(1) God exists as a matter of necessity,
or
(2) It is at least logically coherent to think of God as a necessary being.

You say that (1) obviously entails the desired conclusion, but as you point out, it is worthless because (1) just is the conclusion. So we have to understand the premise as (2). I am not sure what would be wrong with (2). You have said it is too weak, but I'm not sure why. — PossibleAaran

That the second premise seems weak is a point in its favor (whether it really is weaker than the first premise and whether it even makes sense is debatable) - it is what helps to sell it as a premise to someone who does not already believe the conclusion.

(2*) The concept of a being that necessarily exists is logically coherent.
(4) Therefore, it is logically possible that there is a being that necessarily exists.
(5) Therefore, there is a being that necessarily exists.

The inference from (4) to (5) is just collapsing the modal operators in accord with S5. The inference from (2*) to (4) assumes that if a concept is logically coherent, it is logically possible that it is instantiated. — PossibleAaran

Yes, and my point is that this interpretation of possibility makes it unfaithful to the underlying logic, because it suggests that there is some difference between (2) or (2*) and (1), whereas there should be none.

Actually, it is not all that clear what it means to say "The concept of a being that necessarily exists is logically coherent." I hold the same opinion as you regarding necessary existents: with no constraints on possible worlds other than the rules of logical inference, there should not be any. (I am bracketing off "things" like ideas, abstractions, logical and mathematical entities and the like - presumably, when we talk about the existence of God, we are interested in something more than a mere idea of God.) But then it follows that the concept of a being that necessarily exists is inconsistent with this proposition that I already hold to be true, given the rules. So how is it coherent? Of course, as I mentioned earlier, we could play by different rules, stipulating, for example, that the relevant possible worlds are only those in which God exists (in much the same way as in my earlier example, where all relevant possible worlds contained the same immovable walls in the same places). That idea would be coherent - but unfortunately, stipulating such rules begs the question.

But again, the reason I resent Plantiga's argument is that he seems to want to sidestep such close examination of the premise, encouraging the reader instead to accept the premise because it sounds so unassuming and innocent. And so seemingly different from the proposition "God exists in all possible worlds" contained inside it. It is as if we were just picking up that outrageous proposition and looking at it at arm's length. But that feeling is betrayed, once the meaning of possibility is switched in mid-argument.

Let me make some general remarks first, just to make sure that we are on the same page (and to help those who are less conversant with the topic).

1. Modality is a way of thinking, talking, reasoning about the world. Modality can be a property of a proposition, but It makes no sense to talk about modal properties of a thing. Modality is a way of talking about things. So a "necessary being" is just a shorthand for saying that it is necessarily the case that such and such exists.

2. Modality can be understood and deployed in different ways. Those ways differ in their ground rules: what we hold to be fixed about the world, and what we allow to vary. Thus, an epistemic modality is where we reason from available evidence (presumably, also taking certain other things as given, such as known laws of nature). Nomic modality is where we hold just (some) laws of nature as fixed. Metaphysical modality is where we hold certain metaphysical constraints as fixed. And so on. Any set of constraints generates its own modal framework. As a limiting case, a priori (or logical) modality is where only the rules of inference are fixed.

For example, if I need to make my way from my office on the second floor to another office on the fifth floor, there are different ways in which it is possible for me to accomplish this. I can take different corridors, take different turns, use the stairs or the elevator, etc. But whatever I do, I have to contend with certain necessary facts: the fact that there are walls that I can neither move nor destroy (they are necessary beings in this context - they always exist in the same way, whatever course of action I take). I also cannot fly or teleport, there is a limit to the speed of my movement, etc.

3. There are different mathematical theories of modality, or modal logics. A theory is agnostic about the world on which it operates; it is agnostic even about the meaning of modal terms. All it does is it establishes certain rules for manipulating modal propositions. Defining the world and giving meaning to the modal operators gives a particular interpretation to the theory. As long as the rules of the theory are obeyed throughout, you are entitled to make use of its theorems to make meaningful inferences.

