After some thinking,
Revealwhich was prompted by a retort to my friend jokingly saying that I am not X, to which I replied that I am so X that my appreciation for Y surpasses even the metaphysical and transcends into the realm of logical possibility,
forcing me to wonder "What does it mean to transcend the metaphysical into the logical?", I have come to some new conclusions.
When we ask whether something is a
possibility within X, we are naturally asking whether something violates the laws of X or not. Thus, to be metaphysically possible means not to violate the laws of metaphysics. That brings us to: what are the laws of metaphysics?
A quick search online gives us nothing, but the simple confusion of laws of logic with metaphysics.
I thought of the following: if the laws of metaphysics encompass physics but are contained within logic, all laws of metaphysics must attend logical laws, but be above physical laws. In order to make "metaphysically possible" meaningful, it must also be separate from both physics and logic.
So, let us search something that is not "A is A" but that at the same time is true in every possible world.
It is metaphysically possible that the speed of light is 1 meter/second, that gravity is repulsive, that uranium is more stable than helium. It seems that it is metaphysically possible that the physical elements of the universe could be any way. But what about something non-physical?
There are a few three types of objects afaik: physical, mental, abstract. We are acquainted with the former two, but abstract objects are objects that are not spatially or temporally located, and are causally inert; that is, they are not anywhere in time or space, and they don't act on anything. I personally do not think that abstract objects are real objects, but here I will assume they are
Reveal(and I give myself that freedom for reasons I could but will not elaborate on)
. Among abstract objects, we have universals, such as greenness or beauty, and numbers
Reveal(you could argue a number is a universal from an immanent realist point of view, but that is besides the point)
.
Since universals such as greenness and beauty seem to invoke analytic truths, which hinge on the laws of logic, let's leave those aside to focus on numbers instead. What is it about 2 and 4 and 7 that is always true but does not hinge on its definition? That 2 always equals 2 is simply the law of identity. But then, that 1+1=2? One might say that that is a synthetic judgement, as there is nothing in 2 that evokes the definition of 1. However, if we are going off Peano arithmetic, 2 not only invokes 1 but its existence depends on it. It seems abstract objects won't very helpful.
In some previous posts epiphenomenalism is discussed, and we argue about whether the "metaphysical possibility" is not encoded into the semantics of the metaphysical system, making every metaphysical possibility into a logical possibility. What about a law for every metaphysics?
What is something that applies to every metaphysical system we could come up with, be it idealism, physicalism, Cartesian dualism, neutral monism, parallelism, etc? My immediate thought was causality. What are then the laws of causality? Well, I don't think we know any. Is it metaphysically possible that causality works backwards? Yes. Is it metaphysically possible that an effect has many causes? It seems so. I don't seem to find anything in causality that is beyond that which is determined by logic. Even if we want to say that causes can't be their own effects, how are we to prove such a statement beyond appealing to analytic truths? I don't see any way. Maybe if we look at the other two fields, we may find clues.
The laws of physics are familiar, nothing goes beyond the speed of light, gravity is an attractive force inversely proportional to the square of the distance, etc.
The laws of logic seem to invoke, to some extent, analytic truths. Of course, there is also identity, non-contradiction, and excluded middle, which are required for analytic judgements, those are the basic laws of logic. But it is logically impossible that a bachelor is married, or that a colour is transparent, or that a flat surface has three dimensions.
That leave us with synthetic judgements, something that neither physics (necessarily) or logic touches upon. Maybe it is the case that metaphysical laws are simply synthetic necessities.
Someone brought up Kripke's before, so such a conclusion might not be surprising. But it seems that the laws of metaphysics limit themselves only to synthetic necessities. Let us take a triangle. There is nothing about a triangle that invokes its angles adding up to 180º, because it does not always. A triangle projected on Earth can add to more than 180º. It is only when we bring Euclidian geometry into the equation that triangles' angles add up to 180º necessarily, but that law seems to derive from the semantics of Euclidian geometry constraining the semantics of "triangle". "A regular triangle's angles in Euclidean space sums 180º degrees" seems therefore to be an analytic judgement. So we have to search for things that are not only synthetic, but that also scape our definitions, no matter how hard we try to systematise them into axioms and theorems. Well, that would be it for mathematics, as the existence of nominalistic mathematics shows that mathematics does not scape our semantic games.
Therefore, if we want to find something logically possible but metaphysically impossible, we must find a violation of a metaphysical law. We
Reveal(and by 'we' I mean me)
have this intuition that metaphysical laws are synthetic necessities. To find something logically possible but metaphysically impossible, we must find a synthetic necessity and state its opposite.
Searching for a synthetic necessary judgement, I found “A Defence of `Synthetic Necessary Truth’” by Stephen Toulmin, where the example of a knockout game is used (or better, of a raffle).

Here, we see that both King’s and Lady Margaret go to Heat 1, only if they win the game, and only one can win the game. And it is also the case that, no matter how hard they try, neither will get to Heat 2.
Even though we could argue that {2 teams in bracket 1 cannot go to the Heat 1} is inbuilt in the semantics of the game, there is nothing about the definition of Kings that implies it is in bracket 1 with Lady Margaret, thus we have a synthetic statement. If we contradict that synthetic statement, we say that both Kings and Lady Margaret can go to the semifinal. While that statement is metaphysically impossible, because it must be the case in every possible world given the rules established; it is logically possible, as the laws of logic are not violated if, say, both the winning and losing team go to the next bracket while none of the teams in the other bracket go forward, only the laws of the game are violated, which here I call metaphysical laws.
Formulating it plainer:
A: In a knock-out game decided by luck, with 4 brackets (1.1, 1.2, 1.3, 1.4) , each bracket contains two opponents, who knock each other out to go to the next bracket of 2 (2.1, 2.2), then to the bracket of 1 (final), which decides the winner.
B: Bracket 1.1 is composed of Kings and Lady Margaret (synthetic statement, given by the particular condition those two teams find themselves in).
C: It is metaphysically impossible that Bracket 2.1 is composed by Kings and Lady Margaret (derived from both the semantics of the game A and the synthetic statement B).
D: It is logically possible that Bracket 2.1 is composed by Kings and Lady Margaret (no laws of logic are summoned).
RevealA draft:
That morning star and Venus mean the same thing. But a group of workers can be designated by Arxc or Bcxr, that A3x4 and B4x3 references the same worker is true, is it logically possible that it could reference a different worker? If so, what would it mean for it to mean the same worker metaphysically possibly? The meaning of those two systems is given by a language, to use the system A for example, the language maps the first element to a row and the second element to a column. To ask if A3x4 and B4x3 could reference different workers means different things. Could the system (mapping) of each be different? If we change the system, we are changing the meaning of the word ‘bachelor’ to mean something that could be a married man.
Changing the way workers organise would make A3x4 and B4x3 possibly refer to different workers. The system has not changed, yet the result has.
It turns out, relating metaphysics to synthetic necessities is obviously not original:
Synthetic a priori judgments are the crucial case, since only they could provide new information that is necessarily true. But neither Leibniz nor Hume considered the possibility of any such case.
Unlike his predecessors, Kant maintained that synthetic a priori judgments not only are possible but actually provide the basis for significant portions of human knowledge. In fact, he supposed (pace Hume) that arithmetic and geometry comprise such judgments and that natural science depends on them for its power to explain and predict events. What is more, metaphysics—if it turns out to be possible at all—must rest upon synthetic a priori judgments, since anything else would be either uninformative or unjustifiable. — http://www.philosophypages.com/hy/5f.htm