Sunday, July 4, 2010

A Certain Ambiguity

I just finished one of the books I brought along for pleasure-reading during my vacation: A Certain Ambiguity, by Guarav Suri and Hartosh Singh Bal. The book touches on so many of the themes that weave through my own life and philosophical work, as well as the discussions that keep recurring on this blog, that I would recommend it to anyone who finds the issues on this blog captivating.

It is a mathematical novel—one that weaves the philosophy and history of mathematics into a story about the efforts of Ravi, an Indian college student, to understand a transformative episode in his beloved grandfather’s life (and in the process to chart the course of his own life). The mathematical dimensions of the book are captivating in their own right. Reading the book is like having an impassioned math teacher right there with you, inviting you to be as excited as he or she is about Cantor’s proofs of degrees of infinity, or the struggle to prove Euclid’s “fifth postulate” from the other four (and the subsequent emergence of non-Euclidean geometry).

But on a deeper level the book is about the light that these mathematical insights sheds on the prospects (and elusiveness) of certainty, humanity’s quest for meaning, and the complex relationship between religious faith and the kind of intellectual virtues cultivated in mathematics (and other disciplines).

At the heart of the story is the narrator’s discovery that his grandfather, a mathematician named Vijay Sahni, was arrested while visiting a small New Jersey college town in 1919. The charge against him? Blasphemy. For reasons I won’t get into, the young Vijay is motivated to get up in a public forum and discuss the absurdities of Christianity—an act that so offends the community’s sensibilities (after they had gone to such lengths to be hospitable to this strange foreigner!) that he is arrested the next day.

Of course, the New Jersey blasphemy law under which the visiting “Hindoo” is charged does not quite sit comfortably alongside the Constitutional guarantee of free speech, and there is pressure from more progressive voices for the governor to step in and dismiss the charges. The resulting clash of religious conservatives and more progressive constituencies puts the governor in a difficult political situation—one he seeks to extricate himself from by passing the buck.

He does so by sending a respected, conservative judge—a religious man named John Taylor—to review the case and make a legal recommendation concerning whether the case should proceed to trial. The judge decides he needs to interview the foreign blasphemer—and the transcripts of those interviews, along with other relevant documents and newspaper articles that the grandson Ravi uncovers over the course of the novel, tell a story about two intelligent men, one an atheist mathematician from India, the other a Christian judge from America, who form a bond of mutual respect and friendship as their exchanges become about far more than whether Vijay should be put on trial.

Judge Taylor has his own distinctive notion of how and when the blasphemy law can apply without violating the right of free speech—but to make a judgment, he needs to interview the prisoner to discern his motives. Since Vijay claims him motives are rooted in mathematics—more specifically his conviction that mathematics offers the model for how we should go about forming our beliefs—the judge ends up getting an extended lesson in Euclidean geometry. As Vijay's grandson, Ravi, is working his way through these transcripts, he is taking an introductory mathematics course on infinity—in which he is introduced to set theory, including Cantor’s proofs that while the infinite set of integers is equal in cardinality to the infinite set of rational numbers, the infinite set of real numbers has a higher cardinality. In other words, there are degrees of infinity. In fact, there are infinitely many degrees of infinity.

As the story evolves, the sticking point of Euclidean geometry—the fifth axiom, which is more complex than the first four and doesn’t quite seem as if it should be an axiom at all—becomes connected to the sticking point of Cantor’s mathematics—the so-called Continuum Hypothesis, which hold that there is no (infinite) cardinality greater than that of natural numbers but less than that of real numbers.

In both cases, the contested principle defies proof but seems right to many. And yet, when the contested principle is rejected and its negation is assumed, no contradiction emerges. A whole vista of alternative mathematical systems arises instead, depending on what you take to be axiomatic.

And then, of course, the timing of Vijay’s imprisonment takes on meaning. In one of the final documents Ravi uncovers, Judge Taylor and Vijay come face to face with Einstein’s confirmation, in 1919, that space does not conform to Euclidean geometry—that is, it does not fit with the geometry that arises when we accept Euclid’s apparently self-evident fifth axiom (which can be formulated in numerous ways, but is perhaps most simply expressed with the statement that given a line and an adjacent point, you can only draw one line through the point that is parallel to the adjacent line).

What arises is a story about the quest for certainty—for knowledge that can be founded on indubitable starting points—and the epistemic struggles of human beings to figure out what to do when apparently self-evident starting points turn out not to be self-evident after all. What does it mean for human life, for our struggle to understand our world, that we can construct equally coherent geometries or set theories (or interpretive worldviews) out of alternative starting points?

