Construct your own Cosmological Argument

First read this piece by St. Feser:
So you think you understand the Cosmological Argument?

about the traditional structure of Cosmological Arguments, rebutting several popular misconceptions.

Now take the following argument scheme, making suitable choices as needed:

  1. (Major Premise) Every [thing/event] with property X needs a [cause/explanation/reason] outside of itself to [cause/explain/be the reason of it]
    .
  2. (Minor Premise) There is at least one [thing/event] with property X.
    .
  3. (Inductive Principle) You have a choice...
    A.  argue that an infinite regress of [causes/explanations/reasons] for the X's is unreasonable, OR
    B. argue that such an infinite causal chain would itself have property X, OR
    C.  argue that the entire set of X's taken together (which might, depending on X, include the entire physical universe we know and love) has property X.
    .
  4. (Conclusion) Tracing back the [causes/explanations/reasons] back to their ultimate origin, we find that there is [one/at least one] thing which does not have property X, which, taken [singly/together], [causes/explains/gives the reason for] all the things which do have property X.
    .
  5. (Atheist Baiting) Add the famous words: "And this all men call God".  Works best if ~X is a traditional divine attribute, or even better if you can collect several such ~X's and can argue that they all refer to one and the same Exalted Being!

For example, in the debate, St. Craig's kalam argument used "comes into existence" as X, and then used a lumping strategy (3C) to talk about the universe as a whole and ask whether it had a cause.  This form of the Cosmological Argument ended up being strongly dependent on what the Science of the Big Bang actually shows, but most forms don't really depend that strongly on Science.

Other traditional X's include "changing with time", "contingent" (something that might or might not exist), "composite", and some other possibilities mentioned in the link above.   The idea is that there are some features of objects which make us seek out causes for them, for example if an object is composed of several disparate objects, we naturally want to know what brought them together.  Depending on what you pick for X, the Cosmological Argument may be more or less plausible.

You will also want to consider what type of causal concept you want to include in your argument.  A key question is how we know there is such a thing as causation?  If it is primarily for empirical reasons, then presumably we know about it through some type of inductive* argument from experience, in which case we could wonder how applicable it will be in unusual situations.  On the other hand, if it is primarily motivated by reason, through analyzing what types of explanations would make sense of the universe, it may be less dependent on observation.  Or perhaps the truth is somewhere in the middle.

[* Footnote: I somewhat regret using the term "inductive" here, given my previous usage of "Inductive Premise" to label premise 3.  In both cases one is moving from specific applications to more general applications, but for premise 3 I had in mind something closer to mathematical induction, a step which (given the right background premises) is logically necessary, whereas in the paragraph directly above, I am referring to something more like scientific induction, where if you observe something happening enough times you guess that maybe it always happens that way.]

Another thing to figure out is what types of entities are connected by cause-effect relationships.  Does a cause have to determine the effect with certainty, or is it sufficient if it in some way produces it?  For example, if we want to argue that all contingent things were caused by something which is necessary, this is a contradiction in terms unless a necessary thing can produce contingent things, i.e. if causes don't have to be deterministic.  A related question: when we talk about causes, are we primarily talking about beings causing things to happen (a.k.a. agent-causation), or states of affairs causing things to happen (a.k.a. event-causation), or both?

Regarding step (5), note that excessively glib atheist baiting obscures the fact that nearly everyone should accept some type of Cosmological Argument, even if they don't necessarily take it to a Theistic conclusion!  If you are going to talk about causes/explanations/reasons AT ALL (and I really don't see how to avoid this) then you really need an account concerning the domain to which the concept is applicable.  And then it is an interesting fact, that either you must accept infinite or circular chains of [causation/explanation/reasons] or you end up going outside the domain to something else which is different.

This type of reasoning should be interesting, even if you are an atheist.  The trouble is, if people only encounter Cosmological Arguments in the context of Theism, then Atheists adopt an argumentative approach where they just feel the need to poke a few holes in the arguments and then retreat to where they were before.  This doesn't do justice to the fact that there are numerous X's for which the argument's premises are at least plausible, even for people who don't start out committed to any particular religious doctrine.

