Do some inductions require a necessary first cause?
August 21, 2014 — 8:16

Author: Alexander Pruss  Category: Existence of God Uncategorized  Tags: , , , ,   Comments: 5

Suppose that we’ve observed a dozen randomly chosen ravens and they’re all black. We (cautiously) make the obvious inference that all ravens are black. But then we find out that regardless of parental color, newly conceived raven embryos have a 50% chance of being black and a 50% chance of being white, and that they have equal life expectancy in the two cases. When we find this out, we thereby also find out that it was just a fluke that our dozen ravens were all black. Thus, finding out that it’s random with probability 1/2 that a given raven will be black defeats the obvious inference that all ravens are black, and even defeats the inference that the next raven we will see will be black. The probability that the next raven we observe will be black is 1/2.

Next, suppose that instead of finding out about probabilities, we find out that there is no propensity either way of a conception resulting in a black raven or its resulting in a white raven. Perhaps an alien uniformly randomly tosses a perfectly sharp dart at a target, and makes a new raven be black whenever the dart lands in a maximally nonmeasurable subset S of the target and makes the raven be white if it lands outside S. (A subset S of a probability space Ω is maximally nonmeasurable provided that every measurable subset of S has probability zero and every measurable superset of S has probability one.) This is just as much a defeater as finding out that the event was random with probability 1/2. (The results of this paper are driving my intuitions here.) It’s still just a fluke that the dozen ravens we observed were all black. We still have a defeater for the claim that all ravens are black, or even that the next raven is black.

Finally, suppose instead that we find out that ravens come into existence with no cause, for no reason, stochastic or otherwise, and their colors are likewise brute and unexplained. This surely is just as good a defeater for inferences about the colors of ravens. It’s just a fluke that all the ones we saw so far were black.

Now suppose that the initial state of the universe is a brute fact, something with no explanation, stochastic or otherwise. We have (indirect) observations of a portion of that initial state: for instance, we find the portion of the state that has evolved into the observed parts of the universe to have had very low entropy. And science appropriately makes inferences from the portions of the initial state that have been observed by us to the portions that have not been observed, and even to the portions that are not observable. Thus, it is widely accepted that the whole of the initial state had very low entropy, not just the portion of it that has formed the basis of our observations. But if the initial state and all of its features are brute facts, then this bruteness is a defeater for inductive inferences from the observed to the unobserved portions of the initial state.

So some cosmological inductive inferences require that the initial state of the universe not be entirely brute. I don’t know just how much cosmology depends on the initial state not being entirely brute, but I suspect quite a bit.

What if there is no initial state? What if instead there is an infinite regress? Here I am more tentative, but I suspect that the same problem comes back when one considers the boundary conditions, say at time negative infinity. If these boundary conditions are brute, then we’ve got the same problem as with a brute initial state. Likewise, a contingent first cause will not help, either, since the argument can be applied to its state.

It seems that the only way out of scepticism about cosmology is if there is a necessary first cause. And I also suspect that the impact of the argument may go beyond cosmology. Presumably, we continue to come into causal contact with portions of the initial state that we have previously not been in contact with, and couldn’t that affect us in all sorts of ways that undermine more ordinary inductive inferences (e.g., a burst of radiation might kill us all tomorrow, and no probabilities can be assigned to the burst, and hence no probabilities can be assigned to any positive facts about what we will do tomorrow)? If so, then we lose quite a bit of our predictive ability about the future if we hold the initial state to be brute.

The Philosophy & Theology of Immortality: Request for Proposals
September 3, 2013 — 13:44

Author: Matthew Mullins  Category: News  Tags: , , , ,   Comments: 1

The University of California at Riverside, with the help of a very generous grant from The John Templeton Foundation and under the direction of John Martin Fischer, welcomes proposals to investigate, through philosophical and theological research, questions that concern personal immortality. Such questions are central existential concerns that know no geographical or cultural bounds.
We anticipate proposals that fall under one of the following six categories:

  1. Investigation into whether persons survive, or could survive, bodily death. Such investigation could take the form of philosophical or theological treatments of the relevant empirical evidence, philosophical challenges to post-mortem survival (e.g., challenges to the possibility of continuous pre-mortem and post-mortem personal identity) and responses to such challenges, and more besides.
  2. Exploration of some topic related to the issue of immortality, e.g., puzzles about the goodness of post-mortem survival, the rationality of desiring to survive, the implications of believing/not believing in post-mortem survival, “quantum immortality,” longevity and the postponement of bodily death, etc.
  3. . Exploration of the relationship between immortality and views about the meaningfulness of life, even finite life. (E.g., does reflection on the possibility of meaningfulness in an immortal life shed light on what makes even our finite lives meaningful?)
  4. Investigation into the nature of infinity, and our conceptual grasp of infinity, as these relate to immortality. (Sample questions here might include the following: Can we grasp the nature of infinity in a way that is adequate to envisaging an infinitely long life? Insofar as the mathematical nature of infinite magnitudes are different from finite magnitudes, does this make it difficult to grasp infinitely long life? How do the mathematical puzzles of infinity relate to the possibility of immortality?)
  5. Investigation of the relationship between the badness of death and the desirability of immortality. (E.g., if death is a bad thing for an individual, does it thereby follow that immortality is (or could be) desirable?)
  6. Investigation of one or more explicitly theological issues related to the topic of immortality, e.g., investigation into the nature of “the intermediate state” or purgatorial or post-resurrection existence carried out within a Christian theological framework, the nature of karma carried out within a Buddhist or Hindu framework, post-mortem survival and its place in theodicy, etc.

Full application information can be found on the project web site:

On the concept of infinite number
March 17, 2013 — 15:39

Author: Jeremy Gwiazda  Category: Uncategorized  Tags: , , , , ,   Comments: 45

I don’t think it an overstatement to say that the concept of the infinite plays a key role in the philosophy of religion. There are at least two senses in which ‘infinite’ is used. First, ‘infinite’ is often used to mean maximal, as in God’s infinite power, knowledge, and goodness. Second, many arguments in the philosophy of religion discuss ‘infinite number’ or ‘infinitely many’. It is this second sense of the infinite that I focus on in this post. Here are two recent examples of this second sense of the infinite, from Prosblogion, with select quotes (and links to the full posts):


Infinite multiverse, fine-tuning and probability
March 6, 2013 — 14:38

Author: Alexander Pruss  Category: Uncategorized  Tags: , , ,   Comments: 64

The best naturalistic alternative to theistic explanations of fine-tuning is a multiverse where there are infinitely many variations on the constants in the laws of nature, generating infinitely many universes, such that in infinitely many of them there is life–and we only observe a universe where there is life. Typical multiverse theories are committed to:

  1. For any situation involving a finite number of observers, stochastically independent near-duplicates of that situation are found in infinitely many universes.

I will argue that if (1) is true, then ordinary probabilistic reasoning doesn’t work. But science is based on ordinary probabilistic reasoning, so any scientific argument that leads to the typical multiverse theories is self-defeating.

The argument that if (1) is true, then ordinary probabilistic reasoning doesn’t work is based on a thought experiment. You start by observing Jones roll a fair six-sided indeterministic die, but you don’t see how the die lands. You do, however, engage in ordinary probabilistic reasoning and assign probability 1/6 to his having rolled six.

Suddenly an angel gives you a grand vision: you see a countable infinity of Joneses, each rolling a die in a near-duplicate of the situation you just observed. You notice tiny differences between the Joneses, but each of them is rolling an approximately fair indeterministic die, and you are informed that all of these situations are stochastically independent.


Is the multiverse consisting of all worthy universes the best multiverse?
June 30, 2011 — 11:15

Author: Alexander Pruss  Category: Uncategorized  Tags: , , , ,   Comments: 42

Say a universe is worthy iff it’s worth creating.  Let M be the multiverse containing all and only the worthy possible universes.  Is M the best multiverse?  Here is an argument to the contrary.  Somewhere in M, there will be an infinite sequence of universes u1,u2,…, with u2 better than u1, u3 better than u2, and so on, such that these universes differ from one another only in the magnitude of a single minor evil.  For concreteness, suppose that in each of these universes, there is a counterpart of me who has a mosquito bite that doesn’t affect his life.  In u1, the bite itches for one hour.  In u2, it itches for half an hour.  In u3, for a quarter of an hour.  And that’s the only difference.  (Maybe this happens during a time in the person’s life where he does nothing but itch or not itch, and later he forget this time.)  Call the universes from this sequence u-universes.

