I’m delighted to see that Freddie deBoer and Led-the-commenter have delivered excellent pushback on a weak point of my previous post. Their point in brief is that the mere fact that our contingent minds have had remarkable success in explaining the universe so far is no guarantee that they will continue to experience such success. Moreover, it is possible that there are deep fundamental questions that we will never even be able to posit, much less solve.
On these two points, I concede entirely. Both of them are correct! They are not, however, as disastrous for my argument that epistemic despair is unwarranted as they may at first seem. As I said before:
Contingent minds merely undermine the necessity of our being able to comprehend the world … they leave open, however, the possibility of contingent minds that “just happen” to be of the sort that can make sense of the universe in which they happen to be located. Nevertheless, Freddie is right about one thing: once we eliminate necessity, we need reasons to think that our minds are of the right sort;
My post was an attempt to provide such a reason. Not a proof, mind you, but suggestive evidence. It may help to consider my approach to be Bayesian. The mere fact that the sun has risen every day that I’ve been alive is not proof that it will continue to do so, but with a fairly modest set of prior epistemological commitments, it’s reason enough to think that my belief that the sun will continue to rise is justified. Similarly, the prior success of science in describing the universe is not a proof that fundamental reality is accessible to us, but it is, to me at least, strong evidence that our minds are not wholly disconnected from reality as some of the formalists and constructivists would have us believe.
Freddie’s and Led’s challenge still warrants investigation, however, and today is a particularly fruitful day on which to consider it. Today is Great and Holy Saturday, when our thoughts are drawn to the small band of disciples who along with Mary gathered outside the tomb of Christ, waiting and hoping for the resurrection of the Lord, their presence motivated by nothing more than a promise. What Freddie and Led have nicely pointed out is that mathematics and science are based on a similar kind of promise.
I recall another Saturday, several years ago, when I was in college and trying to decide whether to take the plunge and become a math major. Late that night, I ran into an inebriated grad student who, as it happens, was writing his dissertation on non-foundational set theory. The two of us chatted, and I explained my dilemma. His first question was blunt, in the manner of mathematicians: “Are you smart enough?”
“I think so,” I replied, “it seems like most of the hopefuls get weeded out by the first class that requires them to do abstract proofs, and I have no trouble with that, so I should be fine, right?”
He smiled drunkenly and shook his head. ”No, proving things is the easy part.”
He was right of course, the difficulty of proof pales in comparison to the difficulty of stating what you wish to prove. Mathematicians since well before Hardy have been publishing paeans to proof as a creative and intuitive process, but trying to determine which questions are mathematically interesting is a far more daring act. The aesthetic and analytic faculties must operate in full concert, fueled by the belief that what seems like it should be true actually is true… and provable.
Mathematicians have struggled with these doubts ever since Gödel showed that all that is true is not provable and, more importantly, since Matiyesevich and Chaitin showed that many interesting true statements are unprovable, rather than just Gödel’s artificial corner-cases. Setting problems and working as a mathematician, however, requires a further faith — a faith in the overall coherence of mathematics and in our ability to apprehend it.
I think the proper scientific analogue is nicely raised in Max Tegmark’s excellent paper on neo-Platonism. In order to work, the physicist must believe that we do not reside within the “physics doomed” quadrant of the diagram on page 12 of that paper. The point is that physics and mathematics are both epistemologically daring activities. I’ll hasten to add that this in no way implies the truth or validity of the particularly bold prior commitments that the physicist and the mathematician hold, consciously or unconsciously. Freddie and Led have done us a service by reminding us of just how non-foundational these enterprises are. They rest on strong basic beliefs about the nature of the universe and the nature of our minds.
The inevitable response, and one that I expect to see in the comments, is that philosophers of physics and philosophers of mathematics have come up with systems within which these activities make sense even if they are divorced from Truth. Some of these systems even give explanations for the observed coherence, consistency, and success of these fields without making any appeal to correspondence with reality.
This is entirely true, and I won’t contest it, what I will say is that however successful these systems are philosophically, they are laughably out of line with the psychology of actual, practicing mathematicians and scientists. Anecdotally, I have never met a mathematician who, when asked what he does for a living, says: “I shuffle formal symbols in arbitrary patterns that are internally consistent and make sense to me.” Nor have I met a physicist who would reply: “I make tautological statements about internal questions related to the socially constructed version of reality that I’ve received.”
