Platonism, a short introduction

By platonism, I will mean the contemporary view on it in analytic philosophy, and not necessarily Plato’s view.

Platonists believe that the existence abstract objects are needed to make sense of three phenomena: resemblance, subject-predicate discourse, and abstract reference.   By contrast, nominalists think that we can explain the three phenomena without the extra ontology. Some candidates for abstract objects are properties, kinds, relations, propositions, numbers, sets, possible worlds, and states of affairs.  (A platonist needn’t accept all these candidates into their ontology.)

Here is a short summary of those three phenomena.  A more detailed treatment can be seen in Michael Loux’s Metaphysics A Contemporary Introduction.

Apples and roses resemble each other in their redness.  Platonists think this resemblance is explained by the particular apples and roses both exemplifying the abstract object of redness.

Subject-predicate discourse
Consider the proposition “Socrates is wise.”  Platonists argue that in order for this proposition to be true ‘Socrates’—the linguistic object—must be correlated to a non-linguistic object—the person Socrates.  Likewise, ‘wise’ must be correlated to a non-linguistic object.  While the subject ‘Socrates’ operates as a noun—a singular term—the predicate ‘wise’ is an adjective and operates as a general term.  That is, the predicate ‘wise’ can be true of many things like Socrates and Plato.

Abstract reference
Corresponding to the adjective ‘wise’ there is the noun ‘wisdom’. Since objects are referred to by nouns, it seems like the use of a noun implies the existence of a non-linguistic object to be referred to. Nouns also play the role of the subject in a sentence. In its use as a subject in the sentence “Wisdom is a virtue”, it seems ‘wisdom’ is explicitly referring to an abstract object.

Loux, Michael J. Metaphysics: A contemporary introduction. Vol. 2002. London: Routledge, 1998.

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Why is There Anything?

Why is there something rather than nothing?  A common answer is that something is necessary.  In a recent paper, Joshua Rasmussen & Christopher Weaver argue for a thesis they call necessary foundation: “there is a necessarily existing concrete thing or things capable of causing or grounding everything else.”  In addition, they propose some arguments from necessary foundation to theism. They follow in the spirit of recent causal-based arguments for a necessary being.

The argument is as follows (quoting):

  • (P1) It is possible that there is a purely contingent totality event that has a cause.
  • (P2) It is impossible that a cause of a purely contingent totality event is purely contingent.
  • (P3) If, (a) it is possible that there is a purely contingent totality event that has a cause and (b) it is impossible that a cause of a purely contingent totality event is purely contingent, then (c) it is possible that there is a cause that isn’t purely contingent.
  • ∴ Therefore, (c) it is possible that there is a cause that isn’t purely contingent.
  • (P4) If (c) it is possible that there is a cause that isn’t purely contingent, then (d) there is a necessary thing that can be a cause.
  • ∴ Therefore, (d) there is a necessary thing that can be a cause.

The crucial and controversial premise is P1; the other premises seem sound.  The ‘can’ in the conclusion I take to be synonymous with possible. The argument concludes that there is a possible world where the necessary thing is a cause, from which it follows that a necessary thing exists.  This doesn’t entail that the necessary thing is a cause in every possible world.

They offer three lines of reasoning in support of the causal principle in P1: from inductive generalization, from causal relevance, and from conceivability.

Concerning the inductive generalization argument, they argue that the causal principle in P1 “fits with a wide range of data, including (i) our experience with contingent things (states, events, etc.) having a cause, and (ii) our lack of experience with uncaused contingent things.”  William Lane Craig’s arguments supporting the first premise of the Kalam Cosmological Argument are similar in spirit, and can act as additional support.

