Tuesday, March 22, 2011

Infinite lives

Imagine a race of immortals. Nothing can kill them; not disease, old age, etc. They are invincible and they also do not go through the normal aging process of decrepitude of the body and mind associated with mortal aging. If they live forever and these beings are like us in all other ways, they will go through the normal vicissitudes of life, the ups and downs, highs and lows, good times and bad times. So such a life in total will include an infinite positive utility and an infinite negative utility. No matter how good a life one lives, so long as some significant repetition of periods of bad times, they will go through an eternity of suffering as well as good times. Do these times cancel out since both times in bad and in good are infinite in duration? Will such a life ever be worth living if we are to believe that what makes life worth living is experiencing as much good (defined as pleasure or happiness here or "utility") and as few bad (sadness, misery, suffering, etc) as possible? In a finite life, once can experience far fewer bad times than good and vice versa but an infinite life, all experiences, good and bad are equal in amount: both infinite in duration.

Also consider that such an immortal, no matter how virtuous he or she is unless she is perfectly virtuous, will inevitably commit an infinite amount of evil as well as good. Will such evil acts and thoughts be canceled out by her good acts and thoughts? It would appear so as well.

Now consider the human race. If the human race lives on forever (and there is almost no chance of that) then the human race will achieve the same amount of overall collective good and bad. It will achieve (unless it all becomes perfectly virtuous after some period of time continuously) an infinite amount of evil and good collective virtue.


  1. I'm not sure that this would count as an infinite amount of good/evil for most purposes. Just because you have experienced an infinite amount of good and an infinite amount of evil, that doesn't mean there's nothing to choose between manners of life. After all, it is surely the balance of good/evil that counts most, and as you'll recall from calculus, the sum from x of 0 to infinite for a function of x can be finite as well as infinite. For example, the function sine of x balances every time it goes over 0 with an equal segment under 0, so its value in the limit is 0. On the other hand, f(x): sine(x) + .00001 will tend towards infinity, since the negative portions are just slightly outmatched by the positive parts. Just so, an infinite life will be valuable just in case it tends to experience "more" happiness than unhappiness, even should the happiness and unhappiness be infinite by themselves.

  2. I think there may be a more concrete way to put what you're saying into an example, Carl. Tell me if I am not getting what you're trying to say in this example.

    Consider an immortal who has alternate good and bad days (sum of his utility on those days are either positive or negative). His bad days all come on odd numbered days. So days 1, 3, 5, 7,... are all bad and the rest are good days for him. But let's also say that on his bad days, they are a diminishing sequence, say on his first bad day, his summed negative utility is -1 and on his second, -1/2, 3rd day, -1/4, 4th day, -1/8 and so on. So we will have a sequence (-1 + -1/2 + -1/4, + -1/8...). As the negative days approach infinity, his negative utility approaches the finite number -2. On the other hand, his positive utility increases without bound since let us say that for each of those days, it increases by +1. In this case, his positive utility will be infinite while his negative will approach -2; a good outcome for him.

    Now that's the case for that sequence but other sequences tend to increase without bound such as the harmonic series -1, -1/2, -1/3, -1/4, -1/5.... This is a non convergent series. As the days approach infinity, the negative utility does so as well which means that there is equal amount of good and bad for him "in the end".

    But a creature that would go through a converging sequence or any other kinds of sequences with regularity of utility patterns would have to be a very different creature indeed from us and may even have to live in a world with different nomic laws as our utility is dependent on our surrounding environment. In my post, I mentioned explicitly that I was assuming that these creatures are just like us except for the fact that they live forever and do not age (kind of like some kinds of trees found in nature at least in theory can go through life indefinitely never aging or dying). In other words, imagine your life extended forever into the future. There will be some periods of bad and good and no diminishing pattern of good vs bad (or any kind of pattern for that matter) as the days approach infinity.

  3. Yes, you've got exactly what I meant and you've brought up some difficulties I hadn't thought of.