A Deadly Paradox: Death and Induction

I’ve been thinking a lot about paradoxes of induction lately, undoubtedly due, in part, to the Philosophy of Science course that I’m taking. I’ve thought of a peculiar paradox concerning death. There seems nothing unusual about the statement that no one alive today will live for an infinite duration. And yet, how do we know this? Through induction, by the fact that everyone in the past died eventually. But is this a reasonable inference? Because everyone we use as evidence have a common property—they’re all dead, where as the people who we are making the inference about are still alive. It’s interesting, because you can’t say people today will die because “everyone who ever lived has died” because that’s not true; we are among the group of everyone who has ever lived!

I think that I finally see the connection between mathematical induction and scientific induction. Let’s say that we are trying to establish an infinite claim. Let Mx denote “Matter exists at instant x”. We can never look at all of these instants, as there will always be instant that remains in the future. So, in order to establish the universal claim, we must assume that if it holds true for all past instants, it must hold true for all future instances. In mathematics, universal claims can be proven about infinite sets of objects, and in science they can’t be. So for scientific induction, the claim cannot be confirmed in a deductive sense. However, as is often noted, it’s possible in theory (if not always in practice) to disprove a universal statement about an infinite number of objects inductively—just find a counter example. For instance if there is not matter at instant x (excepting, of course, the dubiously assumed observer), then it cannot be true that matter exists at all instants.

But can the universal “All humans die” be disproved, even in theory? We already know that we run into the same difficulty that we did before as far as confirming the universal; in accordance with problem of induction, we must assume that if a statement is true for all humans in the past, it is also true for all humans in the future. But again, it isn’t true that all humans in the past have died—it’s only true that all of the humans in the past that have already died have died.

Over dinner, I thought of a possible connection between Hume’s problem of induction and the Grue paradox. In the case of green vs. grue—let’s temporarily redefine grue as a relational predicate Fx,t where x is the object to be Grue or not Grue, and t is the time that the object must be green before or blue afterwards. We accept green and not grue due to a sort of meta-induction of the like that is found in the paradox of induction. Let’s say t is t=-60 days where 0 is the present. We know that it was true that all emeralds before were green, but no emeralds before t were grue. Thus, we have a sort of “meta-inductive evidence” to favor green.

Again, consider the death scenario. We believe that people will be alive before a time t and dead after a time t because that use of induction worked in the past, only for different values of T. Of course, in both the grue and death scenarios, this solution has a serious complication. I said that we justified induction working in the future on the basis of induction in the past. But there must have been a first case that we observed! Now, how was that first case justified, if there is no initial time to give it credence?

This is interesting! With this view of the problem of induction, the problem isn’t so much that induction begs the question as it is the problem that it can’t be justified ad infinitum.