For example, Carroll himself gives an account of the scope of causation when he says:

Why should we expect that there are causes or explanations or a reason why in the universe in which we live? It’s because the physical world inside of which we’re embedded has two important features. There are unbreakable patterns, laws of physics—things don’t just happen, they obey the laws—and there is an arrow of time stretching from the past to the future. The entropy was lower in the past and increases towards the future. Therefore, when you find some event or state of affairs B today, we can very often trace it back in time to one or a couple of possible predecessor events that we therefore call the cause of that, which leads to B according to the laws of physics. But crucially, both of these features of the universe that allow us to speak the language of causes and effects are completely absent when we talk about the universe as a whole. We don’t think that our universe is part of a bigger ensemble that obeys laws. Even if it’s part of the multiverse, the multiverse is not part of a bigger ensemble that obeys laws. Therefore, nothing gives us the right to demand some kind of external cause.

There seem to be some question-begging moves in this paragraph, but leave that aside.  My point is that Carroll gives a positive account of when he thinks makes the notion of [cause/explanations] make sense.  He endorses a version of (1) whereby the concept of causation makes sense if (a) there are laws of nature, understood as unbreakable regularities, and (b) there is a thermodynamical arrow of time whereby entropy increases, making a distinction between the past and the future.  (Since causes normally precede effects, but the laws of physics don't strongly distinguish between the two directions of time except through thermodynamics, it seems clear that the arrow of time has to play some role in distinguishing causes from effects in physics.)

He also allows (2) that this concept—though not fundamental in his opinion—nevertheless makes sense for certain particular cases.

Then for (3) he allows us to lump together the universe taken as a whole, but claims that this whole does not meet his criterion (1).  He thus comes to an object—the whole universe, apparently—for which, in his view, it wouldn't make sense for it to have a cause (4), although he does not identify it with God (5).  Thus his reasoning has an implicit atheist version of the Cosmological Argument behind it.  Though one can certainly question whether the metaphysical assumptions behind this claim are right.

But it's just possible you came here hoping, not to construct your own Cosmological Argument, nor to deconstruct Carroll's, but instead to find out what I think about it, something which you may think I have postponed saying for quite long enough.  Well, it just so happens that I've written a 16,000 word essay on the Cosmological Argument and related topics, and will be posting it in installments over the course of the next few weeks.

Posted in Metaphysics, Reviews, Scientific Method, Theological Method | 45 Comments

Explanation needed

I've been discussing Sean Carroll's claim that:

The demand for more than a complete and consistent model that fits the data is a relic of a pre-scientific view of the world. My claim is that if you had a perfect cosmological model that accounted for the data you would go home and declare yourself having been victorious.

In my last post, Models and Metaphysics, I tried to argue that there are substantive philosophical questions about causality which Carroll is dismissing unduly as pre-scientific.

But in this post, I thought I'd give a concrete example of a situation where we would not declare victory and go home, even with a complete and consistent model of the universe.  While at some point fairly soon I'd like to give my own take on the Cosmological Argument, my counterexample in this post isn't going to depend on any seriously heavy-duty metaphysics.  Instead I'd like to try to focus on something fairly quantitative and precise, something  "rational almost to the verge of rationalism", in short, an argument that even someone steeped in scientism could love.

Let's imagine that in the future, we come up with a seeming Theory of Everything™ which explains almost everything about the world.  Every single physical phenomenon which has ever been observed has now been explained by a simple equation.  Let us stipulate that the initial state of the universe is itself determined by these equations, leading to a cosmology consistent with what we observe.  If you like, we can also pretend that no supernatural events have ever been verified, and that (after the Great Riot of 2438 C.E., when all the metaphysicians and philosophers were confined to the tops of their Ivory Towers and forbidden to communicate with the ordinary citizens outside) we have all agreed not to inquire to closely into the question of why certain physical states of the brain correspond to conscious experiences.  It is indeed a great triumph for the Scientific Method.

