Matter of opinion.

[Lorenzo]

Dion is a man. Theon is the part of Dion that is
all of Dion but his left foot.

If that's true, then 1=2 except .10%
100 is a hundred. 90 is also 100 minus 10.

It's all names and numbers! What happened to Ockham's Razor?

[Zubivka]

What happened to Ockham's Razor?

I reckon it was traded in for a Norelco chromatic shaver. It's the price of sophistication--in its prime sense.
This often happens to sharp tools when one is not careful. A thin red line...

You could sing "Careful with that blade, Ockham"
--on the tune of "Careful with that axe, Eugene", of course

[Ridseard]

A mathematician wouldn't bother about the fact that Dion and Theon are conceptually distinct and have different histories. Since (after the amputation) Dion and Theon have identical mathematical and physical properties, they would be identified: (amputated Dion) = Theon. This is similar to identifying the fractions 4/8 and 1/2 because they have exactly the same mathematical properties, although they consist of different numerals.

[jim stone]

Yes, it's just that 1/2 and 4/8 really do have all their
properties in common. There is just one fraction in the
story--it's denoted by several numerals.

Similarly 'the morning star,' 'the evening star,'
and 'Venus' all denote the same object, in fact.
But part of what follows from the fact that
the morning star and the evening star
are identical to Venus is that the morning
star, the evening star and Venus share
all their properties, past, present, and future.

Venus is the first 'star' we see in the morning.
The morning star is denoted by 'the evening star.'
The evening star is the star that we first
see in the morning.

This is the Indiscernibility of Identicals:
identical objects must share all their
properties.

Also known as the principle of the alibi.
If the burglar left footprints in the
garden showing that he wore size
7 shoes, and my feet are way to
big to wear size 7, then I wasn't the burglar.

The trouble is that Dion and Theon,
unlike 4/8 and 1/2 and the morning
star and the evening star, do have
different properties, even today,
after the amputation. Dion, but not
Theon, has the property that yesterday
Dion weighed more than Theon,
also Dion, but not Theon, has
the feature that yesterday he included
ten toes; Dion, but not Theon, yesterday
occupied more space than Theon.
Dion contained molecules Theon did not
contain. Identical objects share all their
properties, therefore Dion and Theon
are distinct.

We could deny the Indiscernibility of Identicals,
and allow that one and the same thing
can have different properties from itself.
But that's strongly counter-intuitive.

As to Ockham's Razor, I think that's what this is
about, ultimately. The conclusion of Chrysippus's argument,
that after the amputation there are distinct
physical things occupying the same space,
made of the same molecules, violates
Ockham's Razor. Too many entities!
As David Lewis wrote: 'It reeks of double
counting.' That's why there's a paradox.
But that helps explain what's the matter
with the conclusion. It doesn't yet locate
a fallacy in the forceful argument for
the conclusion.

Russell said that in philosophy we
begin with premises too obvious for
anybody to deny them, and proceed by
apparently inevitable inferences to conclusions
too bizarre for anybody to believe them.

Dion is a man. Theon is all of Dion but Dion's
left foot.

It's hard to see a problem. Dion is a man--well,
there are men, and Dion is one of them.
Theon is all of Dion but Dion's left foot.
Men have parts smaller than themselves.
Theon is a smaller part of Dion.
No problem with Ockham's Razor
here. Dion is bigger than Theon, etc.

Nobody is saying that Dion = Theon,
to the contrary, they are distinct,
today, before the amputation,
and tomorrow, after it.

A man can survive the amputation of
a foot. And Theon survives the amputation,
surely; nothing has been chopped off Theon.

So Dion and Theon both survive and occupy the same
place, but they're distinct; for they have
different properties after the amputation.
From which it follows
that there are two objects there, not one,
which is crazy, I think.

Of course, we can insist that one of
them doesn't survive. But which?
Dion? Or Theon? Best

[Zubivka]

Similarly 'the morning star,' 'the evening star,'
and 'Venus' all denote the same object, in fact.

I bef to digger.

1) Venus names a heavenly body, the second planet of the Solar System, Milky Way, Our-Universe-As-We-Know-It.

2) Morning star, evening star, shepherd's star (etc.) all name the reflection of the sun light over the atmosphere of said Venus (which makes it a "star"), and only as seen from the neighbouring planet Terra, and only at favourable moments from its variable part which at a given time is shadowed from the sun, aka "night".

Infering a 1) + 2) identity implies a confusion between an object and its image from a very particular vantage point.

There are in no way identical concepts, no more than a man and his shadow on the cave wall, the burglar and his footprint, the painting and the pipe... or a recorder and a chromatic instrument.

Russell said that in philosophy we begin with premises too obvious for anybody to deny them, and proceed by apparently inevitable inferences to conclusions too bizarre for anybody to believe them.

Right, but if the premises are deeply erroneous for a start, all you infer is a sophism.
Then, the intuitive cognition known as "common sense" may find a use as a guiderope for a safe landing, the secure end to grab and start unravel the tangled premises.

[Walden]

So, Dion and Theon refer to parts of a whole?

St. Thomas Aquinas said that there is only need of one of that which is incorruptible, but there are multiple individuals of each species of that which reproduces and is corruptible.