Is it psychologically likely that somebody who holds such beliefs would go through the trouble of doing mathematical or scientific research? I doubt it, in my experience they tend to become philosophers of science or mathematics instead. For a less anecdotal take on this, I’d recommend Feyerabend and Norris.
April 3rd, 2010 | 6:18 pm
[...] This post was mentioned on Twitter by Damir Tankovic. Damir Tankovic said: The Peculiar Faith of the Mathematician or Scientist » Postmodern … http://bit.ly/boi9Q0 [...]
April 3rd, 2010 | 6:22 pm
“Nor have I met a physicist who would reply: “I make tautological statements about internal questions related to the socially constructed version of reality that I’ve received.”
What philosophers of physics are supposed to believe this description of the science? (And there is nothing in Feyerabend, by the way, that sounds like your post.)
April 6th, 2010 | 1:28 am
dpm,
I mentioned Feyerabend in this post, and I believe in the previous one, as somebody who has good insights into how the methods with which real scientists actually engage in science do not in any way resemble the idealized portraits presented by many philosophers of science. In other words, I’m mentioning him for his psychological and sociological observations, rather than his philosophical ones.
As for the chunk you quoted, I was being dramatic by creating a caricature composed of a pastiche of views. You can find elements of it all over the place, however, Hacking and Carnap are examples that spring to mind.
April 6th, 2010 | 8:09 am
I’m sorry, but it’s nonsense to suppose that Carnap thought physics was either socially constructed or a set of tautologies, and it’s nonsense to suppose that Hacking thinks science is a bunch of tautologies, even though he has some sympathy with some aspects of the strong programme. And I do think your post pushes a pretty strong discovery/justification distinction, which I don’t find in Feyerabend.
April 6th, 2010 | 11:11 am
A very good response, but I still think there’s some unacknowledged daylight between your position and Freddie’s position. Call it the difference between ultimate and practical epistemology.
On the one hand, there’s the question of the ultimate destiny of the scientific method. To put it in crude mathematical terms, what is the limit of knowledge generation as effort and time expended goes to infinity? Is it a full, comprehensive understanding of the universe, or is it something less? And if it is (as the above persuasively argues, and I heartily concur) less than perfect, what is omitted? While I love thinking about this question, we can hopefully agree it is largely academic.
The more pressing question is, what makes for a proper practical epistemology? What the result of infinite scientific inquiry would be hardly matters, considering that’s unavailable to finite organisms. And this is where there is substantial disagreement between DeBoer and Harris. Harris argues (as I read him) that practically speaking, the only proper epistemology is pure rational inquiry. Anything which cannot be discovered by pure rational inquiry is suspect and requires rational vetting before it can be considered valid. In his attack on Nietzsche’s fact-value distinction, Harris is taking this to a somewhat radical extreme. He’s not content to aver that rational inquiry is the only valid basis for assessing fact, but goes further to say that values are nothing but objectively discoverable facts that we can assess with rationality. This is where DeBoer is crying foul most loudly, as I see it. Because Harris barrels ungracefully through several major logical barriers to his argument, it’s hard to make a single, clear refutation what I see as his half-dozen errors, but you have to start somewhere.
To wit, for starters, it’s not just the non-foundationality of science that’s problematic, it’s the attack on other forms of knowledge (principally here, but not limited to, religious ones) on the basis of non-foudationality. Harris’s acolytes commenting on DeBoer’s blog (and possibly Harris too, but I won’t put words in his mouth) will claim that this invalidates all knowledge, and divorces it from objective reality entirely. (Which, in full disclosure, I do believe in, just not our ability to comprehend it directly.) Not so, says DeBoer, it’s just that the connection to reality is far more contingent, and hence far less self-congratulatory, than that imagined by the pure empiricists and objectivists. And I agree.
I suppose that when you boil everything down, it still comes down to Harris saying that rationality is, almost by examination, so far superior as an epistemology that it invalidates all other forms. I think he’s wrong in this, and that it’s one of the biggest problems with his particular critique of religion.
April 6th, 2010 | 11:49 am
Dear Mr. Wilson,
You wrote: “Nor have I met a physicist who would reply: ‘I make tautological statements about internal questions related to the socially constructed version of reality that I’ve received.’”