In a concluding story (told through Judge Taylor’s person journal) about the reunion of Vijay and Judge Taylor in 1930, when the judge travels to India to visit the friend he’d made in a prison cell, the still religious judge at one point asks Vijay whether he now believes in God. Here’s the response:

He smiled and shook his head. “No, Judge, that is not in my nature.” He then paused, looked me in the eye, and said, “But I can understand why someone might.”

In a way, this response captures the essence of what I’m about in my philosophical work. While not every “axiomatic system” is consistent or provides an adequate template for understanding our lives and our world, our epistemic situation does not allow us to settle conclusively on just one. Some of us gravitate towards a system of one kind, while others gravitate towards another. It is often hard, once we are enfolded within a functioning axiomatic system, to see it as anything other than the indubitable truth, and to see those who disagree with it in favor of an alternative system as deeply misguided, as caring more about psychological comfort than about truth, or as indoctrinated by some cultural ideology. But while these psychological forces are often at the root of our outlooks, the reality of our epistemic situation is much more complex than the way it appears to be from the vantage point of one particular axiomatic system.

My hope, in the grand scheme of things, is that we will come to see this complexity, and so, in the process, be able to say of those who see the world differently, “It is not in my nature to look at things that way, but I can understand why someone (a reasonable person) might.”

In any event, I recommend the book to anyone interested in these issues.(My copy is from an Indian friend, but it looks as if an American edition will be released at the end of this month).


  1. Hi, Eric-

    "(a reasonable person)"

    Therein lies the conclusion that begs the question. Perhaps we can best understand why someone holds some set of different beliefs by assuming that they are not being reasonable about an issue. They may be holding demonstrably irrational or fabulistic beliefs. Such things are not unprecedented, like in the many debates that roil our channels of disinformation- smoking, climate change, evolution, fear of deficits, etc.

    Debate is essential, but at some point, the persistence of intuitive (or self-interested) notions that have insufficient support (e.g. the fifth axiom) begins to look more like psychological attachment than an even-handed exploration of alternate axioms (axia?).

  2. Burk,

    This is the chief bone of contention between us. You are convinced that persons who disagree with your position on certain key matters (e.g. the truth of materialism, the illusory character of free will) are being selectively unreasonable (and, it seems, the only refutation of this view you'll accept is one which aims to show that YOU are the one who is being selectively unreasonable). On these and a range of issues you are convinced that reasonableness only permits one position on the matters.

    While I obviously do think that people can be unreasonable in the positions they adopt, I also think there are areas where reasonable people, BEING reasonable, can adopt disparate perspectives.

    The position you adopt with respect, for example, to beliefs about the transcendent, irks me--not that you deny the veridicality of such beliefs, but that you want to attribute (selective) irrationality to all those who adopt such beliefs. This irks me not merely because the implication is that you think I am being selectively unreasonable, but because it is at odds with my considered judgments about the human epistemic situation--judgments which I've arrived at by wrestling earnestly for years with the question of the scope and limits of human knowledge, and which I find to be far more sensible in the face of human fallibility and cognitive limitations than the understanding advocated by the new atheists, you, religious fundamentalists, etc.

    It also irks me on a more profound level in relation to my years of work in nonviolent conflict resolution. But that is probably an issue for another time.

    In any event, Kant has been influential in shaping my understanding of our epistemic situation, but so has Hegel--which is why I mean to say more about some of his relevant thoughts on this matter soon.

  3. Burk said:

    "Perhaps we can best understand why someone holds some set of different beliefs by assuming that they are not being reasonable about an issue."

    This is a direct contradiction of what is standard practice for philosophers. I majored in philosophy, and we are taught to use what is called the "principle of charity." Roughly speaking, when examining an argument, one should construe an opponent's argument in its strongest possible form, and criticize on that basis.

    Invoking selective stupidity in order to "understand" someone's argument would get you a failing grade in a college philosophy class, and doing so leaves you wide open to finding "flaws" in arguments that are not actually there.

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  5. Evan, Burk and I already had that discussion; I guess it didn't take...

    And the book sounds really interesting, thanks for the recommendation.

  6. Hi Eric, this is off topic:

    William Lane Craig gave a lecture on “Beyond the Big Bang”, in which he presents his KCA. The entire lecture is on youtube and I figured I would share it with you.

    I know you can’t stand WLC authorial voice, but I’m hoping it will be easier on you if you can see Craig talking. Then again, maybe it will be worse?

    Part 1 of 6 of main lecture:






    Q/A part 1 of 4:




    If you're able to watch it, please let me know what you think.

  7. On reflection, I'm thinking we may not be applying the principle of charity to Burk's comment here. The most charitable reading of his comment is not that we should START by assuming that someone is being unreasonable about an issue, but rather that one might eventually come to the conclusion that the best way to understand why they have the commitments they have is to postulate psychological motivations for belief that have nothing to do with the reasonableness of the belief.

