how many beans make a heap?
A bean lies before you on a table. Is that a heap? Assuredly not? Add a second bean to the first. Does that constitute a heap? Still no? Then add a third bean to the pair – and a fourth to the three, a fifth to the four – until they make a ‘heap’.
More and more beans are added to the collection in increments of one. You writhe uncomfortably in uncertainty's grasp; you never had an answer to begin with, but this is getting ridiculous. In your desperation, you eye the growing pile of beans - they seem to be a heap, now! You declare them thus, and count twenty-three of them.
Now remove one bean from the ‘heap’ of twenty-three. Is that still a heap?
“A heap is merely some quantity of abundance. What of one bean less?” you muse. “It is.”
Splendid. Remove another. Is that still a heap? Yes? And another. And another, and yet another, in decrements of one, until you no longer have a heap. Tell me when you get there!
“…”
Logic and legumes do not go together, you decide. You leave in a huff.
----
The following are the two premises of the argument.
Premise one: 23 beans make a ‘heap’.
Premise two: A ‘heap’ of beans minus 1 bean is still a heap.
In spite of the validity of the two premises (which I will not endeavour to prove), one realises that an absurd conclusion will be reached upon multiple applications of the second premise. In other words, one will be forced to admit that one bean constitutes a heap, however intuitively repugnant that may be, because formal logic demands that it must be so.
This is a classic example of a Sorites Paradox (Wiki: σωρός (sōros) being Greek for "heap" and σωρείτης (sōreitēs) a derived adjective meaning "heaped up"), of which there is an abundance of in Stoic philosophy. This particular paradox is often attributed to Chrysippus, the ‘Second Founder’ of Stoicism. An identical paradox that involves sand in the place of beans is ascribed to Eubulides, successor of Euclid, who preceded Chrysippus by a century.
Now why am I waxing lyrical about this? I have no interest in presenting the more complex forms of the paradox, of which there are the conditional, mathematical induction and line-drawing interpretations. I have no interest in presenting philosophical solutions, of which there are a few, and all of which I have not understood.
What I have is not a motion, but an observation.
Policy makers, judges and administrators encounter this paradox in their lines of service everyday. Society needs to agree on ages of consent. Speed limits. Term limits for abortion. In the simple terms employed by Chrysippus in his teaching of the paradox, great difficulty is experienced when we struggle to define fixed quantities as qualities, or predicates. This was brought to my attention by Stephen Fry, who pointed it out to Clive James in a television interview (2007). (Fry attributed the paradox to Zeno, perhaps mistakenly so.)
In philosophy, there are four acceptable responses.
1. Deny that logic applies to soritical expressions
2. Deny some premise(s)
3. Deny the argument’s validity
4. Embrace the paradox.
Society does not care much for this. I am not sure if it can, or should. I have not thought of a way that it can in a manner acceptable to public debate.
The paradox is applicable to society’s making of policy. I have said as much. We do not, however, need to confront the paradox. We circumvent it. Arbitrarily-coined predicates, nebulous in the vagueness of language, require themselves to be defined arbitrarily as well. Society’s solution in a liberal democracy (assuming you live in one, of course) would be to seek group consensus in a democratic fashion amongst representatives at the appropriate levels of the apparatus that is the government. We swap prescriptive linguistics for descriptive linguistics.
If there is a lesson to be learnt, it is that logic did not untie the Gordian Knot - rationality did.
[DAMNIT I spend the night composing this entry, and what do I find? Dinosaur Comics beat me to simpler explanations a few weeks ago!]
----
Resources:
1. Wikipedia, Sorites paradox
2. Stanford Encyclopedia of Philsophy, Sorites Paradox
3. Clive James: Talking in the Library - Stephen Fry 3/3
4. Soren Kierkegaard, M.G. Piety, Edward F. Mooney: Repetition and Philosophical Crumbs, pg 185
5. Bertrand Russell: A History of Western Philosophy
and a few others that I have forgotten.
More and more beans are added to the collection in increments of one. You writhe uncomfortably in uncertainty's grasp; you never had an answer to begin with, but this is getting ridiculous. In your desperation, you eye the growing pile of beans - they seem to be a heap, now! You declare them thus, and count twenty-three of them.
Now remove one bean from the ‘heap’ of twenty-three. Is that still a heap?
“A heap is merely some quantity of abundance. What of one bean less?” you muse. “It is.”
Splendid. Remove another. Is that still a heap? Yes? And another. And another, and yet another, in decrements of one, until you no longer have a heap. Tell me when you get there!
“…”
Logic and legumes do not go together, you decide. You leave in a huff.
----
The following are the two premises of the argument.
Premise one: 23 beans make a ‘heap’.
Premise two: A ‘heap’ of beans minus 1 bean is still a heap.
In spite of the validity of the two premises (which I will not endeavour to prove), one realises that an absurd conclusion will be reached upon multiple applications of the second premise. In other words, one will be forced to admit that one bean constitutes a heap, however intuitively repugnant that may be, because formal logic demands that it must be so.
This is a classic example of a Sorites Paradox (Wiki: σωρός (sōros) being Greek for "heap" and σωρείτης (sōreitēs) a derived adjective meaning "heaped up"), of which there is an abundance of in Stoic philosophy. This particular paradox is often attributed to Chrysippus, the ‘Second Founder’ of Stoicism. An identical paradox that involves sand in the place of beans is ascribed to Eubulides, successor of Euclid, who preceded Chrysippus by a century.
Now why am I waxing lyrical about this? I have no interest in presenting the more complex forms of the paradox, of which there are the conditional, mathematical induction and line-drawing interpretations. I have no interest in presenting philosophical solutions, of which there are a few, and all of which I have not understood.
What I have is not a motion, but an observation.
Policy makers, judges and administrators encounter this paradox in their lines of service everyday. Society needs to agree on ages of consent. Speed limits. Term limits for abortion. In the simple terms employed by Chrysippus in his teaching of the paradox, great difficulty is experienced when we struggle to define fixed quantities as qualities, or predicates. This was brought to my attention by Stephen Fry, who pointed it out to Clive James in a television interview (2007). (Fry attributed the paradox to Zeno, perhaps mistakenly so.)
In philosophy, there are four acceptable responses.
1. Deny that logic applies to soritical expressions
2. Deny some premise(s)
3. Deny the argument’s validity
4. Embrace the paradox.
Society does not care much for this. I am not sure if it can, or should. I have not thought of a way that it can in a manner acceptable to public debate.
The paradox is applicable to society’s making of policy. I have said as much. We do not, however, need to confront the paradox. We circumvent it. Arbitrarily-coined predicates, nebulous in the vagueness of language, require themselves to be defined arbitrarily as well. Society’s solution in a liberal democracy (assuming you live in one, of course) would be to seek group consensus in a democratic fashion amongst representatives at the appropriate levels of the apparatus that is the government. We swap prescriptive linguistics for descriptive linguistics.
If there is a lesson to be learnt, it is that logic did not untie the Gordian Knot - rationality did.
[DAMNIT I spend the night composing this entry, and what do I find? Dinosaur Comics beat me to simpler explanations a few weeks ago!]
----
Resources:
1. Wikipedia, Sorites paradox
2. Stanford Encyclopedia of Philsophy, Sorites Paradox
3. Clive James: Talking in the Library - Stephen Fry 3/3
4. Soren Kierkegaard, M.G. Piety, Edward F. Mooney: Repetition and Philosophical Crumbs, pg 185
5. Bertrand Russell: A History of Western Philosophy
and a few others that I have forgotten.
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