When theoretical statements use terms that refer to objects and properties whose existence seems awkward, puzzling, redundant, or ontologically problematic, there is motivation to analyze or reduce such statements to others that employ better understood terms. Reductionism must be distinguished both from eliminativism and supervenience. Consider two domains of properties M and P (e.g., the mental and the physical). Eliminativism claims that since only P exists, M can be eliminated (e.g., there is no such thing as demonic possession, but only a biochemical problem in the brain). Supervenience asserts that both M and P are real and distinct, though M is determined by P (e.g., headache pain is real, and while not identical to neurophysiological processes, is nonetheless realized by such processes). Reduction, however, asserts that there is but one thing that is both M and P, with P having explanatory priority (e.g., Mary's particular headache pain is just a particular complex neurological event).

Semantic and theoretic reduction

Examples of reductions in philosophy include logicism (reducing statements about numbers into statements of logic and set theory), phenomenalism (reducing statements about external macro-objects into statements of actual and possible experience), logical behaviorism (reducing statements about mental states into stimulus-response conditionals), logical positivism (reducing statements employing theoretical entities to ones referring only to observed objects), and naturalism (reducing normative ethical statements to ones whose terms refer to natural properties only). All these philosophical reductions are semantic, for all use definitional equivalences linking terms of the reduced to those of the reducing statements, (i.e., statements in the reduced theory just mean equivalent statements in the reducing theory). Broadly speaking, semantic reductions have been out of favor in philosophy since the 1950s. This is due in part to four developments: the heightened sensitivity to the "paradox of analysis" (i.e., if a semantic reduction is successful it is not informative and if it is informative it cannot be successful); the realization of the enormous practical difficulties of actually carrying out the proposed reductions; an increasing recognition of the holistic nature of sentence meaning; and the growing doubt about the very possibility of foundational discoveries.

Of more interest to the science-religion conversation is the status of scientific reductions. Consider physics, chemistry, biochemistry, biology, physiology, neuroscience, psychology and sociology. How are these various disciplines related? How does one connect hadrons, atoms, chemical compounds, amino acids, cells, synapses, thoughts, and cultural tendencies? If physicalism is true in asserting that all that ultimately exists are those entities referred to in the most basic physical theory, then in what sense can thoughts and cultural tendencies exist? Should talk of such things be eliminated, or should we understand theories making reference to them to be reducible to more basic theories, and ultimately to theories referring to fundamental physical entities? Theoretic reduction in the philosophy of science attempts to show how entire theories, and the entities and properties specified by them, are reducible to more basic theories.

Unlike semantic reduction, theoretic reduction understands the biconditionals connecting theoretical terms in the reducing and reduced theories to be empirically discoverable bridge laws specifying coextensive property instantiations. While statements in the reduced theory mean something different from statements in the reducing theory, it is nonetheless true that the reduced theory statements are true if and only if their reducing statements are true. Examples of theoretical reduction within science include the reduction of chemistry to physics, the reduction of thermodynamics to statistical physics, the reduction of Mendelian genetics to molecular genetics, and the partial reduction of psychiatry to neurophysiology.

Reductions can also be found in theology and religion, though they are not often presented as such. For example, Immanuel Kant (1724–1804) semantically reduced talk of God to discourse about morality, while Friedrich Ernst Schleiermacher (1768–1834) reduced it to modifications of the feeling of absolute dependence. Karl Marx (1818–1883), Sigmund Freud (1856–1958), and Emile Durkeim (1858–1917) attempted theoretically to reduce religion to economics, psychology, and sociology respectively.

Varieties of reduction

There are different types of reduction, and also different typologies of these reduction types. One might distinguish methodological, epistemological, and ontological reduction. Accordingly, the first is a research strategy in which the behavior of complex wholes is analyzed into their component parts; the second an explanatory strategy claiming that theories and laws at the higher levels are analyzable or otherwise explainable in terms of the theories and laws of the lower levels; and the third an ontological strategy holding that reality is ultimately comprised of nothing but simple components (e.g., quarks, strings) organized in particular ways.

This "nothing but" relation can be understood as reduction's defining characteristic: M reduces to P if and only if M is nothing but P. Accordingly, one can distinguish ontological, property, semantic, theoretical, and causal reduction. Ontological reduction claims that upper-level entities and events are nothing but complex configurations of lower-level entities and events; property reduction asserts that the instantiation of every upper-level property is nothing but the instantiation of a particular lower-level property; semantic reduction declares that the meaning of statements in the reduced theory is nothing but the meaning of statements in the reducing theory; theoretic reduction claims that laws of the reduced theory are nothing but the laws of the reducing theory; and causal reduction asserts that the causal powers of upper-level entities are nothing but the causal powers exhibited by their lower-level physical realizers.

Property reduction and causal reduction are of particular interest in the science-theology discussion. One can hold that while only physical particulars exist, property dualism nonetheless obtains because higher-level properties are not reducible to, and thus not coextensive with, any specific lower-level properties. Some in the science-theology discussion believe such a nonreductive physicalism of emergent mental properties can protect religious discourse and experience from reduction or elimination.

Causal reduction is extremely important for the question of the ontological status of putative emergent entities and properties. If entities at the upper-levels wholly inherit their causal powers from the lower-levels, and if ontological status only pertains to causally efficacious entities, then it seems that emergent phenomena are not fully real. The question of the causal status of emergent properties is at the heart of the controversy about downward causality. Some in the science-theology discussion suggest that the emergent itself can effect the causal distribution at the lower-levels, not just the lower-level realizers of that emergent, (e.g., consciousness itself is causally efficacious.) But if particular lower-level actualizations are sufficient for the instantiation of an emergent property, then it seems that these actualizations are also sufficient for the effects this emergent property is said to cause.

Conclusion

Many in the science-theology discussion wish to provide an account of emergent phenomenon that does not presuppose reductive explanation. Unfortunately, even in the absence of the straightforward reduction of the emergent, the admission of its physical realization seems to accomplish much of what reduction initially sought, for the causal loop still gets closed at the lowest physical levels. It seems that the "something more" of the emergent may be "nothing more" when it comes to the issue of causal reduction. This is not a result that would cheer many in the science-theology conversation.

See also BEHAVIORISM; CAUSALITY, PRIMARY AND SECONDARY; CAUSATION; DOWNWARD CAUSATION; MATERIALISM; NATURALISM; PHYSICALISM, REDUCTIVE AND NONREDUCTIVE; SUPERVIENIENCE

DENNIS BIELFELDT