    And this is surely correct. But one needs to be careful about a few things:

    1) One shouldn't fall prey to the genetic fallacy, that is, the fallacy of rejecting the substance of what someone says based on what motivated it.

    2) One shouldn't conclude that someone is being selectively stupid simply because their views are derived from an axiomatic framework one does not personally accept.

    3) One shouldn't assume that someone's beliefs are unreasonable simply because they conflict with another person's beliefs that ARE reasonable. That is, one shouldn't simply assume that rationality operates in an exclusivist way, such that in disagreements at most one party can be reasonable.

    In brief, the conclusion that someone is being motivated by irrational considerations should be arrived at with great caution, after one has invoked the principle of charity, and after one has studied the person's thinking on its own terms--that is, after one has really tried to see things from their position (as opposed to, say, using one's own position as the standard of rationality and finding their view wanting because it doesn't measure up to that standard).

  8. I see your point. But I guess my biggest problem with assuming someone is being unreasonable, even as a "last resort" used with great caution, is that too often "unreasonable" is simply a code-word for "I disagree with it" or "I don't understand it," while "reasonable" is a code for "an answer which fits within my world-view." A perfect example: today in a bookstore I browsed through one of the innumerable books that are in vogue lately about "the evolution of religion," which promised a "perfectly rational explanation" for the whole phenomenon of religion, as contrasted with a "supernatural" one, in the book-jacket's words. This is an example of what you were talking about, Eric, where answers other than the ones a certain person or group prefers are deemed "irrational" because they do not fit with a certain way of viewing the world. I guess my point is that I would be reluctant to say that someone was being "unreasonable" as an explanation for their beliefs, barring evidence of genuine mental illness or disturbance, because I recognize that I myself am potentially just as prone to label ideas outiside my worldview as "unreasonable" as was the author of that book on the "evolution of religion" that I looked at.

  9. Eric

    What I like most about this blog is well captured by the above discussion. It strikes me that you are attempting to promote the kind of informed discussion that not only allows but indeed encourages disagreement. So while I don't always agree with your views, I find that with a little application I am able to get a sense of why we differ, and in doing this I get to try out and modify my own views as I go. That is to me a tremendous luxury and I want to thank you for that.

    There are many many things I am uncertain about, and I am aware of places in my own thinking where leaps of faith, patching over of contradictions and fastidious ignoring of implications have been put in place as a sort of temporary fix until my understanding improves. I am sure that when my time is up many of these will necessarily remain in place. (I act as though others have agency above and beyond that sanctioned by my deterministic views for example, I can not bring my heart to support the sort of moral relativism my head leads me to, I embrace science for pragmatic reasons yet hesitate to endorse other forms of pragmatism and so forth).

    So, given all of this, of course reasonable people will disagree with me, and frankly if they did not my learning would stall. Why seek that?

    What you are doing here is an excellent example of the teacher's craft. Again, thank you.


  10. Thanks Eric-

    Of course psychological arguments should not be a first resort, since charity, as you say, prompts us to take our interlocutors as sensible beings offering rational argument, especially if they say they are. And it could be our own limitations that lead someone else's argument to not make sense. That is hard to discount, unless one's argument really is based on logic and evidence in some demonstrable way.

    But when we introspect, retrospect, or hear about ourselves from others, we recognize that our reasoning is frequently afflicted by psychological biases, such as confirmation bias, unexamined premises, arguments from authority, self-interest, mood disorders, blind adherence to tradition, and narcissism in general. That is the great virtue of discussion, critique, and especially evidence, which provide outside perspectives, and ideally even unbiased tests, of our ideas and claims. For which I thank you!

    So it is salutary to recognize the power of psychological biases. And what better exemplifies them than the history of religion, with its intensely imaginative parade of gods, doctrines, and certainties of which you believe virtually none, even while attempting to salvage some precious core? Why all this delusion? You would have to agree that something psychological has been, and is still, going on.

  11. Burk, you write:

    "That is the great virtue of discussion, critique, and especially evidence, which provide outside perspectives, and ideally even unbiased tests, of our ideas and claims. For which I thank you!"

    And therein lies the problem. "Evidence" does not provide an "outside" perspective, unless one has the uncanny ability to step "outside" oneself. All evidence is interpreted evidence. And, that is what allows you to write:

    "So it is salutary to recognize the power of psychological biases. And what better exemplifies them than the history of religion..."

