“Certainly, my surety isn’t inviolable. It always starts with some assumption. And as I’ve asked you elsewhere, ‘Are you sure you’re sure?’ Sometimes I say I’m sure, but deep-down doubt surfaces because I can’t be certain that I have considered all alternatives. Plus, I know that I arrive at surety through only two avenues. The first is belief. The second is reason. And there seems to be a strange and unavoidable connection between the two: Both require our inserting meaning as well as deriving meaning. Let me ramble a bit.
“We all ‘know’ the inexplicable through belief. Reason handles the rest, that is, the explicable. Yet, reason rests on the unreasonable, on some assumption, and formal reason rests on axioms like those of geometry. And although scientists argue that what they do is deductive, ultimately, because they cannot know if they have covered all alternatives, they, too, rely on inductive thinking, belief that the specifics sum to the general. What if theorems that are supposed to verify the axioms are incomplete? Quantum physicists, for example, have deduced the Standard Model that appears to ‘explain It all,’ but they leave open the possibility that some new discovery at CERN might reveal a family of new phenomena (particles) that will change the Standard Model. Scientists (I’m generalizing, of course) also argue that there’s a big difference between belief and reason, between what they do, for example, and what religious leaders do. Both, however, arrive at working explanations of the world. In living our complex daily lives, we might argue that whatever works works. Someone can go through life happily on the ground of belief rather than on the ground of science though pretty much everyone uses both belief and reason to get through a day. When we exit the bed in the morning, we infer that the floor will not collapse beneath us. We infer because we reason that the structure of the floor is logically designed to hold our weight and because years of experience guide us to conclude inductively that this morning the floor will be no different from what it was on the previous morning. We’ve experimented over a lifetime, and we believe we have discovered and understand the way the world of floors works.
“You—you don’t mind my calling you you, do you?—are likely saying, ‘There’s nothing new in this.’ And you would be right. Nagel and Newman put it this way, ‘Inductive considerations can show no more than that the axioms are plausible or probably true’ (19). * I suppose what we look for in living our lives is consistency. Consistency removes the unexpected and lends meaning to the world. It would be a heck of a surprise if the sun didn’t rise tomorrow, if we didn’t ‘stick’ to the ground because of gravity, and if the oxygen content of the atmosphere dropped from 20.99% to 15%.
“I just have to quote Nagel and Newman again: ‘In…attempts to solve the problem of consistency there is one persistent source of difficulty. It lies in the fact that the axioms are interpreted by models composed of an infinite number of elements. This makes it impossible to encompass the models in a finite number of observations; hence the truth of the axioms themselves is subject to doubt’ (20). **
“So, you, if you are a ‘believer,’ you woke up this morning with a set of beliefs by which you will operate throughout your day. As long as everything runs consistently, you’ll be happy; life will be good; you will be successful. After all, didn’t those beliefs work for you yesterday? Hasn’t experience taught you that they work? Sure, that’s inductive reasoning on your part, but you have as yet to encounter that exception, that ‘new particle’ in your personal Large Hadron Collider. And that works for you even if you are a nonbeliever, a hardcore skeptic, even a hardcore atheist bent on waging war against ‘foolish’ believers. Hardcore nonbelievers also awake with beliefs.
“Believing is an inescapable part of being human. No finite being, as Nagel and Newman suggest, has an infinite amount of time or space to find that special exception. For all of us, what works, works until it doesn’t work.
“We can refine our refining ad infinitum, never reaching some inviolable Ultimate. Think Democritus and Leucippus and the concept of the indivisible, that is, the atom. Then think nucleons, quarks, strings, and…. And on the other end of the scale, think planet, Solar System, galaxy, the ‘estimated’ two trillion galaxies, other universes, and…. We really do rely on belief.
“The skeptic is right to search through reason for consistency, but is the skeptic ‘more right’ than the believer? And if the believer dismisses the musings of the skeptic as inconsistent with the axioms or tenets of belief, is there any substance to the dismissal? Certainly, dismissals of others’ thinking can vary even among largely like-minded believers.
“Maybe all of us just want consistency, and getting it is a personal matter. Intellectually, we’re like ancient dwellers of rock shelters and caves. Emerging, though necessary for acquiring food for thought, means facing the unknown, some wolf of doubt or contradiction.
“Early on, did you have the same difficulty I had with multiplication tables? With any system of abstract symbols? Think, 2 + 2. But what? Sure, now as an adult with years of experience with things that come in twos, you have no difficulty, but at the outset, 2 + 2 and 2 X 2 make up a meaningless set of symbols. You have to provide some meaning for the symbols, apples for example. Yet, in every math text book, we can see practice problems that employ only the symbols sans some associated object or process. Any calculus, any system of symbols, is meaningless, though consistent. Yet, we accept the calculus as meaningful precisely because it is self-consistent. It works as it—and only it—can work. Another calculus does the same as long as it is self-consistent. As the editor of Nagel and Newman’s book notes, you can give your car a pet name, but the machine works without any designation (27). ***
“Believers have a calculus of one kind, and nonbelievers have a different kind. We can name the calculi as we wish and furnish their symbols with meaning often without acknowledging that they serve the same purpose in different ways: They provide the consistency we all seek.”