Now, returning to Plantiga's argument:

The starting premise is that it is logically possible that a maximally great being exists. If someone believes that a maximally great being does exist, then they surely also believe that it is logically possible. Now consider someone who doesn't already believe the conclusion. Such a person might believe that the concept of a maximally great being is coherent. I think many people who deny the existence of God do believe that the concept is at least coherent. But then, it could be pointed out to them that this premise, which they believe, entails that a maximally great being exists. Why wouldn't that be an effective argument? — PossibleAaran

You want to make use of the so-called S5 modal logic. In this theory, stringing several modal operators together has the same effect as taking just the last of those operators. So, something that is possibly necessary is just necessary. Any model (i.e. true interpretation) of this theory has to respect that rule. So when you propose that "it is ... possible that a ... being [necessarily] exists," that has to be understood as just proposing that "a ... being [necessarily] exists." Whatever interpretation you give to this proposition - however you interpret possibility and whatever properties your proposed being possesses - what I wrote above has to be the case, or else this is not a model of S5.

Yet, the way you want to reason, there seems to be a difference between the following two propositions:

(1) God exists as a matter of necessity,
(2) It is at least logically coherent to think of God as a necessary being.

One is a very strong proposition that obviously entails the conclusion of the argument, and thus it is no good as a premise. The other sounds like a much weaker proposition, one that we could accept without committing to the first proposition. Whether that is actually a reasonable reading of these sentences is not even the point - the fact is that you are trying to equivocate on the meaning of your modal terms. You are insinuating a meaning that is not consistent with the theory whose theorem you then want to use in order to reach the conclusion of the argument. You are not arguing in good faith.

All of this is quite uncharitable to Plantinga. — PossibleAaran

He does define his 'super-duper being' very carefully. He defines a maximally great being as one which is maximally excellent in every possible world, and maximal excellence is defined as entailing omnipotence, omniscience and moral perfection. To wit, the first two premises of his argument from the Nature of Necessity, page 214 — PossibleAaran

Fair enough, I didn't read that book - my recollection is of his own gloss of the argument in a short paper that I no longer have at hand. So let's assume the more careful formulation as you present it.

In that case, he seems to be fairly laying his cards on the table (assuming the reader is paying attention!), thus severely handicapping the argument right from the start. His ontological argument is much weaker than Anselm's; he does not just beg the question: the premise that he asks us to accept is much stronger than the conclusion of the argument. Thus, even those who already believe the conclusion independently may not accept his starting premise. (You seem to be of that opinion, judging by what you said concerning the issue of necessary existence.)

I think there's a fundamental problem with saying that a logical necessity is logically possible. I can't quite put my finger on what that problem is, though, but as I said before, my instinct is that it's related in kind to Tarski's hierarchy of language. — Michael

It is not problematic in the formal system to which Plantinga appeals. But that formal system (modal logic known as S5) basically ratifies your intuition: it posits as an axiom (or is it a theorem?) that adding the qualification of possibility to something that is already necessary changes nothing - it is an empty move devoid of any consequence, like multiplying by one or adding zero. (By the way, the same happens when you qualify possibility with necessity: necessity in that case does no work either.) So when that move is made and expounded on in a natural language formulation that seems to appeal to our informal intuitions concerning possibility, and yet in the end we are assured that "possibility" and "necessity" were used in their strict formal sense all along, you are right to be suspicious.

But then, suppose I don't have this bias. Suppose that I am not such that, when I see that a premise entails that God exists, I will not accept that premise. — PossibleAaran

I hope I explained why this is not the reason that neither I nor anyone who understands the argument that Plantinga is making - not in retrospect, but right as it is unfolding - would be likely to accept it.

You also say that it is illegitimate to predicate necessary existence. Why? You say that Michael's argument shows why. But which argument of Michael's do you mean? — PossibleAaran

It is what @StreetlightX and @Michael (and, no doubt, others who have criticized Anselm's argument) have said about predicating existence (necessary existence, as has been discussed, has even more severe problems). Having properties implies existence. So when we predicate a property of something, the qualification "provided that the thing exists" is already implied. When we define a unicorn as "a horse with a single horn," the same definition could be equivalently restated as "a being, such that if it exists, it exists as a horse with a single horn." The actual predicate here is still "being a horse with a single horn," nothing more. So when we "predicate" existence of a being, that is equivalent to saying "a being, such that if it exists, it exists" - which is just a tautology that applies to any hypothetical being.

Do you mean the argument that we can tack 'necessary existence' onto any concept and then create an argument for its existence, regardless of what the concept is? — PossibleAaran

That, too. Plantinga's argument is, if anything, even easier to parody than the original. Those attributes of Super-Dupeness Maximal Greatness do no work in the argument - they ride free and thus can be replaced with anything whatsoever.

Perhaps we could argue that the world is the necessary thing, as it seems tautological to say that the world exists in every possible world. — Michael

Possible worlds for the World are just all the ways in which the World could possibly be (where the sense of "possibility" is left open).

