Tuesday, December 4, 2012


       Taxonomy as an ontological question (2) falls under the purview of what is meant by a definite description.  On the basis of Frege’s analysis, we are told that a singular common noun is a referring expression (4; Sinn), and I use this notion to ground taxonomy within a pluralist context. Questions concerning life, particularly the taxa we devise for it, necessarily refer to those components which we can observe. When the biologist splits reptiles and birds as separate classes, she is referring to a list of features extracted from observations made about those individuals within them. In evolutionary biology, such a list will generate a number of splittings depending on the algorithm used. For example, algorithm A may place alligators and chickens into a closely-related clade, whereas algorithm B would recognize alligators as being distinctly separated from Aves within the taxonomy. As well, the organization and collection of data is instrumentation-dependent, which subsequently “co-evolves” with the observer community and vice versa. From this phenomena stems plurality. The referent components analyzed and subsequently categorized are in a dynamical flux on the basis of evolving methods for collecting novel features in the specimen under study. What was previously invisible to the senses will become “real” in the future. For example, Darwin could create taxonomies without knowing genetic sequences, although the supposed “transforming principle” underlying evolution did not refer in this case. Darwin could simply not see DNA with his eyes, a direct result of unavailable instrumentation. The beauty of Frege’s analysis is that it allows for gappy propositions (5), and I suppose that the referents collected for each individual take the object position of the gap within Frege’s calculus.  I will contrast this allowance with Russell’s method to show why gappy propositions are vehicles for pluralism and potentially high-dimensional spaces.

In Russell’s view, particularly the On Denoting period, singular common nouns cannot be referring expressions because they are merely symbols which quantify objects in space and time; our observable, “actual world”. If statements of this quantified form are computable, then we cannot implement it within taxonomy without sacrificing the transforming nature of life in the program’s output. To say that a symbol quantifies an object in the actual world is to select a finite subset of characters and assigning it the value of a string, which is a referential data type for denoting alphabetical expressions. Consider the following sentence:
(1)  The present King of France is bald

First recognize that “the present King of France” (a string denoted by X) has some unique properties as a definite description. It is temporally restricted to the present time. Using tuple notation, an object X has some monadic property/universal Y (denoted as “is bald”; the universal is the state of being bald) at time t, which can be read as A = <<X, t>, Y>. On the case of what is meant by present, view the following set B = {...,<<X, t – 1>, Y>,< <X, t>, Y>, <<X, t + 1>, Y>,...}. B informs us of a fatalist state of affairs, where the dot notation denotes the object X for all time-points in the history of our universe of discourse far in the past and the future, and is subsequently true for all time. When discussing what is meant by the present, it is precisely the behaviour/property Y of X at that time-point which is not t - 1 and t + 1. The implication of this view is that when we are discussing X, we have one, already presupposed its existence; and two, the arrow of time can be constrained to single points in a continuous life history. However, t “right now” and t in “the future” (t + 1) are both denoting expressions for what is already the present. The king of France may have been bald when he was alive (eg. t - 1), but certainly his “monadic status” in the world has since passed. B taken as a set would fall under having a truth value of false. Furthermore, time flows forward, and to make a statement about an object at t + 1 is to say that we will definitely know the dynamics of the object in all future flows of time as well; Y is not necessarily universal across all time, and certainly not when Y is with respect to biological evolution. Unfortunately for Russell, it seems that truth is not as static as he would like in this context, his purports on linguistic rules are too tight for generating dynamic taxonomies for biological entities in this instance and leaves no room for the imagination when considering the instrumentation problem.

On the other hand, the consideration of a “gap” within a proposition about a species acts as a placeholder which may be presupposed to be those adjacent possible (3) properties that emerge from available resources in the future. We cannot know the morphology and functions biological structures will take in the future, but the development of techniques such as genetic stochastic modeling allows us to account for theoretical properties and derived traits from current information extracted from the species being classified. In the scheme of devising an effective ontology for discerning “useful” taxonomies from ones that have no utility, using incomplete, gappy propositions allows the [in silico] experimentalist to consider higher dimensions in which they capture the level of resolution being studied in the set of species being classified. For example, the set  C = {...<X, t - 1>, Y0, Y1, Y2...>>, <Z, t>, Y0, Y2, Y5...>>, <   , t + 1>, Y0, Y2, Y3...>>,...} contains gaps in the object position of future elements and now recognizes an existential difference between an object X and Z versus an undetermined adjacent structure in the future falling under a suspected list of properties. If the presupposition of such empty structures fail to generate references within our model, the list is rejected for a better optimization and we may derive a stronger taxonomy for our species set with a more effective predictive power.

1. Russell, B. "On Denoting." Mind 14 (1905): 479-493.
2. Ereshefsky, M.  “Species, Taxonomy, and Systematics.”  In Rosenberg and Arp.
3. Kauffman, SA. “Investigations.” Oxford University Press (2002): 22.
4.  Frege, G. “. Über Sinn und Bedeutung.” Zeitschrift für Philosophie und philosophische Kritik, (1892): 25-50.
5. Everett, G. “Empty Names and ‘Gappy’ Propositions’.” Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition, 116(1), (2003): 1-36.

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