Concerning the causal relevance argument, they ask:

Does a totality of purely contingent events differ from other purely contingent events in a way that is causally relevant? We’ll give one reason to think not. To begin, consider the following states of affairs:

  • s1: there being exactly 1 purely contingent event
  • s2: there being exactly 2 purely contingent events
  • s3: there being exactly 3 purely contingent events

Notice that these states differ by a mere quantity of events. You might think mere quantitative differences aren’t normally relevant to causal possibility. That is, if there could be a cause of s3, then there could be a cause of s2, and if there could be a cause of s2, then there could be a cause of the smaller state, s1. This inference is supported by what Rasmussen (2014) calls “modal continuity.” … We don’t expect it to be controversial that there could be a cause of s3 … . For example, there could be two purely contingent events that give rise to a third. In this situation the two events jointly cause s3 to obtain. So, by causal uniformity, we have some reason to expect that it is possible that there is a cause of s1.

Their idea is that it is uncontroversial to say that s3 could be caused; and since the only difference between s3, s2, and s1 is mere quantity, it seems (from modal continuity) that s1 could be caused.  But what kind of thing could cause s1? The only thing that could cause s1 would have to be a necessary thing, since if a contingent event caused there to be exactly 1 contingent event, it would have to cause itself—an impossibility.

In reply, what reason is there to think there could be a cause to s2 and s3 but not s1 if the difference is mere quantity?  The immediate answer for those coming into the argument skeptical of necessary concrete things is that there is a prior belief that all of concrete reality is exhausted by contingent things.  The causally relevant feature for why s1 can’t be caused is that you can’t have a cause to the totality of concrete things without something causing itself, which is impossible.  This response will push the debate to why we have those prior beliefs, but, for the moment, the causal relevance argument is defused.  The same reasoning defuses the inductive generalization argument.

Thirdly, there is the conceivability argument.  Here we make use of a principle famous from Chalmers’ zombie argument in philosophy of mind.  The principle states that if you can conceive of a certain statement then that is a guide to its metaphysical possibility.

Since Chalmers’ methodology plays perhaps the central role in modal reasoning, a primer will be helpful.  Chalmers distinguishes between negative and positive conceivability for some statement S.

The central sort of negative conceivability holds that S is negatively conceivable when S is not ruled out a priori, or when there is no (apparent) contradiction in S.

Positive notions of conceivability require that one can form some sort of positive conception of a situation in which S is the case. One can place the varieties of positive conceivability under the broad rubric of imagination: to positively conceive of a situation is to in some sense imagine a specific configuration of objects and properties. It is common to imagine situations in considerable detail, and this imagination is often accompanied by interpretation and reasoning. … Different notions of conceivability correspond to different notions of imagination. One such notion is tied to perceptual imagination. … For example, one can perceptually imagine that a pig flies by forming a visual image of a flying pig, where this can be understood as an image that relevantly resembles a visual experience as of a flying pig. … There is a sense in which we can imagine situations that do not seem to be potential contents of perceptual experiences. One can imagine situations beyond the scale of perception: e.g. molecules of H2O, or Germany winning the Second World War. One can imagine situations that are unperceivable in principle: e.g. the existence of an invisible being that leaves no trace on perception.

Since positive conceivability—i.e. the ability to imagine—is a richer type of conceivability it is considered to be preferable over negative conceivability.  Chalmers notes two types of positive conceivability: one is perceptual, and the other, I’ll call, conceptual.

Following Chalmers’ test, Rasmussen and Weaver say:

With Chalmers conceivability tests in hand, let us now return to our causal principle, [P1], which says that possibly, there is a cause of a purely contingent totality event. Does conceivability justify [P1]? According to Chalmers, it does to the extent that we can imagine a situation in which a totality event has a cause. So consider the following scenario. There is a supremely powerful entity E (whose nature we leave unspecified), which is capable of causing any and every purely contingent event, including a totality event. We may imagine, for example, that whatever event can occur could be caused by E. Or if that is too much to imagine, then imagine merely that E causes whatever purely contingent events happen to occur. Or if even that is too much, then imagine a particularly big contingent event, which is known to be causable, like a galaxy forming, and then imagine that E causes that event. Now add to your imagination empty space around the caused event so that there are no other purely contingent events. The imagined galaxy is now a totality of purely contingent events, and no incoherence is revealed by supposing that it still has a cause. These imaginations are … coherent, and thus, by Chalmers’ lights, they provide … evidence for the metaphysical possibility of the imagined situation. We have thus identified a third line of potential support for our causal principle.

