Ironically I might also be guilty of using some technical terminology incorrectly here!
I had in mind the discussion on valuing actions with imperceptible effects from the âFive Mistakes in Moral Mathematicsâ chapter in Reasons+Persons (relevant to all the examples mentioned in the IVT section of this post), where if I remember right Parfit makes an explicit comparison with the âparadox of the heapâ (I think this is where I first came across the term).
It feels the same in that for both cases we have a function from natural numbers (number of grains of sand in our potential heap, or number of people voting/âbuying meat) to some other set (boolean âheapâ vs ânot heapâ, or winner of election, or number of animals harmed). And the point is that mathematically, this function must at some point change with the addition of a single +1 to the input, or it can never change at all. Moreover, the sum of the expected value of lots of potential additions must equal the expected value of all of them being applied together, so that if the collective has a large effect, the individual effects canât be smaller, on average, than the collective effect divided by the number of consituents.
I suppose the point is that this paradox is non-trivial and possibly unsolved when the output is fuzzy (like whether some grains of sand are a heap or not) but trivially true when the output is precise or quantitative (like who wins an election or how many animals are harmed)?
The relatively more orthodox view amongst philosophers about the heap case is roughly there is a kind of ambiguous region of successive ns where it is neither true nor false that n grains make a heap. This is a very, very technical literature though, so possibly that characterization isnât quite right. None of the solutions are exactly great though, and some experts do think there is an exact ânâ where some grains become a heap.
Also, pretty much every empirical outcome is potentially fuzzy in some possible situation. (Elections can be tied, whether an experience is painful and hence harm or neutral can be unclear etc.)
Maybe, although an election being tied is about the only way that particular example can be fuzzy, and there is a well defined process for what happens in that situation (like flipping a coin). There is ultimately only one winner, and it is possible for a single vote to make the difference.
Whether an experience is painful or not is extremely unclear, but if your metric is just something like ânumber of animals killed for meat each yearâ then again that is something well defined and precise, and it must in principle be possible to change it with an individual purchase.
It can also be indeterminate over a short time who the winner of an election is because the deciding vote is being cast and plausibly there is at least some very short duration of time where it is indeterminate whether the process of that vote being cast is finished yet. It can be indeterminate how many animals were killed for food if one animal was killed for multiple reasons of which âto eatâ was one reason but not the major one. Etc. etc.
Ironically I might also be guilty of using some technical terminology incorrectly here!
I had in mind the discussion on valuing actions with imperceptible effects from the âFive Mistakes in Moral Mathematicsâ chapter in Reasons+Persons (relevant to all the examples mentioned in the IVT section of this post), where if I remember right Parfit makes an explicit comparison with the âparadox of the heapâ (I think this is where I first came across the term).
It feels the same in that for both cases we have a function from natural numbers (number of grains of sand in our potential heap, or number of people voting/âbuying meat) to some other set (boolean âheapâ vs ânot heapâ, or winner of election, or number of animals harmed). And the point is that mathematically, this function must at some point change with the addition of a single +1 to the input, or it can never change at all. Moreover, the sum of the expected value of lots of potential additions must equal the expected value of all of them being applied together, so that if the collective has a large effect, the individual effects canât be smaller, on average, than the collective effect divided by the number of consituents.
I suppose the point is that this paradox is non-trivial and possibly unsolved when the output is fuzzy (like whether some grains of sand are a heap or not) but trivially true when the output is precise or quantitative (like who wins an election or how many animals are harmed)?
Thanks, I get what you meant now.
The relatively more orthodox view amongst philosophers about the heap case is roughly there is a kind of ambiguous region of successive ns where it is neither true nor false that n grains make a heap. This is a very, very technical literature though, so possibly that characterization isnât quite right. None of the solutions are exactly great though, and some experts do think there is an exact ânâ where some grains become a heap.
Also, pretty much every empirical outcome is potentially fuzzy in some possible situation. (Elections can be tied, whether an experience is painful and hence harm or neutral can be unclear etc.)
Maybe, although an election being tied is about the only way that particular example can be fuzzy, and there is a well defined process for what happens in that situation (like flipping a coin). There is ultimately only one winner, and it is possible for a single vote to make the difference.
Whether an experience is painful or not is extremely unclear, but if your metric is just something like ânumber of animals killed for meat each yearâ then again that is something well defined and precise, and it must in principle be possible to change it with an individual purchase.
It can also be indeterminate over a short time who the winner of an election is because the deciding vote is being cast and plausibly there is at least some very short duration of time where it is indeterminate whether the process of that vote being cast is finished yet. It can be indeterminate how many animals were killed for food if one animal was killed for multiple reasons of which âto eatâ was one reason but not the major one. Etc. etc.