On the Vagueness of Species, Part 5: Excluding Some Higher Order Vagueness


In several earlier entries in this blog, I’ve discussed the vagueness of species, the idea that our identification of an individual life form with one species and not another can be vague. I’ve suggested that the concept of rough sets can be usefully applied to Darwin’s species concept.

Epistemic concepts of vagueness say that there really is an exact count of grains where a group of grains are a heap, or an exact count of hairs where a head becomes bald, but that we do not know what that number is. This differs from the more common idea that our terms themselves are vague in application to an exact world.

Where does the rough set concept come in in those differing ideas of vagueness? Is it a vagueness of our concept or of our knowledge of the concept? It is both.

First, as applied to whether a given individual is definitely a species member, definitely not a species member, or vaguely a member, the vagueness is either in our terms or in the members themselves: if an individual life form is only vaguely an orange tree, that is either that we do not have sufficient precision in the orange tree definition to decide, or the tree is the kind of hybrid which is vaguely an orange tree by its nature. In these cases we don’t generally think there are any further unknown facts which would decide the matter.

Second, the rough set concept is without any need for secondary, higher-order vagueness. Such higher-order vagueness is said to be when

in addition to the unclarity of the borderline case, there is normally unclarity as to where the unclarity begins. In other words ‘borderline case’ has borderline cases. This higher order vagueness seems to show that ‘vague’ is vague”

according to the Stanford Encyclopedia of Philosophy. However, with rough set theory, there should be no question regarding whether an individual is definitely a species member or vaguely a species member. If there remains a question of species membership at all, this puts the member entirely into the vague category, which removes the question of whether the member is vaguely vaguely a member: all such border cases are vague ones. The rough set concept thus collapses all secondary vagueness of that sort into the primary vagueness portion of the rough set.

How is this an epistemic view of higher-order vagueness? Between the life forms that are definitely in the species and those that are vaguely so there is a definite boundary. More than this, it is one we should be able to know.

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