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Paradox of the Heap

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Paradox of the Heap

TecnoTut
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Posted 07/01/03 - 01:57 PM:	#1
This is a paradox due to vagueness of a given predicate. With a single grain of sand, you cannot make a heap. If you cannot make a heap with the grains you have, you cannot make one with just one more. So even with 10 million grains you cannot make a heap -- but it seems counterintuitive to assert that 10 million grains do not constitute a heap. Here's another way of looking at the problem on vaguness: 1 is a small number, and any number bigger by 1 than a small number is small; so all numbers are small. Responses include: denying the major premiss, that is, affirming that there is a sharp cut-off (even if we don't know where); and (alternatively) avoiding the conclusion by revamping classical logic and semantics.
He that dies pays all debts - Shakespeare's Stephano from The Tempest Truth is its own measure - Spinoza, Ethics IIp43s Those who deny [Aristotle's] first principle should be flogged or burned until they admit that it is not the same thing to be burned and not burned, or whipped and not whipped. - Ibn Sina (Avicenna)

wuliheron
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Posted 07/01/03 - 07:01 PM:	#2
The sorites heap paradox is thought by logicians and philosophers to have more to do with semantics and vagueness than logic. Words like bald, heap, etc. are vague. Edited by mod to keep topic on track

TecnoTut
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Posted 07/01/03 - 07:54 PM:	#3
Wrong again. An argument consisting of categorical propositions that can be represented as (or decomposed into) a sequence of categorical syllogisms such that the conclusion of each syllogism except the last one in the sequence is a premise of the next syllogism in the sequence. An example is ‘All cats are felines; all felines are mammals; all mammals are warm-blooded animals; therefore, all cats are warm-blooded animals’. This sorites may be viewed as composed of the two syllogisms ‘All cats are felines; all felines are mammals; therefore, all cats are mammals’ and ‘All cats are mammals; all mammals are warm-blooded animals; therefore, all cats are warm-blooded animals’. A sorites is valid if and only if each categorical syllogism into which it decomposes is valid. In the example, the sorites decomposes into two syllogisms in (the mood) Barbara; since any syllogism in Barbara is valid, the sorites is valid. At least we're talking about sorites now.
He that dies pays all debts - Shakespeare's Stephano from The Tempest Truth is its own measure - Spinoza, Ethics IIp43s Those who deny [Aristotle's] first principle should be flogged or burned until they admit that it is not the same thing to be burned and not burned, or whipped and not whipped. - Ibn Sina (Avicenna)

wuliheron
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Posted 07/02/03 - 01:15 AM:	#4
I did not say logic had nothing to do with the paradox, merely that the actual paradox itself has more to do with semantics than logic. Logistics does not assign truth values to paradoxes. It can argue their validity and strive to disprove they are really paradoxes, but in the case of the Sorities it is thought to be more an issue semantics might possibly resolve rather than logistics.

TecnoTut
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Posted 07/03/03 - 06:09 PM:	#5
I did not say logic had nothing to do with the paradox, merely that the actual paradox itself has more to do with semantics than logic. Logistics does not assign truth values to paradoxes. . . in the case of the Sorities it is thought to be more an issue semantics might possibly resolve rather than logistics. If by 'logistics' you mean logic, then I disconcur. Many logicians view the problem exclusively as a many-valued logic problem.
He that dies pays all debts - Shakespeare's Stephano from The Tempest Truth is its own measure - Spinoza, Ethics IIp43s Those who deny [Aristotle's] first principle should be flogged or burned until they admit that it is not the same thing to be burned and not burned, or whipped and not whipped. - Ibn Sina (Avicenna)

wuliheron
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Posted 07/03/03 - 06:29 PM:	#6
Fortunately, logicians do not rule the world, much less this website whioh is dedicated to philosophers. Here is the Stanford website on this paradox: http://plato.stanford.edu/entries/sorites-paradox/

TecnoTut
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Posted 07/03/03 - 06:40 PM:	#7
I see nothing here that shows that the sorties paradox is more a matter of semantics than logic. I am not saying semantics is irrelevant -- but I am saying that there is an arbitrary claim whenever one states that semantics is more relevant than logic, or logic is more relevant semantics. By the way, I found this sentence in the link "Though soritical predicates are admittedly indeterminate in their extension the indeterminacy is not semantic. " Although I believe the paradox can be contrued semantically, I just want you to know that there are some professionals who think it has nothing to do with semantics
He that dies pays all debts - Shakespeare's Stephano from The Tempest Truth is its own measure - Spinoza, Ethics IIp43s Those who deny [Aristotle's] first principle should be flogged or burned until they admit that it is not the same thing to be burned and not burned, or whipped and not whipped. - Ibn Sina (Avicenna)

Solar Wind
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Posted 07/03/03 - 06:49 PM:	#8
Originally posted by TecnoTut This is a paradox due to vagueness of a given predicate. With a single grain of sand, you cannot make a heap. If you cannot make a heap with the grains you have, you cannot make one with just one more. So even with 10 million grains you cannot make a heap -- but it seems counterintuitive to assert that 10 million grains do not constitute a heap. Here's another way of looking at the problem on vaguness: 1 is a small number, and any number bigger by 1 than a small number is small; so all numbers are small. Responses include: denying the major premiss, that is, affirming that there is a sharp cut-off (even if we don't know where); and (alternatively) avoiding the conclusion by revamping classical logic and semantics. What might this say about the POSSIBLE "consciousness" of the very small (elementary particles) and the very large (the Universe Itself) and Everything in between (us, lizards, dogs, trees, bugs & rocks)? In other words, what is the cut-off point for consciousness? If a bee can give directions to his hive mates with a wiggle of his butt, might not this be a form of consciousness (awareness of self and/or others...as well as awarenss of context)? And if a bee can be conscious, why not a roach. And could one make a case for the consciousness of elementary particles as explaining the interconnectedness of all things -- a NETWORK of interconnections on the non-physical level -- with "forces" like gravity acting upon seemingly remote "points" without a conductive medium (ether?) in between? Humor me.

TecnoTut
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Posted 07/03/03 - 06:53 PM:	#9
Who said a roach and a bee cannot be conscious? And who said a particle is conscious?
He that dies pays all debts - Shakespeare's Stephano from The Tempest Truth is its own measure - Spinoza, Ethics IIp43s Those who deny [Aristotle's] first principle should be flogged or burned until they admit that it is not the same thing to be burned and not burned, or whipped and not whipped. - Ibn Sina (Avicenna)

Woods
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Posted 07/03/03 - 06:54 PM:	#10
Someone's been reading Leibniz again . . . but that's not a bad thing initself. So, are you saying that things with nothing to call a brain -think?

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