They offer three scenarios for us to imagine.  If we can imagine any of those situations, then we have support for its metaphysical possibility, from which a necessary being follows.  The first scenario seems to be a conceptual imagining, and the second and third scenarios seem to be a perceptual imagining.  I will consider the 2nd and 3rd perceptual case for two reasons: (1) if we are considering the argument and have the option to use perceptual imagining, it seems like a plus and not a minus since adding more detail doesn’t seem bad, and (2) the use of perceptual imagination is where I think the argument runs into counterintuitive results.

Consider the third scenario: “imagine a particularly big contingent event, which is known to be causable, like a galaxy forming, and then imagine that E causes that event.”  It seems easy to perceptually imagine that the cause is a gas cloud.  Then I can imagine the cause of that stretching back to a singularity.  If you followed the original argument, it should be clear that, since the galaxy formation is the totality of purely contingent events, the singularity has to be a necessary concrete being—an unintuitive result.  We can construct similar scenarios to open up a Pandora’s box of necessary concrete beings.

One possible move is to say that the singularity should have been included in the totality of purely contingent events in the first place.  I think to do that would be to give up on this causal part (where we imagine the possibility of cause) of the argument and go back to whatever method we were using in the first place.  Essentially, the causal part of the argument is vetoed by whatever our primary method (e.g. Chalmers’ test) is for figuring out whether concrete things are necessary or contingent. At best, the causal part can offer suggestions, but it’s not the final arbiter.

The next phase of their argument provides a path to theism.  They propose that the necessary being must have omnipotence, which is plausibly a great-making property.  Their reasoning follows the spirit behind modal continuity.  (I will only offer a short paraphrase.)  The idea is that it seems arbitrary for there to be some cutoff to what this necessary being can cause.  For example, why think the necessary being can cause a galaxy forming but not a tree forming?  Presumably, if you think the galaxy forming can possibly be the totality of purely contingent events and possibly have a cause, you also think the tree forming can possibly be the totality of purely contingent events and possibly have a cause.  So, to avoid arbitrariness, it seems that the totality of necessary concrete beings must be able to cause all possible totalities of purely contingent events, and, therefore, be omnipotent; otherwise, there seems to be an arbitrary break in modal continuity.  It is here that the causal part of the argument does play some role.

They further argue that N, the totality of necessary concrete beings, must not have a geometry.

In other words, we have reason to think that if N has a geometry, it could have had a different one.

This result is especially significant if N’s contingent states can be caused. For then N can be an ultimate cause of geometric reality. Moreover, to avoid causal circularity, N can lack a geometry altogether—prior to its causing there to be a geometric reality. There is more. Suppose one thinks that whatever has a geometry must have a geometry. Then one may infer that N is essentially geometric-less and thus immaterial.

I don’t find this plausible, since by parallel reasoning we could imagine N not being geometric-less.  Additionally, one might think that geometric reality exhausts all of concrete reality, which entails that there can’t be a cause to geometric reality.

They “leave open whether the N picks out a single thing, sum of things, or a plural of things.” It is likely they have further arguments (outside of this paper) that the totality of the necessary causal foundation can’t be a plurality of things, but, for the moment, their argument seems to support a Pandora’s box of necessary concrete beings (which would satisfy the omnipotence requirement.)

Chalmers, David. “Does conceivability entail possibility?” Conceivability and possibility (2002): 145-200.
Rasmussen, Joshua & Weaver, Christopher. “Why is There Anything?” Two Dozen (or so) Arguments for God: The Plantinga Project (forthcoming).