There's one catch.  The remaining (non-meta)physicists tell us that there is one universal constant of nature in the theory, designated by a capital alpha A, whose numerical value needs to be fixed before any predictions can be made.  This constant is dimensionless, meaning that all the units cancel out, so that it isn't measured in meters per gram, or joule-seconds, or anything like that, but is just a real number.  For example, it might be the ratio of two things with the same units.  Because this constant A is dimensionless, it's numerical value is independent of the choice of units used to measure this parameter.

(In real life there are currently about 26 or so dimensionless constants in the Standard Model plus General Relativity—not counting inflation or dark matter—the most famous of these constants being the fine structure constant, which is approximately 1/137.036\ldots.)

Since the equations work equally well no matter what the value of A is, we have no choice but to do experiments to see what its value is.  Let us suppose (rather unrealistically) that the scientists have measured this parameter to 800 decimal places, and that—lo and behold!—the answer is exactly

A = \frac{2\pi}{7}.

No one knows why, that's just the way things are. 

(Note: this situation is different from the usual Fine-Tuning Argument, because I am not supposing that there is any reason why life requires the constant to take on this precise value.)

I submit to you that, notwithstanding the fact that this TOE™ gives a complete description of everything in the universe, we ought not to declare victory and go home.  Because it is plain as day that this number 2\pi / 7 requires some sort of explanation which has not yet been given.  In other words, we don't just demand that our models completely explain the data.  We also demand that they be complete in the sense of providing explanations for anything which seems to require an explanation.

True, 2\pi / 7 is not an extremely complicated number; in most computer languages one can write a fairly short computer program that spits out this number.  But I didn't become a physicist in order to compress my sense-data into as few bits of information as possible; WinZip does a better job of data compression than I ever could.  I became a physicist in order to understand how and why the world works the way that it does.

So I wouldn't be completely satisfied with this TOE™ as it stands, even though it would be a big improvement on our current best theories of physics.  Instead I would start asking naïve questions like:

"Why is there a 2\pi in the formula for A, given that we all know that 2\pi is the ratio between a circle's circumference and its radius?  Where do circles come into it?"

and

"What's so special about 7?  Is this just a random whole number that was pulled out of a hat?!?  Why is the denominator even an integer at all?  What is 7—a sufficiently awkward prime that it seldom comes up in physics formulae—doing in the most fundamental equation of the universe?"

Now I don't know whether all of these mutterings about sevenths of circles would get me shoved up a Tower or not.  But I am convinced that this question would be meaningful, that it must have an answer, and that any red-blooded human being with basic curiosity about the world should hope to find the answer.

Or, to speak in Bayesian terms, nearly all of my prior probability would be placed on there is an explanation for this odd fact that I don't know yet, and nearly none on this is just an inexplicable basic fact about the universe which has no explanation at all.  I'm not sure how to convey this intuition to you if you don't already share it.  But it seems to me that basic inexplicable facts about the universe shouldn't fall into patterns which seem to indicate the existence of a deeper layer of reality, unless there actually is a deeper layer of reality behind the shadows we see on the cave wall...

"What's that? Yes officer, I was just headed for that Tower over there right now!  Please don't let me trouble you any further.  No, I just stepped out for a moment.  Yes.  Look I'm heading back right now.  See?"

Of course, just because I would think that there must be an explanation, doesn't mean that we would ever find out what that explanation is.  Life can be a bummer that way:

All this I have proved by wisdom.
I said, “I will be wise”;
But it was far from me.
As for that which is far off and exceedingly deep,
Who can find it out?
(Ecclesiastes 7:23-24)

I would be potentially open to any explanation involving either "natural" or "supernatural" elements, so long as it in fact explained the parameter.

Of course, if the explanation involved more ad hoc elements than the thing being explained, then that would raise questions about whether it was really the best or simplest explanation.  And even if I thought of a good explanation, I might wonder if there were some other equally good explanation. Or conversely, I might not be able to think of any good explanation at all.  So at the end of the day I might have to be an agnostic about what type of explanation should be considered.

But that wouldn't change the fact that I'd think there'd be one.

Posted in Metaphysics, Reviews, Scientific Method, Theological Method | 5 Comments

Models and Metaphysics

In my previous posts about the Carroll-Craig debate, I've been skirting around the edges of an important claim by Carroll which summarizes the main reason he doesn't buy the Cosmological Argument.  That's because I was focusing on the question of whether the universe had a beginning.  Now I want to grapple with his more philosophical claim.