"A twofold distinction is found in things; one is a formal distinction as regards things differing specifically; the other is a material distinction as regards things differing numerically only. And as the matter is on account of the form, material distinction exists for the sake of the formal distinction. Hence we see that in incorruptible things there is only one individual of each species, forasmuch as the species is sufficiently preserved in the one; whereas in things generated and corruptible there are many individuals of one species for the preservation of the species. Whence it appears that formal distinction is of greater consequence than material. Now, formal distinction always requires inequality, because as the Philosopher says (Metaph. viii, 10), the forms of things are like numbers in which species vary by addition or subtraction of unity. Hence in natural things species seem to be arranged in degrees; as the mixed things are more perfect than the elements, and plants than minerals, and animals than plants, and men than other animals; and in each of these one species is more perfect than others. Therefore, as the divine wisdom is the cause of the distinction of things for the sake of the perfection of the universe, so it is the cause of inequality. For the universe would not be perfect if only one grade of goodness were found in things." [St. Thomas Aquinas, SUMMA THEOLOGICA]

[Lorenzo]

Theon is the part of Dion that is
all of Dion but his left foot.

Theon is all of Dion but Dion's
left foot.

It's hard to see a problem.

Theon is all of Dion but Dion's left foot.

Nobody is saying that Dion = Theon
to the contrary, they are distinct,
today, before the amputation,
and tomorrow, after it.

See the difference?

Unless you say what you mean by staying with the "words" you say...I would agree that, "It's hard to see a problem." But in your first example, if "Theon is the part of Dion that is all of Dion but his left foot" then you are saying "that Dion = Theon" except for the left foot.

[Jerry Freeman]

What we end up with here, it appears to me, is that the difference between Deon and Theon is something abstract.

The difference between Deon and Theon is their past. Physically, in the present, they are identical. But they can be said to be different because Deon used to have two feet. That's an abstract thing. It's a memory.

On the one hand, one could argue that it doesn't make Deon and Theon distinct. That, to me, would be perfectly reasonable, and I would say, "You're right, they're not distinct. They're identical."

On the other hand, you could argue that they are distinct because of their different pasts. I would say, "You're right. They have different pasts. They're distinct."

As to the issue of two things occupying the same space -- that's very similar to the problem with the statue and the piece of bronze occupying the same space. The thing that gives a statue its statueness is abstract. The thing that distinguishes Deon and Theon is abstract. It seems to me that any number of abstract things can occupy the same space without violating any laws of physics or common sense.

Another way to go at this would be to consider what Theon is in the first place. He's something abstract. Really, he's just an idea. There's no distinct, obvious entity that anyone would naturally distinguish and say, "Yep. There's Theon. Hi, Theon." So again, we have an abstraction. And as I said, any number of abstractions can occupy the same space without violating any laws of physics or common sense.

[Martin Milner]

I agree with Jerry & Lorenzo, having a part of you called by a separate name is just playing around with words. Theon is just a concept, not a separate person or thing.

I might as well say my left arm is called Jeremy. Therefore Jeremy and my left arm occupy the same space at the same time, and I don't even need to have an amputation.

To paraphrase Leonardo,

Deon = Theon + left foot

Deon - left foot = Theon

This doesn't make Deon and Theon separate things to me.

Still they have some different properties:
Dion alone has the property that yesterday
he included a left foot as a part.

Therefore they are distinct.

Therefore there are two physical things
in the same place at the same time,
(which Chrysippus thinks is Koo Koo,
which is why this is called Chrysippus's Puzzle.)
This is an argument, with premises,
inferences, and a conclusion.

History is not a physical property.

[Walden]

History is not a physical property.

That's right. History isn't a physical property.

[Lorenzo]

But in jimstone/Chrysippus's defense, I realized that Dion was a man..."By a man I just mean a human animal."

It was never stated, or implied (if I remember correctly) that Theon was a man. I now realize that Jim carefully chose his words, and avoided a description of Theon. Theon could actually be a reference name describing Dion's trunk, or a major section of his torso, except he uses the word "all" which implies the whole person.

But Jerry and others offered a new and valid angle too, with which I agree, solving the puzzle.

I'm with Martin though, unless you find the idea in the puzzle that one is LIKE the other, then because of common understanding of language, one must be the other.

[Jerry Freeman]

Extending what Lorenzo has proposed,

If Theon is something physical, like Deon's trunk, and Deon is the whole person, then again the problem sorts itself out.

Then Deon, the whole person, is the abstraction. You have Deon (the whole person), Deon's body (before and after losing the foot), and Theon (all of Deon's body except for the foot). After losing the foot, Deon's body and Theon are identical, but Deon (the whole person) and Theon are not identical, though they occupy the same space. I am not identical with my body, though I at least appear to occupy the same space.

Where the problem becomes interesting, though, is when it's extended to the issue of Jim, sans all but Jim's brain. And what about Jim without Jim's brain? Then we get into what I would consider the really intriguing questions about what a person is, what is consciousness, does consciousness emerge from matter or does matter emerge from consciousness, etc.

Best wishes,
Jerry

[Walden]

Where the problem becomes interesting, though, is when it's extended to the issue of Jim, sans all but Jim's brain. And what about Jim without Jim's brain?

I say we let Jim keep his brain.

[Lorenzo]

I am not identical with my body, though I at least appear to occupy the same space.

Pretty clever! I'd like to see that! When's your next appearance, or do you just show one? How is "I" different from "my body?"

And how would you know...and know you know? Of course, we may think we know ourselves as well as anyone possibly could, but what we think may only be true unless someone knows us better, like our mothers.

The first principle of objective self analysis is never trust your opinion of yourself (unless you've never been wrong, nor can be). Care to turn yourselves over to the authorities?

[Jerry Freeman]

Hi, Lorenzo.

This is a tough one.

I can tell you I do know categorically that I am not my body.

I suppose one could go at it logically. Every molecule of my body has been replaced many times, and I'm still me. If I'm my body, which model am I? The 1965 model? The 1993 model? I'm sure I was me in 1965, 1993 and 2003, but my body was not the same body.

But that's indirect, and subject to debate, anyway.

It gets to the big question, "What am I?"

I believe the answer to that question is different for different people, according to different experiences, and I would also say, different states of consciousness.

Best wishes,
Jerry