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William Lane Craig says he does not know how they would respond to his three points against Atheistic Moral Platonism

In this video Craig offers three criticisms to what he calls atheistic moral Platonism.

(I suspect Christian Platonists about morality, like Terence Cuneo, would object to this term. And, I have never seen any metaethicist ever use this term. It should simply be called Moral Platonism or a robust non-naturalism à la Enoch, as opposed to Parfit’s Quietism.)

When asked by a questioner, Craig says that he does not know how the atheist moral Platonist would reply to his three criticisms. Really? I don’t expect Craig to accept their reply, but I find it odd that he wouldn’t even know how they would reply. I’ll quote Craig’s criticisms in full then offer standard replies.

Criticism 1: The view seems unintelligible. What does it mean to say, for example, that the moral value justice, just exists? It’s hard to make sense of this. It’s easy to understand what it means to say that some person is just, but it’s bewildering when somebody says that, in the absence of any people, justice itself just exists. It becomes even more bewildering when you reflect on the fact that justice itself is not just anymore than loyalty is loyal or intemperateness is intemperate. So, if there were no people around who are just, then how could justice exist? It seems like there wouldn’t be any justice, this abstract object is not just, there aren’t any just people, so justice wouldn’t seem to exist, which contradicts the view that justice just exists on its own as an idea. Moral values seems to be properties of persons, and so it’s hard to understand how moral values like justice can exist as an abstraction.

Reply: This first criticism doesn’t seem to be specifically about atheism or morality, but about Platonism from someone with Aristotelian leanings.  (Briefly, on Platonism, there are external abstract properties that are exemplified by particulars, and there are such things and unexemplified properties.  On the Aristotelian view, all properties are immanent in the particular, and there are no unexemplified properties.)  We can equally imagine Craig saying: It’s easy to understand what it means to say that some concrete object is red, but it’s bewildering when somebody says that, in the absence of any concrete objects, redness itself just exists. Since one of Craig’s philosophical specialties has to do with abstract objects, I’m sure he’s heard of the third man argument; so he should know the reply. The idea is that it seems to the Aristotelian that the form of red must itself be red, but, then it seems we need another form to account for the redness of the form of red and we’re off to an infinite regress, in which case Platonism never solves the original problem of accounting for the redness of a particular, say, an apple. One reply, given here and here, is to say:

Plato’s theory of forms proposes that for any irreducible simple element F exhibited by particulars, the primary function of the form F is to explain (give being or existence to) the F-ness of those particulars that partake of F.   Specifically excluded from Plato’s description is any attempt to explain the F-ness of F.   Plato does not open the possibility of an infinite regress of forms of F-ness, each of which explaining the F-ness of the forms of F-ness below it in the hierarchy.   The form of F can explain the F-ness of the original plurality of F particular things.   But it cannot explain the F-ness of F.   That requires no explanation because he maintains that F-ness is equivalent / identical to F.   Hence, the move in the Third Man Argument to demand a “higher level”Form in order to explain the F-ness of the larger set of things that includes the Form of F is specifically invalid.

Criticism 2: Secondly, this view provides no basis for moral duties. It tries to give a basis for moral values, but it has nothing to say by way of an explanation of our moral duties. Let’s suppose for the sake of argument that moral values like justice, loyalty, mercy, forebearance, and so on, just exist. How does that result in any moral obligations for me? Why would I have a moral duty to be, say, merciful? Who or what lay such an obligation on me? Notice that on this view moral vices such as greed, hatred, rapacity, selfishness, and sloth also exist as abstractions. So, why are we morally obligated to align our lives with one set of these abstractions rather than with some other set of these abstractions. Atheistic moral Platonism, lacking a moral law giver, has no grounds for moral obligation.

