Philosophy and Faith in the NYT
August 6, 2010 — 16:12

Author: Matthew Mullins  Category: Atheism & Agnosticism Religious Belief  Comments: 38

Garry Gutting has a nice piece on faith and philosophy in a recent New York Times article. An excerpt:

The standard view is that philosophers’ disagreements over arguments about God make their views irrelevant to the faith of ordinary believers and non-believers. The claim seems obvious: if we professionals can’t agree among ourselves, what can we have to offer to non-professionals? An appeal to experts requires consensus among those experts, which philosophers don’t have.
This line of thought ignores the fact that when philosophers disagree it is only about specific aspects of the most subtle and sophisticated versions of arguments for and against God’s existence (for example, my colleague Alvin Plantinga’s modal-logic formulation of St. Anselm’s ontological argument or William Rowe’s complex version of a probabilistic argument from evil). There is no disagreement among philosophers about the more popular arguments to which theists and atheists typically appeal: as formulated, they do not prove (that is, logically derive from uncontroversial premises) what they claim to prove. They are clearly inadequate in the judgment of qualified professionals. Further, there are no more sophisticated formulations that theists or atheists can accept — the way we do scientific claims — on the authority of expert consensus.
In these popular debates about God’s existence, the winners are neither theists nor atheists, but agnostics — the neglected step-children of religious controversy, who rightly point out that neither side in the debate has made its case. This is the position supported by the consensus of expert philosophical opinion.

Those with an interest in social epistemology might find some of Gutting’s comments of particular interest. Thanks to Stephen Grimm for passing this along.

Comments:
  • The move from:
    1. The arguments do not logically derive their conclusions from non-controversial premises
    to:
    2. The arguments are inadequate
    is quite problematic. Adequacy is relative to a telos, and arguments do not have a unique telos. If the aim were to derive something from non-controversial premises, 2 would follow from 1. But if the aim is to derive the something from premises that reasonable people ought to accept, 2 does not follow from 1. And if the aim is to derive something from premises that many people (or many reasonable people) accept, 2 still does not follow from 1.

    August 6, 2010 — 16:47
  • Keith DeRose

    Perhaps when we ask “inadequate for what purpose?”, the best reading of Gary’s use of the term here is “inadequate for the purposes of proof”–(& he’s using “prove” here to mean “logically derive from uncontroversial premises”). On this understanding, 2 (from Alex’s comment above) isn’t a conclusion inferred from 1, but a restatement of 1. If so, Alex is right to stress that even given Gary’s claim, the arguments in question can still be “adequate” for other important purposes. But Gary is still making a point that, if correct (& I think it is), is important to convey to the general public.

    August 7, 2010 — 12:19
  • I am not sure “inadequate for the purposes of proof” is the right reading. If memory serves me, Gutting concludes further on that the agnostic is the one who is made best off by the current state of the art. But inadequacy for the purposes of proof is compatible with the arguments’ making agnosticism irrational, or with their being such as to convince many agnostics, etc.

    August 7, 2010 — 20:35
  • Keith DeRose

    I have difficulties with understanding just what’s meant when someone is called an “agnostic.” But not to go into all that, on almost any good way of dividing folks up into atheist/theist/agnostic, outcome 1 seems to favor the theist, outcome 2 the atheist, and outcome 3 seems to favor (though not as decisively) the case of the agnostic:
    1. God’s existence has been proved
    2. God’s non-existence has been proved
    3. Neither God’s existence nor God’s non-existence has been proved
    Gary writes, “In these popular debates about God’s existence, the winners are neither theists nor atheists, but agnostics.” Even if outcome 3 doesn’t completely settle things in favor of the agnostic, they can be said to be the “winners” here in that the possible outcome that favors and that most favors their case has turned out (so far) to be the actual outcome.
    But that all depends on dividing the possible outcomes into just those three. Alex’s point may be that there may be more fine-grained specification of possible outcomes — perhaps of the “neither has been proved, but …” variety — that are arguably or perhaps even actually actual, and that hurt agnosticism.
    I guess I’m inclined to persist in trying to endorse the points I take both Gary & Alex to be making … 🙂

    August 7, 2010 — 22:14
  • Mike Almeida

    It’s hard to tell what exactly the disagreement is about the adequacy claim (worries compounded by what looks like Keith agreeing with Alex’s disagreement with him ….:). It’s pretty clear what Gutting means by the adequacy claim. He says,
    There is no disagreement among philosophers about the more popular arguments to which theists and atheists typically appeal: as formulated, they do not prove (that is, logically derive from uncontroversial premises) what they claim to prove. They are clearly inadequate in the judgment of qualified professionals.
    These arguments are inadequate IF their aim is to prove (in Gutting’s stipulated sense) their conclusions. And that seems right. No one has any interesting proofs in that sense.
    On the other hand, the objection seems to be that there are other aims for arguments and these arguments are not inadequate for those aims. But who could deny it? Such arguments might still convince lots of people, or they might provide lots of entertainment, or they might put the children to sleep really fast, etc.

