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It's logically possible for reductionism to be the case, but not metaphysically possible.
There has to be a whole binding all the parts of something from the top-down for it to be coherent, you can't actually building anything by "combining parts" without that, despite what a pragmatic heuristic it is to think so.

It seems logically possible for syntax to be sufficient for semantics. It just turns out when we investigate with thought experiments like the Chinese room argument, that syntax is actually insufficient for semantics. But without knowing that beforehand, it appears possible that we might understand the meaning of some symbol purely by looking at the instructions of which it is a part.

After doing some thinking, I am not so sure whether physicalism implies the equivalence of metaphysical and physical possibility. — Lionino

What do you have in mind as something physically impossible, but metaphysically possible?

You also refer to "possible worlds". There can only be non-actual possible worlds if there is contingency in the actual world. The only known, true contingency in the world is quantum indeterminacy. Do you have something else in mind?

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Yes, by possible world I mean for example, a world where the speed of light is less, the gravitational constant is 10 times greater, etc. Those are not necessary exactly because they could have been otherwise. — Lionino

Conceivability does not track metaphysical possibility. What makes you think the gravitational constant (or speed of light...) could have been different? Wouldn't that entail a deeper law that produces those values?

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Let's assume for the sake of the argument that 'finite' is not included in the definition of 'person' (henceforth also called 'subject', so that it may also imply supernatural beings), so it does not figure a logical contradiction. If an infinite subject is that which encompasses the whole universe, it is metaphysically possible that this subject exists. If by infinite however we mean something that spans not only its world but all worlds, then it is not metaphysically possible because we know at least one world which he does not span: ours. However, I would say that by then, the definition of infinite is twisted to mean something that actually reflects "necessary (in all possible worlds)", after all. — Lionino

Infinity itself is a tricky concept. I once started a thread on the topic and got brutally pummeled by less than charitable mathematical folk for the terminology I employed. So I’ll here employ different terminology for it.

We often enough think of infinity in terms of quantity. Even Cantor’s Absolute Infinity, for example, is postulated to a number bigger than any other quantity. Going back to its roots, though, infinity signifies that which is devoid of limits and boundaries. In this sense then, to be bound, for example, to any aspect of space (distance), time (duration), or number (quantity) is to be finite, this rather than infinite. The Ancient Greek notion of Anaximander’s Apeiron gives one example of this latter notion of the infinite.

Most infinities we can think of are thereby in some respects bounded and only in some others unbounded. For example, Cantor’s Absolute Infinity is yet bounded to, and hence limited by, quantity. For the sake of convenience, I’ll here label these bounded infinities, or else the boundedly infinite—and contrast these to unbounded infinity, or else the boundlessly infinite. A line, a geometric plane in Euclidian space, and Cantor’s Absolute Infinity are all then bounded infinities; whereas the Apeiron is one example of that which is boundlessly infinite.

Given all that, what then does the phrasing of an “infinite subject” intend to imply?

I presume that “a subject” entails being a subject of awareness, which I further take to entail being aware of other. If so, all subjects are boundedly infinite in some regard—for one example, their/our awareness can, I think, be safely deemed infinitely divisible in principle. For instance, I see a rock + background: the rock has infinitely many aspects I could address in principle (variations in color, texture, curvature, etc.; relations between these; similarities and dissimilarities to other things I could be aware of; etc.)—given that I don’t get bored in so doing and that I would so address for all eternity. And this is not to yet get into the rock’s background.

We might by the just stated then affirm—in a rather bizarre formulation—that all subjects (of awareness) are thereby infinite at all times for as long as they occur. This on grounds that their awareness of other, by which they are principally defined, can only so be. (I might add, I can’t yet fathom of anything spatiotemporal that can’t be deemed to be boundedly infinite in at least one respect; as one example previously mentioned for an “infinite dog”, the mapping of anything physically spatial via geometric points leads to an infinite quantity of geometric points constituting whatever it is that is being addressed, thereby making the thing boundedly infinite. But if all items in a set of items are infinite in the same respect, this characteristic ceases to be any difference between them: an infinite apple then equals a plain old apple, so there then is no reason for the adjective of “infinite”.)

So no, when thus understood, an infinite subject would not be a logical contradiction—thereby allowing for metaphysical postulates wherein infinite subjects of awareness are interpreted to hold an awareness that encompass this world or that. (Don’t we as subjects of awareness in at least some ways encompass the very possible worlds we are aware of?)