Reply: Craig says that our moral duties are constituted by divine commands, but in the 17th century, theologian Ralph Cudworth noticed that this type of divine command theory cannot account for all moral obligations.  (This criticism survives today and is talked about by metaethicists like David Baggett, C.S. Evans, and Terence Cuneo.)  It seems that Craig would agree that we’re obligated to obey God’s commands, but what accounts for that obligation? On a DCT, where all duties are constituted by God’s commands, God would have to command us to obey his commands in order for us to be obligated to obey his commands. But why are we obligated to obey that 2nd order command? God would have to command us again, and we’re off onto an infinite regress. It seems, for Craig, there has to be at least one obligation that can’t be accounted for by God’s command—namely, the obligation to obey God’s commands—in which case DCT is false. Maybe it’s just a necessary truth that we’re obligated to obey God’s commands, but that opens the door to say that it’s a necessary truth that we’re obligated to follow the golden rule (or whatever). If at least one obligation is not accounted for by a command, it wouldn’t be queer, in the Mackian sense, that a second is.

Criticism 3: And, finally, number three, it’s fantastically improbable that the blind evolutionary process should spit forth precisely those sorts of creatures who correspond to the abstractly existing realm of moral values. This seems to be an utterly incredible coincidence when you think about it. Remember that this realm of moral values as an abstract realm is utterly independent of the natural realm. It is causally unconnected with the natural realm. So how is it that exactly that kind of creature should emerge from the blind evolutionary process that corresponds to this independently existing moral realm. It’s almost as though the moral realm knew that we were coming. I think that it’s far more plausible to think that both the natural realm and the moral realm are under the authority of a God, who gave us both the natural laws and the moral law, than to think that these two independent realms of reality just happen by coincidence to mesh. So for those reasons, I think that atheistic moral Platonism is a less plausible theory of ethical values and duties than is theism.

Reply: Here, there seems to be two criticisms: (1) an epistemological problem for platonists, (2) an argument similar to Plantinga’s EAAN. As for (1), one way for the Platonist to reply, for abstract objects in general, is given by Michael Loux in his Metaphysics A Contemporary Introduction book:

And they will argue that the Aristotelian’s contention that the Platonist faces insoluble epistemological problems is overblown. They will insist that while some universals have no instances in the spatiotemporal world, many do; and they will claim that our knowledge of exemplified universals can be captured by a thoroughgoing empiricism. As they see it, we come to have cognitive access to these universals simply by experiencing the spatiotemporal particulars that exemplify them; whatever other knowledge we have of universals is grounded in our knowledge of these exemplified universals. Thus, we come to know about some unexemplified universals by extrapolation from our empirically based knowledge of instantiated properties, kinds, and relations (p. 43).

On how “moral realm knew that we were coming”, the most famous reply is David Enoch’s pre-established harmony—to borrow a phrase from Leibniz. The idea is that there is a pre-established harmony between what is evolutionarily advantageous and what is good—a happy coincidence.  For another, similar reply, see Knut Olav Skarsaune’s Darwin and Moral Realism.  Skarsaune proposes that:

if pleasure is usually good and pain usually bad, then the required relation between evolutionary pressures and the evaluative facts (realistically understood) exists [since] evolution has caused us to value reproductively beneficial things by making us such that we take pleasure in these things, and caused us to disvalue reproductively harmful things by making us such that these things cause us pain. … But now if … pleasure is usually good (for the subject), then to the extent that evolution has influenced our evaluative beliefs through the mechanism just described, that influence has been truth-conducive.

As for (2), the literature on Plantinga’s EAAN is vast—too much for me to want to repeat here.  See James Beilby’s Naturalism Defeated and Plantinga & Tooley’s Knowledge of God.

The point isn’t that these replies to Craig are good (I’m skeptical of reply 1 and 3), but that it is odd that Craig would say that he’s not aware of the responses.

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A New and Improved Argument for a Necessary Being

Here is John Turri’s argument for a necessary being, which captures the essentials of a previous argument by Joshua Rasmussen.