    August 8, 2010 — 10:38
  • Of course the concluding abduction to agnosticism is inadequate even on its own terms, since (as most of us here probably will agree) the agnostics have not made their case.

    August 8, 2010 — 11:35
  • Mike Almeida

    Of course the concluding abduction to agnosticism is inadequate even on its own terms, since (as most of us here probably will agree) the agnostics have not made their case
    This actually raises an interesting paradox. On Gutting’s view, it can be true that neither theism nor atheism nor agnosticism has an adequate proof, since none of them follow from uncontroversial premises. But, of course, if it is reasonable to believe p only if there is an adequate proof for p, then it’s not reasonable to believe any of these views. But you can’t suspend belief on all of them. On the other hand, if it is reasonable to believe p and there is no adequate proof for p, then you can reasonably believe theism or atheism or agnosticism.

    August 8, 2010 — 18:35
  • I think we can cut through some of the confusion if we’re more clear on what these terms mean. One popular way of dividing people up is to think of theists as those who believe that God exists, atheists as those who believe that God does not exist, and agnostics as those who don’t believe one way or the other.
    I think a better way of using the terms might be this: theists believe that God exist, atheists lack that belief, and agnostics lack knowledge on God’s existence or non-existence (or, at least, they claim to lack knowledge). From there you can have positive atheists (those who believe that God does not exist) and negative atheists (those who neither believe that God exists nor believe that God does not exist) as subsets of atheists in general, and a subset of agnostics who say that knowledge on God’s existence or non-existence is impossible.
    Let’s take the more popular way of parsing these terms. On this view, there’s something intuitively wrong with being a theist if there aren’t good reasons to believe that God exists. (I’m bracketing here both prudential arguments and Plantinga’s claim that theistic belief can be properly basic.) And there’s something intuitively wrong with being an atheist if there aren’t good reasons to believe that God does not exist. But there’s nothing wrong with being an agnostic unless you’re just missing the obvious evidence for God’s existence or non-existence. That said, though, the lack of definitive proof one way or the other doesn’t favor agnosticism as much as Gutting seems to think, since there can still be pretty strong reasons to believe in God even if there isn’t proof in the sense that he stipulates, in which case theism is intuitively the position to go for.
    Now on the other way of using these terms, it’s just wrong to pit theists, atheists, and agnostics as three groups that are against each other. Both theists and atheists can be agnostics, and the lack of definitive proof for or against God does indeed look like a pretty good reason to be agnostic, though that doesn’t say anything about whether you should be an atheist or a theist. Using these definitions, you should be a theist if there are good reasons to believe that God exists, and you should be an atheist otherwise. To think of agnostics as a third category would just be mistaken.
    It looks to me that Gutting is using the words in the more popular sense. But then it is just mysterious why he thinks that the lack of proof one way or the other should be a victory for agnosticism. I imagine that a lot of what we believe is not capable of being proven in his stipulated sense, but that doesn’t mean that we shouldn’t believe it.
    By the way, Mike, if I’m right about the way that Gutting is using the words, then it’s not clear that it makes sense to say that “it can be true that neither theism nor atheism nor agnosticism has an adequate proof, since none of them follow from uncontroversial premises.” To prove theism is just to prove that God exists, and to prove atheism is just to prove that God does not exist, but if agnosticism is just being used as the lack of belief one way or the other, then what does it mean to “prove agnosticism”? The view is by definition a lack of a belief, so there’s no content to prove. It also wouldn’t make sense to say “you can’t suspend belief on all of them.” Again, this would be because there is no content to believe for agnosticism. Does that seem right?

    August 8, 2010 — 23:38
  • Mike Almeida

    By the way, Mike, if I’m right about the way that Gutting is using the words, then it’s not clear that it makes sense to say that “it can be true that neither theism nor atheism nor agnosticism has an adequate proof, since none of them follow from uncontroversial premises.” To prove theism is just to prove that God exists, and to prove atheism is just to prove that God does not exist, but if agnosticism is just being used as the lack of belief one way or the other, then what does it mean to “prove agnosticism”?
    You can prove agnosticism in Gutting’s sense of ‘prove’ if you provide an argument for it from uncontroversial premises. All you need is an argument for broad skepticism. But there are countless arguments for skepticism, if one of them has uncontroversial premises, then you have the sought-after proof.