Now, let M* be a multiverse containing all and only the worthy possible universes other than u1.
If M is the best multiverse, M has to be better than M*.  But this is far from clear.  There is a one-to-one correspondence f between the universes of M and M*, where universes that aren’t in the sequence u1,u2,… correspond to themselves (f(u)=u), while f(u1) = u2, f(u2) = u3, and so on.  Then, for any universe u in M, either f(u)=u, or f(u) is just like u, except that my counterpart have a shorter length of itching from the mosquito bite in u than in f(u).  How can M be better than M*, then?
Well, M is surely not aggregatively better.  How could it be, given the correspondence?  We describe the difference between M and M* as follows: M is just like M*, except that if anything it has some more itching.  
So if it is better, it must be in virtue of a non-aggregative value.  The best proposal, which Klaas Kraay made in response to my arguments in the previous multiverse post, is that M maximally exemplifies the value of diversity.  But notice that M and M* exemplify the same diversity of goods.  The only difference is that M exemplifies a greater diversity of bads: it contains a u-universe with my counterpart having an hour of itching from the relevant bite, while M* does not contain that u-universe.  However, both M and M* contain the same countable infinity of u-universes, and they contain all the same diversity of goods from the u-universes and the non-u-universes.


A probabilistic argument against actual infinities
March 17, 2010 — 8:45

Author: Alexander Pruss  Category: Existence of God  Tags: ,   Comments: 3

I find the idea that an actual infinity is impossible very counterintuitive, but sometimes arguments can establish something very counterintuitive. Actually, even if the following argument does not show that actual infinities are impossible, it will, I think, show that one cannot make any probabilistic inferences in an infinite multiverse. And that’s an interesting conclusion in its own right. (That said, I have some technical qualms about the argument that I can’t articulate.)

Begin with the Parity Principle: If it is almost certain (i.e., if it has probability one) that (a) the basic properties Q and R have exactly the same distribution at t1, and that (b) x is a substance existing at t1 and a member of basic kind K, and no other information is available about x, then the probability that x has Q is equal to the probability that x has R. (Here, I allow such probability values as “undefined”, “inscrutable” as well as intervals, vague values.)

For my argument I will need the assumption that it is possible to have indiscernibles–objects that have all the same basic properties. I actually think this assumption is false, but I am hoping that this assumption can be relaxed.

The possibility of indiscernibles and the Parity Principle are going to be the only potentially controversial assumptions in the argument. If you trust me on this point, you can stop reading the argument, and just argue against these two assumptions. Though you might want to read on to see how exactly I understand the “same distribution” condition in the Parity Principle.


Two more arguments against an infinite past
October 6, 2009 — 8:23

Author: Alexander Pruss  Category: Existence of God Free Will  Tags: ,   Comments: 26

In my earlier post, I gave a Grim Reaper based argument against an infinite past. Here I want to give two more arguments. Unlike the earlier argument, these two arguments are not going to be useful for arguing for the existence of God, since they make use of premises that the atheist is likely to deny (in one case, a version of the Principle of Sufficient Reason, and in the other, the existence of God). But they are useful in a broader sense, namely they help show what might be wrong with an infinite past.

Argument 1. If there is an infinite past, we could imagine that each January 1 in the infinite past somebody looks around and checks if there are any rabbits. If there are, she does nothing. If there aren’t, she makes a breeding pair. Of course, once a breeding pair of rabbits exists, there will be rabbits forever. Nobody and nothing but one of these potential rabbit-makers makes a rabbit. The setup entails that there have always been rabbits, and the rabbits have not been made by anybody or anything, contrary to a causal version of the Principle of Sufficient Reason.

Argument 2. If there is an infinite past, the following scenario should be possible. The universe contains nothing but bobs, and at no time is there more than one. A bob is an asexually reproducing person who lives for a century. At the end of the century he dies, but at the end of his existence he has a choice whether to reproduce or not, and can choose either way. If he freely chooses to reproduce, a new bob comes into existence out of the old bob’s body after death. So, this is a universe where every bob has always chosen to reproduce, though they could have chosen otherwise. But now consider the following very plausible Thesis:
(*) Necessarily, if a world contains at least one contingent being, then there exists something in that world determined into existence by God’s will.
But the story in Argument 2 seems to violate (*), since each bob’s existence is partly dependent on the free choice of the preceding bob. Maybe God has determined, then, not the fact that there is a bob, but that there is some initial infinite sequence of bobs, without determining which initial infinite sequence there is. But even that there is an initial infinite sequence of bobs already depends on bob-made choices.

Argument 2 won’t impress theological compatibilists.