Sunday, July 24, 2011

Grow up or shut up

I’ve pointed out that the argument so many atheists like to attack when they purport to refute the cosmological argument -- namely “Everything has a cause; so the universe has a cause; so God exists” or variants thereof -- is a straw man, something no prominent advocate of the cosmological argument has ever put forward.  You won’t find it in Aristotle, you won’t find it in Aquinas, you won’t find it in Leibniz, and you won’t find it in the other main proponents of the argument.  Therefore, it is unfair to pretend that refuting this silly argument (e.g. by asking “So what caused God?”) is relevant to determining whether the cosmological argument has any force.    

I’ve also noted other respects in which the cosmological argument is widely misrepresented.  Now, in response to these points, it seems to me that what a grownup would say is something like this: “Fair enough.  I agree that atheists should stop attacking straw men.  They should avoid glib and ill-informed dismissals.  They should acquaint themselves with what writers like Aristotle, Aquinas, Leibniz, et al. actually said and focus their criticisms on that.”  But it would appear that Jason Rosenhouse and Jerry Coyne are not grownups.  Their preferred response is to channel Pee-wee Herman:  “I know you are, but what am I?” is, for them, all the reply that is needed to the charge that New Atheists routinely misrepresent the cosmological argument.  

In particular, Rosenhouse, who is curiously silent on this charge -- though it is, after all, the point at issue -- has decided to change the subject.  Like the teenager who, when caught red-handed with the evidence of his drug use, responds by criticizing Mom and Dad’s drinking habits, Rosenhouse  works himself into an adolescent dudgeon over how I’ve allegedly misrepresented Robin Le Poidevin.  And how exactly have I misrepresented him?  That is never made clear.  I said that Le Poidevin presents a variation of the straw man as if it were “the basic” cosmological argument.  And he does.  I said that Le Poidevin presents the “more sophisticated versions” he considers later on in his book as “modifications” of that straw man.  And he does.  I did not deny that Le Poidevin addresses these more sophisticated versions.  I explicitly noted that he does.  Nor did I say that Le Poidevin claimed that Aristotle, Aquinas, Leibniz, et al. actually defended the straw man argument themselves.  Indeed, I quoted Le Poidevin as acknowledging that “no-one has defended a cosmological argument of precisely this form.”  Rather, I said that readers who are unfamiliar with what Aristotle, Aquinas, Leibniz, et al. actually wrote are liable to come away from a discussion like Le Poidevin’s with the false impression that what the major defenders of the cosmological argument are up to is, essentially, merely an attempt at a patch-up job on a manifestly feeble argument.  And I explicitly said that I was not claiming that Le Poidevin was deliberately trying to give this false impression, but rather that he should know better. 

So, again, how exactly did I misrepresent him?  It turns out that Rosenhouse’s real complaint, to the extent he has any, reduces to another adolescent trope.  My problem, you see, is that I need to lighten up.  I’m “overreacting” to what was merely a “pedagogical” exercise on Le Poidevin’s part.  Beginning his treatment of the cosmological argument with the straw man was simply Le Poidevin’s gentle way of ”introducing” a complicated topic to undergraduates.  

Well, we all know why this dodge won’t work.  Suppose a creationist writer began his exposition of Darwinism by presenting the claim that “Monkeys gave birth to humans” as “the basic” claim of the theory, of which the “more sophisticated versions” of Darwinism he would consider later were variants.  Naturally, he would have little trouble showing that this claim (which no Darwinist has ever made) is false.  But suppose he defended this odd approach as merely a “pedagogical” technique for “introducing” Darwinism to his readers.  And suppose he also held that any biologist who finds this procedure outrageous is merely “overreacting.”  Rosenhouse and Co. would, quite rightly, be unimpressed.  And neither should we be impressed by Rosenhouse’s lame defense of Le Poidevin. 

To be sure, Rosenhouse thinks he has preempted such a comparison: 

The claim that a monkey gave birth to a human is not an oversimplified version of Darwinism that might serve as a helpful stepping stone into a complex topic.  It is just a completely made up idea tossed off specifically to make evolution look foolish.  

