Take the movie Interstellar for example (spoilers), at the end, the main character returns to Earth just as he had left, but his daughter is on her deathbed.

If we say there are three types of time — historical time, chronological time, and biological time —, the main character is younger than his daugher in all but historical time.

If we say there are three types of time — historical time, chronological time, and biological time —, the main character is younger than his daughter in all but historical time. — Lionino

I would say there are historical (Earth or chronological) time and phenomenological time. If biological processes would be slowed down, reduced to almost zero at near light speeds, what would a person on a craft travelling at such speeds experience? Such travel may well be physically impossible in any case, but allowing for the sake of argument its possibility, I can only imagine that during such a journey, even if it lasted a thousand years, the passengers would experience almost no time, or even no time at all, if travelling at light speed.

So, yes if that were possible then the main character would be biologically younger than his long dead daughter. On the other hand, since Earth time is really what counts for us, we would say he has been gone for a thousand years, and is thus one thousand plus years old, even though relatively unaged.

Should we count age as being the time of duration or physical change? — Janus

There's a fable I was acquainted with as a kid in which the hero overcomes many an obstacle to at long last arrive in a kingdom where life occurs without death and without aging (though physical changes generally speaking do occur there: folks move about, talk, etc.). Being a magical place, he looses track of time. Nevertheless, after what by all accounts is a short stay there, he becomes nostalgic and wants to see his family again - not having seen them since the commencement of his journey a long time back. Though warned against leaving the kingdom, he leaves to return to his homeland. Once he arrives back from where he started his quest, he finds that eons had gone by since his departure, with everything he once knew and loved now gone.

At this juncture in the story, should we deem the protagonist to be millennia old or, conversely, twenty-some years old?

Long story short, I don't find this question to be answerable via any one of the two options presented alone. Rather, I find the issue of his age fully relative to the conceptual context addressed. Such that in the story both appraisals of his age are simultaneously actual but in different respects.

And, although I personally find this fable far more telling in terms of possible metaphysics of time (i.e., of duration), the same can be said of Highlander movies or of any vampire story: that the the character lives for hundreds of years or more while remaining of a constant age makes conceptual (else, metaphysical) sense. These stories would all be utterly unintelligible otherwise.

This to better illustrate the following stance: The answer to the question of whether "a child can be older than her parents" - this as a metaphysical possibility - will be relative to the semantics employed for the concept of age.

So, in durational terms she is always going to be older than her daughter, and since the very meanings of 'mother' and 'daughter' presuppose that the mother exists antecedently to the daughter, then to say that the child could be older than the mother would involve a logical contradiction. — Janus

As per my previous post, I agree with this in full.

An addendum for improved clearness as regards my last post, just in case it might be needed:

In the fable presented, the protagonist’s age as measured by his own personally experienced duration of time will factually be that of twenty-some years. This though, in the fable, relative to the duration of time as would be measured by all those he departed from on his initial quest, he will factually be millennia old. In both cases his age is yet measured by duration, but this relative to the vantages of different actual or (being now dead) potential observers. (This as can be just as validly said of various scenarios concerning time dilation within the theory of relativity.)

Also noteworthy, physical changes occur in both of these duration-grounded appraisals of the protagonist’s age. So the division between age as measured by “duration of time” and by “physical changes” becomes largely spurious - although I do get what you intend by the dichotomy.

Secondly, and entwined with the just mentioned, there then will not be one objectively true vantage point of the protagonist’s age, this such that the other vantage point becomes falsity. The protagonist will hence factually be both ages at the same time, with each age being factual from a different vantage point.

As regards metaphysical possibilities, this then to me sets the fable apart from the Adeline movie scenario - as well as from vampire stories, etc. - in terms to the metaphysics of time. It basically seems to addresses the metaphysics behind the theory of relativity without the implied physicalism (and the block universe model) that is typically ascribed to the theory.