Carroll says this:

So, I think I can make these points basically by following Dr. Craig’s organization starting with the kalam cosmological argument, and unlike what he said I should be doing I want to challenge the first of the premises: If the universe began to exist it has a transcendent cause. The problem with this premise is that it is false. There’s almost no explanation or justification given for this premise in Dr. Craig’s presentation. But there’s a bigger problem with it, which is that it is not even false. The real problem is that these are not the right vocabulary words to be using when we discuss fundamental physics and cosmology. This kind of Aristotelian analysis of causation was cutting edge stuff 2,500 years ago. Today we know better. Our metaphysics must follow our physics. That’s what the word metaphysics means.

[Well, many scholars think that Aristotle's book on causation/God was called Metaphysics because it was the book immediately following his Physics in the traditional order of the canon.  But perhaps Carroll knows this and is simply introducing his thesis in a joking way...]

And in modern physics, you open a quantum field theory textbook or a general relativity textbook, you will not find the words “transcendent cause” anywhere.  What you find are differential equations.

[Of course, because QFT and GR concern the interactions between various material entities (excitations of fields).  Their interactions (i.e. their causal relationships) are indeed described by differential equations.  And therefore the subject matter does not concern transcendental or ultimate causes, any more than economics or psychology textbooks discuss the weak force.  What he really ought to say to make his argument, is that the term "cause" does not appear in many modern physics textbooks (apart from the use to mean "logically implies") due to its lack of usefulness in specifying the precise form of the laws of physics.

It is, however, a separate question whether concepts of causation are implicit in the fact that some particular differential equation holds.  It does not seem outrageous to state that the state of the fields at a given point are caused by the state of the fields just beforehand in the past lightcone; indeed this concept is called causality in contemporary physics.  This concept may indeed be different in some ways from traditional philosophical ideas of causality, but it is not sheerly different, and there is room for argument about the precise relationship between these ideas of causation.  Carroll continues:]

This reflects the fact that the way physics is known to work these days is in terms of patterns, unbreakable rules, laws of nature. Given the world at one point in time we will tell you what happens next. There is no need for any extra metaphysical baggage, like transcendent causes, on top of that. It’s precisely the wrong way to think about how the fundamental reality works. The question you should be asking is, “What is the best model of the universe that science can come up with?” By a model I mean a formal mathematical system that purports to match on to what we observe. So if you want to know whether something is possible in cosmology or physics you ask, “Can I build a model?” Can I build a model where the universe had a beginning but did not have a cause? The answer is yes. It’s been done. Thirty years ago, very famously, Stephen Hawking and Jim Hartle presented the no-boundary quantum cosmology model.

[See here for my discussion of the claim that the Hartle-Hawking model leaves no room for a Creator.]

The point about this model is not that it’s the right model, I don’t think that we’re anywhere near the right model yet. The point is that it’s completely self-contained. It is an entire history of the universe that does not rely on anything outside. It just is like that. The demand for more than a complete and consistent model that fits the data is a relic of a pre-scientific view of the world. My claim is that if you had a perfect cosmological model that accounted for the data you would go home and declare yourself having been victorious.

Carroll seems to be saying that the ability to construct a mathematically precise and consistent model of the universe is the only important criterion for the fundamental laws of physics, aside from fitting the data.  Presumably he would add something about simplicity if we were considering two rival models which both accounted for the same data, but I think he doesn't mention that since his primary concern is saying what counts as a possible model according to the contemporary set of informal procedures that cosmologists use, rather than asking how we decide between models once we have them.

This is probably the most important claim that Carroll made during the debate.  I appreciate the fact that he was able to state his view in such a clear and accessible way.  Now, there is one important point in which I agree with Carroll, and one important way in which I disagree.

