What is an abstraction?
Abstract objects are difficult to specify. In the Stanford Encyclopedia of Philosophy entry on abstract objects, Gideon Rosen notes that the distinction before the 20th century was primarily about words, and the general and particular distinction of the nominalist debate. In modern philosophy following Frege's theory of logic, abstractions become objects. Basically an abstract object is something that exists in virtue of being an objective property of universals. A universal, as I have discussed before, is something common to all actual objects ("particulars"). Nominalists think that universals exist only in the head. So how can there be abstract objects at all?
We aren't here concerned with any abstract object, but with the abstract objects of science, and in particular of biology. What numbers may be can be left for philosophy of mathematics. Nor are we concerned that some abstract objects can be family-resemblance based. In fact, in biology we might expect that many classes of organisms would be family resemblance classes; they are families after all. Phylogenetic classes are families - and some abstract objects of biology, such as "homology", are due to family descendance. Homologies are caused by by being descended from the "same" parts of ancestors. The problem lies in finding out what the sameness is.
One of the ways indicated by the Rosen article for explaining abstract objects is called by David Lewis the "way of abstraction", and it is this that is relevant here. We identify something that is common to more than one organism or biological phenomenon, and eliminate that which is unique to some subset (including each individual particular), and we call that the class. Another way to identify universals is the Non Spatiality Criterion, which has been axiomatised by Edward Zalta. According to Zalta, an abstract object is something that does not exist in space or time. But biological entities do exist in space and time, and any class, such as a taxon or homology is spatially bound - it exists in a given area, at a particular period in history. It is, as philosophers say, time and space indexed.
So homologies are concrete things. But the generalisations we make are in our heads, so they are also concrete things. It is only in our descriptions, that is, in our language, that they lack time indices. The confusion this sometimes causes leads people to think that form is an explanatory abstract object. The classical form versus function argument that one finds popping up again and again is based on this. Form is abstract. It explains nothing except the form itself. It is that it suits us to say that something common to all of the class is had by a particular object in biology, and so it shares all the concomitant properties of the form. Here I include such "forms" as equations like the Lotka-Volterra cycle, or the Hardy-Weinberg equilibrium. Exploring the properties of these abstract objects helps us, to be sure, but it is only that we understand these mathematical forms and can make inferences about the form (that the cycle is reaching its downturn for the prey species, say, rabbits, for instance, and so, if the L-V equation holds true, the predator species, say, foxes, will also peak soon). But if the foxes also eat voles as well as rabbits, then the L-V equation won't hold true, and nothing about the abstract model will help us find that out. What explains the actual dynamics is the physical causes - that foxes eat rabbits, which means they have the energy budgets to reproduce. The equation, or in other contexts, the morphology of the organism, is only a sketch of the real explanation, without the messy but necessary details.
As a side note, it is for this reason that I prefer the clumsy but specific nomenclature of cladistics. When one talks about a homology, it is unclear what the referent is, but if you talk about an autapomorphy or a symplesiomorphy it is precisely clear. They are still abstractions, but a given apomorphy is not - it's a leg length or a number of bristles, or whatever. Homologies often include homoplasies (convergently evolved traits, like a bat's and a bird's wing). As Gould notes, E. Ray Lankester, who coined "homoplasy", also suggested "homogeny" for homologies that were still the feature being compared (like the bones of the forelimbs of bats and birds), and it would have resolved a lot of confusion had that term been adopted.
We aren't here concerned with any abstract object, but with the abstract objects of science, and in particular of biology. What numbers may be can be left for philosophy of mathematics. Nor are we concerned that some abstract objects can be family-resemblance based. In fact, in biology we might expect that many classes of organisms would be family resemblance classes; they are families after all. Phylogenetic classes are families - and some abstract objects of biology, such as "homology", are due to family descendance. Homologies are caused by by being descended from the "same" parts of ancestors. The problem lies in finding out what the sameness is.
One of the ways indicated by the Rosen article for explaining abstract objects is called by David Lewis the "way of abstraction", and it is this that is relevant here. We identify something that is common to more than one organism or biological phenomenon, and eliminate that which is unique to some subset (including each individual particular), and we call that the class. Another way to identify universals is the Non Spatiality Criterion, which has been axiomatised by Edward Zalta. According to Zalta, an abstract object is something that does not exist in space or time. But biological entities do exist in space and time, and any class, such as a taxon or homology is spatially bound - it exists in a given area, at a particular period in history. It is, as philosophers say, time and space indexed.
So homologies are concrete things. But the generalisations we make are in our heads, so they are also concrete things. It is only in our descriptions, that is, in our language, that they lack time indices. The confusion this sometimes causes leads people to think that form is an explanatory abstract object. The classical form versus function argument that one finds popping up again and again is based on this. Form is abstract. It explains nothing except the form itself. It is that it suits us to say that something common to all of the class is had by a particular object in biology, and so it shares all the concomitant properties of the form. Here I include such "forms" as equations like the Lotka-Volterra cycle, or the Hardy-Weinberg equilibrium. Exploring the properties of these abstract objects helps us, to be sure, but it is only that we understand these mathematical forms and can make inferences about the form (that the cycle is reaching its downturn for the prey species, say, rabbits, for instance, and so, if the L-V equation holds true, the predator species, say, foxes, will also peak soon). But if the foxes also eat voles as well as rabbits, then the L-V equation won't hold true, and nothing about the abstract model will help us find that out. What explains the actual dynamics is the physical causes - that foxes eat rabbits, which means they have the energy budgets to reproduce. The equation, or in other contexts, the morphology of the organism, is only a sketch of the real explanation, without the messy but necessary details.
As a side note, it is for this reason that I prefer the clumsy but specific nomenclature of cladistics. When one talks about a homology, it is unclear what the referent is, but if you talk about an autapomorphy or a symplesiomorphy it is precisely clear. They are still abstractions, but a given apomorphy is not - it's a leg length or a number of bristles, or whatever. Homologies often include homoplasies (convergently evolved traits, like a bat's and a bird's wing). As Gould notes, E. Ray Lankester, who coined "homoplasy", also suggested "homogeny" for homologies that were still the feature being compared (like the bones of the forelimbs of bats and birds), and it would have resolved a lot of confusion had that term been adopted.
posted by John S. Wilkins @ 11:45 pm
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