Which then directly ties in with this:

So, yes if that were possible then the main character would be biologically younger than his long dead daughter. On the other hand, since Earth time is really what counts for us, we would say he has been gone for a thousand years, and is thus one thousand plus years old, even though relatively unaged. — Janus

When impartially addressed, neither the character's vantage of his own age nor our own Earth-dwelling vantage of his age is privileged. Again culminating in the conclusion that both appraisals of his age are true, i.e. conform to what is factual - but this from different vantage points of observation.

All this stands in contrast to the notion that there is a universally applicable, objective, singular time frame.

But this is not to imply there is a discord between what I've said and what you've expressed.

In the fable presented, the protagonist’s age as measured by his own personally experienced duration of time will factually be that of twenty-some years. This though, in the fable, relative to the duration of time as would be measured by all those he departed — javra

This puts me in mind of some of Kant's CPR i've gone over in the alst couple of days.
The relation of time is individual in that an external impression of another person doesn't exist in their time, it exists in the perceiver's time. I would think that this means we can just see any subjective notion of time as legitimate. It only exists as a relation, so there's no other benchmark.

Is that silly, or somewhat reasonable?

This puts me in mind of some of Kant's CPR i've gone over in the alst couple of days.
The relation of time is individual in that an external impression of another person doesn't exist in their time, it exists in the perceiver's time. I would think that this means we can just see any subjective notion of time as legitimate. It only exists as a relation, so there's no other benchmark. — AmadeusD

It is commonly enough known that we perceive time in subjective manners (the linked Wikipedia article gives a nice presentation). This I think fits into part of what you are saying. But this can’t then be the only benchmark for time, otherwise there would be no way of discerning between time which is subjectively perceived (and which can vary by individual) and that time which is objectively occurring (and is equally applicable to all causally interacting, or else causally entwined, observers).

As concerns objective time, however, the same dichotomy between a relativistic time and cosmically absolute time will present itself. With all indications now pointing to time being relativistic rather than absolute. So, in extreme time dilation scenarios, for one example, an individual can still have two distinct ages that are both objective (and hence not subjective) by breaking away from a commonly shared time frame (for example, the time frame that Earth dwellers more or less all inhabit (though minor forms of time relativity still apply here on Earth)) and then subsequently rejoining it.

To illustrate the distinction between subjective and objective time via a simple example: In a given conversation, time might by going slow for one individual and might be going fast for the other (this due to each individual’s separate chronoception) but will nevertheless be commonly applicable (hence, impartially applicable and, in at least this sense, objective) to both individuals in terms of the back-and-forth dialogue of the conversation - e.g., both will know who said what prior to whose reply, etc., thereby facilitating the possibility of a conversation. And if there were a clock present to both during the conversation, both could potentially pinpoint at which commonly shared, objective time a certain statement was made in durational relation to some other - this despite the differences in chronoception between the two individuals.

Its a very complex topic, this metaphysics of time. But that's my best answer so far.

As concerns objective time, however, the same dichotomy between a relativistic time and cosmically absolute time will present itself. With all indications now pointing to time being relativistic rather than absolute. — javra

And yet the claim is that the Universe began around 14 billion years ago. Time perhaps does not exist apart from change, and when you think about it the general durations of processes of change probably don't vary that significantly because no macro-objects are travelling at anywhere near the speed of light, and they also are not subject to massive time variations due to gravity either.

And yet the claim is that the Universe began around 14 billion years ago. — Janus

Unless I'm mistaken, there is no other way that estimate can be established other than via the theory of relativity - coupled, of course, with empirical evidence. So instead of contradicting the relativity of time, it will be one derivation from it.

Right, but what I was angling at is that the age of the Universe would not vary depending on where you are in it; there would seem to be a sense in which there is a current state of the Universe. And in general, when we talk about the age of anything, existing things which came into being earlier than other existing things are considered to be the older. On this criterion a daughter could never be older than her mother while they are both still alive, although of cause the daughter could live to a greater age.

And in general, when we talk about the age of anything, existing things which came into being earlier than other existing things are considered to be the older. On this criterion a daughter could never be older than her mother while they are both still alive, although of cause the daughter could live to a greater age. — Janus

I've already agreed to this, upheld it even before you mentioned it. But I don't see how this then contradicts the theory of relativity as regards a person potentially holding two actual ages in different respects - given the circumstances previously specified.

