Scientific Explanation, Philosophical/Theological "Reasons" and Abstract Entities

A basic, yet crucial, distinction in philosophical explanations concerns the difference between abstract and concrete entities. An abstract entity is not located in space-time and does not stand in causal relations to other entities (e.g. numbers and propositions). A concrete entity is located in space-time and does stand in causal relations to other entities (e.g. rocks, rivers, mountains and stars). Philosophers frequently reference both types of entities when providing explanations for various phenomena. Typically, abstract entities are taken up to explain why concrete entities are the way they are.

For example, Plato invoked forms, abstract entities which explain why things are the way they are, how they are meaningful to us, and how we can recognize disparate instances of them.  A chair, as the theory goes, is meaningful by its participating—this is not a causal relationship as forms qua abstract entities don’t enter into causal relations—in the form of chairness. That form is what we intuit when we look at a chair. It provides an explanation of how the particular chair is meaningful and how we can recognize objects that are completely dissimilar as chairs. Further, in an elaborate myth of how the world was created, Plato posited a demiurge that modeled concrete, physical objects after the intelligible forms. Christians, who appropriated Neo-Platonism would later claim that the forms reside in the mind of God and that God used these intelligible principles to model the world. This schema leads to the beautiful conclusion that whenever you have an experience of meaning—which is during every conscious moment—it is because your consciousness is subtly enveloped in the mind of God in such a way that entities are illuminated for you. Each conscious experience is made possible by being wrapped up into the mind of God—the ground of all Being.

Currently, however, there is a trend amongst the scientifically minded and among philosophers that wish to model philosophical explanations after scientific ones, to completely discredit the existence of abstract entities. Foremost amongst philosophers in this regard is David Armstrong. In arguing for the nonexistence of abstract entities, Armstrong invoked Ockham’s Razor—a primary tool in distinguishing between parsimonious scientific theories and those which are over-encumbered with unneeded explanans (i.e. things which explain). In short, Ockham’s Razor is the requirement that “entities are not to be multiplied without necessity.” Russell, Our Knowledge of the External World as a Field for Scientific Method in Philosophy (London: Routledge, 1914), 107. Drawing upon this time honored principle, Armstrong levels the following argument against abstract entities:

(1) Abstract entities, unlike concrete entities, do not exist in space-time.

(2) If objects do not exist in space-time they are not causally related to other objects.

(C1) So, even if abstract entities exist, they would make no causal difference to concrete entities. (By modus ponens with the implicit premise that concrete entities are in space and time and thus are causally related).

(C2) Abstract entities, even if they exist, provide no causal explanation for concrete entities.

(C3) Thus, there is no reason to suppose the existence of abstract entities.

See Armstrong, D.M., Nominalism and Realism: Universals and Scientific Realism, vol. 1 (Cambridge: Cambridge University Press, 1978), 130.

This argument, demonstrating no “reason” for the existence of abstract entities, is intended to take us to the conclusion that without a reason for the existence of some entity, we ought not believe that it exists—i.e. we have the epistemic duty to withhold belief. Armstrong’s argument may appear detached from any practical concerns of daily life. However, if his argument succeeds, much of traditional philosophy and western religious theology will have been undermined. Further, the reason that I selected Armstrong’s argument is because it is representative of many attitudes of the scientifically inducted. I have oft heard individuals claim that since science does not need to invoke abstract entities, including God, to explain concrete/physical phenomena, then there is no reason to believe in those things. Armstrong captures with precision these sentiments.

However, Armstrong’s conclusion rests on a questionable inference. C2 speaks of “causal explanations.” Thereafter, Armstrong’s argument abruptly turns to “reasons;” “there is no reason to suppose the existence of abstract entities.” In other words, Armstrong seems to be claiming that causal explanations are the only types of explanations that provide reasons for believing one way or the other. This is unsurprising since scientific theorizing rests, more often than not, upon plotting out the causal connections underlying phenomena as a way of reductively explaining them. Yet, causal explanations are not the only type of explanation which provides “reasons” for believing. The principles in geometry and statistics are used heavily in various scientific fields as bases of scientific explanations. These appropriated principles are often, importantly, not causal. In fact, much of the scientific reasoning underlying all of scientific theorizing (e.g. verificationist and falsificationist schemes) is not causal in nature. Causality is not the only type of explanation which provides reasons for believing things. And even though the scientist qua scientist is urged, more often than not, to ignore non-causal explanations for purposes of the scientific process, we ought not, as the scientifically minded Positivists frequently quipped, mistake our scientific models for reality.

Reality is broader and various forms of explanations, not just causal explanations provided by concrete entities, provide a roadmap in understanding it. The wisest of philosophers and theologians have for centuries recognized this principle. Their struggle to find a rational explanation for reality as such has repeatedly led these sages to posit abstract entities. Does this mean that abstract entities (e.g. numbers, forms and certain notions God) must exist? Well, if the ancients are correct, abstract entities oft provide the very best explanation, and at time the only explanation, for various concrete phenomena. In these extreme instances it appears that they must exist. This philosophical argument has not, importantly, proven that abstract entities do conclusively exist. What is has attempted to demonstrate is that the prevailing attitude which snubs abstract entities as sound principles for explanation, since science doesn’t need to rely on them, rests upon faulty reasoning. Barring stronger arguments from scientific materialists, we should not be ashamed to invoke non-causal, philosophical/theological explanations for the world around us—assuming of course that the explanations we invoke are grounded upon sound reasons.