*Nagel, Ernest and James R. Newman, Gödel’s Proof, Revised Ed., edited by Douglas R. Hofstadter. New York University Press, New York, 2001.
**The same
***The same
“We all ‘know’ the inexplicable through belief. Reason handles the rest, that is, the explicable. Yet, reason rests on the unreasonable, on some assumption, and formal reason rests on axioms like those of geometry. And although scientists argue that what they do is deductive, ultimately, because they cannot know if they have covered all alternatives, they, too, rely on inductive thinking, belief that the specifics sum to the general. What if theorems that are supposed to verify the axioms are incomplete? Quantum physicists, for example, have deduced the Standard Model that appears to ‘explain It all,’ but they leave open the possibility that some new discovery at CERN might reveal a family of new phenomena (particles) that will change the Standard Model. Scientists (I’m generalizing, of course) also argue that there’s a big difference between belief and reason, between what they do, for example, and what religious leaders do. Both, however, arrive at working explanations of the world. In living our complex daily lives, we might argue that whatever works works. Someone can go through life happily on the ground of belief rather than on the ground of science though pretty much everyone uses both belief and reason to get through a day. When we exit the bed in the morning, we infer that the floor will not collapse beneath us. We infer because we reason that the structure of the floor is logically designed to hold our weight and because years of experience guide us to conclude inductively that this morning the floor will be no different from what it was on the previous morning. We’ve experimented over a lifetime, and we believe we have discovered and understand the way the world of floors works.
“You—you don’t mind my calling you you, do you?—are likely saying, ‘There’s nothing new in this.’ And you would be right. Nagel and Newman put it this way, ‘Inductive considerations can show no more than that the axioms are plausible or probably true’ (19). * I suppose what we look for in living our lives is consistency. Consistency removes the unexpected and lends meaning to the world. It would be a heck of a surprise if the sun didn’t rise tomorrow, if we didn’t ‘stick’ to the ground because of gravity, and if the oxygen content of the atmosphere dropped from 20.99% to 15%.
“I just have to quote Nagel and Newman again: ‘In…attempts to solve the problem of consistency there is one persistent source of difficulty. It lies in the fact that the axioms are interpreted by models composed of an infinite number of elements. This makes it impossible to encompass the models in a finite number of observations; hence the truth of the axioms themselves is subject to doubt’ (20). **
“So, you, if you are a ‘believer,’ you woke up this morning with a set of beliefs by which you will operate throughout your day. As long as everything runs consistently, you’ll be happy; life will be good; you will be successful. After all, didn’t those beliefs work for you yesterday? Hasn’t experience taught you that they work? Sure, that’s inductive reasoning on your part, but you have as yet to encounter that exception, that ‘new particle’ in your personal Large Hadron Collider. And that works for you even if you are a nonbeliever, a hardcore skeptic, even a hardcore atheist bent on waging war against ‘foolish’ believers. Hardcore nonbelievers also awake with beliefs.
“Believing is an inescapable part of being human. No finite being, as Nagel and Newman suggest, has an infinite amount of time or space to find that special exception. For all of us, what works, works until it doesn’t work.
“We can refine our refining ad infinitum, never reaching some inviolable Ultimate. Think Democritus and Leucippus and the concept of the indivisible, that is, the atom. Then think nucleons, quarks, strings, and…. And on the other end of the scale, think planet, Solar System, galaxy, the ‘estimated’ two trillion galaxies, other universes, and…. We really do rely on belief.
“The skeptic is right to search through reason for consistency, but is the skeptic ‘more right’ than the believer? And if the believer dismisses the musings of the skeptic as inconsistent with the axioms or tenets of belief, is there any substance to the dismissal? Certainly, dismissals of others’ thinking can vary even among largely like-minded believers.
“Maybe all of us just want consistency, and getting it is a personal matter. Intellectually, we’re like ancient dwellers of rock shelters and caves. Emerging, though necessary for acquiring food for thought, means facing the unknown, some wolf of doubt or contradiction.
“Early on, did you have the same difficulty I had with multiplication tables? With any system of abstract symbols? Think, 2 + 2. But what? Sure, now as an adult with years of experience with things that come in twos, you have no difficulty, but at the outset, 2 + 2 and 2 X 2 make up a meaningless set of symbols. You have to provide some meaning for the symbols, apples for example. Yet, in every math text book, we can see practice problems that employ only the symbols sans some associated object or process. Any calculus, any system of symbols, is meaningless, though consistent. Yet, we accept the calculus as meaningful precisely because it is self-consistent. It works as it—and only it—can work. Another calculus does the same as long as it is self-consistent. As the editor of Nagel and Newman’s book notes, you can give your car a pet name, but the machine works without any designation (27). ***
“Believers have a calculus of one kind, and nonbelievers have a different kind. We can name the calculi as we wish and furnish their symbols with meaning often without acknowledging that they serve the same purpose in different ways: They provide the consistency we all seek.”
*Nagel, Ernest and James R. Newman, Gödel’s Proof, Revised Ed., edited by Douglas R. Hofstadter. New York University Press, New York, 2001.
**The same
***The same
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