So that we're on the same page in terms of the theory of relativity's reality:

How does this connect with General Relativity and GPS? As predicted by Einstein’s theory, clocks under the force of gravity run at a slower rate than clocks viewed from a distant region experiencing weaker gravity. This means that clocks on Earth observed from orbiting satellites run at a slower rate. To have the high precision needed for GPS, this effect needs to be taken into account or there will be small differences in time that would add up quickly, calculating inaccurate positions. — https://www.nasa.gov/image-article/einsteins-theory-of-relativity-critical-gps-seen-distant-stars/

The theory of relativity does operate in terms of Earths own otherwise general time frame. So if travel even between different solar systems were to be possible, it would operate in these circumstances as well.

Yes, if the theory of relativity is in fact correct it operates everywhere. Since the different gravitational forces would not make for much of a difference, and it may well be impossible for objects to travel at anywhere near the speed of light, such thought experiments as would allow for huge differences in the progress of biological processes, and hence significant differences in aging probably remain in the realm of fiction or fantasy.

Since the different gravitational forces would not make for much of a difference, — Janus

The example I just gave of GPS evidences the significant difference between the gravitational force that a satellite is in and the gravitational force that a Earth-bound human is in. But I guess considering what is a "significant difference in different gravitational forces" would embark us too far astray.

and hence significant differences in aging probably remain in the realm of fiction or fantasy. — Janus

... and in the realm of metaphysical possibility, which this thread is in part about.

But I guess considering what is a "significant difference in different gravitational forces" would embark us too far astray — javra

I would say it would be difference great enough to make a significant difference to biological "age".

... and in the realm of metaphysical possibility, which this thread is in part about. — javra

We don't know what is metaphysically possible, and we only know what is physically possible given the assumption that our understanding of natural laws is correct and comprehensive.

We don't know what is metaphysically possible, — Janus

As a friendly reminder, we do know that different ontologies are metaphysically possible.

Although we also know logically that contradictory ontologies (e.g., that of physicalism vs. that of idealism vs. that of substance dualism) cannot all be accurate models of the physical, or better yet actual, world (needless to add, this at the same time and in the same respect).

As a friendly reminder, we do know that different ontologies are metaphysically possible. — javra

How do we know that?

I'll say that, if by no other means, then via acquaintance with there so being different ontologies out there, all of which are metaphysical possibilities regarding what the actual world in fact is. These are all metaphysically possible rather than physically possible in the same way that a possible world is metaphysically possible rather than physically possible - only that in the case of ontologies, one of them might be a more accurate mapping of the actual than the others.

Why ask such a question?

It seems we may have very different notions of what 'metaphysically possible' means. As I see it, if there is only one world then what is metaphysically possible would just be what is physically or actually possible. If there were other worlds, then different sets of physical laws might be metaphysically possible and actual. If there were a non-physical world, then whatever constraints operated in that world would be metaphysical (and of course logical) constraints. But all of this is only, for us, in the realm of the imagination, pure speculation: we have no way of knowing otherwise. If you have an alternative understanding, I'd be happy to hear about it.

If you have an alternative understanding, I'd be happy to hear about it. — Janus

My take was stated in this post in the thread, which is itself based on this SEP entry (you can quickly look at the SEP entry's section 1's two definitions of metaphysical possibility).

Thanks...these are the definitions given there:

p is metaphysically possible iff p is true in at least one possible world.
p is metaphysically necessary iff p is true in all possible worlds.

p is metaphysically possible iff p is consistent with the laws of metaphysics.
p is metaphysically necessary iff p follows from the laws of metaphysics.

I see the first as being circular and uninformative, because we don't know what worlds (if any other than our own) are possible unless we count possibility as being simply what we can coherently imagine.

I see the second as also being uninformative because we don't know what the laws of metaphysics are, unless, again, they are what we can imagine without contradiction.