But so construing all subjects of awareness to be infinite is intuitively odd. We typically by “infinite” want to convey something more. I venture that oftentimes (if not always) this something more will turn out to be logically contradictory: as I find to be the case with an omniscient, else omnipresent, else omnipotent subject (of awareness).

At any rate, the notion of “a boundlessly infinite subject” can only be a logical contradiction: at the same time and in the same respect that addressed is a) bounded to being a subject of awareness (entailed by being a subject) and b) is in no way bounded to being a subject of awareness (entailed by being boundlessly infinite). To use the same example I previously mentioned, the Apeiron cannot logically be a subject of awareness which thereby is cognizant of things which are other than itself—for, if for no other reason, this would then limit the Apeiron to so being a subject of awareness, which contradicts the Apeiron being perfectly limitless in all respects. (While I question Anaximander's notion of the Apeiron on logical grounds, another possible to conceive of boundless infinity is that of Nirvana without remainder, this among yet others, such as the Ein Sof; none of which are subjects of awareness that thereby dwell in a duality between self and other)

(In a bit of hurry at present so I’m not double checking the just written. If there’s glaring mistakes in it I’m sure someone will let me know.)

Not being logically contradictory just means it's logically possible. God's existence is logically possible, but no physicalist would consider God's existence to be metaphysically possible.

Here's my view:
Under physicalism, if it is truly possible for the speed of light to have differed, it would have to be because the speed of light is contingent upon some law that is more fundamental. We don't know if there is such a law, and therefore we don't know if the speed of light is truly contingent. Consequently, we can't say that an alternative speed of light is truly metaphysically (or physically) possible. We can only say an alternative is conceptually possible.

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I think what you're getting to is something similar to "broad logical necessity". It's not uncommon to equate this with metaphysical necessity. It does constitute common ground for evaluating metaphysical systems. It has its place, but can also lead to confusion - such as with a modal ontological argument.

I agree with this. But I would like to add that, if we accept causality, aren't the changes in the laws of nature caused by something? And if so, isn't that cause something that we could consider to be a more fundamental, subjacent, law of nature? — Lionino

If the laws of nature have evolved then we might understand that as a kind of universal tendency towards habit-forming, just as things seems to have a universal tendency to dissipate over time. Causes are usually understood as local influences, exchanges of energy, whereas habit-forming or dissipation might be better understood as global tendencies or constraints.

Metaphysical impossibility is any proposition which violates the presupposed metaphysical theory, no different than how actual/physical possibility is predicated on our scientific theories. The main difference is that metaphysical theories are way more controversial than scientific theories (and there is absolutely no consensus on the former).

E.g.,:

For some in philosophy of mind, philosophical zombies are metaphysically impossible, but actually and logically possible.

For some theists, it is metaphysically impossible for there to be more than one god; for something to exist which is not contingent on God; etc.

For some in metaethics, it is metaphysically impossible for moral facts to exist, albeit actually and logically possible.

For physicalists, it is metaphysically impossible for there to be a mind which is more fundamental than matter (or whatever fundamental mind-independent entities constitute their theory).

And the list goes on and on, and is contingent on the specific metaphysical theory (worldview) in play.

metaphysically impossible, but actually and logically possible. — Bob Ross

What does 'actually possible' mean? I would have thought that metaphysical impossibility precludes actual possibility.

Red things are coloured things, right?

This is logically possible: something red which isn't coloured. They're different predicate symbols.

Is it physically possible to have a red object which is not coloured? If being coloured is interpreted as a judgment of frequency bands of light, and red as a frequency band of light, any world where judgements did not occur would have red objects which are not coloured.

Metaphysically possible? Well, if metaphysics is about coming up with an account of the world we live in and nature at the same time, any model where red objects are necessarily coloured would make it metaphysically impossible for there to be a red object with no colour. IE red objects are necessarily coloured. Which I think is, if any such thing exists, a relation between the folk notion of red and coloured in their standard uses.

Food for thought.

Actual, or also called physical, possibility is a mode of thought in modality whereof something is possible iff it does not violate the laws or currently held beliefs about nature (about the physical world).

I would have thought that metaphysical impossibility precludes actual possibility.

It very well might, depending on whether one believes in a higher 'realm', so to speak, than nature herself--e.g., it is, for some theists, actually impossible for someone to jump to the moon, with nothing but their bare body, from San Francisco but it is metaphysically possible for a God-incarnate to.