There are many versions of it, some intensely complicated. The OPs version is Anselmian, and those arguments typically run:

(1) If God exists then God necessarily exists. (G -> nG) [Partial Definition of God]
(2) If its logically possible that God exists then God exists (pG -> G) [From (1)]
(3) It is logically possible that God exists. (pG) [Premise]
(C) God exists (G) [From 1-3]. — PossibleAaran

This doesn't really have much to do with Anselm's argument, other than being a species of an a priori "ontological" argument, one that, in a way of magical thinking, attempts to reify logical constructs.

Imagine a being, such that it cannot fail to exist.
Therefore, it exists. — SophistiCat

You see I don't think so. None of the premises of the argument say 'imagine a being such that it cannot fail to exist'. — PossibleAaran

I glossed possibility as conceivability - perhaps not quite what Plantinga was trying for. In his version he actually breaks the premise into two in order to obfuscate his meaning. It goes something like this:

First he asks us to accept that a Super-Duper Being is at least within the realm of the possible (not his exact words, of course, but that doesn't matter, since he doesn't explain what the words mean in this premise). Hopefully, a charitable and careless reader will not ask what a Super-Duper Being is and will grant this premise for the sake of an argument.

Then he spring the trap: a Super-Duper Being is one that, among other things, exists necessarily (cannot fail to exist). And he further stipulates that the words "possible" and "necessary" were being used in a technical sense of the S5 modal logic, where stacked modal operators collapse into one.

In the possible world semantics, a Super-Duper being is such that, if it exists in one possible world, it exists in all possible worlds. So the premise then is simply that it does exist in at least one possible world. Of course, stated this way, no one who does not independently believe the conclusion would go along with such an argument (and those who do ought not go along with it either).

But necessary existence is a property, and is immune to the criticism which Kant makes. — PossibleAaran

It is illegitimate to predicate existence in all possible worlds, just as it is illegitimate to predicate existence in some possible worlds. And @Michael's argument neatly shows why it makes no sense to predicate existence.

The 'argument' may as well read:

There exists a being, such that, it exists.
Therefore, it exists. — StreetlightX

Or,

Imagine a being, such that it cannot fail to exist.
Therefore, it exists.

(That's Plantinga's version, only he obfuscates it a bit.)

I don't know about circular arguments, but concepts are sometimes said to have a circular dependency. (Specifically, we are talking here about a "tight" circle, involving only a few concepts.) The dependency is not vicious if it is unavoidable on the one hand, and on the other hand the whole construct works reasonably well.

For example, it is argued that time and clock have such a virtuous circular dependency. Neither concept can be understood without the other, but together they seem to make sense.

When TheMadFool, Bahman, this "programming god" guy vomit up several new topics each day, any deletion for "low post quality" is going to look arbitrary at best, malicious at worst.

Nice video.

The material ontology consisting of inert, amorphous matter substrate as a distinct existent, with form and/or animating spirit or force or process acting on it as another distinct component of existence is both ancient and surprisingly ubiquitous and persistent. For example, ancient materialists, who you would not think of as natural allies of Plato, also believed something like this. And this sort of thinking is still current.

Of course, proponents of this view would not be much discouraged by your exploding elephant - they would just push "matter" to lower, sub-cellular scales (as, of course, has long since been done in the normal process of scientific reductionism).


Another thing that this video reminded me of (again): You often hear people say how machine-like biological mechanisms appear to be - surely, a hallmark of design! I think this is just a superficial impression that is an artifact of the way we analyze and present scientific models, which is like engineering in reverse (or reverse engineering). The impression I get is the opposite. When you look at living things with an unprejudiced eye, as well as when you learn the bewildering array of biological facts, such as those described in the video, it strikes you just how messy and complicated and thoroughly alien these things are. They are so obviously not designed by anything like a human designer*, but grown, evolved through billions of generations across billions of individuals in a blind and unthinking, but massively integrated process: integrated across all physical scales, all the way to the bio-chemical and even quantum mechanical level.

And what role does this inert, formless "matter" play in all this? It seems like a useless kludge, and we should rid our thinking of it.

* And it's no use saying that the designer is totally unlike a human designer: that just removes any reason for inferring design in the first place.

to do philosophy really well you have to be able to write clearly and precisely. — Sam26

You mean there are really people who think this is not the case? I find that amazing — Sam26

I take it you weren't exposed to much Continental philosophy in your curriculum ;)

Well, there are purely conceptual resolutions based on disentangling equivocations about words such as "good" and "evil."