But of course, this is no answer at all, but merely reinforces my point.  For the straw man version of the cosmological argument we’ve been discussing is no less a completely made up idea, one tossed off to make the cosmological argument look foolish.  How do we know this?  Well, here’s some pretty good evidence: First, as I keep pointing out -- and, you will note, as Rosenhouse and his ilk never deny (because they can hardly deny it) -- Aristotle, Aquinas, Leibniz, and the other prominent defenders of the cosmological argument never gave the straw man argument.  Second, the only people who ever do pay the straw man argument much attention are atheist critics of the cosmological argument, and they typically present precisely it as a reason to dismiss the cosmological argument as foolish.

So, the cases are parallel and Le Poidevin’s procedure is no more defensible than that of our imaginary creationist.  No doubt Rosenhouse, as is his wont, will at this point just stamp his foot some more.  “The cases are not parallel!  Are not!  Are not not not not not!” 

But then, Rosenhouse isn’t one to notice when he’s merely making unsupported assertions or begging the question.  For example, in an earlier post, he had written: 

Feser seems rather taken with [the cosmological argument], but there are many strong refutations to be found in the literature.  Off the top of my head, I found Mackie's discussion in The Miracle of Theism and Robin Le Poidevin's discussion in Arguing for Atheism to be both cogent and accessible. 

I then pointed out that this merely begged the question against defenders of the cosmological argument, which (given the context) it quite obviously does.  But the obvious is never obvious enough for Rosenhouse, who in his latest post writes: 

My point was simply that I think the cosmological argument is not very good, and that I think Mackie and Le Poidevin provided cogent and accessible refutations of it.  How could I have been clearer?  I have no idea what question I was begging by expressing those particular opinions. 

Well, Prof. Rosenhouse, here’s a clue:  Whether the cosmological argument is “not very good” and whether writers like Le Poidevin and Mackie have actually “refuted” it are precisely what is at issue between yourself and defenders of the cosmological argument like me.  And merely to assume some proposition which is at issue instead of arguing for it -- as you did when, in response to my advocacy of the cosmological argument, you asserted matter-of-factly that the argument had been “refuted” by the likes of Mackie and Le Poidevin -- is a textbook instance of what logicians call “begging the question.”  But then, in between all those volumes on Aquinas and Leibniz you haven’t read, it seems there are a few logic textbooks you haven’t gotten to either.

Those who are interested in other curious examples of undefended assertion are directed to the rest of Rosenhouse’s post.  But beyond providing us with Exhibit 2,345 of the Higher Cluelessness that is the New Atheism, Rosenhouse’s remarks on this controversy are absolutely devoid of interest.  As I’ve said, in response to the points I made in my earlier post, an atheist who is also a grownup would at least be happy to acknowledge that atheists should not attack straw men and should deal instead with what the major defenders of the cosmological argument actually said.  Yet Rosenhouse can’t even bring himself to do that much before launching into his botched “Gotcha!” exercise.  And that pretty much says it all.

609 comments:

  1. One Brow,

    "You can offer personal judgments about the values of one result or another, but that won't change the autonomy of the practice of mathematics."

    I've tried to make it clear that my interest in this issue is about how math-truth relates to nominalism. If math is supposedly 100% autonomous then there is no standard by which we can test its truth claims. It might as well be astrology. So if grodrigues is correct, then mathematics poses no problem for nominalism. If I'm correct, it poses no more of a problem for nominalism than words like "apple" do. Either way, math itself is irrelevant in the nominalism debate.

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  2. @djindra:

    "If it's just a matter of appealing to a favored philosophical school, I choose empiricism in this matter. Clearly you don't accept that. So your "answer" says nothing."

    I have purposely strayed away from the philosophical foundations of mathematics. I explicitly stated that there are other sources to justify the axioms and, what is more important, I simply do not need to make appeals to philosophy to show that mathematics is an autonomous discipline, which is another, different question, from the justification of its axioms. The fixation with nominalism is yours, not mine -- I never set out to refute it, or to defend any philosophy of mathematics for that matter. Nominalism is simply irrelevant to the question of the autonomy of mathematics.