I agree that Modern Science has involved some shifts in how we think about causation in the physical universe.  This shift, which occurred sometime around the beginning of the 20th century (give or take a couple hundred years) involved a move away from mechanistic notions of causation, towards more abstract mathematical models.  As a characteristic example, in the 19th century it was presumed that light waves couldn't exist unless they were supported by a medium, called the luminiferous aether.  When Einstein developed special relativity, he showed that no such aether was necessary.  If you can write down a satisfactory equation for the way the electromagnetic field propagates, there's no need to ask questions like "In what medium does it propagate?"  (Of course, this philosophical point could have been made in the time of St. Maxwell as well, but it wouldn't have been as compelling then, since before Einstein's theory of relativity an aether was needed to preserve the principle of relativity).

Another example concerns normal forces of the sort that prevent two solid bodies from occupying the same space.  A premodern physicist would have said that solid bodies have a property of solidity or massiness which, using our everyday intuitions, prevents two bodies from occupying the same position.  In Lucretius' atomic theory, the atoms were in solid shapes like billiard balls (but not necessarily round) which excluded each other due to their solidity.  Very different was St. Roger Joseph Boscovich's 1763 proposal that atoms are merely mathematical points exerting force on other mathematical points.

In modern physics, there's nothing inherently wrong in general with two objects occupying the same position, since you can write down equations in which this is allowed.  The default, in the absence of interactions, is for two bodies to pass right through each other.  That this does not occur for real solid bodies is due to a combination of electromagnetic forces and the Pauli exclusion principle for electrons.†

So I agree with Carroll that there have been changes in our attitude to causality in Physics.  Now let's see whether this should change our views about Metaphysics.  As a reminder, Metaphysics is the branch of philosophy which studies the fundamental nature and relationships between various beings (abstracting from the particular descriptions of the particular things as studied by more specialized fields like Physics or Biology).  It asks questions like these:

Do individual things have a particular essence or nature which does things? 
In what sense does causality exist, and if so what kinds are there? 

Is there really a physical universe?
Are there really minds?
Can everything be reduced to physics, or
can everything be reduced to mental properties, or are these two independent realities, or are they both dependent on something else?
In what sense do mathematical entites like "7" or "isoscoles triangles" exist?
In what sense does morality exist?

Does some type of God exist, and if so what is he/she/it like?
What are the relationships between these different types of existence?
 
Do the "holes" in doughnuts really exist, or are they merely the absence of doughnut?
Are the questions I just asked even meaningful, or are some of them silly word games?

(The subset of questions about what exists are also sometimes also called Ontology.  In case you're wondering, analytic philosophers really do debate the one about holes.  Personally I consider the one about God to be more important.  But I figured that given my last question, I needed to include at least one question which I consider to be a silly word game...)

Now, these questions raise some difficult and contentious issues, and philosophers have been debating them for thousands of years.  But rather then tackle them head-on, let's ask to what extent developments in Physics and other Sciences help answer these questions.

There are two opposite extreme approaches one might take:

1.  One is the view that our Metaphysics should essentially follow immediately from our Physics.  Once we learn from experiment what specific Laws of Physics are true, that tells us everything we need to know about Metaphysics.  People with this view tend to be scientistic and dismissive of philosophical arguments.  (You might think from the quotation above that this is Sean Carroll's view, that once we work out the correct physical model there are no more interesting questions to ask.  But in fact his view is more subtle, since he acknowledges that there are interesting philosophical questions not obviously resolved by Science.)

2. The opposite extreme would be to say that developments in Physics have little or no bearing on Metaphysics.  For example, there are modern day followers of St. Thomas Aquinas (typically but not always Roman Catholics) who believe that something similar to Aristotle's metaphysical views follow necessarily, given that the world is rationally explicable at all, and that the very possibility of doing Science depends implicitly on accepting them.  In this view, the basic concepts of metaphysical reality such as substance/accident or act/potency are written in stone, although identifying the particular "substances"‡ which actually exist, and their properties, depends on empirical Science.  One such philosopher is St. Ed Feser, whose blog is on my sidebar.  (I recently read his book Scholastic Metaphysics in which he presents his arguments for this position.  On a first pass, I found it serious and interesting but ultimately unconvincing, though giving my reasons would take this post too far afield.)