Another consideration is that we are not always presented with a binary choice of good vs. evil. In any morally non-trivial situation we end up doing some sort of moral balancing, choosing the least evil or the good that seemingly outweighs the attendant evil. And different people in different epistemic situations will balance the scales differently, hence one person may judge another person's choice as evil on the balance.

Also, Socrates assumes a perfectly rational agent, but people are not perfectly rational agents. What constitutes intentional action or desirable action is not always clear. Sometimes we do something we seemingly don't want to do, even without being forced. Sometimes we do what we know we ought not to do. I don't think these ambiguities can be satisfyingly fixed with conceptual analysis, because there is no unambiguous fact of the matter, not in such simple terms.

I don't understand what's the issue either. Maybe let me restate the question. Does determinism apply to a situation where all outcomes can and are realized? — Posty McPostface

In a deterministic universe every possible outcome can and is realized (in its time), since every event realizes the only outcome that is possible at the moment when it happens.

Does this answer your question?

Do you even have any clear idea about what you are asking? I get a strong impression that you don't.

No, it doesn't.

"In such a universe" - what universe? You mentioned interpretations, plural. Are you thinking of some particular interpretation?

And why would determinism not makes sense?

Really, why do you start a thread if you can't even express your thought in a few coherent sentences?

I honestly have no idea what you are talking about.

Just a simple question, seemingly. — Posty McPostface

I don't understand the question.

R. M. Hare, a non-cognitivist (non-objectivist) moral philosopher, recognized that there was a difference between expressions of emotion and moral utterances, between "I don't like liver" and "murder is wrong", and agreed that Emotivism is unable to account for the normative force of moral claims. He articulated the view, which became to be called Prescriptivism, that moral claims have an imperative, or prescriptive, element. To say that murder is wrong says both "I disapprove of murder" AND "Do thou likewise!" — Mitchell

I agree, moral attitudes seem to be prescriptive: they are aimed at compelling or constraining actions, which other attitudes such as pleasure, disgust, sadness, gratitude, fear, tenderness, etc. do not do in and of themselves. And they tend to have a more-or-less general character: not just do that in this particular instance, but whenever anyone finds themselves in similar circumstances, they ought to do something like that. So an argument can be made that moral attitudes can be grouped into a natural kind distinct from other attitudes (although the boundary is going to be somewhat fuzzy).

But that is a modest, commonsensical conclusion of conceptual analysis: it only assures us that the predicate "moral" is meaningful and expressive. It doesn't tell us much about the metaphysics of morality.

After all, morality certainly seems to appear to us as "objective", as a command-from-afar, an imperative, something we must do out of free will. — darthbarracuda

What you describe sounds like morality simpliciter. What is particularly "objective" about it? Or, to put it another way, what would a non-objective morality be like in your view?

Regarding Emotivism, which is being expressed by some of these responses, there seems to me to be a crucial difference between "I don't like liver" or "Boo, Liver!", on the one hand, and "Torturing children for fun is wrong", on the other. — Mitchell

Of course there is a difference. There is even a difference between "I don't like liver" and "I don't like Brussels sprouts." But, assuming emotivism for the sake of an argument, what is "crucial" about this difference, other than the strength of the emotion?

That is not a rhetorical question, but an invitation to elaborate the point. "Emotion" is one word, but that doesn't mean that all emotions are of the same sort. Is there a difference here that cannot be accommodated under some ordinary idea of emotion?

Science is a social endeavor. There are universities and research centers that produce research. There are scientific journals and book publishers that publish research. There are conferences that organize meetings and presentations. There are governmental and non-governmental agencies that distribute funds and commission and stimulate research programmes. There are educational institutions that teach science fundamentals, and government institutions that issue educational guidelines and select textbooks. There are entrepreneurs and corporate R&D departments that turn research into practical applications.

All of these institutions, each in their own capacity, are engaged in evaluating science, one way or another. At the most basic level, that comes down to the question: Is it even science? So it is no use to stamp your feet and rail against those who ask and answer that question, @darthbarracuda. They have to. And no, science, or "science," is not going away, and thank god for that.


As for the demarcation criteria, in the real life they can be vague and messy, and vary depending on who is asking the question. But I think that what is known as "falsifiability" does get at some important, though fairly obvious, idea. It is inherent in the very notion of empirical knowledge. In order to qualify as such, empirical knowledge has to be sensitive to observations. And the more sensitive it is, the more engaged it is with empirical observations - the more relevant it is.