    Of course, one could also talk about the psychological bias of philosophical naturalism, but such is lost on the person who believes that everyone else is biased but himself. As I’ve pointed out many times before, if you or anyone else on this blog is aware of some “evidence” or “fact” that theists/Christians are not, as to God’s existence or nonexistence, please do tell. You could wrap up this whole, “does God exist or not” question rather quickly. Since you have been unable to answer that question, perhaps you should move on from the “I base my beliefs on the evidence,” while everyone else is irrational and to be pitied- response to everything.

    Eric would caution me here that charity requires a different response, but as I read Burk and Rich Griese’s responses in most of these posts I would have to summarize their position as basically equating to this assertion: “You know what’s wrong? Everything I don’t understand.”

  12. Hi, Darrell-

    Yes, quite so. But I think the qualities of the evidence differ, leading to my mantra. The theist evidence with regard to mind questions typically amounts to ... it feels like there is something special going on in my head (or in the heads of famous mystics) that there is no natural explanation for, ergo it is reasonable to make supernatural claims.

    This just seems rather light-weight to me, not to mention prone to all sorts of psychological biases, special pleading, and sophistic constructions. History is full of intuitions which we have had to wrench out of their original tracks in light of better knowledge. My intuition is still that the earth is flat, after all!

    On the other hand is all the evidence that minds happen in the brain, with ever-increasing precision from interventions, scanning, unfortunate accidents, and so forth. Also the general evolutionary argument about how brains and minds came to their current state. All this is so much more solid and determinative that keeping with our admittedly age-old and venerable intuition/superstition seems untenable.

    But that is just me and my reading of the evidence, even the meta-evidence, as it were. If something more interesting and solid comes along against naturalism, I will be highly interested, of course.

  13. Burk,

    You write: "qualities of the evidence differ, leading to my mantra."

    You miss the point. Again, the evidence and what you would consider is "quality" or the "best" evidence is known by theists and Christans. You agree, correct? If not, please tell us which piece of evidence it is we are unaware of.

    If you do agree however, then it comes down to the question of why we interpret the evidence differently. If so, you need to move on from the "I, the rational actor, base everything on the evidence and the rest of you have psychological issues" approach to everything. Not the best way to gain a hearing by the way.

    Putting that aside, since you don't believe in Free-Will, how do you know that your belief in philosophical naturalism is not simply a psychological bias? If you say, "Because I know it is true based upon the evidence," you are simply begging the question.

    Further, if there is no Free-Will, then it matters little if you believe in such things as "truth" or "reason" or even "evidence" as there is no way to discern whether or not you would or could choose to use "reason" or choose to know the "truth" or choose the best interpretation of the "evidence." Beyond that little problem, it assumes there is a "truth" to choose, a "best" way to use reason, and a "best" way to interpret evidence. That is even a bigger problem for you. You haven't even scratched the surface as to how your philosophical naturalism is even plausible. The hurdles are insurmountable in my view. That is why it is almost comical the way you throw the word "evidence" around. It doesn't help you in the slightest. Move on.

  14. Dustin,

    You write: “So I guess if it not evident to you that you are having subjective experiences, we can go ahead and say that you are not going to be impressed by the argument. Of course, this doesn't make the argument pointless, because the vast, vast majority of people will agree that it is self-evident that they are having subjective experiences.

    If I understand Bernard’s position correctly, what he means is not that he is not sure that he has subjective experiences, but rather that he is not sure that his subjective experiences are anything over and above his body’s physical processes and/or predispositions to behave in a certain way. So, he figures, by understanding the latter better (which is an ongoing scientific project) we *may* find out that subjective experience really is nothing more that these physical processes and/or predispositions.

    I have the feeling that many naturalists, when confronted with the famous problems related to the philosophy of mind, make the following inductive argument: There have been many cases in the past where science explained on purely physical grounds phenomena which everybody thought must have a transcendental source. A famous example is how people used to think about living things: "The behavior of living things is so dramatically different than the behavior of non-living things, that it can’t possibly be the case that living things consist of exactly the same kinds of physical bits that non-living things consist of and nothing more. Rather some non-physical 'breath of spirit' or 'life force' or 'soul' must exist which animates non-living matter and makes it a living organism." Yet science proved that no such non-physical things were necessary to explain life, for, as we now know, life is nothing more than a complex but entirely physical electrochemical reaction. Similarly, consciousness does now appear to be a phenomenon that is so different from everything else that it can’t possibly be explained on purely physical grounds. But, as has been the case so many times in the past, science may yet find a way to explain consciousness on purely physical grounds. Indeed brain science is discovering knowledge about the most complex thing there is in the universe, namely the human brain. Perhaps future discoveries will be such that all mysteries related to the mind will simply evaporate. Given the huge success of science in the past, how can we be certain that science won’t surprise us once again?