    August 9, 2010 — 8:47
  • Keith:
    I’ve tended to take agnosticism in the weaker sense to be neither believing that God exists nor that God does not exist. On reflection, that’s not right because trees and cats aren’t agnostics, and I don’t quite know what else to add (“after considering whether God exists, while still being capable of belief on the issue”?). There is also a stronger notion that I’ve met with in Msgr. Van Noort’s Dogmatic Theology, which is that an agnostic is someone who believes that it cannot be known whether God exists.
    Yeah: the finer-graining is a nice way of putting my point. Suppose that Sally plays poker (it’s been years since I’ve played poker, and it was only against my PC, and I barely remember any of it, so the example might not work, in which case change it to some other game) and overall she loses. But she loses only by the tiniest amount, and she happened to always have been dealt a really bad hand, while others have been dealt really good hands. Now, consider the question of who is a good poker player. In one sense, the evening’s play disfavors Sally, because she lost. But that’s only if we partition on win/tie/lose. If we partition more finely, as we should, the evening’s play favors Sally.
    Maybe my real worry is this. One often finds non-philosophers who think that it’s only reasonable to believe in moral claims or God if there is a proof in Gutting’s sense. I am sure you’ve heard sceptical statements starting with “Nobody’s proved…” from undergrads. Of course, these folks either don’t think this about other areas of investigation, or are really confused about how we in fact find things out (e.g., they think scientists prove things). Anyway, the worry I have is that even if Gutting means to make only a really modest point, many of the readers are apt to take it to be a more substantive point, such as that the arguments do not make it rational to believe or disbelieve that God exists. And when we write for the general public, there is a special challenge to take into account the audience’s irrationalities (actually, this is true for any audience).

    August 9, 2010 — 11:47
  • Keith DeRose

    Agreed, Alex. I’m just adding that since there are those (on both sides) who claim that one position or the other has been decisively proved to be right, it’s also worth stressing the relatively modest point I take Gary to be making. But, yes, this should be accompanied by your warning.

    August 9, 2010 — 12:36
  • Keith:
    To my ears, “decisively proved” does not sound like something that entails “proved from non-controversial premises”. Whether an argument is decisive seems to me to be the question whether (a) its premises and rules of inference must be accepted on pain of (severe?) irrationality; and (b) the conclusion follows from the premises by the rules of inference in the way indicated. Typically, the question is about (a), and that’s a normative question, while the question whether a premise is non-controversial is sociological. But that may just be how I would use “decisively”.

    August 9, 2010 — 13:00
  • Mike, you wrote: “You can prove agnosticism in Gutting’s sense of ‘prove’ if you provide an argument for it from uncontroversial premises. All you need is an argument for broad skepticism. But there are countless arguments for skepticism, if one of them has uncontroversial premises, then you have the sought-after proof.”
    I was thinking of proving a position in the sense that you show it to be true. Theism can be true, and atheism can be true, but agnosticism (defined as the lack of a belief one way or the other) cannot be true, because it lacks a truth value. There is no content to be true or false.
    You could say, though, that a proof for God’s existence would be a reason to accept theism, and a proof for God’s non-existence would be a reason to accept atheism, and a proof of some skeptical argument would be a reason to accept agnosticism. But in this sense, it looks like agnosticism itself would not have been proven. What will have been proven is that there is a very good reason to be agnostic. It seems to me that there’s a difference here, but I’m not sure if it’s an important difference.

    August 10, 2010 — 13:26
  • John H.

    Why is are so many Catholic intellectuals struggling for proof, whether it be understood as possessing premises reasonable people ought to accept or non-controversial ones? The 1913 Catholic Encyclopedia clearly states that the arguments can only be “motives of credulity”, i.e. probabilistic, and are even if they can establish belief, they cannot bestow faith, which necessarily is a supernatural gift and is certain. There might be some things here to question, such as the certainty condition, but this seems to be a moderate, sensible position, far more so than demanding proof.
    It is true, of course, that Catholicism teaches that God’s existence can be discovered by reason. I’m not certain, however, such a discovery requires a proof in either of the above senses.
    Also, Gutting states that he can see how theistic belief can be warranted a la Plantinga, but not Christian belief. Well, what about WCB? Does Gutting have a rejoinder to Plantinga on this somewhere in the literature?
    /Soapbox/ It seems to me that Catholic philosophers should focus less on natural theology and more on developing a “Counter-Reformed” epistemology. For instance, if Catholic belief is basic, a Catholic need only appeal to the magisterium in interpreting Scripture; a Protestant is faced with the lack of consensus Gutting mentions and so the average layman will not be in a position to know what much of it means.

    August 10, 2010 — 18:05
  • Mike Almeida

    I was thinking of proving a position in the sense that you show it to be true. Theism can be true, and atheism can be true, but agnosticism (defined as the lack of a belief one way or the other) cannot be true, because it lacks a truth value.
    I’m not sure what you mean by the claim that skepticism lacks a truth value. It is either true or false that we can know whether theism is true or false. Suppose it is false that we can know whether theism is true or false. The truth of theism is unknowable just as, perhaps, it is unknowable whether a particular color shade is red. That theism is unknowable in this sense is the content of agnosticism that might be proven true.

    August 10, 2010 — 19:14
  • Mike,
    I didn’t say that skepticism lacks a truth value, I said that agnosticism (defined as a lack of belief one way or the other) lacks a truth value.
    You seem to be treating agnosticism in the other sense that I defined it earlier (something regarding a lack of knowledge, or even the stronger claim that one cannot have knowledge).

