When one is presented with some subject on which there are several viewpoints, and exhorted to look at things “dialectically,” one might ask what this means.

Wikipedia says of classical dialectic that the point is to generate either a refutation of one viewpoint or a synthesis — to reach a better conclusion. But it doesn’t say what form the better conclusion is in. Similarly, it says of Hegelian dialectic that the point is to reach a synthesis by combining the common points of a thesis and an antithesis.

These models of truth-finding appear to be rather limited. Besides the fact that in some sense they are specialized to dual or opposing viewpoints numbering two (or even if we extend it, a finite number), they are restricted to finding truth only in the intersection or union or some other simple-minded method of synthesis. I argue for a more general way to model truth-finding. This is inspired by engineering, as usual.

The truth in this case is like an object that lives in some high dimensional space. The viewpoints, any number of them, are projections of the truth onto different subspaces. Some subspaces may be larger than others even. The point is each “view” will see something different out of the same object.

Truth-finding is to combine the viewpoints in the sense of inverting the projections, so as to recover the original object. This is not a simple or even unique process, but there is probably a most parsimonious way to do it a la estimation. But it has the benefit of giving not only the complex and rich object in its original form or some approximation of it, but also the capability to support projection to an infinite number of other subspaces or viewpoints not present in the original argument. This is what dialectics cannot provide.