Popper was not the first to realize this, nor the last. He was just one of the philosophers of science and epistemologists who were trying to formalize this empiricist intuition and incorporate it into his own theory. In the end, it seems, his theory didn't prove to be all that influential (most of those who name-drop Popper know very little of it), but he did succeed in popularizing some terms and basic notions.

How can anybody assert that the state of some event outside our sphere 'is' in any particular state? Our definition sort of assumes a measurement taken from 'here', and by that definition, those distant events have no measurement and are in complete superposition. — noAxioms

Superposition states are states too (they are also called "mixed" states, as opposed to "pure" states). But I think I get your point: if we haven't been in contact with some remote region of the universe, then within that interval of time its wavefunction has been evolving independently from us, and there is no coherence between us and any one of its branches.

In an infinite universe, aren't we almost surely guaranteed a world where our doppelgangers walk through walls (the molecules align just right) after saying an incantation? Maybe doppleganger Jesus really did take a stroll on the water. — Marchesk

Yes, I think Vilenkin entertains similar fun scenarios, but frankly, not having followed the derivations, I am a little hesitant to commit to such specific predictions.

The case of a simple bound system, such as a hydrogen atom, is easier to analyze than a more general case: we can actually solve the quantum equations and enumerate every possible state. There is, however, a theorem for the general case in quantum mechanics, which puts a limit on the number of possible states, or degrees of freedom, given a volume and energy density within that volume.

The general point that I wanted to make is that if there are separate systems with a finite number of possible states between them, then for them to be found in the same state at some moment, they do not have to have identical histories up to that moment. Even in a purely deterministic universe, as these systems transition from one state to another, they may end up in the same state at some point simply by chance. What that chance is - high, low, "almost surely" - will depend on a more detailed analysis.

I skimmed that article you linked and was interested to note that Vilenkin makes statements like:

"there are an infinite number of O-regions with identical histories up to the present"

where I think what he means is "there is almost surely an infinite number of .....". That is, I think he over-simplified his statement, presumably because he wanted to make it more accessible to the non-physicist reader, since it is a non-technical article.

I note that in your post you included the crucial qualifier "almost certainly", although it does not occur in the paper. Interestingly, Tegmark also omits the qualifier (bottom of first column on page 4 of this article you linked) but, like Vilenkin, gives no explanation for the omission, and his article is also more pop science than academic.

Do you have a view on why they omitted the 'almost certain' qualifier from their articles? — andrewk

Well, I cannot answer for Vilenkin or Tegmark, but I think they were speaking informally.

How we interpret these results depends on how we think about probability. If we interpret probability as a quantitative measure of credence, or degree of belief, then there isn't really a difference between "almost surely" and "surely": in either case, the credence is exactly zero. This failure to make a distinction between possibility and impossibility may be a deficiency of the epistemic interpretation of probability (not to mention the problems of formal probabilistic modeling that have been raised here).

But if we further think about our concepts of probability and possibility, this might be argued to be a distinction without a difference. We can hardly tell the difference in credence between an event that has a probability of 10^-10 in a single trial and one with a probability 10^-100. We stop making a difference long before "almost surely".

There is still a possible/impossible distinction though. But is there, really? If "an event A is impossible" means for you that you should live your life as though A will never happen, then events with an extremely low probability are as good as impossible. You live your life assuming that the air will not suddenly evacuate the room through the window, leaving you choking on the floor, even though science says that such an event is possible (and even has a well-defined, finite probability!)

Let's bring down the scale to a manageable size to explore this concept. Instead of Earth, let's consider one hydrogen atom. Now, an atom has a finite number of configurations, or states that it can possibly be in (10 for hydrogen, I think). Since there are obviously a lot more hydrogen atoms than that, there have to be a lot of atoms that are absolutely identical, regardless of their prior histories.

You can see how this can be scaled up by adding more atoms and particles to the system: they each have some finite number of states, and so do their combinations, even allowing for interactions. The number of degrees of freedom rises dramatically as you expand outwards, but the principle remains the same.

I won't vouch that the math actually works out for macroscopic systems, i.e. that the number of possible states increases slower than the size of the system, but that is the argument that Vilenkin and some others make.

As I recall reading, and this was actually mentioned in Edward Feser's Scholastic Metaphysics, powers are just formal-final causes under a different name. — Marty

I don't know, I am not a fan of powers and propensities on the one hand, and I don't know what Feser's argument is. Maybe he proposes a reduction to final causes, but that wouldn't mean that the two accounts are actually one and the same.