But it seems to me that the correct view is in the middle, that Physics has some bearing on Metaphysics but it doesn't fully determine it.  Physical models and metaphysical views have, not a 1-to-1 relationship, or even a 1-to-many relationship, but a many-to-many relationship!

People who agree on the Laws of Physics (to the extent that we are able to discover them at present) can still have radical disagreements about Metaphysics.  Of these metaphysical views, some seem irrational and silly, like the Monadic view that all distinctions are illusory and that only one thing exists.  But it seems to me that there are several possible reasonable (i.e. non-crazy) views.  So even after we agree on a single physics model, multiple metaphysical views can be reasonable.  The variety of interpretations of Quantum Mechanics is one prominent example.  Choosing between these interpretations requires philosophical arguments; doing an experiment is not enough.

On the other hand, it seems rather unlikely that the philosophical considerations by themselves are sufficient to pin down an exact Metaphysics either.  That would be to say that every single view about the nature of Being, besides one, can be decisively refuted by philosophical arguments.  That would seem to me almost as surprising as a claim that the Laws of Physics can be deduced from pure Reason.  There are just too many possible sets of belief, and logical consistency plus noncraziness is too weak of a constraint.  (Especially since our notion of noncraziness needs to be flexible enough to include things like interpretations of QM and the mind-body problem, where nearly all views seem "crazy" in one way or another.)

Given that there are multiple possible views about Metaphysics, we need all the help we can get to choose one.  So it would be absurd not to rely on Physics to some extent, especially as it impinges on relevant questions.  How could anyone have an informed position on the nature of time without thinking about what General Relativity says about spacetime?  But we also need to recognize that Physics is not enough, and that abstract arguments about what "makes sense" are also called for.  Even together these are not sufficient to bring all reasonable Philosophers into agreement.

That means that Carroll is moving much too quickly when he says that "This kind of Aristotelian analysis of causation was cutting edge stuff 2,500 years ago. Today we know better. Our metaphysics must follow our physics."

If there are multiple possible metaphysical views, then we can't just dismiss the views of Aristotle (or whoever) just for being old, without carefully thinking about their compatibility with Modern Science.  Maybe people switched to modern views because of updates in physical knowledge (some of which, like Determinism, may themselves be out of date!).  Or maybe they changed because of philosophical arguments, in which case we need to check whether those arguments are good or bad.  Or maybe the old views simply became unfashionable.  Most likely, it was some combination of these four causes, and we need to be careful!  As St. Lewis writes concerning Owen Barfield:

In the first place he made short work of what I have called my "chronological snobbery", the uncritical acceptance of the intellectual climate common to our age and the assumption that whatever has gone out of date is on that account discredited.  You must find out why it went out of date.  Was it ever refuted (and if so by whom, where, and how conclusively?) or did it merely die away as fashions do?  If the latter, this tells us nothing about its truth or falsehood.  From seeing this, one passes to the realization that our own age is also a "period", and certainly has, like all ages, its characteristic illusions.  They are the likeliest to lurk in those widespread assumptions which are so ingrained in the age that no one dares to attack or feels necessary to defend them.

While I don't accept St. Feser's arguments that Aristotelianism is compulsory, I think that studying it is a useful antidote to thinking that there's only one possible view.  Certain aspects of modern thought might be unreasonable inheritances from the Enlightenment, or from Positivism.  The easiest way to notice that we are making unnecessary presuppositions, is by comparison to what previous thinkers have thought.  If we dismiss previous metaphysical views out of hand, that makes it hard to notice our own modern blindness towards certain issues and problems.

We need to be especially careful given the tendency for theories to be expressed in the language of the existing philosophical structures.  This can cause us to think that those theories depend on a certain Metaphysics, when really they don't.  Just because theologians expressed Trinitarian doctrines using Aristotelian terminology, or early 20th century physicists expressed QM using Positivist concepts, doesn't necessarily mean that these ideas can't be transplanted to certain other systems.

Aristotelianism became unpopular long before QM was discovered.  But suppose that somehow the medieval European or Muslim world had discovered QM.  I bet that their "interpretations" would have been radically different from anything we have now, even if the mathematics which they developed ultimately turned out to be equivalent to ours (as happened to Heisenberg and Schrödinger)!

