Monday, August 28, 2023

Are we finite?

Here’s a valid argument with plausible premises:

  1. A finite being has finite value.

  2. Any being with finite value may be permissibly sacrificed for a sufficiently large finite benefit.

  3. It is wrong to sacrifice a human for any finite benefit.

  4. So, a human has infinite value. (2 and 3)

  5. So, a human is an infinite being. (1 and 4)

That conclusion itself is interesting. But also:

  1. Any purely material being made of a finite amount of matter is a finite being.

  2. If human beings are purely material, they are made of a finite amount of matter.

  3. So, human beings are not purely material. (5, 6 and 7)

I am not sure, all that said, whether I buy (2). I think a deontology might provide a way of denying it.

And, of course, work needs to be done to reconcile (5) with the tradition that holds that all creatures are finite, and only God is infinite. Off-hand, I think one would need to distinguish between senses of being “infinite”. Famously, Augustine said that the numbers are finite because they are contained in the mind of God. There is, thus, an absolute sense of the infinite, where only God is infinite, and anything full contained in the divine mind is absolutely finite. But surely there is also a sense in which there are infinitely many numbers! So there must another sense of the infinite, and that might be a sense in which humans might be infinite.

Nor do I really know what it means to say that a human is infinite.

Lots of room for further research if one doesn’t just reject the whole line of thought.


Rob said...

I like the argument, and would like to see it developed in greater depth somewhere. To that end, here's a reservation I feel about it.

One way of pushing back would be on the nature of value. One could plausibly take value to be in a sense objective yet perspectival. For instance, couldn't an Aristotelian say that humans are valuable because we properly relate to them as things we should care about, given our nature? This is plausibly an aspect of why we don't believe it to be a defect for a lion to eat a human, since the lion's nature does not require the same relations to humans. I can think of a couple ways of responding to this consideration. Firstly, that being is convertible with goodness. Since value has something to do with goodness, this might provide a non-perspectival sense of value to things. The issue here is that one can't get to infinite value for persons on this account since humans aren't pure act. Secondly, it could be objected that humans are made in the image of God, which provides them with infinite value. However, this cuts against the force of the argument, since it limits the argument's scope to those who already accept that humans are made in the image of God.


SMatthewStolte said...

Speaking generally, the ‘finite’ is another name for the limited. Numbers are limited insofar as they are all only quantities, but the numbers we call ‘transfinite’ are not limited by any (integer) quantity. When we say “finite numbers,” we are using the term finite in order to describe a particular way of being finite.

It feels a little silly to say the following, but I think it might be right: numbers keep going, to large cardinals and beyond, but there is no cardinal so large that it is a substance. So all numbers are finite.

I find the argument you attribute to Augustine to be pretty uncompelling, since the divine ideas are not strictly distinct from God himself. The divine ideas of numbers are only finite with respect to their objects: they are of the finite though in themselves they are infinite.

Human beings are finite in a lot of different ways. Most obviously, we are none of us omniscient.

There is a sense in which human beings have infinite value, and it is this: the sort of value we have is not well-represented by assigning it a finite number. (Contrast this with the sort of value that money has.) And so human value does not have a finite quantity. But I don’t think it is especially well-represented by assigning it an infinite number either. Probably the best way to understand human value is to work out a bunch of its implications and say something like, “it is that feature in us which has such-and-such implications.”

SMatthewStolte said...

One further point. I think electrons have a certain kind of inner worth as well and that their inner worth is not especially well-represented by quantities (though for some different reasons than in the case of human value). So if I were to accept the first half of your argument, I would either reject premise 6 or I would have to deny that electrons are purely material.