Afternoon.
Carol is cooking sauerkraut and pork. Smells good to Richard who just finished
Chapter Eight of Wolff's Fire and Fury.
** **
Chapter eight. In Fire and Fury the inner WH political triumvirate are Bannon, Priebus
and Kushner doing power struggles among themselves. Pence rests elsewhere to up
for his master's bidding in the inner war fitting. Late in the chapter eight
game the questions is asked what the President's priorities are. No one knows.
Round and round and round this goes while the West Wing rapids of wonder flows.
** **
1348 hours. We had a
leisurely morning with no errands. Jadah is crying for attention at the top of
the stairs. I'll have to see to her needs.
Later, my man. - Amorella
2057 hours. We watched NBC
News and the latest "This Old House Hour". Time for Rachel Maddow. I
am hooked on how we are in the political mess both nationally and
internationally.
Later. - Amorella
You watched most of Rachel Maddow (only
one 'a' in Rachel). Then checked out a few days old Quora. You love paradoxes
and Martin Freeman has one so you dropped it in. - Amorella
2208 hours. What I love
about this paradox is that it shows the logic might be clear but that words
without specific definition, i.e. a pile of sand cannot be fully clarified.
People know what a pile of sand is and they also know what a heap of sand is
until you compare them. This reminds me of the question: "How many Angels
are there on a pinpoint or head of a pin? First, one has to define an Angel, a
spiritual being (not a material being) by size. What?
** **
Paradoxes: What defines a pile of sand?
Martin Freeman
Answered Dec 30
|
The Heap Paradox or
the Sorites’ paradox was first proposed by the greek philosopher Zeno of Elea.
It basically says that you first take a pile of sand, containing thousands of
individual grains of sand, and this pile is known as a heap.
Using tweezers, we
start removing grains of sand one at a time. We keep doing this until there is
only one grain of sand left. Is it a heap? If not, why not? When did the pile
become “not a heap”?
The paradox can be
stated logically in premises as follows:
1000000 grains of
sand is a heap of sand (Premise 1)
A heap of sand minus
one grain is still a heap. (Premise 2)
By continuously
applying these two premises, which are demonstrably true by induction (one
experience-based method of learning knowledge about the world, we are forced to
accept the conclusion that one grain of sand is a heap.
We can also work
backwards. If we start with one grain of sand, and keep adding on grains of
sand, when does the collection of grains become a heap?
There are five main
solutions to the Heap Paradox. The main differences come about because some
emphasize perception as reality while others emphasize being as
reality.
•
Vagueness. Holds that Language is inherently vague. The use of words like
“heap” are used when the speaker wishes to communicate a lack of knowledge or
emphasize that the precise amount is meaningless.
•
First,
we must realize that many other words in language such as “bald” and “ocean”
work this way. We could construct the same paradox by removing liters of water
from the ocean. At one liter, is the ocean still an ocean? We could do the same
also with hairs on a head.
The
use and manipulation of these words dates back to Supervaluationism. Basically,
if I said of the greek god Zeus, “Zeus likes chocolate”, the statement is vague
and is useless to evaluate since we have no information on Zeus’ chocolate
preferences.
This
view holds that all language is a compromise between the speaker, who wants to
use the most vague words possible for minimum effort, and the listener, who
wants the most specific words possible for minimum mental effort as well.
•
Fuzzy logic. Fuzzy logic is given to all systems of logic devised after the
1930s. Everything before the 1930s was put in a single package called Classical
Logic. The main difference of Fuzzy logic is its rejection of the Bivalence
Principle. Basically, the Bivalence Principle says that every statement is
either true or false, and Fuzzy Logic rejects that.
•
Take
probability statements, for example. What if I said: “It will rain in 10 days”?
How do we evaluate the truth value of that statement? It cannot really be said
to be definitely true or false. The same applies to combinations of statements
involving predictions and statements about the present.
So,
Fuzzy Logic came up with a system of dividing truth values, instead of the
binary system of 0 for false and 1 for true, into fractions. 0 represents
definitely false, ¼ represents mostly false, ½ represents half true, ¾
represents mostly true, and 1 represents wholly true. This can be subdivided
into as many fractions as is applicable to the statement.
Puzzled?
Let’s take the example of a keyboard which is designed to electronically
simulate a piano. Using classical logic, we could evaluate statements as either
“the key is pressed” or “the key is not pressed.” If the key is pressed, then a
sound is made. But this is not how a real piano works. Using Fuzzy Logic, a
press is assigned a value. Not pressed= 0, which means no sound comes out.
Softly pressed= ¼ truth value, little sound comes out. Moderately pressed =½
truth value, which means a medium-volume sound comes out, and so on.
Fuzzy
logic basically approaches this paradox by saying that the statement “this is a
heap” is more true at certain points than others. So at 100,000 grains of sand,
it is definitely a heap. At 10,000 grains of sand, it is mostly a heap,
at 1,000, maybe a heap, at 100, mostly not a heap, and at 1, definitely not a
heap.