    As far as the core of the dispute, according to you, what I have said about the autonomy of mathematics is not a fact. Since we are talking about matters of fact, it should be pretty easy to establish that you are right and that I am wrong. You only have to do two things:

    1. Show that you understand what is meant by autonomous discipline.

    2. Show that mathematics is not an autonomous discipline.

    Responses such as an appeal to examples of applied mathematics do not work. I never disputed that there is such a thing as applied mathematics (this is misnomer, but for my purposes here let this pass) and it matters not one whit to the autonomy of mathematics. Or in other words, it only matters *if* you can show that *all* mathematics, as practiced by mathematicians today, is nothing but applied mathematics. Either way, put up or shut up.

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  3. djindra said...
    I've tried to make it clear that my interest in this issue is about how math-truth relates to nominalism.

    That's simple. Mathematics is a formal discipline, like logic, philosophy, or law. Mathematical truths are determined by consistentcy/provability within the preferred axiom system using teh preferred truth calculus, much like the truths of philosophy, logic, or law.

    If math is supposedly 100% autonomous then there is no standard by which we can test its truth claims.

    You are correct. Formal systems can be relatively reliable or unreliable models of reality, but they are not tested in ther sense scientific theories are tested, in part becasue the nature of formal systems is to make no empircal claims.

    It might as well be astrology.

    Last I checked, astrology made empircal claims. So no, not like astrology.

    So if grodrigues is correct, then mathematics poses no problem for nominalism. If I'm correct, it poses no more of a problem for nominalism than words like "apple" do. Either way, math itself is irrelevant in the nominalism debate.

    Since you can adopt a nominalistic or and realist apraoch to mathematics, and still do mathematics, I agree mathematics is irrelevant to the "nominalism debate". On the other hand, since nominalism and realism themselves are merely formal constructs, how could it be otherwise?

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  4. Grodrigues:

    >> You insist on using adjectives like "true" and "false" (no capitalization this time) in an equivocal manner. That some branch of mathematics has some practical application does not make it more true in any reasonable sense of the word. In particular, your statement "without it, mathematics is just spinning its wheels in the air without traction" is one of those sloven illiteracies that only someone who does not know or understand mathematics can produce.

    As I mentioned above, there are a number of senses of “true” when it comes to mathematics. There is true1, which is true relative to the assumptions of a particular system. There is true2, which is true relative to real state of affairs in the world. That Harry Potter wears glasses is true1, but not true2, for example. Sometimes true1 is coextensive with true2, such as mathematical theorems that are applicable to empirical reality. In other words, all cases of true2 must be true1, but not all cases of true1 must be true2.

    My argument is that mathematics is always true1, but not always true2. I am more interested in truth2 than truth1, because truth2 actually refers to independent reality, and is what most people mean when they say that something is “true”.

    >> Mathematics is an independent and autonomous discipline, with its own conceptual framework and its own standards of value. It is not the handmaiden of whatever discipline you think more important.

    I agree with everything that you just wrote. However, one can also say that literary criticism is equally “an independent and autonomous discipline, with its own conceptual framework and its own standards of value”. Does it follow that the conclusions of literary criticism are true2? Of course not. (See: Potter, Harry.) If your focus of interest is truth1, then be my guest and knock yourself out. If your main interest is in coherence rather than correspondence, then I will not denigrate your interests or your efforts. All I can say is that I am equally interested, if not more so, in truth2 and correspondence to reality than in truth1 and logical coherence.

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  5. @dguller:

    "As I mentioned above, there are a number of senses of “true” when it comes to mathematics. There is true1, which is true relative to the assumptions of a particular system. There is true2, which is true relative to real state of affairs in the world."