As for counterfactual dependence, I'm not sure what it means to say “If A had not occurred, C would not have occurred” without wondering why that claim is the case. In virute of what? — Marty

Well, you could pose the same question in response to any account of anything whatsoever, couldn't you? But to address your question more directly, counterfactual accounts of causation are more conceptual analysis than metaphysics. "What we talk about when we talk about causation."

A bit off topic, but I've always noted that the orientation of the three spatial axes (X, Y, and Z) is arbitrary. If there is an actual x axis, which way is it? But if the universe is a 3-torus, all three axes have a preferred orientation, and this defines a preferred frame as well, even if not an inertial one. If the spatial axes are fixed, the temporal one, orthogonal to the others, is fixed as well.
This is only a minor violation of the principle of relativity, but it galls me enough to discount the significant probability of such a finite topology. — noAxioms

Even in Euclidean space, as soon as you introduce something to break the symmetry, you already have some kind of "preference." For example, in a universe that is a flat space with one black hole there is an obvious "center." This does not violate the principles of relativity, though it may violate some esthetic demand for perfect symmetry. (Of course, the principle of relativity is itself a kind of demand for symmetry.)

Without the axiom of infinity, each number has a successor but there is no set of all the numbers; no infinite set; and no calculus — fishfry

Sure, you are right. Though "the axiom of infinity" is just a name for an axiom that posits the existence of a set with certain properties. But those properties do not include being "infinite" in some basic sense. But thanks for the qualification.

This does not change what I was saying though: like it or not, most of modern physics does use calculus. You can claim that most of modern physics is misguided (for what that would be worth), but you cannot deny the facts.

I never dismissed the possibility. I pointed out -- correctly -- that current theory says that the universe is finite. Your own examples support this. — fishfry

I take back the bit about not denying facts! And this is why I don't usually engage this person.

I can see now that an infinitely large number of planets is not needed for the argument, so thanks for correcting me on that.

I remained unconvinced, though, that an infinite number (can there be more than one?) could be specified; because it would seem that any specifiable number must be finite. This is not to deny that an unspecifiable number might be useful for mathematical operations. In any case I see no reason to believe there are infinitely many planets; but admittedly I am no expert on cosmology. — Janus

I have alluded to some more exotic mathematics in which an infinite number can actually be specified (and yes, more than one) - that goes all the way to Cantor. But that's really beside the point. All these fanciful cosmologies that are bandied around here are backed by nothing more exotic than standard calculus. And while calculus used be called "infinitesimal calculus," it has long since eschewed any explicit references to the infinitely small or the infinitely large. When we say things like "an infinite number," that's just a shorthand that, in a more rigorous formulation, unpacks into the kind of weaselly formulation that I gave you above, where I offer you to play a game: give me any number and I can give you an even bigger (but still finite) number. It turns out that that's all we need to get going.

Which is good, because contemporary physics holds that the universe is finite. — fishfry

Note that fishfry's source for this claim is, apparently, the bizarre little argument that follows it, and not what scientists actually write, which would be something like the following from a NASA site:

We now know (as of 2013) that the universe is flat with only a 0.4% margin of error. This suggests that the Universe is infinite in extent; however, since the Universe has a finite age, we can only observe a finite volume of the Universe. All we can truly conclude is that the Universe is much larger than the volume we can directly observe. — NASA

Actually, when they say that the near-flatness of the universe "suggests that the Universe is infinite in extent" - that's an oversimplification. A locally flat(tish) universe is compatible with some finite topologies, such as a 3-torus. These guys did some serious number-crunching with WMAP data and came to the conclusion that out of several likely topologies that they considered, a certain compact (finite) topology provided a better fit than the infinite flat topology.

Be that as it may, you would be hard-pressed to find many cosmologists who dismiss the possibility of an infinite universe on such preposterous a priori grounds.

The idea of an infinitely large number is not as unintelligible as you think - don't underestimate the intelligence of mathematicians ;) But we don't even need to invoke infinitely large numbers here. It is enough to suppose that there is no limit to the number of planets: for any number that you may choose, there are (supposedly) more planets than that. That's all we need to assume for Vilenkin's argument.

And the classification of multiverses is given in Tegmark's Parallel Universes.

I think you misunderstood; the point is that there is no actual infinite distance. Even if you traveled away from Earth, for example, forever you would never reach an infinite distance from earth. — Janus

True, but I don't understand how this is relevant to what noAxiom was saying.