Why does the “psychology of actual, practicing mathematicians and scientists” matter here? Does the psychology of actual practicing Buddhists have any impact on the existence of the Christian God?
If you accept Freddie deBoer’s point, which you do with your statement, “This is entirely true, and I won’t contest it,” then it should follow that we are incapable of discerning whether (to borrow your terms) our “reality” is the “Truth.” We are INCAPABLE. It appears that you get this in the beginning of your post. However, with your quote about physicists above, it appears that you fall right back into the trap of assuming that non-believers hold “Truth” in higher regard than “reality,” hence your insertion of the qualifying statement. They do not, as it would not make sense for them to do so.
In a crude analogy, imagine two people playing Monopoly, the board game. One of the players is on the verge of opening a real estate investment fund, his / her first ever foray into the real estate market. Throughout the game, this investor constantly uses her in-game strategy as an empirical testing ground for her real-life fund. She calculates her returns, “30% in one trade! That would make my whole year!” She analyzes her approach, “Hmmm, I tried to target the mid-range properties in this game and I’m kind of struggling there. For my fund I had better go for either the high- or low-end properties instead.” And on and on.
In this analogy, “reality” is the Monopoly game, “Truth” is the real world of real estate investing, the investor is the believer and other player is the non-believer. While the believer certainly would acknowledge the inadequacies of the Monopoly game as a model for her fund, she still thinks it helps to think these things through with whatever tools she currently possesses. After all, what if a certain Monopoly game happens to coincide EXACTLY with the conditions of the real estate market she is about to enter? That would be worth the trouble!
The non-believer thinks, Monopoly is a game. It works as a game within the confines of its alternate reality. The reason to play the game is that it may be interesting or fun in and of itself. Sure, it’s probably possible to extract SOME lessons about the real estate market from playing / analyzing the game, but those lessons still would be embedded within the rules of the game. And once confronted with the realities of the market, it is almost impossible to imagine those lessons being anything more than symbolic. Therefore, efforts to analyze the game should be done on their own merits (playing Monopoly is fun!). Analysis of the real estate markets should be conducted with data from actual real estate markets.
Now imagine further that the investor is not entering the real estate markets anywhere on planet Earth, but on some Alien planet billions of light-years away (or, if you prefer, back in time, in Imperial China) and that she has no prior knowledge of how these markets are set up. Her attempts to graft the Monopoly model onto what would be a very different market model seem even more absurd. As we imagine more and more outlandish settings for the investor’s “real estate market,” the game of Monopoly becomes more and more inadequate as a tool for understanding that market. Keep pushing the boundaries of this “real estate market” and eventually you will approach the limit of human understanding. Then it takes just one more little push beyond that point and the game of Monopoly becomes COMPLETELY IRRELEVANT to the “real estate market.”
To non-believers, “Truth” lies beyond that frontier of understanding and our “reality” is self-contained. The non-believer therefore views all attempts (especially his/her own) at “Truth-seeking” to be fundamentally mislabeled — you cannot even SEEK, let alone FIND, “Truth” if your tools are embedded in “reality.” Therefore the search for “Truth” holds NO SPECIAL PRIORITY in the minds of non-believers. It has value as a philosophical exercise to the extent that we can fool ourselves into mimicking a pursuit of something we cannot even comprehend, and then enjoy doing so! But it is not elevated to sacred status – it cannot supersede “reality” since that is all we are capable of knowing. This is not to say that non-believers are uninterested in human origins or in the question of our morality. Rather, in addressing these questions, non-believers simply view the pursuit of “Truth” as a distraction from and an illusion of reality.
Thanks,
ISOK
April 6th, 2010 | 3:00 pm
[...] takes the point and salvages his larger argument. Possibly related posts: (automatically generated)Quantum [...]
April 7th, 2010 | 4:58 pm
[...] Will Wilson at PomoCon, responding to Freddie: Freddie’s and Led’s challenge still warrants investigation, however, and today is a particularly fruitful day on which to consider it. Today is Great and Holy Saturday, when our thoughts are drawn to the small band of disciples who along with Mary gathered outside the tomb of Christ, waiting and hoping for the resurrection of the Lord, their presence motivated by nothing more than a promise. What Freddie and Led have nicely pointed out is that mathematics and science are based on a similar kind of promise. [...]
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