Joe comes to visit Fred and finds Fred sitting on his porch, sharpening his axe.

"That's a fine looking axe, Fred," says Joe.

"I think so too," says Fred, "I've chopped firewood with it every day for over twenty years and it's never failed me."

Joe, a little surprised, asks "How have you kept it in such good shape, using it every day like that?"

"Well," says Fred, "it's had a half-dozen handles and I've replaced the head twice in that time, so it's always been good to work."

"Yup, it's a fine looking axe, Fred," says Joe.

''How many axes has Fred had?''

This story raises an interesting question about '''identity''' and how it's handled in different environments. 
* According to Codd, every time he changed a head or a handle, Fred got a new axe. 
* According to U.S. and Canadian firearms law, each handle was a new axe. 
* According the universal vehicle registry, each head was a new axe. 
* According to Object Oriented Design principles, Fred had only one axe for lo' those twenty years.
* According to Agile development principles, Fred's axe is still under construction.
* According to LogicProgramming principles, ?
* According to FunctionalProgramming principles, ?

-- MarcThibault

By the way, you aren't MarcThibault! I met Marc several years ago, and you don't have a ''single molecule'' in common! -- the water bag previously known as IanOsgood

''Remote molecular analysis? Amazing!''

And think about rivers.

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This is a variation on the "Ship of Theseus", a classic illustration of notions of identity and persistence, and how they are affected by change. See http://faculty.washington.edu/smcohen/320/theseus.html

''The ship wherein Theseus and the youth of Athens returned had thirty oars, and was preserved by the Athenians down even to the time of Demetrius Phalereus, for they took away the old planks as they decayed, putting in new and stronger timber in their place, insomuch that this ship became a standing example among the philosophers, for the logical question of things that grow; one side holding that the ship remained the same, and the other contending that it was not the same.'' -- Plutarch

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Doesn't this come down to the issue of Interfaces and BlackBox? The interface between the woodsman and the tree is still an ax, which has the same general set of properties: A handle with a length and a head with one or two blades, either of which may have a particular sharpness. -- Wyatt Matthews

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''so the class of Fred's axe is constant, but how many instances?'' -- mt
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CategoryPolymorphism