Smarandache Sorites Paradox
Carol Harlestle Jr.
following:
Our visible world is composed of a totality of invisible particles.
a) An invisible particle does not form a visible object, nor do two
invisible particles, three invisible particles, etc.
However, at some point, the collection of invisible particles becomes
large enough to form a visible object, but there is apparently no
definite point where this occurs.
b) A similar paradox is developed in an opposite direction. It is always
possible to remove a particle from an object in such a way that what is
left is still a visible object. However, repeating and repeating this
process, at some point, the visible object is decomposed so that the
left part becomes invisible, but there is no definite point where this
occurs.
References:
[1] Smarandache, Florentin, "Invisible Paradox" in "Neutrosophy. /
Neutrosophic Probability, Set, and Logic", American Research Press,
Rehoboth, 22-23, 1998.
[2] Smarandache, Florentin, "Sorites Paradoxes", in "Definitions, Solved
and Unsolved Problems, Conjectures, and Theorems in Number Theory and
Geometry", Xiquan Publishing House, Phoenix, 69-70, 2000.
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Before you buy.
Daryl McCullough
>
>How can we resolve the Smarandache Sorites Paradox, which is the
>following:
>
>
>Our visible world is composed of a totality of invisible particles.
>
>a) An invisible particle does not form a visible object, nor do two
>invisible particles, three invisible particles, etc.
>However, at some point, the collection of invisible particles becomes
>large enough to form a visible object, but there is apparently no
>definite point where this occurs.
>
>b) A similar paradox is developed in an opposite direction. It is always
>possible to remove a particle from an object in such a way that what is
>left is still a visible object. However, repeating and repeating this
>process, at some point, the visible object is decomposed so that the
>left part becomes invisible, but there is no definite point where this
>occurs.
To me, the way to solve this type of paradox is to replace absolute
judgements (is this collection of particles a visible object?) by
probabilistic judgements (what is the probability that the collection
of particles will be seen?). When an object is made up of one million
and one particles, the probability of its being seen is very slightly
greater than an object made up of only one million particles.
Of course, you can reinstate the paradox in terms of probabilities:
At what point does it become 100 percent certain that the object will
be seen? But I think that the reasonable answer is "never". Even if
you are in the same room as an elephant, there is a itsy-bitsy, teeny
tiny, wee, small probability that you won't see it.
--
Daryl McCullough
CoGenTex, Inc.
Ithaca, NY
Neil W Rickert
>How can we resolve the Smarandache Sorites Paradox, which is the
>following:
>Our visible world is composed of a totality of invisible particles.
>a) An invisible particle does not form a visible object, nor do two
>invisible particles, three invisible particles, etc.
>However, at some point, the collection of invisible particles becomes
>large enough to form a visible object, but there is apparently no
>definite point where this occurs.
I don't see any paradox.
>b) A similar paradox is developed in an opposite direction. It is always
>possible to remove a particle from an object in such a way that what is
>left is still a visible object. However, repeating and repeating this
>process, at some point, the visible object is decomposed so that the
>left part becomes invisible, but there is no definite point where this
>occurs.
I don't see any paradox there either.
Why do you take these to be paradoxical?
Neil W Rickert
>> >How can we resolve the Smarandache Sorites Paradox, which is the
>> >following:
>> >Our visible world is composed of a totality of invisible particles.
>> >a) An invisible particle does not form a visible object, nor do two
>> >invisible particles, three invisible particles, etc.
>> >However, at some point, the collection of invisible particles becomes
>> >large enough to form a visible object, but there is apparently no
>> >definite point where this occurs.
>> I don't see any paradox.
>It is really a paradox, i.e. a typical Sorites paradox, i.e. when the
>frontier is not
>exactly found between visible and invisible.
A typical sorites paradox (the paradox of the heap) depends on the
intuition that the property of being a heap is a monotone function of
the number of grains in the heap.
Our intuition for visibility is very different. In particular, it is
our intuition that visibility depends on all kinds of additional
things such as the distance, the ambient light, whether the observer
is paying attention, etc.
>And the Smarandache Sorites Paradox is connected with a more general
>Smarandache Paradox. I copy from
>http://www.andrews.edu/~calkins/math/biography/topparad.htm:
It seems that should be
"http://www.andrews.edu/~calkins/math/biograph/topparad.htm"
Carol Harlestle Jr.
> >following:
>
> >Our visible world is composed of a totality of invisible particles.
>
> >a) An invisible particle does not form a visible object, nor do two
> >invisible particles, three invisible particles, etc.
> >However, at some point, the collection of invisible particles becomes
> >large enough to form a visible object, but there is apparently no
> >definite point where this occurs.
>
>
always
> >possible to remove a particle from an object in such a way that what
is
> >left is still a visible object. However, repeating and repeating this
> >process, at some point, the visible object is decomposed so that the
> >left part becomes invisible, but there is no definite point where
this
> >occurs.
>
>
> Why do you take these to be paradoxical?
>
>
It is really a paradox, i.e. a typical Sorites paradox, i.e. when the
frontier is not
exactly found between visible and invisible. Daryl McCullough is right
too.
See, for example:
http://www.madsci.org/posts/970594003.Ph.q.html
http://www.madsci.org/posts/970594003.Ph.r.html
And the Smarandache Sorites Paradox is connected with a more general
Smarandache Paradox. I copy from
http://www.andrews.edu/~calkins/math/biography/topparad.htm:
<A Smarandache Paradox is one with the meaning of "All is possible, the
impossible too.">.
Andy
Carol Harlestle Jr. wrote:
It's not different from the liar's paradox.
For example, with regards to the particles, in reaity there is a threshold
that is different for different people under which some particles cannot be
visibly discerned. To say "Our visible world is composed of a totality of
invisible particles." does not imply paradox, it just means that people
can't discern minute particles with their eyes. So, it is false in
implication.
With regards to "All is possible, the impossible too.", it is false because
if all is possible then nothing is impossible a priori, in the first place,
and at the same time if anything is impossible, then not all is possible.
I don't believe there are paradoxes, or rather I believe there are not
paradoxes.
--
contact Andy
company Apex Internet Software
email in...@apexinternetsoftware.com
website http://www.apexinternetsoftware.com/
Mark William Hopkins
>How can we resolve the Smarandache Sorites Paradox, which is the
>following:
>Our visible world is composed of a totality of invisible particles.
The "visible world" (which here actually means your "visual field') is
composed of those millions of enormously tiny and rapidly fluctuating
specks you see when you look carefully at the smallest parts of your visual
field. The specks I'm referring to are the ones you see when you focus on
your own visual field at resolutions around 1/100000 radians or so (hard
to estimate since they're smaller than everything else that's visible and
very hard to make out individually), and which appear to be 'shimmering' or
'vibrating' chaotically at around 20-50 Hz, almost like specks of sunlight do
on the surface of an ocean seen from miles up.
They're easiest to see when you're looking directly at a uniform background,
and are always there (eyes open or shut), rigidly fixed to the visual field
(no matter how you move your eyes).