Paradox: objective meaninglessness of concept of similarity?

February 1, 2012 1:58 AM

Has anyone heard of the mathematical "proof" that the concept of similarity is objectively meaningless?

A couple of years ago, if I recall correctly, some mathematicians or philosophers showed that because real-world objects have an infinity of properties, you could cherry-pick as many properties as you wanted to counterintuitively "prove" that, for example, an orange is more similar to a roll of aluminum foil than to an orange segment. (For example, both the orange and the aluminum foil roll are round and weigh more than an ounce, properties the orange segment doesn't share.)

Can anyone point me to an article about the proof or "proof" of the meaninglessness of similarity, with the names of the originators of the concept? Thanks.

posted by rwhe to religion & philosophy (8 answers total)

I think you're thinking about Nelson Goodman, who wrote "Seven strictures on similarity." The central idea was precisely as you say: there are always an infinite number of possible ways two things could be alike (e.g., both of myself and a potato have mass, are over 90 million miles away from the sun, etc etc). Goodman's point spawned a lot of discussion, but I believe he was the originator.

Full citation:

Nelson Goodman (1972). Seven Strictures on Similarity. In Problems and Projects. Bobs-Merril.
posted by forza at 2:34 AM on February 1, 2012 [6 favorites]

(Of course, the basic ideas underpinning this overlap considerably with problems of induction dating all the way back to Hume. But I think Goodman was the first person, or at least the first major person, to relate it all to similarity).
posted by forza at 3:42 AM on February 1, 2012

You might be interested in this (original paper here) which tries to disqualify Leibniz's identity of indiscernibles: two things are identical if and only if they share all the same properties.

Max Black tries to argue against this by counter-example: imagine two spheres identical in all their properties. Aren't they still two rather than one and the same thing?

This turns your question upside down to pick apart the notions of 'similarity' and 'identity' - two things may be different even if they are exactly similar, I don't know if this would be useful to you but it's an interesting angle I think.

I'm not aware of any 'proof' that similarity is objectively useless. To my understanding it is actually useful in various logical languages and to philosophers and mathematicians alike.
And real world objects have a variety of shared properties that are not considered relevant from certain perspectives.
posted by mkdirusername at 4:41 AM on February 1, 2012 [2 favorites]

In quantum mechanics, any two particles are indistinguishable if you interchange their position, that is, they aren't really two separate things.
posted by empath at 6:25 AM on February 1, 2012

It's not exactly the same thing, but Radiolab did an episode called Stochasticity which was about randomness and coincidence. The first segment addresses basically what you are talking about, although not with math.

This is more an-interesting-thing-that-may-be-on-topic than it is an answer.
posted by gauche at 6:33 AM on February 1, 2012

Seconding forza -- I bet you're thinking of Goodman.
posted by enlarged to show texture at 6:49 AM on February 1, 2012

because real-world objects have an infinity of properties, you could cherry-pick as many properties as you wanted to counterintuitively "prove" that, for example, an orange is more similar to a roll of aluminum foil than to an orange segment.

You can generate real-world proof of this concept by playing the game French Toast.
posted by alms at 7:22 AM on February 1, 2012 [4 favorites]

forza, thank you! I'm sure the recent discussion I saw was philosophical fallout from Goodman's paper. Bingo.

mkdirusername, thanks. I am also interested in the (similar?) concept of the identity of indiscernibles.

gauche, I heard most of that episode but don't recall that segment. I'll have to give it a second listen.

alms, great game! I will try to get this played at my next game night.
posted by rwhe at 11:46 AM on February 1, 2012