Agree with djbinder on this, that âinfinities should only be treated as âidealized limitsâ of finite processesâ.
To explain what I mean:
Infinites outside of limiting sequences are not well defined (at least that is how I would describe it). Sure you can do some funky set theory maths on them but from the point of view of physics they donât work, cannot be used.
(My favorite example (HT Jacob Hilton) is a man throws tennis balls into a room once every 1 second numbered 1,2,3,4,⌠and you throw them out once every 2 seconds, how many balls are in the room after infinite time and which balls are they? Well if you throw out the odd balls (2,4,6...) then 1,3,5,.. are left but if you throw out the balls in the order they are thrown in (1,2,3,4...) then after infinite time no balls are left. The lesson: âinfiniteâ is not a precise enough term to answer the question.)
As far as I understand it, from a philosophy of science point of view doing physics is something like writing the simplest set of mathematical formulas to describe the universe. These formulas need to work. So you will never find a physicist that uses infinites in the way this post does. If physics is ever able to succeed at mapping the universe it will have to do it without using infinite sets, except where they can be well defined as limits (unless there is drastic change to what physics is).
As such doing infinite ethics of the type done in this post makes as much sense as doing any other poorly defined by physics thought experiment (see example in my other reply about what if time travel paradoxes are true).
Of course there could still be infinites in limits. E.g. one happy person a day tending forever (as Joe flags in his comment). But hopefully they are better defined and may avoid some of the problems of the post above (certainly it breaks the zones of happiness/âsuffering thought experiment). I am not sure.
Agree with djbinder on this, that âinfinities should only be treated as âidealized limitsâ of finite processesâ.
To explain what I mean:
Infinites outside of limiting sequences are not well defined (at least that is how I would describe it). Sure you can do some funky set theory maths on them but from the point of view of physics they donât work, cannot be used.
(My favorite example (HT Jacob Hilton) is a man throws tennis balls into a room once every 1 second numbered 1,2,3,4,⌠and you throw them out once every 2 seconds, how many balls are in the room after infinite time and which balls are they? Well if you throw out the odd balls (2,4,6...) then 1,3,5,.. are left but if you throw out the balls in the order they are thrown in (1,2,3,4...) then after infinite time no balls are left. The lesson: âinfiniteâ is not a precise enough term to answer the question.)
As far as I understand it, from a philosophy of science point of view doing physics is something like writing the simplest set of mathematical formulas to describe the universe. These formulas need to work. So you will never find a physicist that uses infinites in the way this post does. If physics is ever able to succeed at mapping the universe it will have to do it without using infinite sets, except where they can be well defined as limits (unless there is drastic change to what physics is).
As such doing infinite ethics of the type done in this post makes as much sense as doing any other poorly defined by physics thought experiment (see example in my other reply about what if time travel paradoxes are true).
Of course there could still be infinites in limits. E.g. one happy person a day tending forever (as Joe flags in his comment). But hopefully they are better defined and may avoid some of the problems of the post above (certainly it breaks the zones of happiness/âsuffering thought experiment). I am not sure.