None of what I have said here is a positive argument for Theism.  It is merely my attempt to sweep away Carroll's strong claim that once we have a physical model, all of our work is done and there is no place to ask further metaphysical questions.  On the contrary, we can continue to ask questions, and we can judge possible answers to those questions by whether they make logical or intuitive sense to us.

Perhaps at the end of the day, a person might conclude that the certain questions about the origin of the Universe are meaningless, or that that they are meaningful but that Theism is not the correct answer to them.  But that has to come after considering the merits of different rival views, not beforehand.

Notes:
† The Pauli exclusion principle forbids two fermions from occupying the same state, which sounds a bit like the principle that solid objects cannot occupy the same space, except that:

(i) ``state'' refers not just to position but rather to all properties including both position and velocity (to the extent that both can be simultaneously measured in Quantum Mechanics).

(ii) It follows from a much more abstract mathematical principle, which I will cite without explaining, that identical types of fermions (e.g. electrons) have antisymmetric wavefunctions.  This means that the complex number describing the quantum mechanical amplitude for one electron to be in position x and the other in position y is minus the amplitude for the first to be at y and the other at x.  This is called Fermi-Dirac statistics.

(iii) It doesn't apply to bosons, which have symmetric wavefunctions.  Therefore you can have a bunch of identical bosons in the same state, as in lasers or Bose-Einstein condensates.

‡ "Substance" is a technical term in Aristotelian metaphysics.  It means an individual entity which possesses existence independently, as opposed to an "accident" which "inheres" in a substance and can be changed without affecting the underlying nature of the thing in question.  Sort of like the difference between nouns and adjectives.  Not to be confused with the more recent chemical notion of substances.  This confusion of terminology causes great misunderstanding when Roman Catholics try to explain their doctrine of transubstantiation to modern people!

Posted in Metaphysics, Reviews, Scientific Method, Theological Method | 28 Comments

Chalcedon

A reader writes in with the following questions concerning the Incarnation:

1. Since Jesus was a Jew (born of a Jewish mother, Mary), and Jesus Christ is one of the 3 persons of the Trinity, is God a Jew? But God is spirit. I am not sure if there is a difference between the Son (before creation) and the Son who later took human form in a Jew named Jesus. In other words, the Son was eternal (part of the Trinity) but Jesus was not. The Son – who is neither male nor female but spirit being God – became flesh, a Jewish rabbi.

2. In Matthew 24:36 Jesus says: “But of that day and hour no one knows, not even the angels of heaven, but My Father only.” Why wouldn’t the Son know if he’s an equal person in the Trinity? Again, I’m tempted to think this is Jesus the man who is speaking, and not God the Son (who must know when he would return, or else is not omniscient).

I do realise the Trinity is ultimately a mystery in the Christian faith, but I’d like to hear what you think about these two questions. Aside from these questions, I have no problem with the Christian understanding of a personal God in the life of Jesus..

You're in good company. This is actually the exact question of Christology which started being controversial in the 400's, the century following the adoption of the Nicene creed by the Councils of Nicea and Constantinope (known as the 1st and 2nd Ecumenical Councils). Once it was settled that Christ is God (contrary to the heretical teaching of Arius), the next question to work out is the relationship between the divine and the human in Christ.

Catholic, Orthodox, and Protestant Christians are all agreed about the answer, which is that Christ has two different natures (divine and human) but these natures are united in one person and one being, the Christ.

The controversy started as a result of Nestorius, who claimed that there were two separate persons in Christ, a divine person united to a human person.  He was unwilling to say that Mary was the Theotokos (God-bearer) but preferred the term (Christ-bearer). This was condemned as heretical by the Third Ecumenical Council of Ephesus.  Nestorius went over to the Assyrian Church of the East (which exists to this day and is neither Catholic nor Protestant nor Orthodox).

Then later there were the Monophysites/Miaphysites who said that Christ had just one nature, which was both human and divine. This was condemned at the Fourth Ecumenical Council of Chalcedon [pronounced with a hard "Ch", like "Christ"] in the year 451 AD.  However, the Coptic Church and others didn't agree with this, and so there was a schism between them and the (not-yet-divided) Catholic/Orthodox church, which exists down to the present day.

