Yes Virginia, There Is a Universe. (Part Four--Moon in June)
Initially I thought that my arguments had taken care of this thread. Indeed there was no response to my three "Virginia" posts for 16 days. But ultimately Virginia came back one day to tell me of Jimmy K.'s latest outrages and of
Richard J. Hanak's lengthy reply.
"OK Virginia, let's start with his arguments about classes and sets. They're particularly stinky!"
Quote:
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Originally Posted by Richard J. Hanak
Classes and sets are abstract ideas and exist only in the mind. All that can be attributed to a class or set is its rules of membership. An abstract class or set cannot have physical properties (density, entropy) or histories (BB, SS) attributed to it.
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"That's wrong right off the bat. Can you think of a property every set has?"
Virginia though about it a moment, and then asked, "The number of elements in it?"
"Yes, every set has a cardinality, the number of elements in it, either zero or some finite number or possibly even infinitely many. Colloquially we consider the properties of the members to be the properties of the set. We can consider, for example, the set of all stars within 1000 light-years of Earth. Once we have this list we can ask how many stars are in this set, what is the total luminosity of the stars in this set, what percentage of stars in this set have spectral type G and so on. We can always use the locution 'the attributes of this set's elements' or 'the history of this set's elements' but everybody understands that this is what is meant by 'attributes of this set' and 'history of this set'."
"And sets don't even have to be homogeneous for us to assign meaningful attributes to it. I can define a set that consists of a lion, a witch, and a wardrobe. I can determine how many doors it has by counting the doors of the wardrobe."
"How many teeth does your set have?" Virginia catches on quickly!
"I could determine the total number of teeth by counting if only the lion and the witch will let me!
RJH continues:"
Quote:
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Originally Posted by Richard J. Hanak
Look what happens if we try to define a thing as a set. Let's take the moon as an example. We can begin with 'the moon is a set of atoms.' The earth and the sun are also sets of atoms, so our definition of the moon as a set is not sufficiently narrow. We could add another membership rule to define which atoms can be members of the moon set. Any way you try to define that membership you ultimately wind up with 'the moon is the set of atoms that constitute the moon.' Unfortunately a thing cannot be defined in terms of itself. In such a definition if we replace the word 'moon' wherever it occurs by 'the set of atoms that constitute the moon' we soon have 'the moon is the set of atoms that constitute the set of atoms that constitute the set of atoms that constitute the set of atoms ......' without end, and we can never attain a definition. (The 'fin' in 'definition' means 'end'.)
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"I challenged him to define the Moon himself, and
RJH continues with this:"
Quote:
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Originally Posted by Richard J. Hanak
In the quote CM refers to above, I tried to show the kind of problems that can arise if we try to define a real thing as a set or class. We have no such problems when real things are not defined as a set or class. Modern definition: The Moon is the Earth's natural satellite. Ancient definition: The Moon is the largest and brightest thing wever seen in the night sky.
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"Only problem is, he hasn't defined the Earth, he hasn't defined satellite, and he hasn't defined what 'natural' means in the context of his definition.
"Now I know that words have to be defined in terms of other words, and ultimately there are going to be words that cannot be defined but whose meanings must be taken to be understood, but
RJH does not extend this courtesy to me in the definition that I give later of the Universe.
"And even if we do accept
RJH's definition of the Moon, it is still ultimately a collection of atoms and it has the attributes that it does by virtue of this fact. Because the Moon is a collection of atoms, it has a total mass and an inertia tensor, it has a history (its position at each moment of time), it has velocity, linear momentum and angular momentum. All of these are things that matter very much to me as a celestial mechanic. It has all of these things by virtue of being a collection of atoms. Now we could please
RJH by always saying things like 'the collection of atoms that constitutes Earth's natural satellite has a total mass of 7.3483E+22 kg', but that would be pedantic."
To be continued...