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The following Figure is largely self-explanatory.

The following Figure is largely self-explanatory.

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Figure 1.  On Being Human

Figure 1.  On Being Human

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The way the joke goes, the straight man "defines" a human being H as an "apterous biped" A B, a two-legged critter without feathers, and then the wiseguy hits him over the head with a plucked chicken, and by dint of this koan, he achieves enlightenment about the marks that distinguish kindness of the artless kind from the crasser kinds of artificial kindness.  Leastwise, at any rate, that's the way that I heard it.

The way the joke goes, the straight man "defines" a human being H as an "apterous biped" A B, a two-legged critter without feathers, and then the wiseguy hits him over the head with a plucked chicken, and by dint of this koan, he achieves enlightenment about the marks that distinguish kindness of the artless kind from the crasser kinds of artificial kindness.  Leastwise, at any rate, that's the way that I heard it.

Suppose that we are clued into the fact that not all sets in Pow(X) are admissible, allowable, material, natural, pertinent, or relevant to the aims of the discussion in view, and that only some mysterious 'je ne sais quoi' subset of "natural kinds", Nat(X) c Pow(X), is at stake, a limitation that, whatever else it does, excludes the set P and all of that ilk from beneath GLB(A, B).  Though it is difficult to say exactly how we are supposed to apply this global information, we "know" it in the sense of being able to detect its local effects, for instance, giving us the more "natural" lattice structures that are shown on the right sides of Figures 2 and 3.  Relative to these "natural orders", we can observe that H = GLB(A, B), more precisely, the result of the lattice operation associated with the conjunction, GLB, or intersection of A and B gives us just the lattice element H.  Thus in this more natural setting the proposed definition works okay.

Suppose that we are clued into the fact that not all sets in Pow(X) are admissible, allowable, material, natural, pertinent, or relevant to the aims of the discussion in view, and that only some mysterious 'je ne sais quoi' subset of "natural kinds", Nat(X) c Pow(X), is at stake, a limitation that, whatever else it does, excludes the set P and all of that ilk from beneath GLB(A, B).  Though it is difficult to say exactly how we are supposed to apply this global information, we "know" it in the sense of being able to detect its local effects, for instance, giving us the more "natural" lattice structures that are shown on the right sides of Figures 2 and 3.  Relative to these "natural orders", we can observe that H = GLB(A, B), more precisely, the result of the lattice operation associated with the conjunction, GLB, or intersection of A and B gives us just the lattice element H.  Thus in this more natural setting the proposed definition works okay.

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Figure 2.  Arbitrary Kinds Versus Natural Kinds

Figure 2.  Arbitrary Kinds Versus Natural Kinds

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An alternative way to look at the transformation in our views as we pass from the arbitrary lattice Pow(X) to the natural lattice Nat(X) is presented in Figure 3, where the equal signs (=) suggest that the nodes for G and H are logically identified with each other.  In this picture, the measure of the interval that previously existed between G and H, now shrunk to nil, affords a rough indication of the local quantity of information that went into forming the natural result.

An alternative way to look at the transformation in our views as we pass from the arbitrary lattice Pow(X) to the natural lattice Nat(X) is presented in Figure 3, where the equal signs (=) suggest that the nodes for G and H are logically identified with each other.  In this picture, the measure of the interval that previously existed between G and H, now shrunk to nil, affords a rough indication of the local quantity of information that went into forming the natural result.

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Figure 3.  Arbitrary Kinds Versus Natural Kinds

Figure 3.  Arbitrary Kinds Versus Natural Kinds

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===Incidental Note 3===

===Incidental Note 3===