In philosophy, parallelism is a theory devised to solve the long-standing mind/body problem. Briefly put, the mind/body problem states that it is impossible to give a plausible account of the causal interaction between mind and body, given that they are such radically different substances. One is mental, and the other is physical. Causation only takes place between physical objects in space, so how is it possible for the mind, which isn't a physical object, to cause movements in the body?
Parallelism tries to get around this problem by arguing that mental and bodily events are perfectly coordinated without any causal interaction between them. In his philosophical masterpiece The Ethics, the rationalist philosopher Spinoza held that there was only one substance, God (or Nature), of which mind and matter were two attributes. They are two different but related ways of comprehending the same reality.
The mind and the body are therefore simply two sides of the same coin; they do not causally interact but instead parallel one another. For Spinoza, whatever happens in the body always occurs in tandem with the contents of our mind, and vice versa.
Spinoza's is only one of the many attempts to deal with the mind/body problem using parallelism. But all of such efforts share the same common notion: that mind and body are related in a non-causal manner. This approach has been criticized on the grounds that the constant correlation posited by parallelism lacks scientific veracity.
Science deals with empirical procedures that, in order to account for the interaction between two phenomena, operate on the assumption of some kind of cause taking place. Parallelism, because it deals with the mind, avoids this procedure, avowing instead that a constant correlation between mind and body is all that can reasonably be established.
Yet, this has been criticized as an example of question-begging, assuming something that needs to be proved. And if something cannot be proved, so the critics of parallelism claim, then it has no validity. If we are to account for the relationship between mind and body, critics argue, then we need to treat the mind as if it were a species of matter. Such a materialistic conception of the mind, whatever its shortcomings—is the mind really material?—does at least have the benefit of allowing us to establish a possible causal connection between mind and body.