    August 10, 2010 — 19:39
  • Mike Almeida

    I didn’t say that skepticism lacks a truth value, I said that agnosticism (defined as a lack of belief one way or the other) lacks a truth value
    Agnosticism follows from general skepticism. If I can prove that the skeptical position is right, then I can prove that agnostic position is right. I’m using ‘agnosticism’ in the standard sense of neither affirming nor denying theism. So if I have an argument for skepticism then I have an argument that neither theism nor atheism is justified. The only justified position (of the three) is to neither believe nor fail to believe theism. So it is TRUE that a rational person neither believes nor fails to believe theism.

    August 11, 2010 — 7:38
  • Joshua Rasmussen

    the worry I have is that even if Gutting means to make only a really modest point, many of the readers are apt to take it to be a more substantive point
    I have the same worry. Consider that the modest sociological point (about arguments built on uncontroversial premises) is compatible with the thesis that there are decisive (or knock-down, or nearly knock-down, or knock-down with respect to certain sets of beliefs widely held by non-philosophers) arguments for or against God’s existence and that included among them are some of the familiar, less technical arguments.
    One reason I have for thinking that the sociological point is fairly insignificant (and not worth telling the general public) is that I’ve found that the average “expert” on arguments for and against theism is aware of but a tiny percentage of the standard arguments and their possible lines of defense. Indeed, I’ve discovered through personal interaction with many philosophers who publish arguments for and against God that there are typically many instances of each type, as well as possible lines of defense, which even philosophers who publish on that type (myself included) have not considered. I’ve found that there isn’t a battery of standard or traditional arguments of which certain experts are all aware and have deemed inconclusive. Things just aren’t nearly that simple.
    Also, if a layperson thinks X is a good argument against theism, I don’t think she will be much troubled by the revelation that philosophers aren’t in agreement over whether or not the premises in X are true once we make this layperson aware that philosophers aren’t in agreement over whether or not there are tables and chairs, over whether or not people can survive the loss of a single proton, over whether or not there’s a half an ear in a causally isolated universe, over whether or not it’s permissible to torture babies to maximize the welfare of the many, over whether or not time is real, over whether or not everything is nothing more than ideas in a mind, or over whether or not modus ponens is valid. Tell her those things, and I doubt if she’d be bothered by the lack of consensus over X. She shouldn’t be.
    I think it’s more important to share with lay people some of the advances made in philosophy of religion and to point out places where philosophers have achieved broad agreement. For example, there’s broad agreement that if certain widely-accepted modal axioms are true, then the mere possibility of a necessary being entails that a necessary being exists. I think most lay persons would be very surprised to find out that among those philosophers aware of the Gale-Pruss cosmological argument there is a broad consensus that if any contingent fact so much as can have an explanation, then there is a necessarily existing concrete particular, or that among those aware of my “modal kalam argument” for a necessary being, there’s a consensus that if any beginning so much as can have an explanation, then there is necessarily existing concrete particular. There’s broad agreement that the existence of a perfect being is logically compatible with the existence of evil. There’s broad agreement that some philosophical propositions can be conclusively and uncontroversially demonstrated (e.g., for example, we can conclusively demonstrate that the proposition just mentioned cannot be conclusively proven false). Ok, the last one isn’t philosophy of religion, but I throw it in there because I’ve seen MANY non-philosophers surprised to discover it. Rather than reinforce the stereotype that philosophers have nothing useful to say, why not instead highlight a few “building block” propositions about which philosophers have gained broad consensus?

    August 11, 2010 — 8:10
  • I think Josh’s point is very important. There are a number of important conditionals that there is broad (but not unanimous) agreement of experts over. Let me add three more, two in philosophy of religion and one in applied ethics:
    1. If there is gratuitous evil, there is no God.
    2. If abortion is permissible throughout the first trimester not just in exceptional cases, then six-month-old infants are not persons (variant: then some living individual members of the human species are not persons and may be permissibly killed despite being neither aggressors nor guilty).
    3. If the PSR or a broad Causal Principle is true, there is a necessarily existing first cause.
    There will be disagreement on how exactly to spell out gratuitous evil, exceptional cases and the PSR/CP, but the basic agreement seems to be there.
    And the conditionals are ones that are in fact important to public debate. For instance, among the general public, very few accept the consequent of (2) (or even the variant one–this is shown by the way the public thinks the abortion debate is over when “human life begins”), and most would accept the antecedent of (3) if asked. (I think that people in our culture will have less agreement with regard to the antecedent of (1), because many have a strong intuition that evil always works out for a good.)
    Or to put the point differently, it would be surprising and interesting to the public to see just where much of the main philosophical debate lies: that it lies over the antecedents of (1) and (3), and the consequent of (2) (and its variant), and about the details of the formulation, rather than about the conditionals in a broad sense. Of course, this might just make the public think that philosophers are crazy.