•
The Time dimension. I mentioned the higher dimensions here:
After
you’ve read that answer, realize that the Higher Dimension method involves
recognizing that logic is incomplete in three dimensions, even supposing a
one-dimensional time.
The
paradox may be illustrated thus:
Heap
------------------------------------------>
<------------------------------------------------- a="" few="" grains="" o:p="">
As
seen, you can start with a heap and move downward, taking grains off as you go.
However, the pile retains the “heap” status until only a few grains are left.
Or, you can start with a few grains and move upward, retaining the “few” status
even when there are so many, perhaps more than the “heap”. The paradox only
arises when you try to consider both statements as happening simultaneously.
Therefore, you get a paradox. If you start from the beginning of both arrows
and move inwards, you will find, at any vertical line you can draw through both
arrows (a moment in time) that around the middle, the same number of grains can
be called both a “heap” and a “few” depending on where you starting from. And
this is the contradiction.
However,
this is unlike “fuzzy logic”, because it does not propose fractions, only
states of superposition, where once time becomes meaningless, a statement can
be both true and false at the same time.
The
paradox only arises when you start from a certain point and try to loop back.
It can be avoided entirely by changing the definition of heap based on the
original arrangement of the grains (whether there was a lot at first or only a
little) and once we look at this from “above” time the statement is both true
and false.
•
4.
The Perception is Reality solution. Basically, this solution holds that
if the first word that is aroused in your consciousness (when you look at the
pile of sand) is the word “heap”, then it is a heap. If the first word that
comes to your head is “pile” or “mountain”, then it is not a heap. Of course,
this solution accepts that the definition of heap will change for each person,
i.e. that it is subjective.
•
You
can do this involving group consensus as well. If Mike’s “heap” trigger for his
brain lies in looking at a pile of between 1,000 and 500,000 grains, and Adam’s
trigger is between 20 and 40,000 grains, then one would average them out.
Alternatively,
one can predict whether a pile can be considered a “heap” based on only the
overlapping zones for each person. The reason this method works is that most
humans’ brains are wired similarly.
Solution
also accepts that vague words like this were created by humans to address sets
that are inherently subjective. In other words, the subjective reality
predates the word.
•
5.
There is a definite value and cut-off of a “heap”, we just haven’t found
it out yet. This solution is supported by Quantum Mechanics and the realization
that the universe is discrete. Infinite variations in terms of getting smaller
in size are simply not possible.
•
This
view holds that the human brain thinks in many logical neural networks, and
that if we were to untangle the many neurons and synapses, we could actually
find out what the conscious mind considers a “heap.”
However,
there is a problem with this approach. It does not consider the arrangement of
sand grains. So ten thousand grains of sand spread over a square foot may not
be considered a heap, but the same amount spread over a few square inches is
called a heap due to its shape.
Selected
and edited from quora dot com.
** **
2217 hours. I have the
same sort of problem if I want to know the 'stuff' of Amorella, is she a
spiritual substance or an imaginary substance. How does one define a difference?
** **
spiritual - adjective 1 relating to or affecting the
human spirit or soul as opposed to material or physical things: I'm
responsible for his spiritual welfare | the spiritual values
of life. • (of a person) not concerned with material values or
pursuits. 2 relating to religion or religious belief: the tribe's
spiritual leader.
**
spirit - noun 1 the nonphysical part of a person which is the
seat of emotions and character; the soul: we seek a harmony between body and spirit. • the nonphysical part of a person regarded as a
person's true self and as capable of surviving physical death or separation: a year after he left, his spirit is still
present. • the nonphysical part of a person manifested as
an apparition after their death; a ghost. • a supernatural being: shrines to nature spirits. • (the Spirit) short for Holy Spirit.
** **
imaginary - adjective 1 existing only in the
imagination: Chris had imaginary conversations with her.
**
imagination - noun the faculty or
action of forming new ideas, or images or concepts of external objects not
present to the senses: she'd never been blessed with a vivid
imagination. • the ability of the mind to be creative or resourceful: technology
gives workers the chance to use their imagination. • the part of the mind that
imagines things: a girl who existed only in my imagination.
Selected
and edited from the Oxford/American software
** **
2228 hours. Pray tell, how
does one argue what is spiritual and what is imagination without further
definition. Which is the larger, the spirit or the imagination?
Young man, you attempt to make a point where one cannot be imagined. -
Amorella
2231 hours. You mean I cannot
imagine an Angel or a Spirit?
Well, can you? - Amorella
2233 hours. I am shaking my
head 'no' and smiling deeply at the same time. (It is strange that I cannot imagine either in a physical or spiritual reality because I cannot fully define reality. - 2244 hours)
Post. - Amorella
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