For those interested, the argument that, as a generic consequence of inflationary cosmology, there almost certainly exist exact duplicates of Earth (among other interesting things) is given here: Many worlds in one, J. Garriga, A. Vilenkin, Phys.Rev. D64 (2001). (This is still within the parameters of "level-I multiverse.")

Yeah. I have no idea what what a nonteleological account of causation is without making your nature Humean. — Marty

Well, the most popular account of causation nowadays is probably counterfactual dependence, which seems to be as far from teleology as you could get. Causal processes, causal powers - those aren't obviously teleological either. Not that I necessarily subscribe to any of those accounts - just pointing out that a nonteleological account of causation isn't something unheard of - not by a long shot.

In biology, largely for historical reasons, it is common to talk about things in a teleological fashion. This is a residue of the science's history, not a logical necessity, and is a feature not shared by most other sciences. — andrewk

There may be good objective reasons for teleological language in biology, other than it being a holdover from the prescientific era. This is most obvious in behavior science: behavior is, pretty much by definition, goal-directed. But, less obviously, it has been argued that even in other biological contexts we find features that are isomorphic to goal-directedness.

So what's your ideal world? — MountainDwarf

If you are going to imagine a fantastic alternative world that is not "broken," as you say, then why fiddle with all these little details like minimum wages? Why not go for the essence of what you think is broken in this world and eliminate that? That is, imagine a world without suffering?

There, done.

Don't see much food for thought here though.

Starting from premise (2) (potentiality/actuality) the argument heavily relies on idiosyncratic and antiquated Aristotelian metaphysics, which I feel no obligation to accept, and which in any case is not at all clear in this brief summary (if at all). And this is why this argument has no pull on me. Just my opinion.

Let's take gravity as an example. On a Humean account, gravity is just a shorthand for objects behaving in a similar attractive manner, such that bowling balls and feathers fall at the same rate on Earth, or the planets orbit in the same manner around the sun.

But Einstein notices a connection between acceleration and gravity, and posits the acceleration of objects through curved space as the gravitational force. So now you've moved from a shorthand for particulars to a very general principle. — Marchesk

Why should Humean account (as you describe it) be confined just to Newton's theory of gravity? This contrast between Newton's and Einstein's theories that you keep invoking is quite puzzling. Both are empirical theories that are aimed at explaining certain categories of observations. Relativity has a wider scope of application and, where it can be applied to the same observations as Newtonian physics, it fits some of them better.

Nevertheless, you could paraphrase Einstein's theory in terms of what you call the Humean account just as readily as you did it with Newton's theory: Relativity is just a shorthand for objects [and all of the observables to which the theory applies] just happening to behave [as far as we know] as the theory says they should behave, as a matter of brute fact, without any underlying metaphysical powers of causation constraining or impelling them.

Now, I am curious: how would you distinguish such a "Humean" universe from one that is "enriched" with your favored metaphysics?

Beliefs about ethics aren't 'free floating' somewhere in a purely abstract domain, they concern concrete ethical decisions - if the systems aren't sensitive to variations in ethical decisions then they lose their core content.

More generally, the idea that there are 'purely philosophical problems' is something I don't believe, nor do I believe that 'the love of wisdom', originally founded in ethics, is done justice by the want to entertain abstractions devoid of real problems. — fdrake

Well, I am not sure what a 'purely philosophical problem' would entail for you, but I tend to regard such problems as language problems. And like it or not, a lot of discussion in philosophy comes down to arguments about language - or so it seems to me, from my admittedly superficial amateur perspective. While I admit that working out precise language is akin to fashioning the tools of the trade for an analytical philosopher, I don't much care for such discussion myself - especially when it pretends to be substantive discussion. Still, like good therapy or surgery, a trenchant analysis of philosophical discourse can dissolve pseudo-problems and clear up confusions, and that is a good thing.

But what would constitute substantive discussion of ethics? In addition to laying out and defending the principles for living a good life, I would also include meta-ethics in that category. Although a lot of that discourse would, again, be ultimately about language, it doesn't have to be 'free-floating' if it connects to other ideas and things that matter to us.