  1. It is possible that the first contingent thing is caused to exist. (Premise)
  2. In the possible case where the first contingent thing is caused to exist, a causally powerful necessary being must cause it to exist. (Premise)
  3. A causally powerful necessary being possibly exists. (From 1 and 2)
  4. A possibly causally powerful necessary being necessarily exists.

To see why 2 is true, notice that a prior contingent thing can’t cause the first contingent thing—for that prior thing would itself be the first contingent thing; therefore, only a necessary being could cause the first contingent thing.  This seems like a valid argument; if you accept 1, the conclusion follows.  So, we should focus on the controversial premise 1. As Turri notes, all the conclusion entails is that there is a necessary being that is causally powerful in some possible world and not in every world.  In other words, there are other possible worlds where a necessary being is not a cause.  (Modest premises in, modest conclusion out.)

There’s a simple—maybe too simple—response to this argument.  Many people will have the intuition that there can’t be a concrete necessary being (using conceivability to possibility as a guide).  People with this intuition will think that all concrete things are contingent; therefore, on this view, the first contingent thing can’t be caused to exist—for there would have to be a causally prior contingent thing that would itself be the first contingent thing.  Simple.

This may seem all too quick and some may still have the intuition that the first contingent thing can have a cause—for suppose the first contingent thing is a water molecule: Why isn’t it possible that the first contingent water molecule be caused by, say, the prior bonding of a hydrogen and oxygen atoms? (The water molecule example comes from Joshua Rasmussen.)

Consider this parody:
1’. It is possible that the first non-infinite-sized thing is caused to exist. (Premise)

Suppose the first non-infinite-sized thing is caused to exist.  It’s possible that that first non-infinite-sized thing is a tiny water molecule.   You may have the intuition that this water molecule could be caused to exist by the bonding of hydrogen and oxygen atoms.  But the thing that caused the water molecule to exist can’t also be non-infinite-sized—for if that were so, then that thing would be the first non-infinite-sized thing; therefore, only an infinite-sized thing can be the cause of the water molecule.   The truth of 1′ entails the possible existence of an infinite-sized (and causally powerful) thing.

Returning to 1 … suppose that the first contingent thing is a water molecule.  We have the intuition that this water molecule could be caused to exist by the prior bonding of hydrogen and oxygen atoms.  If we keep with this intuition, we’ve just shown that hydrogen and oxygen are necessary beings—and the proofs for other necessary beings wouldn’t stop here.

Consider another parody:
1’’. It is possible that the first non-square-circled thing is caused to exist. (Premise)

For simplicity, we can use the water molecule as an example of the first non-square-circled thing.  An unsuspecting reader might have the intuition that this water molecule could surely be caused to exist.  But this can’t be right, since it would prove the possible existence of a square-circled thing.  This shows that—in thinking of the entailments—we should consider the conclusion (the possible existence of a square-circled, causally powerful thing) in advance, if we want to accurately assess 1’’.

If we reason this way, then 1’’ (and 1) should not persuade someone who is already skeptical of the conclusion.   In 1, what first seems like an independent argument for a necessary being is not one anymore than 1’’ is an independent argument for a possible squared-circle.

Turri, John. “A New And Improved Argument For A Necessary Being.” Australasian Journal of Philosophy 89.2 (2011): 357-359.
Rasmussen, Joshua. “A New Argument for a Necessary Being.” Australasian Journal of Philosophy 89.2 (2011): 351-356.

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The Fine-Tuning Argument

I recently ran across Jonathan Weisberg’s interesting paper The Argument from Indifference.

Before getting to the argument, let’s first set up the fine-tuning dialectic.

We’ve always known that the laws and constants were life-permitting.  After all, if the laws and constants weren’t life-permitting, we wouldn’t be here.   What we didn’t know is if the life-permitting range of the constants is narrow or wide.  The recent discovery that the constants needed to be in a narrow range was said to be evidence for design.

The fact that there is life is old data—we’ve always known that life exists.  The new data is that the constants need to be in a narrow range for the universe to be life-permitting.  This new data gave rise to a new breed of fine-tuning arguments; and the new data is supposed to provide additional support for design over and above the old data of life.