In both cases if metaphysical possibility is just what we can, without contradiction, imagine, then metaphysical possibility would seem to collapse into logical possibility.

The meaning of modalities is in their use, which is inadequately represented by picture-theories of modalities, especially the silly Venn diagrams stemming from the naive depiction physical possibilities as being a proper subset of metaphysical or logical possibilities.

First of all, are modalities empirical claims about reality, or they normative rules of convention that refer to the use and interpretation of a model, or are they both? And besides, how does the empirical content of a model relate to the application of it's rules? Can Kripkean semantics, or any other plum-pudding depiction of possible worlds do justice to the complicated use meaning of modalities?

Consider the fact that physical impossibility cannot be empirically falsified, at least not in the naive way that people presume. For example, the physical impossibility of faster than light travel cannot be directly tested nor understood by measuring the speeds of various objects, for we cannot observe what isn't observable, and the literal claim that nothing can travel faster than the speed of light cannot be directly verified by any finite number of experiments. Nor can a philosopher directly imagine faster than light travel in a thought experiment (for what would that look like, exactly?). So both the empirical and theoretical meaning of the impossibility of faster than light travel is far from straightforward and definitely not obvious. Furthermore, the literal English meaning of "faster than light travel" cannot even be translated into the language of Special Relativity, for SR maps the English sentence "faster than light travel" to infinite Lorentz factors that are extensionally meaningless.

The empirical meaning of SR is demonstrated by the experiment and results of the Michelson Morley experiment that partly motivated it. This empirical meaning does not refer in any obvious way to the sentiment that "faster-than light travel is impossible". If a physicist is asked to describe the meaning of this impossibility, he will likely refer to empirically observable Lorentzian relations that he argues are expected to hold between observable events. In other words, his use-meaning of the "physically impossible" is in terms of the physically possible!

So physical impossibilities shouldn't be thought of in terms of impossible worlds, but rather as referring to the application of a linguistic-convention that supports the empirical interpretation of language.

I'll say that, if by no other means, then via acquaintance with there so being different ontologies out there — javra

There are different ontological theories; there is one ontological subject and object of study, which is existence. Having different ontological hypotheses doesn't alter the nature of the real.

What is possibility? It is "possible" that string theory is true, e.g. that it aligns with reality. It is possible that a rolled dice will come up six. Which only means that, in the actual unfolding of actual events someone rolls the dice and it comes up six. It doesn't mean that there actually are alternate realities in which every case of every event is realized. Ex hypothesi, if these alternate realities exist, they are mutually exclusive, in which case, they represent metaphysically exclusive cases. So there is still only one overriding metaphysics, that which governs each exclusive modal set. That spirals off into an infinite set of infinite universes, which is absurd. The whole nature of the universe, as quantum physics explores, is to consume these possibilities. Information decoheres from a state of superpositions to realized specific configurations which are "preferred" and which, qua pointer states, correlate with specific physical properties.

what would something metaphysically impossible but logically possible be? — Lionino

It's logically possible that abstract objects exist, but their existence is metaphysically impossible if physicalism is true.

In general one would judge as metaphysically possible, anything that is consistent with one's prior ontological commitments. If contradicted by ontological commitments, you'd judge it metaphysically impossible.

If you prefer to judge metaphysical possibility from a perspective that's devoid of ontological commitments, then metaphysical possibility = broadly logical possibility.

The empirical meaning of SR is demonstrated by the experiment and results of the Michelson Morley experiment that partly motivated it. This empirical meaning does not refer in any obvious way to the sentiment that "faster-than light travel is impossible". If a physicist is asked to describe the meaning of this impossibility, he will likely refer to empirically observable Lorentzian relations that he argues are expected to hold between observable events. In other words, his use-meaning of the "physically impossible" is in terms of the physically possible!

So physical impossibilities shouldn't be thought of in terms of impossible worlds, but rather as referring to the application of a linguistic-convention that supports the empirical interpretation of language. — sime

Of course, I must agree that physical impossibility is grounded in physical possibility; there is that which is physically possible, and the rest is not; so I'm not sure what you are aiming at with that.

