I never thought I would hear a plausible defence of slippery slope arguments.
An interesting analogy is with the Sorites or ‘heap’ paradox, and mathematical induction. In the paradox you show that one grain of sand is not a heap, and that two grains are not a heap, and three.… so you generalise that for if N grains of sand is not a heap then N+1 grains is also not a heap. Therefore 10^1000 grains of sand cannot be a heap, and there are no heaps!
Obviously the problem is that the premise isn’t true for any arbitrary N, (unlike cases of mathematical induction where you prove them to work for an arbitrary number).
Similarly with slippery slope arguments, proving that you can move between two points does not mean you can equally easily move to any other point. For example it is plausible that if abortion term limits were changed from say 16 weeks to 17 they might be more likely to move t0 18 in the future. But That doesn’t logically imply we will therefore kill born babies.
Edit: Not sure why this has been downvoted so much, did I misunderstand something about the post?
Thanks, I’ve seen that before. What interested me about the reaction to it was every commentator decried them for suggesting babies should be killed, said that it would give weight to the arguments of anti-abortionists or that it showed how out of touch academics were with public opinion. But no-one gave an argument in response about why an 8 month abortion and a born baby are different in a morally relevant way. I had underestimated how much in general public discourse even discussing a morally condemned act was itself condemned.
In the context of slippery slopes, again this is moving between two adjacent points not showing you can just as easily move to any point on the scale.
Obviously the problem is that the premise isn’t true for any arbitrary N
This is a tangent, but...
This is certainly not obvious (I submit that if it were, the Greeks would have noticed) and I don’t think it’s true either.
Treating heapness as a boolean, the Sorites paradox indeed implies that there are no heaps, or that any number of grains is a heap. If N grains of sand together are not a heap, then N+1 grains of sand also are not; the piles are visually the same, and so anyone who knows what ‘heap’ means would look at them and classify them as both “heap” or “not heap”. I submit that if you ran that experiment for different values of N (showing each respondent only one instance of N and N+1), you would find no N for which most respondents classified one as a heap and the other as not a heap.
Since this is a paradox, we know there’s a problem with one of our assumptions. These days, the obvious one is that heapness is not a boolean. There’s a cluster in thingspace we call “heap”, and some things are clearly part of the cluster, like a pile of 2000 grains of sand, and some things are clearly not part of the cluster, like a single grain of sand.
Then to do our mathematical induction, we must agree that for any arbitrary N, if N is clearly part of the cluster then N+1 is also clearly part of the cluster. But there is some point at which you become uncertain. I submit that there is some N such that N grains of sand is clearly not a heap, and N+1 grains of sand may or may not be a heap; also, there is some N such that N grains of sand may or may not be a heap, and N+1 grains of sand is a heap.
Though really if we wanted to formalize this, we’d probably set different thresholds depending on whether we’re adding or removing grains of sand; the N at which something stops being clearly a heap is lower than the N at which something starts being clearly a heap, and we might even cut out the “uncertain” category from this model. And this would probably match people’s intuitions if they watched people adding or removing grains of sand and were told to classify.
Or, you can still treat “heapness” as a boolean and still completely clobber this paradox just by being specific about what it actually means to have us call something a heap.
I never thought I would hear a plausible defence of slippery slope arguments.
An interesting analogy is with the Sorites or ‘heap’ paradox, and mathematical induction. In the paradox you show that one grain of sand is not a heap, and that two grains are not a heap, and three.… so you generalise that for if N grains of sand is not a heap then N+1 grains is also not a heap. Therefore 10^1000 grains of sand cannot be a heap, and there are no heaps!
Obviously the problem is that the premise isn’t true for any arbitrary N, (unlike cases of mathematical induction where you prove them to work for an arbitrary number).
Similarly with slippery slope arguments, proving that you can move between two points does not mean you can equally easily move to any other point. For example it is plausible that if abortion term limits were changed from say 16 weeks to 17 they might be more likely to move t0 18 in the future. But That doesn’t logically imply we will therefore kill born babies.
Edit: Not sure why this has been downvoted so much, did I misunderstand something about the post?
You may want to look at this.
Thanks, I’ve seen that before. What interested me about the reaction to it was every commentator decried them for suggesting babies should be killed, said that it would give weight to the arguments of anti-abortionists or that it showed how out of touch academics were with public opinion. But no-one gave an argument in response about why an 8 month abortion and a born baby are different in a morally relevant way. I had underestimated how much in general public discourse even discussing a morally condemned act was itself condemned.
In the context of slippery slopes, again this is moving between two adjacent points not showing you can just as easily move to any point on the scale.
Yes, and then we move to a point adjacent to the new point, and then to a point adjacent to the next point. This is how slippery slopes work.
He means adjacent without ascension/descension: lateral movement, i.e. change in non-morally relevant variables.
This is a tangent, but...
This is certainly not obvious (I submit that if it were, the Greeks would have noticed) and I don’t think it’s true either.
Treating heapness as a boolean, the Sorites paradox indeed implies that there are no heaps, or that any number of grains is a heap. If N grains of sand together are not a heap, then N+1 grains of sand also are not; the piles are visually the same, and so anyone who knows what ‘heap’ means would look at them and classify them as both “heap” or “not heap”. I submit that if you ran that experiment for different values of N (showing each respondent only one instance of N and N+1), you would find no N for which most respondents classified one as a heap and the other as not a heap.
Since this is a paradox, we know there’s a problem with one of our assumptions. These days, the obvious one is that heapness is not a boolean. There’s a cluster in thingspace we call “heap”, and some things are clearly part of the cluster, like a pile of 2000 grains of sand, and some things are clearly not part of the cluster, like a single grain of sand.
Then to do our mathematical induction, we must agree that for any arbitrary N, if N is clearly part of the cluster then N+1 is also clearly part of the cluster. But there is some point at which you become uncertain. I submit that there is some N such that N grains of sand is clearly not a heap, and N+1 grains of sand may or may not be a heap; also, there is some N such that N grains of sand may or may not be a heap, and N+1 grains of sand is a heap.
Though really if we wanted to formalize this, we’d probably set different thresholds depending on whether we’re adding or removing grains of sand; the N at which something stops being clearly a heap is lower than the N at which something starts being clearly a heap, and we might even cut out the “uncertain” category from this model. And this would probably match people’s intuitions if they watched people adding or removing grains of sand and were told to classify.
Or, you can still treat “heapness” as a boolean and still completely clobber this paradox just by being specific about what it actually means to have us call something a heap.
Any feasible number (free PostScript version) of grains of sand is not a heap.