, debatable). That would mean necessitarianism is true and all counterfactual sets of laws of nature are logically impossible (I don't mean to suggest Oppy thinks necessitarianism is true. Here I'm invoking Amy Karofsky).

If all of that works, then it's logically necessary that the foundation of the universe be what it is, it's logically necessary that this foundation would produce the laws of nature it does, and thus the laws of nature themselves are logically necessary. All counterfactual sets of laws of nature would be not only impossible, but logically so, as ultimately they lead to the contradiction of saying the logically necessary foundation has its particular nature and does not have its particular nature. But then that would mean what's physically impossible just is what's logically impossible.

Sure, we can imagine physically impossible things in a way we cannot imagine logically impossible things. But some things have their logical impossibility more and less immediately accessible; some things are more obviously contradictory than others. That's the point of the distinction of explicit vs implicit contradictions. So physically impossible things are not ultimately consistent, but they are apparently consistent at first. That "surface level consistency" is why we can imagine some impossible things to some degree, but other impossible things cannot be imagined to any degree.

We can imagine a group of people who stumble upon the idea of a square circle. They can conceive of a square circle... partially. They can conceive of its squareness. They can conceive of its circularity. But they cannot conceive the whole thing all at once. They are unsure whether the object is impossible or not, because they must first investigate all that it means to be a square and all that it means to be a circle. At first, they cannot see the contradiction. Eventually, through investigation, they realize that circles cannot have angles, and squares must have four right angles, and thus by definition the square circle is self-referentially incoherent; it's a contradiction.

That could be like us with God. Because of the ontological argument, God is either metaphysically necessary or metaphysically impossible. Which, per the above discussion, means God's existence is either implicitly contradictory, or God's non-existence is implicitly contradictory. No one thinks God's existence or non-existence is explicitly contradictory. God is, and has been, a common belief among humans. So clearly we can at least imagine God partially. But even Christians emphasize how we cannot conceive of God in God's entirety; God is too great a being for our earthly minds to comprehend. So like the simple people and the square circle, we must investigate all that it means for something to be God, and see if there are any contradictions therein. This is the area of philosophy called the coherence of theism, and many tensions have been noted between God's attributes. Some philosophers suspect that God is incoherent (if you're an atheist, then you must suspect this, because if God does not exist, then God is impossible per the ontological argument), and some may even outright argue that way. But I don't think any philosopher would say God is as obviously incoherent as a square circle or a married bachelor.

I've heard of the distinction between something being epistemically possible versus logically possible. If something is epistemically possible, then that means, for all I know, or for all I can tell, that thing is possible. In the case of the simple people and the square circle, the existence of the square circle was epistemically possible for them; for all they knew, there were square circles. But after they conducted their investigation, square circles became epistemically impossible; they came to see that they cannot exist. Likewise, some objects could be epistemically possible to us at first until investigation reveals they are not. While it's easy to see the whole picture when it comes to square circles or married bachelors, and thereby see their impossibility, it's much harder to see the whole picture when it comes to more complicated ideas like God.

So when we imagine fictional objects like Harry Potter and Hogwarts, we can imagine these things to a degree. They aren't explicitly contradictory. But really we are only partially imagining them. We run into problems when we try to really take Harry Potter seriously. Think of all the parodies made and plot holes pointed out about Harry Potter. This is how it is for any fiction (and, dare I say, for theology) when you take it too seriously. It falls apart and stops making sense. To truly imagine fictional stories as real, we'd have to imagine history having unfolded differently. We'd have to imagine different laws of physics, ones that allow magic or sci-fi technology. When fans ask lore questions, they are testing the fictional world in exactly this way, for consistency, and to see how far they can make sense of the fictional world. The more sensible the fictional world is, the more seriously we can take it. The less sensible the fictional world is, the more vulnerable it is to parody.

I cannot fully comprehend the real universe, so of course I cannot fully imagine a counterfactual universe down to the smallest detail, which is what I'd have to do to take any fiction fully seriously. This is why we can only partially imagine fictional objects, why they are only partially possible. To imagine the fictional whole, we'd have to imagine a different past and different laws of nature, which would mean imagining, via the argument from contingency, the logically necessary foundation of the universe being what it must be and not being what it must be at the same time. And there we have our contradiction, reducing physical possibility to logical possibility.

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Since I'm going through Alyssa Ney's introduction to metaphysics, I might as well record what she says about possibility. In chapter 10, on modality, she gives two definitions:

Nomological possibility: What's possible according to the laws of nature. (nomos means law in Greek)

Logical possibility: What does not entail any contradiction.

Notably, Ney uses round squares and married bachelors as examples of logically impossible things. She uses the example of an object moving faster than the speed of light as an example of a logically possible but physically impossible thing (special relativity precludes it).

Ney never mentions metaphysical possibility.

Alex O'Connor recently uploaded a video questioning where the laws of logic come from. They "come from" the necessary foundation of reality, or are part of it. But it does sound weird to say the laws of logic are logically necessary. That sounds circular. But if we just say the laws of logic are necessary, it sounds like we're saying the laws of logic are metaphysically necessary. But we can't say that if metaphysical necessity reduces to logical necessity.