In retrospect, it is not so clear that these other groups were quite so heretical as they were made out to be.  Unlike the controversy with the Arians, it is a bit hard to be sure when the two groups actually disagree, and when they were just using different language for the same thing. But I believe that the Chalcedonian language is, at the very least, the most clear and accurate way to describe the union of the divine and human natures in Christ.

The complete Chalcedonian Formula is as follows:

"Therefore, following the holy fathers, we all with one accord teach men to acknowledge one and the same Son, our Lord Jesus Christ, at once complete in Godhead and complete in manhood, truly God and truly man, consisting also of a reasonable soul and body; of one substance with the Father as regards his Godhead, and at the same time of one substance with us as regards his manhood; like us in all respects, apart from sin; as regards his Godhead, begotten of the Father before the ages, but yet as regards his manhood begotten, for us men and for our salvation, of Mary the Virgin, the God-bearer [Theotokos]; one and the same Christ, Son, Lord, Only-begotten, recognized in two natures, without confusion, without change, without division, without separation; the distinction of natures being in no way annulled by the union, but rather the characteristics of each nature being preserved and coming together to form one person and subsistence, not as parted or separated into two persons, but one and the same Son and Only-begotten God the Word, Lord Jesus Christ; even as the prophets from earliest times spoke of him, and our Lord Jesus Christ himself taught us, and the creed of the fathers has handed down to us."

Applying this to your question, we see that Jesus possessed BOTH the attributes of divinity (eternal, omniscient, sexless, etc.) and the attributes of (a particular) human nature (Jewish, born of Mary, male, limited, etc.), but without sin, having a complete human body and soul. Since the divine nature is eternal, immutable and cannot change, we cannot say that God was transformed into a human being, but must instead say that he assumed or took on human flesh.  "Not by conversion of the Godhead into flesh; but by assumption of the Manhood by God", says the (so-called) Athanasian Creed.

However, there is just one person—the divine Son of God, Second Person of the Trinity—who is and does both of these sets of things.  (Without this, the Atonement wouldn't work, because in order to be saved we need for God to have fully shared in our human afflictions.) As a result, it is also correct to say that God was Jewish, and that he suffered and died on the Cross, or that Mary was the Mother of God, or (going in the other direction) that the human being Jesus pre-existed, was begotten by the Father before time began, and that through him all things were made; so long as we remember that that we are speaking of the experiences of the united person who has both natures, and not attributing properties of one nature to the other nature.  This way of speaking is called communicatio idiomatum, i.e. the "communication of attributes", and you can find articles by both Catholics and Protestants online, explaining it.

Your second question was about Christ's knowledge.  The divine nature of God the Son is omniscient and eternal, and therefore the divine nature of Christ must know when he will return.  However, his human nature started out ignorant and could learn things, as we know from Luke 2:52: "Jesus grew in wisdom and stature", and also from Hebrews, when it says that Jesus was made like us in every way (sin excepted).  But we cannot divide the human and divine natures, so it is also true that "God the Son", the divine person, experienced what it is like to possess human ignorance.

Thus God the Son could both know and not know the same thing at the same time.  How is this possible?  I think it helps to remember that any time we know something, we know it in a particular way. For example, you can know something intuitively but not logically, or vice versa, or both ways simultaneously.  The divine nature knows things by being the perfect being; the human nature knows things by forming neural connections in the brain that somehow represent or imitate the behavior of the things we know.  Jesus did both.

One analogy I find a bit useful is that of roleplaying where you pretend to be a character in a fictional universe.  It is possible for a situation to arise when the person playing the game knows something the character doesn't know.  But now imagine that the universe the character lives in is real, not pretend and that you experience fully everything the character experiences (including what it feels like to be ignorant).  That would be a little like what happened with the Incarnation, I guess.

The Trinity and the Incarnation are great mysteries, so our language and analogies must necessarily break down in certain ways. But that doesn't mean we can't make an effort to make our language as un-misleading as possible.

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