    You insist on the mistake of using the word "true" equivocally. There is only one of sense of truth when it comes to mathematics. What you call true2 is either meaningless or completely circular. That Euclidean Geometry is true of the world, just like that, without any extra qualifications, is a meaningless statement. What is true or false, as far as it concerns the outside physical, mind-independent world is that some model or physical theory that happens to use Euclidean geometry is true or false, in the sense that it is falsified or not by the observations -- what we can call empirical truth. That some model or physical theory is true or false has nothing to do with the mathematical truth of Euclidean geometry or whatever mathematical theory it happens to use; it is a category mistake to confound the two.

    "My argument is that mathematics is always true1, but not always true2. "

    This is not an argument, it is a statement, and as I said, a meaningless one.

    "I am more interested in truth2 than truth1, because truth2 actually refers to independent reality, and is what most people mean when they say that something is “true”."

    So you are interested in mathematics only as it concerns what we usually call the natural world? That is a fairly common attitude among non-mathematicians. As far as your last statement, I doubt very much that that is the sense of truth that most people think of, but that hardly matters. And for the record, what you call truth1 or mathematical truth, is also an independent reality in the sense that mathematical truth is not subjective or dependent on the vagaries of historical or cultural contingency. In fact, mathematical truth, contrary to empirical truth, is necessary truth and as such eternally true: if the premises are true (including the premises that are usually left implicit, like the basic axiomatic system in which we are working), the conclusions are true.

    "However, one can also say that literary criticism is equally “an independent and autonomous discipline, with its own conceptual framework and its own standards of value”."

    Indeed it is.

    "Does it follow that the conclusions of literary criticism are true2? Of course not."

    This is a stupid (and yet, revealing of your confusion) analogy for the simple reason that *no* literary critic (or anyone else for that matter) has ever contended that the statements produced by the literary criticism are empirical truths or even more generally, truths about the "real world". Methinks, you are fighting mere figments of your imagination.

    "If your focus of interest is truth1, then be my guest and knock yourself out. If your main interest is in coherence rather than correspondence, then I will not denigrate your interests or your efforts. All I can say is that I am equally interested, if not more so, in truth2 and correspondence to reality than in truth1 and logical coherence."

    Do not turn the tables; I never expressed a value judgment about what is more interesting or important so telling me to "knock myself out" is completely misplaced. You on the other hand, have made it quite clear what is more interesting and important to you. As I said, opinions like that are perfectly normal, even healthy and defensible, at least up to a certain point.

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  6. Grodrigues:

    You insist on the mistake of using the word "true" equivocally.

    How is that possible when I have specified unequivocally what the two senses of “true” are that I am using?

    There is only one of sense of truth when it comes to mathematics. What you call true2 is either meaningless or completely circular. That Euclidean Geometry is true of the world, just like that, without any extra qualifications, is a meaningless statement.

    This may help.

    Euclidean geometry states that the internal angles of a triangle will add up to 180 degrees. This is a truth of mathematics, or what I would call an example of true1. Say I was to draw a triangle with a ruler, and then add up the internal angles, and they added up to 180 degrees. I contend that I can say that the Euclidean geometric truth is equally true in the empirical world, and thus is true2.

    It is like deducing a hypothesis from some assumptions, and then testing it to see if the world works in the way that the hypothesis predicts. The hypothesis, having been deduced from assumptions, is true1, but we are interested in seeing if it is equally true2, because we want to know if we can use that information in our lives in the material world.

    This is all that I mean, and I honestly cannot see how this is meaningless. Either mathematical truths, which are all true1, can also be confirmed to be operative in the empirical world, and thus be true2, or they cannot, and then they are just true1.

    As far as your last statement, I doubt very much that that is the sense of truth that most people think of, but that hardly matters.

    I know that when someone tells me that it is raining, what I think of is that the proposition, “it is raining”, is derived from assumptions according to the rules of logic and reason. But anyway, this “hardly matters”, unless you want to remain dry.

    And for the record, what you call truth1 or mathematical truth, is also an independent reality in the sense that mathematical truth is not subjective or dependent on the vagaries of historical or cultural contingency.