Let N = the new data of narrow range constants, D = Design, and O = the old data of life.  The fine-tuning argument in a likelihood formulation says:

(FTA) P(N|D & O) > P(N|¬D & O).

That is, the probability of the narrow constants given design and life is greater than the probability of the narrow constants given blind chance and life.

  • The Likelihood Principle says: if P(E|H) > P(E|¬H) then E supports H over ¬H.

Given the likelihood principle, the FTA says that new data of fine-tuning supports design over blind chance (given the old data of life).

But is the FTA true?  To figure that out Weisberg first introduces some assumptions that should seem plausible to the fine-tuning proponent.

  • Divine Intent: P(O|D) = 1. The designer will always create life.  (Some may say that this is unfairly high, given free will, and that it unfairly helps the FTA, but let’s put this at 1 for the sake of the argument.)
  • Blind Indifference: if there is no designer, P(.|O&¬D) is a uniform distribution among the O-possibilities.  In other words, given mindless chance, each O-possibility is equally probable.
  • Divine Indifference: if there is a designer, P(.|O&D) is a uniform distribution among the O-possibilities.  In other words, given a designer, each O-possibility is equally probable, since she does not favor any O-world over the other.  All she cares about is to have a life-permitting world.

Blind Indifference and Divine Indifference entail Divine and Blind Irrelevance.  That is, D and ¬D is irrelevant to the probabilities of the O-possibilities since any O-possibility is equally probably given either D or ¬D.

These assumptions, which should be plausible to the design theorist, entail that the new fine-tuning data N supports blind chance (¬D) over design (D).  More formally:

(1) P(N|¬D) > P(N|D)

Here’s an intuitive way to think why this is so.  A designer will only pick among O-worlds (life-permitting worlds), and blind chance will be indifferent to the O-worlds.  Let’s define robust laws are laws that permit life given a wide range of constants, and fragile laws as laws that permit life on only a narrow range of constants.  Since most of the O-worlds have robust laws rather than fragile laws (given that it’s easier to have life if a wide range of constants are life-permitting) , the designer is more likely than blind chance to pick a world with robust laws, which is identical as saying that N (narrow range) is more likely on blind chance than design.  More formally,  P(N|¬D) > P(N|D), which says that the new data N favors blind chance over design.  (In the paper, Weisberg gives a mathematical proof for P(D|N) < P(D), which is equivalent to the above likelihood formulation, since P(H|O) > P(H) iff P(O|H) > P(O|¬H).)

The previous likelihood did not include O (that life exists) in our background knowledge.  So what happens when we put O in to our background knowledge?  Using the assumptions of Blind Indifference and Divine Indifference, we can directly see that:

(2) P(N|D&O) = P(N|¬D&O).

That is, given that life exists, the new data does not support design or blind chance—they have equal support.  This can be seen intuitively: given Blind Indifference and Divine Indifference, all O-possibilities are equally probable on both design and blind chance. Blind chance and design have the same random selection mechanism.

Darren Bradley, in his reply to Weisberg, argues that there is still an argument to be made for fine-tuning; more specifically, Bradley argues that the amount of support O gives to D increases as N gets narrower—so N acts as indirect support for D.  To see this, let B stand for maximally broad constants where all constants support life.  In that case, we have:

  • P(O|D&B) = P(O|¬D&B) = 1.

In other words, given B, life will surely exist on both design and blind chance.  Since the probabilities are equal, O is indifferent between D and ¬D (given B).  But now suppose that the constants need to be in a narrow range to permit life, which we represent as N.  Then we’d get: P(O|D&N) = 1 (assuming Divine Intent) and P(O|¬D&N) < 1 (assuming blind chance).  So that:

(3) P(O|D&N) > P(O|¬D&N).

In other words, given N, life supports D over ¬D. (And the narrower N is, the more D is supported.)