    August 11, 2010 — 9:10
  • Minor points about the Almeida/Hedrick disagreement:
    1. Agnosticism lacks a truth value, because agnosticism is an attitude rather than a proposition, sentence, doctrine, belief, or some other kind of (primary or non-primary) truthbearer. The proposition towards which agnosticism is an attitude has a truth-value, but because the proposition towards which agnosticism is an attitude is <There is a God&rt;, it makes no sense to identify the truth value of agnosticism with the truth value of that proposition.
    2. Associated with agnosticism, however, there is the normative doctrine that the agnostic attitude is the one that should be taken. And that doctrine has a truth value (at least relative to a disambiguation of “should be taken”). Call this doctrine agnosticism*.
    3. Agnosticism* is not parallel to the doctrines of theism and atheism. Theism and atheism considered as doctrines, rather than as attitudes, are the doctrines that there is or is not a God; considered as attitudes, they are believings in the respective doctrines. There are further normative doctrines, which we can call theism* and atheism*, that we should believe or disbelieve that there is a God, respectively. But these second-order doctrines should not be identified with theism and atheism, just as the view that we should believe in common descent should not be identified with common descent.
    4. Atheism as a doctrine is compatible with each of atheism*, agnosticism* and theism*. Prima facie, theism as a doctrine is compatible with each of atheism*, agnosticism*, and theism*, though maybe it’s only ultima facie compatible with theism*. Neither atheism* and theism* is prima facie compatible with agnosticism*.

    August 11, 2010 — 9:29
  • “It is true, of course, that Catholicism teaches that God’s existence can be discovered by reason. I’m not certain, however, such a discovery requires a proof in either of the above senses.”
    Catholics are dogmatically required to believe that the existence of God can be known with certainty by natural reason. While the wording of the First Vatican Council on this point may leave open the question whether a “proof” in any sense is possible, I think it’s fair to say that magisterium has tended towards the demonstrative interpretation. For instance, the Oath Against Modernists says: “And first of all, I profess that God, the origin and end of all things, can be known with certainty by the natural light of reason from the created world (see Rom. 1:90), that is, from the visible works of creation, as a cause from its effects, and that, therefore, his existence can also be demonstrated”.
    What exactly “demonstration” means is a hard question, but it does seem to mean a deductive argument from privileged premises. I don’t think the privileged premises have to be uncontroversial, but it seems plausible that they at least have to be such that a person not suffering the effects of an earlier irrationality would be rationally required to accept them.
    At the same time, it is logically compatible with the Oath that the demonstration will never actually be found. And it may be that earlier irrationalities are so wide-spread that even if the demonstration were given, few would be convinced.
    As for the question of the importance of natural theology, I do think it is important. For instance, beyond apologetics, it has consequences for state-and-religion issues. For instance, if the existence of God is demonstrated by reason, then it is prima facie reasonable for God to be invoked in public contexts by officials of a secular state.

    August 11, 2010 — 9:46
  • Mike Almeida

    Agnosticism lacks a truth value, because agnosticism is an attitude rather than a proposition, sentence, doctrine, belief, or some other kind of (primary or non-primary) truthbearer
    But belief (that God exists) is an attitude, too. So we might as well say theism lacks a truth-value. Is your belief in God true? One could answer, ‘attitudes don’t have truth-values’. But that’s just being oddly fussy. What the person is asking is whether the propositional object of the belief is true. Something similar happens with agnosticism, if again, we don’t get pointlessly fussy about it. The agnostic has a meta-attitude. He believes that certain beliefs are unjustified (or unwarranted, or whatnot). The object of his meta-belief is a proposition that is either true or false.

    August 11, 2010 — 12:47
  • John H.

    Alexander: I am aware that the historical trend has been the demonstrative interpretation, but I am not convinced that the dogma demands this (note: I am a Catholic). The historical trend of interpreting Extra Ecclesiam nulla salus certainly underwent a shift; I see no reason to think this couldn’t happen in other cases.
    At any rate, there certainly isn’t a dogmatic prescription to believe that Christian dogmas can be demonstrated to be revealed; there are some “motives of credibility” – such as the historical arguments Vatican I mentions – but this will not take you to faith. And it is justifying Catholic beliefs that Gutting seems particularly concerned about.
    I do think evidential arguments can justify belief that God exists, albeit not prove. However, I’m not sure this would be useful in any public context, as too few properties of God are known to provide much information about our moral obligations.

    August 11, 2010 — 12:56
  • John H.:
    “At any rate, there certainly isn’t a dogmatic prescription to believe that Christian dogmas can be demonstrated to be revealed” — Right. If anything, the tradition inclines against the idea that Christian doctrines can be demonstrated to be revealed.
    As for how many properties of God can be known by reason, I think that depends on how well the arguments in Part I of the Summa work. A number of them do seem to work, but it would be a large task, which one day I want to take up (or maybe have a grad student take up), to go through them carefully and see what can be established. The move from simplicity to the omniproperties seems very promising to me.
    Still, even if God is just known to be a supernatural creator with good ends, that might be enough to trigger a duty to be grateful to him.