This is logically possible: something red which isn't coloured. They're different predicate symbols. — fdrake

This is only possible for a logic that is is purely syntactical. However such a logic would be meaningless (ex hypothesi, since meaning requires semantics). In which case so is the attribution of "possibility" to it, since possibility implies a realization.

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So, basically, when we say, it is metaphysically impossible for something to happen in a metaphysical system, we are saying, given a metaphysical system M and a proposition X, "In M, X is impossible", it seems that whether X is possible or not boils down to the semantics of M, that is, whether some of the properties or consequences of X are in contradiction to the axioms of M, making untrue analytic statements — Lionino

Wouldn’t the boundaries of a metaphysical system be defined not by what it deems logically impossible, but what appears from the vantage of that metaphysics as unintelligible, senseless and incoherent? What is logically possible and impossible would seem to be reciprocally implied, and both would define what is included WITHIN the system, not what is other than it.

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This is only possible for a logic that is is purely syntactical. However such a logic would be meaningless (ex hypothesi, since meaning requires semantics). In which case so is the attribution of "possibility" to it, since possibility implies a realization. — Pantagruel

Aye. I don't think it's possible to make red not imply coloured when you interpret those symbols with their everyday use. But ultimately, as you say, that's a semantic rather than syntactical constraint.

it deems logically impossible, but what appears from the vantage of that metaphysics as unintelligible, senseless and incoherent
— Joshs

Aren't those the same thing? — Lionino

Is logical impossibility the same thing as nonsense? Doesn't what is logically impossible conform to the criteria of meaning that allow a judgement of its meaningful incompatibility to be made? For something to be outside of this metaphysical criteria would be for it to appear as random, chaotic, not subject to logical judgement at all.

So, basically, when we say, it is metaphysically impossible for something to happen in a metaphysical system, we are saying, given a metaphysical system M and a proposition X, "In M, X is impossible"

Correct.

it seems that whether X is possible or not boils down to the semantics of M, that is, whether some of the properties or consequences of X are in contradiction to the axioms of M, making untrue analytic statements.

I wouldn’t say that metaphysical impossible is derived solely from the semantics of M but, rather, the underlying meaning associated with those semantics. Semantics is just the analysis of words, not its underlying contents.

I guess you could say the same about physical statements, in a sense.

Correct, the physical/actual mode of modality is analogous to both the logical and metaphysical modes thereof: it is possibility, necessity, contingency, and impossibility juxtaposed with the presupposed mode of interpreting them.

But the issue is that the laws of physics are given to us through the scientific method, while metaphysical laws are not, each person has their own metaphysical views

A contention about the methodology of physics vs. metaphysics is of no concern to the definition of metaphysical impossibility.

However, as a side note, I agree that metaphysics is a much looser study than physics; however, there are actual methodological conventions which (good) metaphysicians adhere to. The difference mainly is that there is far less education on what metaphysics is let alone what the proper method is for its inquiry, so most people who engage in it do it very poorly.

Then the statement P1 "In S, light goes faster than c" is logically impossible

No. “In S, light goes faster than c” is logically possible because the logic, if generated within a truth table, does not result in every result being false (e.g., there is no logical contradiction in it); whereas it is physically/actually impossible given our current scientific knowledge.

Remember, the logical mode of modality is only concerned with, well, logic, which pertains solely to the form of reasoning. P1 is just a proposition, p, which cannot itself entail a logical contradiction: you would need to demonstrate, in the form of the argumentation, that, in its most abstract, a truth-table of the formula results in false all the way down.

On the issue of metaphysics, however, for a metaphysical system M and a self-consistent proposition X that violates the laws of that system, "In M, X" seems to be logically impossible

It will always be logically possible so long as the logic does not always produce false (e.g., has no contradiction in it), even if M is internally incoherent (viz., ‘incoherence’, as I use it here, does not refer to a logical contradiction but, rather, a looser contradiction in the system such that two propositions held as true in M seem to strongly oppose each other, although there is no logical contradiction therein).

So in the case of epiphenomenalism, we end up with a logically impossible statement or a logically possible statement that has no evaluation in metaphysics yet

I am not sure I followed this part, so I can’t really comment.