I realize that an hypothesis such as that travel faster than light is impossible can never be verified by any number of observations. I was only concerned with the notion that there should, or even merely might, be physical impossibilities, regardless of whether we can know what they are or even whether there are such impossibilities.

If we adhere to the idea of universal natural law and assume that what we understand about that law is valid and reflects necessary or universal invariances, then within that context, we can talk about physical impossibilities. But the caveat will always be 'given that the laws of nature are themselves invariant".

The idea that there might be worlds (or universes) which enjoy very different laws would then transcend this notion of physical impossibility which is based on our familiar laws. So, I would refer to that as metaphysical possibility. The question then would be as to whether there should or must be any constraints on metaphysical possibility other than those of a merely logical nature.

Being fundamentally a skeptic, of course I will answer that we can raise these kinds of logically derived questions, but we cannot decidedly answer them. They remain exercises of the speculative imagination.

I would say there are historical (Earth or chronological) time and phenomenological time — Janus

Yes, basically. What I meant to be specific was that he is older in historical time (1000 years or so), but younger in chronological time (because he has not lived for as long as his daughter in his experience) — or as you call it durational time —, and also younger in biological age because his body has aged a certain amount (equal to chronological time in this case).

In any case, the example given of a mother younger than her daughter does not fit the bill.

unless we count possibility as being simply what we can coherently imagine. — Janus

That would be it. Possible worlds are every state of affairs that could have been, t.i., not logically contradictory.

we don't know what the laws of metaphysics are, unless, again, they are what we can imagine without contradiction — Janus

The laws of metaphysics do not follow necessarily from logical possibility.

It's logically possible that abstract objects exist, but their existence is metaphysically impossible if physicalism is true.

In general one would judge as metaphysically possible, anything that is consistent with one's prior ontological commitments. If contradicted by ontological commitments, you'd judge it metaphysically impossible.

If you prefer to judge metaphysical possibility from a perspective that's devoid of ontological commitments, then metaphysical possibility = broadly logical possibility. — Relativist

Good post. I agree. I would also raise that if physicalism is true, metaphysical possibility = physical possibility.

I would also raise that if physicalism is true, metaphysical possibility = physical possibility. — Lionino

100% agree.

deleted

If we adhere to the idea of universal natural law and assume that what we understand about that law is valid and reflects necessary or universal invariances, then within that context, we can talk about physical impossibilities. But the caveat will always be 'given that the laws of nature are themselves invariant". — Janus

If naturalism is true, and there are laws of nature, I suggest the true natural laws would be invariant. The way they manifest might be contingent on local conditions. That's why I think its important to refer to laws of nature, as you have done, rather than the laws of physics- which are based on our current understanding, and subject to revision as we learn more.

The laws of metaphysics do not follow necessarily from logical possibility. — Lionino

I agree with you, but would just repeat that we don't, can't, know what the laws of metaphysics (if there be such) are. Logical possibility informs us only about what is possible, not about what is necessary.

If naturalism is true, and there are laws of nature, I suggest the true natural laws would be invariant. The way they manifest might be contingent on local conditions. That's why I think its important to refer to laws of nature, as you have done, rather than the laws of physics- which are based on our current understanding, and subject to revision as we learn more. — Relativist

The Laws of nature may evolve (as Peirce thought) but if that were so they would still be invariant over long periods (unless there were some kind of "punctuated evolution" as S J Gould postulated in regard to biological evolution). The laws of nature may be understood simply as the 'observed habits of nature as formulated by us).

There are different ontological theories; there is one ontological subject and object of study, which is existence. Having different ontological hypotheses doesn't alter the nature of the real. — Pantagruel

Of course: one ontic reality (whatever it might in fact be) and many ontologies (each with its own proposed metaphysical laws) trying to accurately map it - often enough in manners that end up being contradictory to other ontologies.

After some thinking, 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 . Among abstract objects, we have universals, such as greenness or beauty, and numbers .
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 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).



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