    August 12, 2010 — 9:04
  • Mike:
    “The agnostic has a meta-attitude. He believes that certain beliefs are unjustified (or unwarranted, or whatnot).”
    I am not sure that’s always true. Suppose I am simply unconvinced by the arguments for and against p. Do I always then have a belief that belief and disbelief in p is unjustified? To say that in general would seem to be an unwarranted empirical generalization.
    It seems that sometimes the result of hearing the arguments is a first order attitude of being unconvinced either way, without any second order attitude of being convinced that one should be unconvinced. In fact, I am pretty sure this is right. After all, sometimes we’re unconvinced by an argument, but we are not convinced that we should be unconvinced–we allow that there might be something to the argument, and that maybe we should find it compelling, but we just don’t find it compelling.
    So one would expect that there would be some agnostics who do not have a second order belief that they are justified in being unconvinced. One might call these “diffident agnostics”. There probably are also diffident theists and diffident atheists: they find themselves believing that God does or does not exist, but they are convinced of the frailty of their rationality and hence do not commit themselves to their belief being justified. A diffident theist is a theist, and by analogy a different agnostic is an agnostic. But while the diffident theist does have a relevant belief whose truth value can be assessed–viz., that God exists–the diffident agnostic does not. Hence, not all agnostics have a relevant belief whose truth value can be assessed.

    August 12, 2010 — 9:13
  • Dan Johnson

    I’m in broad agreement with Alex and Josh in thinking that Gutting’s remarks are misleading at best. I’d like to approach it from a different direction, though: Gutting’s definition of “proof” (as a valid argument from uncontroversial premises) is quite obviously inadequate.
    First, let us suppose that mathematics is the model for what counts as a “proof,” such that no empirical scientific discovery ever counts as a proof. This is a really strong notion of proof, arguably not the notion commonly invoked in popular discussions. But Gutting’s definition is too strong even to capture this very strong notion of proof! The mere sociological fact that the premises of a mathematical proof are controverted by someone surely isn’t sufficient to deny it the status of a proof. Even the mere sociological fact that the premises are controverted by informed people surely isn’t sufficient to deny it the status of proof — the rejection of the law of contradiction by somebody very informed and smart like Graham Priest surely doesn’t mean that every argument that employs the law fails to be a proof.
    If we weaken Gutting’s definition of a proof to “a valid argument from premises it is irrational to reject,” to eliminate the problematic sociological factor from the definition, two interesting things result. (1) It is no longer widely agreed that no theistic argument meets this standard. (2) Even this standard is too strong for “proof.” Plenty of people can reject or withhold from believing mathematical premises simply because their complexity means they don’t understand them, or because their complexity means that it is easy for them to mistakenly think that there is a problem with the premise. Someone who sees more clearly may have no such problem — and I think that a valid mathematical argument employing such premises can still count as a “proof.” Arguably, the PSR has precisely these properties. It may be self-evident and yet some may withhold on it without irrationality because their comprehension (their ability to appreciate its self-evidence) is weaker than that of others.
    I don’t know how to weaken the definition further, but any further weakening will only make it easier to think that some theistic argument meets the standard of “proof.”
    Second, on top of all this, it isn’t even clear that the ordinary person’s concept of proof is this mathematical concept anyway. Almost every ordinary person thinks that science can prove things. We have a choice: we can stick to the mathematical model and say that the ordinary person is just mistaken about that, or we can admit that their concept of “proof” is broader than, perhaps merely an analogue of, mathematical proof. If so — if strong inductive evidence counts as “proof” — then many will affirm that theistic arguments meet the standard of “proof.”

    August 12, 2010 — 11:36
  • Dan:
    “Almost every ordinary person thinks that science can prove things.”
    This is fascinating! I’ve noticed this, too, and I’ve always taken it that the ordinary person is just mistaken about how science works. But maybe you’re right, and we should more charitably read the ordinary person as having a much broader sense of proof.
    After all, compare the notion of “prove beyond reasonable doubt.” This suggests two things. First, that there is a notion of “proof” operative that’s not deductive. For the things that are “proved” in court are typically not deductively proved. Second, that one can prove while allowing reasonable doubt–otherwise “beyond reasonable doubt” would be otiose.
    I now wonder what the ordinary person means by “proof”? Do they simply mean something inferential that is knowledge-conferring? Something inferential that confers practically-certain knowledge? I’d love to know. But now I must go back to my modality ms proofreading.

    August 12, 2010 — 14:13
  • Dan Johnson

    Alex, the reference to “proof” in a legal context is very helpful. If things can be “proved” in a courtroom, then surely many philosophers would think that some theistic arguments constitute proofs! And I’ll bet the ordinary person’s concept of “proof” is more tightly bound to the legal use of the term than it is to the mathematical use of the term.
    The word “proof” seems to call out for a rigorous analytic-style conceptual analysis, and this is of special importance for philosophers of religion in evaluating theistic arguments.
    I think a study of the history of the term could help some as well (though of course it wouldn’t determine the current meaning) — is the word most closely associated with mathematics historically, or did it originate in a different context?