    I can agree with that. So maybe I have to add a true3 to my zoo of truths, i.e. “not subject to variation according to historical and cultural changes”. In that sense, what is true1 and true2 would also be true3.

    In fact, mathematical truth, contrary to empirical truth, is necessary truth and as such eternally true: if the premises are true (including the premises that are usually left implicit, like the basic axiomatic system in which we are working), the conclusions are true.

    And Harry Potter will have glasses and lightning bolt on his forehead for all eternity, given the assumptions of Rowling’s imagination. That is why I would put mathematical truths and literary truths in the same category of true1.

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  7. grodrigues:

    This is a stupid (and yet, revealing of your confusion) analogy for the simple reason that *no* literary critic (or anyone else for that matter) has ever contended that the statements produced by the literary criticism are empirical truths or even more generally, truths about the "real world". Methinks, you are fighting mere figments of your imagination.

    First, that is irrelevant to the argument. Just because someone claims to be doing X does not mean that they are, in fact, doing X. A homeopath claims to be utilizing the law of opposites to heal illness, but that is not what they are doing at all, because it is all placebo.

    Second, literary critics’ work is operative on the assumption that they are describing a fictional world that does not exist in our world, but can still be objectively described and debated about. In a sense, this is similar to mathematicians, who study a mathematical world that also does not exist in our world, because its subjects are perfect and immutable, whereas our world is imperfect and mutable. I’m afraid that there are parallels between the two fields. And the bottom line is that I have no problem with either of them studying their respective worlds, but I reserve special respect for the conclusions of either that happen to also be operative in our empirical world, because we can use them to implement changes to better our lives.

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  8. @dguller:

    "There is only one of sense of truth when it comes to mathematics. What you call true2 is either meaningless or completely circular. That Euclidean Geometry is true of the world, just like that, without any extra qualifications, is a meaningless statement.

    Euclidean geometry states that the internal angles of a triangle will add up to 180 degrees. This is a truth of mathematics, or what I would call an example of true1. Say I was to draw a triangle with a ruler, and then add up the internal angles, and they added up to 180 degrees. I contend that I can say that the Euclidean geometric truth is equally true in the empirical world, and thus is true2."

    Since you cannot point to any triangles in the real world, to do what you propose you have to interpret what a mathematical triangle is in the real world, in other words, you have to have a model or a physical theory to mediate between the mathematical and the real world. The reason you are blinded to this simple fact is that the examples you have in mind are deceptively simple and the interpretative act seems so obvious that pointing out is just pedantry. But things are more complicated when you start talking about Hilbert spaces and self-adjoint operators (quantum mechanics), manifolds and Riemannian metrics (general relativity), connections on vector bundles (Yang-Mills gauge theories), spin networks (loop quantum gravity), etc.

    To take up your example; suppose you draw a triangle, measure the internal angles and do *not* get 180 degrees -- for example, if you drawed the triangle in the surface of the earth. You will *not* say that Euclidean geometry is "false"; you will simply realize that your model is botched and that using Euclidean geometry is wrong. Or to put it in other words, there is no falsifiability criterion for mathematical statements, which is obvious since they are not statements about the physical universe. That is why your talk is either meaningless, or if you add qualifications like you did in your example, then you are talking about truth of the model or physical theory, not truth of the Euclidean geometry, at least not in any reasonable sense of the word.

    "As far as your last statement, I doubt very much that that is the sense of truth that most people think of, but that hardly matters.

    I know that when someone tells me that it is raining, what I think of is that the proposition, “it is raining”, is derived from assumptions according to the rules of logic and reason. But anyway, this “hardly matters”, unless you want to remain dry."

    My bad here. "Hardly matters" should be "hardly matters for the point I want to make", or "I am just nitpicking".

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  9. doesn't cosmological argument say that "everything that HAS A BEGINNING needs a cause"?
    Or put it in different terms, only contingent beings need cause.
    Since God does not have a beginning, and is not a contingent being, He does not have, nor need, a cause.

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