While Weisberg thinks that Bradley may be right that as N gets narrower it increases the support O gives to D, it is still the case that learning N after we learn O does not increase the net support for D.  This is because the disconfirmation of D given by (1) exactly balances out the support for D given by (3), since (2) shows us that learning N after learning O neither favors design nor blind chance (they have equal support).

A note on evidence
The notion of evidence used here is Bayesian.  Evidence, alone, only boosts the degree of credence of the hypothesis one way or the other; it does not determine the overall plausibility of the hypothesis.  On a Bayesian view, what you should believe given the new evidence will depend on prior probabilities of beliefs.  To use John Hawthorne’s example, the existence of cheese is evidence for a God with a cheese fetish; but, given the low priors we don’t actually find the cheese fetish God plausible.

Evidence comes in degrees—sometimes weak, sometimes strong.  Suppose a raffle exists with a 100 tickets.  If I bought 1 ticket, that would be weak evidence that I would win—yet it is still evidence.  Given the weakness of the evidence, it wouldn’t be plausible that I would win.  If I bought 99 tickets, it would be strong evidence that I would win; and it would be plausible that I would win.

Additional worries
The first worry is the normalizability problem.  Timothy McGrew, Lydia McGrew, and Eric Vestrup explain the normalizability problem:

Probabilities make sense only if the sum of the logically possible disjoint alternatives adds up to one … But if we carve an infinite space up into equal finite-sized regions, we have infinitely many of them; and if we try to assign them each some fixed positive probability, however small, the sum of these is infinite.

The design theorist could restrict herself to a probability distribution over a finite range to avoid this problem—something like Robin Collins’ “epistemically illuminated region”.

A second worry has to do with Divine Indifference.  So far, our designer hypothesis has had the auxiliary hypothesis that the designer is equally likely to pick among any of the O-worlds.  If we changed our auxiliary hypothesis by giving the designer certain intentions, it could turn out that N is evidence for design (given O) as John Hawthorne explains in this video.

What Hawthorne doesn’t mention is that, on other auxiliary hypotheses about Divine intentions, it could turn out that N is evidence against design (given O).

A note on skeptical theism
As Hawthorne notes, near the end of the video, the skeptical theist is not in a position to use fine-tuning arguments.  Skeptical theism is a response to the evidential problem of evil.  The skeptical theist reasons that given our finite human epistemic position, we are in no position to make empirical judgments about the existence of gratuitous evils; for God could have morally sufficient reasons beyond our ken.  Effectively, skeptical theists block off empirical/Bayesian reasoning concerning the appearance of gratuitous evils to the conclusion that a good God does not exist.  Given skeptical theism, one should also accept that one is in no position to know that God couldn’t have morally sufficient reasons to create robust laws.  So this should also block off empirical/Bayesian reasoning concerning fine-tuning.

It seems the skepticism should be even deeper in the case with robust/fragile laws than with the gratuitous evil case, for what information does the skeptical theist have about God’s preferences concerning laws?  In the moral case, the skeptical theist can at least point to some of the moral properties of God—like lovingness, honesty, and generosity.  Given these properties, it should give us some general idea about what God would do; but the skeptical theist denies this.  In the fine-tuning case, what properties of God can we point to that allows us to say, with some confidence, which laws or type of laws God would create?  It seems none.  So it seems skepticism on fine-tuning is more warranted than skepticism about gratuitous evil.

I’ve ignored talk of multiverses so far and assumed a single universe hypothesis.  Things change once we consider multiverses.  Some interesting papers concerning the multiverse are Roger White’s Fine-Tuning and Multiple Universes,  Kai Draper & Paul Draper & Joel Pust’s Probabilistic Arguments for Multiple Universes, and Darren Bradley’s A Defense of the Fine-Tuning Argument for the Multiverse.


Bradley, Darren. A Reply to Weisberg.
Weisberg, Jonathan. The Argument from Divine Indifference.

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