    August 12, 2010 — 14:41
  • Mike Almeida

    But Gutting’s definition is too strong even to capture this very strong notion of proof! The mere sociological fact that the premises of a mathematical proof are controverted by someone surely isn’t sufficient to deny it the status of a proof.
    Hi Dan,
    There is no plausible reading of what Gutting is asserting that makes it true that a controverted premise is sufficient to undermine a proof. He’s talking about controverted proofs among professionals. Nor is it indicated that a premise is controversial iff. someone controverts it. This surely fails right to left.
    This aside, I think Gutting is exactly right about the notion of proof. It is not quite a mathematical proof he has in mind. What’s offered in mathematics are ‘demonstrations’, which are proofs from necessary premises. That’s the best you can have. Those are proofs of course, but so are weaker arguments whose premises are unconroversial and not necessarily true. In other cases you do not have a proof. You have an argument. That’s a distinction that is worth preserving.
    Finally, it’s regrettable the number of theists who assimilate proofs to arguments whose conclusions it is ‘rational to believe’ given the premises. The ‘rational to believe’ phrase is truly the last refuge of scoundrels. I can’t tell you the number of times I’ve seen theists obviously using that phrase for cover.

    August 12, 2010 — 19:36
  • Finally, it’s regrettable the number of theists who assimilate proofs to arguments whose conclusions it is ‘rational to believe’ given the premises. The ‘rational to believe’ phrase is truly the last refuge of scoundrels. I can’t tell you the number of times I’ve seen theists obviously using that phrase for cover.
    Mike, care to give a representative scoundrely example of such a use? This is an intriguing remark, but I’m not 100% on just what sort of phenomenon you’re talking about?

    August 12, 2010 — 20:05
  • Joshua Rasmussen

    I think Dan’s insights are right on.
    One could think that every “theistic proof” has been controverted by a relevant professional, while still thinking that some theistic proofs are as powerful (self-evident) as certain uncontraverted mathematical proofs.
    Arguing against the second thesis isn’t as easy as merely making a sociological observation (contra what my humanity’s professor freshman year seemed to think…)

    August 13, 2010 — 8:31
  • Mike Almeida

    Mike, care to give a representative scoundrely example of such a use? This is an intriguing remark, but I’m not 100% on just what sort of phenomenon you’re talking about?
    When we make estimates of what it is rational to believe given a set of premises the standard in argumentation, we’ve effectively licensed the following move: ‘utter the following words when you’re in dialectical trouble, “as I see it, it is rational to believe p based on those premises”‘ or worse “I can see how someone might find it rational to believe p based on those premises”. That dialectical move is sometimes used in good faith, but mainly it’s abused. That’s why I’d like to discourage it. It makes argumentation a little like playing chess with one additional rule: ‘if you find yourself in check, you may move your king off the board on to the mantelpiece’.

    August 13, 2010 — 8:43
  • Mike Almeida

    One could think that every “theistic proof” has been controverted by a relevant professional, while still thinking that some theistic proofs are as powerful (self-evident) as certain uncontraverted mathematical proofs.
    I don’t know, Josh. It’s hard to see much point in disputing any particular thesis if that’s true. When it’s all said and done, you may (rationally, no less) just believe what you want. It makes being a theist or being an atheist or agnostic too much like joining a club. Just join the club you like.

    August 13, 2010 — 8:54
  • Mike:
    “What’s offered in mathematics are ‘demonstrations’, which are proofs from necessary premises.”
    I am not at all sure of this. First of all, that doesn’t fit with how working mathematicians phrase their “theorems”. Here is a theorem I once published: “Let D be a simply connected domain which is reflection symmetric about the real axis and which contains the interval [0,R). Then, w_r(D) <= w_r(D*), whenever 0 < r <= R.” Before that, the paper contained definitions of w_r and D* (D* is a radial rearrangement of a two-dimensional region: basically, you slide any hole-like things in D outward from the origin to form a region D* with the property that any ray from the origin to a point in D* is wholly contained in D*; w_r(D) is a harmonic measure, which is equal to the probability that a Brownian motion starting at the origin will get distance r away from the origin before hitting the boundary of D).
    I think a reasonable way, given the practice of ordinary mathematicians (except those working in foundations and logic), is to take this not as a proof from necessarily true uncontroversial premises, but a proof from assumed premises:
    1. D is a s.c. domain in R^2 containing [0,R).
    2. (R^2,+,.) satisfies the axioms of the real line.
    3. We’re working in a set theory satisfying something like ZF. (I suspect the typical mathematician is not very clear on this, nor very clear on exactly which axioms she uses, with the exception of a clarity on whether Choice is used. For instance, I don’t think my result relies on the Axiom of Regularity anywhere–it would hold just as well in a set theory with ur-elements.)
    Now, the philosopher may want to transform this into a non-hypothetical universally quantified claim:
    (*) For every system that satisfies ZF, for every quadruple (R,<,+,*) that satisfies the axioms of the real-line, for every simply-connected domain D in R^2 containing [0,R), …
    or into a conditional:
    (**) If ZF and …, then …
    I think (*) is dubious, because it is not clear what the quantification over systems that satisfy ZF comes to. It seems to presuppose, over and beyond the paradise of sets and classes, a paradise of systems (ZFC-sets, ZFD-sets, NF-sets, etc.) And I don’t know that the working mathematician wants to be committed to that. I think (**) has more hope. But note that (**) is trivially true if it turns out that ZF is in fact false (mathematicians use “If …, then …” to indicate the material conditional in practice). However, I hypothesize this: Suppose the working mathematician reads philosophy of math and comes to conclude that ZF is false. She would not conclude that all her theorems are trivially true and that their negations are true as well. Rather, she would say: “OK, let’s go back and see exactly what assumptions from ZF I made use of in my proof, and what was used upstream in the theorems I drew on. Aha! I didn’t use the Axiom of Foundations. And that’s the axiom I now think is false. So what I really proved is not that if ZF, then …, but if ZF*, then ….” Ordinary mathematics is open to revision at the foundational level in such a way that to take it to be proving a conditional of the form “If ZF, …” seems mistaken.

