metonymy4u

The problem of induction has had many faces over the last 250 years, since inductive reasoning was first articulated as the guiding light of the new science in western Europe. Besides the ontological proof, here are some additional ways of conceptualizing the dilemma:

Space travel: if you get up to cross the room to get a cup of coffee, first you have to travel half the distance from here to your coffee. But then you have to travel half of that remaining distance. But then you have to travel half of that remaining distance, but then…and so on…Presumably, each of these distances you travel requires a certain amount of time. So the problem of an infinitely divisible continuum of space and time is that it appears that to travel any finite distance, takes an infinite amount of time. So how can we account for any sort of movement in space and time?

Moreover, how can we account for the beginning of the universe, given that any arbitrary starting point could have been preceded by another starting point, ad infinitum? Are we to accept the absurd conclusion that there was no starting point, and that therefore we ourselves don’t exist?

Ethics and duty: to say that someone ought to do something is to imply that they should not let anything stand in their way of doing it. For example, if we say one ought not to lie, then lying is immoral no matter what benefits might accrue. For to say that lying is ok in some circumstances and not in others is not to talk about duty, but to talk about prudence. So to say that “X” is a duty is to imply that one should not let any concrete extenuating circumstance get in one’s way of performing “X.” But this implies that one could actually eliminate all of those extenuating circumstances in order to guarantee performance of “X.” Because if that’s not possible, then one is just talking about some hypothetical “X” that no one could ever actually accomplish, and to talk about a duty to do something that is not EVER actually physically possible to accomplish is absurd. So how can we ever talk about duties with anything but absurdity, given that it’s probably impossible to eliminate all extenuating circumstances?

The solution, quite simple really, also proposed 250 years ago, involves the concept of the limit of an infinitely inductive series. So time and space are not infinitely experienced across a well defined interval, because we developed a technology (integral calculus) to describe the limit of the infinitely divisible continuum. Likewise we could also describe the limit of our contingent approximations to what we would like to do if we had God’s strength and power. And so God would then be defined as the limit of the infinitely inductive series of spacetime approximations to an arbitrary boundary condition, as well as the limit of an infinite series of attempts to remove all contingencies to the accomplishment of the promptings of duty.