Look at Trump. There are plenty of people like him and even admire him. His principles as a manager are (to me at least) repulsive and immoral. — schopenhauer1

One Soviet writer and intellectual who was jailed and later exiled for publishing a book of fiction abroad, once quipped: "My disagreement with the Soviet regime is purely esthetic." The first time I heard this, I thought his remark was flippant and paradoxical. Only later did I come to appreciate its truth and apply it to myself. I suspect that such "esthetic" disagreements run deeper than any articulated principles. We can argue circles around each other about policy and such, but if you are not repulsed by Trump's very demeanor, then I know that there is a moral gap between us that no principles can bridge.

I think you're interpreting my ire towards ethical systems as a kind of quietism towards them - that theory is irrelevant for motivating ethical decisions, considering what we should and shouldn't do. Rather I'm trying to advocate a subordination of ethical systems to ethical decisions. The subordination I'm advocating is that ethical systems should allow a user to think in concrete circumstances about what to do - they should have some heuristic import to applied ethics. If they don't have the ability to give heuristics; using 'heuristic' as 'a method of informing about choices'; then they can no longer have an impact on ethical decisions.

This is related to my claim in the OP, admonishing the idea that people 'pretend that they live their lives by an ethical system they just invented'. This gets the direction of influence wrong; subordinating ethical decisions to theoretical constructs, rather than using theoretical constructs to make ethical decisions. I'm sure that you've also met people who have in their mind a theoretical guarantee that their actions are always right - and these people are assholes. Or, rather, they always get to decide whether what they did was right or wrong, failures in character and lack of relevant experience to a specific context of decision be damned. — fdrake

I read these passages a couple of times, and they still confuse me somewhat. In keeping with my earlier is/ought distinction, I would distinguish descriptive systems and prescriptive systems. These can be the very same systems, but their import is different. A descriptive system is subordinated to ethical judgments in the sense that preexisting judgments inform the construction of the system, and the soundness of the system is tested against ethical problems whose solutions are arrived at independently from the system (such as the trolley thought experiment). Ethical judgments always trump a descriptive system.

On the other hand, ethical judgments are subordinated to a prescriptive system, in the sense that the system dictates the judgments. And this is precisely the case where you have a theoretical guarantee that your actions are right: if you follow a prescriptive system, then actions that are in keeping with the system cannot fail to be the right actions (the only remaining uncertainty is whether the actions really do conform to the system).

In reality, I think, the split between descriptive and prescriptive systems is not so clear-cut. Those people who consciously follow some system of ethics will have chosen the system to follow at some point, and their choice would likely be informed by preexisting ethical judgments. And in practical ethical decisions they would often let intuitive judgments trump whatever principle they are supposed to follow, or they would simply neglect to invoke principles in great many practical situations. We turn to abstract principles in cases of uncertainty, and even then it is often hard to say how much the eventual decision was informed by the "head" and how much by the "heart." Or else we use ethical principles as heuristic shortcuts - so that we don't have to closely examine our conscience for every trivial decision.

If there are no differences - no applicable heuristics that can be 'derived' from the system - then they cannot inform the procedure of ethical decision. Which is supposed to be the core action of these theories. — fdrake

Is it though? This is what I've been questioning. You are, again, implying that the only admissible ethical inquiry is one that can result in practical guidance. I disagree on general principles, and would like to again put this in a broader context of human endeavors. Not everything we do or think about is aimed at immediate practical ends.

The one thing on which I would agree with you is that we should not pretend. We should not pretend that a theoretical difference makes a difference in practical ethical decisions if in reality it doesn't. And we should probably be more mindful of this point when discussing ethics. But I don't think that every discussion of ethics is infected with such pretension.

Let me try and formulate the converse then. 'I don't care about how to live ethically, I only care about what it means to live ethically'. — fdrake

Come now, you know better than that! This is not the converse: what I said was not an either/or proposition.

Indeed, but who is doing that?

And what influence the study of ethics may have depends on the kind of study. Specifically, whether the study concerns the is or the ought. Only the latter provides what you are asking for, i.e. immediate guidance for ethical decisions, but the former can be a subject for ethical inquiry as well.

What's interesting is that, as much as your ire is directed against ethical systems, I can't think of any ethical inquiry other than system-building that can inform one about practical ethical decisions. As I understand it, developing ethical systems is akin to science or engineering, wherein one tries to discover or create overarching structures that bridge the gaps between particular instances of ethical knowledge and thus enable us to find answers where we don't already have them (the counterpart in science would be predicting observations where they are not already available).

If one is skeptical of such enterprise, as I am, then one is left with looking into the is of ethics. I suppose that too can influence one's ethical behavior in some cases, but the influence wouldn't be so direct and obvious.