    August 13, 2010 — 9:24
  • Mike Almeida

    I am not at all sure of this. First of all, that doesn’t fit with how working mathematicians phrase their “theorems”.
    Fair enough. But wouldn’t you say that the domains you describe in setting up the theorem exist necessarily, if at all? What I don’t think are assumed in mathematical proofs are contingently true premises. What’s a contingently true mathematical proposition?

    August 13, 2010 — 9:31
  • There are two places that “it is rational to believe” enters in that are worth separating. The first is with a proposed requirement that the premises of the argument be rational to believe (or maybe more strongly: it is irrational not to believe them once you understand them). The second is with replacing the deductiveness of proof with a requirement that the premises make the conclusion rational to believe (or maybe more strongly: it is irrational not to believe the conclusion given the premises, or something like that). I don’t think either of these moves need be particularly weaselly.
    The alternative to the first move is either requiring something sociological like uncontroversialness in the notion of proof, and then people in the past would have been able to give proofs of the flatness of the earth (“The earth is flat; therefore, the earth is flat”), or making the notion of proof entirely relative to one’s interlocutor (which isn’t a bad move, but I think doesn’t fit with what the people that Gutting is criticizing are doing).
    The second move seems entirely appropriate, in the ordinary sense of “proof”. For instance, suppose that the jury gets very reliable testimony to the following premises:
    1. Patrick was alive and well before Sally went into his room, and he was sleeping soundly on the bed, on his stomach.
    2. Sally went into Patrick’s room with an unbloody knife.
    3. The door of Patrick’s room was constantly observed, the windows were not openable, there were no other openings, and no one but Sally went in the door.
    4. Sally left Patrick’s room, carrying a bloody knife, and remarked to several witnesses: “Serves him right for having an affair with his accountant! I’ve wanted to kill him for years, and I’m glad I finally did it!”
    5. After Sally left Patrick’s room, Patrick was dead of a wound in his back that exactly matched the shape of the knife Sally was carrying. He was lying on his stomach on the bed, and the bloodstains were such as would be expected from his being stabbed on the back while asleep on his stomach on the bed.
    6. Patrick lacked the dexterity to stab himself in the back.
    I think that, barring further evidence, the jury would conclude they had a “proof” of Sally’s having stabbed Patrick to death. But 1-6 obviously do not entail that she did it. There is, for instance, the hypothesis that she affixed the knife on the floor, blade upwards, as a temporary art installation, and Patrick accidentally fell off his bed onto it, whereupon Sally took his body, placed it back on the bed, and wiped the bloodstains on the floor, to make herself look as a murderer, as she always wanted to see what it’s like to be in jail.
    Now, we can make the above into an explicit deductive argument about probabilities, but I think that’s not faithful to how ordinary people think.

    August 13, 2010 — 9:59
  • Mike:
    If a contingently existing structure satisfies the axioms, the theorem applies to that structure. If, for instance, it turns out (it’s looking unlikely) that spacetime is Euclidean and that the points in it are real and contingent entities, then my theorem will apply to a domain D made out of these real and contingent entities, as long as all the implicit axioms are satisfied.

    August 13, 2010 — 10:07
  • Mike Almeida

    Alex,
    If a contingently existing structure satisfies the axioms, the theorem applies to that structure.
    Well sure. But the abstract structure is the focus of mathmatical attention (the physicist might worry about the instantiation of that structure) and that abstract sturcture is necessarily existing.
    I don’t think either of these moves need be particularly weaselly.
    I didn’t say they ‘need be weaselly’, I said that they generally are so. Of course I’m speaking from arguments I’ve had with both theists and non-theists. Let me press the chess analogy further, since it’s not quite accurate as is. It is like playing chess with someone where it is agreed that, if some time during the game it seems to someone that it really should be a rule that you can move out of check onto the mantel, then that’s enough to show that it really is a legitimate move. Can you see any problems with this methodologically?

    August 13, 2010 — 11:03