Traditionally, the two types of explanation are synthesis and analysis. Leibniz defined synthesis as “the process in which we begin from principles and …[proceed to]…build up theorems and problems,” and analysis as “the process in which we begin with a given conclusion or proposed problem and seek the principles by which we may demonstrate the conclusion or solve the problem.” (Philosophical Papers and Letters, p 286) It seems trivial to suppose that a complete explanation would of course include both types. However, if we do attempt a complete explanation, we will end with paradoxes.
Each and every explanation of anything may be challenged. A new explanation may be demanded of the terms in the original explanation. To meet this demand, new terms are required, otherwise the new explanation is circular. Yet, a third explanation can be demanded of the new terms introduced in the second explanation of the first explanation, and ad nauseaum. There are two resolutions to this: either continue introducing new explanations for an eternity, or end somewhere, out of sheer exhaustion or self-indulgent satisfaction.
In either case the explanation will be incomplete, in the former case, by definition, and in the latter, the terms of the last explanation will not themselves be explained. Therefore, the nature of explanation is that the explanation of anything will always be incomplete.
In science, for that matter, ultimate explanations are offered in terms of matter, natural forces and scientific laws. Matter may be further analyzed in chemical formulae, the table of elements, fundamental particles. The natural forces are energy, gravitation, magnetism, electricity, etc. And the laws of science describes the regularities of matter in motion according to these natural forces. But the terms “matter,” “energy,” “scientific law” themselves remain unexplained, and the scientist turns the project over to the philosopher. These final explanations explain everything else, but remain unexplained. Hence, science can never give the ultimate insight into the mystery of existence. Their explanations do shift the locus of that mystery, but never explain it.
The same thing applies to mathematics: the entire edifice of demonstration totters on a foundation of axioms and rules which are themselves not demonstrated, but assumed. Ditto for the laws of logic: the attempt to justify them involves circularity, because they themselves are the justification procedures in discourse. Logical justification, by definition, is a demonstration that the laws of logic have been obeyed or followed. The limits of explanations for science, mathematics, and logic is the breeding grounds of the fundamental problems of philosophy.
It seems like synthesis is not prone to the dangers of analysis (infinite regress or arbitrary terms). According to synthesis, we can relate things to other things, until we have identified all the relations there are between everything there is, and that would be the natural and necessary end of synthesis. There wouldn’t be anything left to be related, and nothing else left to relate to it. The totality of all things would be a comprehensible whole that exhibits all its internal relations. Apparently, synthesis does not suffer the same theoretical issues of analysis.
This human need of further explanation for everything, the totality of human experience, is typical, and a consistent theme throughout human history. Because, by definition, there’s nothing else to which everything can be related, we, almost inevitably, recourse to an explanation outside of this totality, an explanation with transcendental terms. The known is explained by the terms of the unknown, or, the knowable in the terms of the unknowable. However, given that the unknowable is unknowable, no such total explanation can ever be validated.
It isn’t the case that the total explanation requires our faith or authority. They can only be taken on faith, for they have no other basis. Of course there are such explanations in the majority of the world’s religions. However they are incompatible with one another. Once their explanations are in conflict, we have no way of deciding between them, except for faith or authority. The attempt to explain the known in the terms of the unknown is the inversion of intelligible procedure, a flight into “cloud cuckoo land.”
Both types of explanations make things less clear than they are. Worse yet, both types involve statements about what is unknown or unknowable, and this is at best, self-indulgence, if not self-deception, and at worst, charlatanry. Even the great mathematician, Bernhard Riemann, in his The Mechanism of the Ear, admitted that both approaches, when rigorously adopted, are impossible. Each synthesis relies on the results of a preceding analysis, and each analysis requires a subsequent synthesis in order to be confirmed. They are at best complimentary methods that presuppose one another.
We have to swallow our pride and admit the limits of human apprehension: whatsoever is permanently inaccessible to the capacities of human apprehension is permanently unknown to us. Moreover, the nature of anything is utterly incomprehensible. “The sense of the world must lie outside of the world…. what we cannot speak about we must remain silent about.”