"There are three good reasons to think that reduction will fail on any likely development of social sciences: (1) multiple realizations of social events are likely; (2) individual actions have indefinitely many social descriptions depending on context; and (3) any workable individualist social theory will in all likelihood presuppose social facts. Each of these claims, if true, rules out reduction as defined here." -- Harold Kincaid (quoted in J. E. King (2012)).
Kincaid is arguing against strong methodological individualism. To help explicate his first reason, I want to consider a different domain, biology, and some literature crossing over between biology and computer science.
I suppose I ought to first state the reductionist theory I want to oppose: The theory of evolution can be reduced to the biochemistry of DNA.
A large body of literature explores the logical structure of reproduction, including reproduction with mutations, independently of consideration of the structure of DNA. I think of Von Neumann's work on celluar automata, which, despite the publication date of the work Burks edited, pre-dates the discovery of the molecular structure of DNA. As I understand it, Von Neumann described a structure in which a part simultaneously functions as a blueprint for the next generation and as a component that is duplicated in reproduction.
Von Neumann described a celluar automaton with many states, but his logic can be implemented in a particular celluar automata with only two states, namely Conway's Game of Life. Plausibility arguments that this celluar automata can be used to form a universal computer were available before Paul Rendell implemented a Turing machine in the game of life. Basically, one can identify mechanisms for implementing a memory and an array of gates (for example, AND, OR, and NOT). The gates apply to bits flowing across a wire, in some sense. Jacob Aron has create another interesting pattern in the game of life relevant to my thesis, namely a self-replicating creature.
Some researchers have also explored the role of mutations in self-replicating automata. As I understand it, they typically assume the existence of an assembly language for a virtual machine. One can imagine small programs being executed in parallel in some sort of common memory. One needs some way of introducing random changes in some of the instructions over time cycles and a way of rewarding successful programs with, say, more energy, in some sense.
The different artificially alive creatures in these simulations do not reside in separate protected memories. They have the capability of overwriting one another and resisting such overwriting. Some have even arranged tournaments, called core wars, in these simulations. In some sense, the literature I am referencing includes some bits of recreational mathematics.
I have never seen much more than what the literature says in the little bit of exploration of the above I have done. I did once write an implementation of Conway's Game of Life in which the rules were configurable. I was able to create crystal-like growth, but nothing as interesting as in the original game.
I have pointed to some work exploring a logic of reproduction above the level of the biochemistry of DNA. DNA is one means of instantiating this logic. I have not pointed out any other non-virtual mechanisms for instantiating this logic. I do not know if mitochondrial DNA differs sufficiently from regular DNA to count. Silicon-based life forms on other planets is a standard trope in science fiction. Apparently, Reaves et al. (2012) show the supposed discovery of arsenic-based life forms in certain California lakes has not worked out. But does this anti-reductionist argument require the actual existence of another instantiation, or merely the demonstration of the possible existence of one?References
- J. E. King (2102). The Microfoundations Delusion: Metaphor and Dogma in the History of Macroeconomics.
- Lenski, Richard E., Charles Ofra, Robert T. Pennock, and Christoph Adaml (2003). The Evolutionary Origin of Complex Features, Nature, V. 423 (May): pp. 139-144.
- Poundstone, William (1984). The Recursive Universe. William Morrow.
- M. L. Reaves et al. (2012). Absence of detectable arsenate in DNA from arsenate-grown GFAJ-1 cells.
- Thearling, Kurt and Thomas S. Ray. Evolving Multi-Cellular Artificial Life.
- Von Neumann, John (1966). Theory of Self-Reproducing Automata (ed. by A. W. Burks).