I hope this post was not jumbled and that it was understandable to you, as I think you drive a good point that suffers from the issue I posed above. Maybe I made some grammar mistakes or skipped a word which made a sentence unintelligible; tell me so, so I can fix it.

I appreciate your response, and I hope my response here is adequate enough to address your points!

Bob

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Can you elaborate on this? I am not sure what you mean by underlying contents or underlying meaning, as something that could be beyond semantics. Do you mean the relationship of that semantic content with other semantemas?

Semantics is about words—i.e., what is the best or chosen word to describe something—and not the what those words reference themselves (i.e., their underlying content). “Car” is a word, comprised of 3 characters and is from the english language, which refers to that which we call a ‘car’: the underlying content which the word ‘car’ refers to is a car (I denote the word—viz., the semantics—with quotes and the underlying content it references without it here). You may come along and say: “but, bob, what you call a ‘car’ would be much better described, in english, as a ‘biscobbo’” and I say something to the effect of “I don’t even think that is a word in the english language and therefore, within the context of english, is not a better suited word to describe what I mean by a ‘car’”--this is semantics.

When I say X violates the laws of M, I mean that the proposition X is the opposite of one of the laws of M. So basically, by stating M, we state all its axioms, and by definition of X, one of its axioms would be ¬X. By stating X and M, we entail a logical contradiction therefore, no? Because we are stating X∧¬X.

Firstly, metaphysical impossibility does not entail that it is derived from an axiom of the system. In its most abstract, a proposition, X, is metaphysically impossible for a metaphysical theory, M, iff M → Y ^ !(Y ^ X) [i.e., M entails a proposition, Y, which is incoherent, but not necessarily logically contradictory, with X]. In this form, it is clear that something could be metaphysically impossible yet logically possible, because Y ^ X is not a logical contradiction; instead, the argument rests on the idea that Y strongly, in a non-logical sense, opposes X.

Secondly, you threw a curveball here because you posited !X as itself simply affirmed in M, so, of course, affirming M ^ X leads to a logical contradiction (in this case). However, it is important to note that the logical contradiction here does not lead to X being logically impossible, it leads us to X ^ !X being logically impossible--which is not what you are trying to argue. This is because M ^ X leads to a logical contradiction which is only due to the fact that one also affirms M which leads to !X—so X is not logically impossible but, rather, it is logically impossible for it to be true that M ^ X in this case because it can be expanded to [M → !X] ^ X.

My main point here is that metaphysical impossibility does not entail, necessarily, logical impossibility.

while I am using a definition that also talks about whether one of the premises of a statement contradicts the other statement.

You may, then, be using it in the sense of a non-logical contradiction, which is perfectly fine; but that would not get you to logical impossibility. Only by conflating non-logical contradictions (like actual/physical and metaphysical contradictions) with logical ones would one be able to bridge that gap.

P1 Socrates is a human
P2 Every human is a non-reptile
C Socrates is a non-reptile
P3 (C) Socrates is a non-reptile
P4 Socrates is a reptile

No this is a logical contradiction, not a non-logical contradiction or incoherence. The abstracted form is essentially:

ϕ := ∀x (Human<x> → !Reptile<x>)
φ := ∃x (Human<x> ^ Reptile<x>)

The logical contradiction is that ϕ ^ φ → ∃x (!Reptile<x> ^ Reptile<x>)

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Is logical impossibility the same thing as nonsense? Doesn't what is logically impossible conform to the criteria of meaning that allow a judgement of its meaningful incompatibility to be made? For something to be outside of this metaphysical criteria would be for it to appear as random, chaotic, not subject to logical judgement at all. — Joshs

Yes. Consider the logical touchstone of analytic truth. If x is red then x is coloured. Its analyticity derives from the metaphysical reality of the species-genus relationship. If you denude a proposition of all connection to this categorical content, you are left with a purely formal construct that has no meaning.

By incoherence, I mean the strong opposition of two things. That I have both long and short hair, right now, seems very incoherent given the standard understanding of the property of longness and shortness with regards to hair; but it is, nevertheless, not a logical contradiction for someone to have it because the form is ∃x (Bob<x> ^ LongHair<x> ^ ShortHair<x>).

Semantics is about words—i.e., what is the best or chosen word to describe something—and not the what those words reference themselves (i.e., their underlying content). — Bob Ross

I think this is misleading. You cannot abstract semantic meaning from its putative external correspondences. Semantics deals with the nature of signs and the relationship to their referents.