There was a typo in my statement of the transitive property. I also approached my OP from the wrong angle. |
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So here's the deal. We want the word to be what mathematicians call an "equivalence relation" but it's not. What does this mean? It means that we want three things to be true. |
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Last edited by PhilosopherStoned; 03-18-2011 at 06:16 AM.
Previously PhilosopherStoned
There was a typo in my statement of the transitive property. I also approached my OP from the wrong angle. |
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Last edited by PhilosopherStoned; 03-18-2011 at 07:54 AM.
Previously PhilosopherStoned
Your model is insufficient. You're ignoring key information by trying to treat species as members of a set. |
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Just to clarify, I'm trying to treat organisms as members of a set and species as a partition (or equivalence relation) on that set. So if O is the set of all organisms, then a species would be a subset of O. I'm not sure what the problem is but I'll think about it. I'm pretty sure that there is absolutely no problem with taking the set of all organisms. |
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Previously PhilosopherStoned
Species is really just an arbitrary label we use for convenience. |
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Last edited by Photolysis; 03-19-2011 at 12:38 AM. Reason: Typoo. Yes I'm aware that itself is a typo. OR IS IT?
You're going to have to tell me. As near as I can determine, my model is perfectly sufficient for proving that there is no correct way to define species. Specifically, any partition of the set off all organisms with the property that an organism is in the same segment as both it's parents and its offspring must be the trivial partition. But on the other hand, we certainly expect a "species" to have this property. Actually, either "is the same species as its parents" or "is the same species as its offspring" are equivalent and either breaks everything. This is all utterly trivial. |
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Previously PhilosopherStoned
The main purpose of using such labels in the first place is for the ease of communication. It's not best suited for situations like these where we're dealing with many shades of grey, but labels are useful in general, and besides, a lot of people feel the need to categorize things. |
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Species is unambiguous at any given time, it's worth pointing out. There is no way of using transitivity to make any living bonobo make fertile offspring with a chimpanzee. |
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Last edited by Xei; 03-21-2011 at 04:16 PM.
I'm surprised I haven't pointed that out. Of course it's because the last common ancestors of bonobos and chimpanzees aren't alive so the "female parent of X" operator will only build a chain 2 or 3 elements long and you can have a non-trivial partition on the organisms alive at any given time. |
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Last edited by PhilosopherStoned; 03-21-2011 at 08:47 PM.
Previously PhilosopherStoned
It's also worth pointing out that even with the at-any-given-time clause, the common definition only applies for species that reproduce sexually. Which seems pretty odd. |
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Yes, I'm quite unsatisfied with the notion that a species is defined by the potential to breed with another organism and produce fertile offspring. If we really wanted to be pedantic, than this would exclude non-fertile members of a species as well. If a woman couldn't have fertile offspring for some reason, then according to that definition, she wouldn't be a member of any species. Of course we "know" that she's still homo sapiens but we have to bend the definition to make it work. |
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Previously PhilosopherStoned
There is no single definition of species. I'm aware of ten definitions/concepts that are regularly used, the biological one (based on reproductive characteristics) being only one of them. |
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