What do we do when our logic seems to befool us? when we run the numbers, check the math, yet we are left with unresolved contradictions? In philosophy and biblical studies, this comes up a lot: the perennial response to the doctrine of the Trinity is the accusation of bad math—how can God be both 3 and 1?—and many theologians deduce bad theology from biblical premises (God is love, therefore he must give prevenient grace to all men; yet the Bible teaches that He doesn’t). There are many causes for these dilemmas, for the appearance of contradiction in the biblical narratives and bad theology derived from good theology, but the idea of a limiting concept can help us Christians be consistent and solid in our reasoning, both in our internal discussions over theology and our apologetical discussions with unbelievers. In this post, I want to give a brief explanation of limiting concepts; in another post, I will outline why they matter.
First, a definition: what is a limiting concept? By limiting concept, an idea I have picked up from Cornelius Van Til, I am not referring to any thing–there is not a thing called a limiting concept–but a function that propositions (simple truth statements: e.g., the block is red) take in logic and reasoning. That is, statements are limiting concepts when they serve to prevent conclusions from being reached that would otherwise be valid—abstract I know, we will get to the practical… eventually. Representing propositions algebraically (A, B, C, etc.), we could give a formula for the function of a limiting concept like this: if it seems to be the case that “A therefore B,” but we know that “C then not-B”; when C is true, “A therefore B” is false. In this logical equation, A is a true statement (e.g. “It is wet outside”) and B is a statement that may be true or false (e.g. “it is raining”). C is another statement that excludes B from being true (e.g. C = “it is too cold to rain”) and is functioning as a limiting concept. That is, at first glance A “It is wet outside,” therefore B “It is raining” seems reasonable—this makes sense! Yet the presence of C “it is too cold to rain” causes us to revisit our initial reasoning. Because we cannot deduce B from A, we must consider other possibilities—of which there are many (e.g. D “a man is spraying the sidewalk with a hose”; E “there is a heater melting the snow”; etc.)! The limiting concept here reveals a problem in the initial logic itself: though B implies A, A does not necessarily imply B.
The function of limiting concepts become very important when we consider worldviews, or systems of truth. A system of truth, for our purposes, is the sum total of true and false statements that accurately describe our world. To properly understand any one detail in a system of truth, one needs to have perfect understanding of the whole: to give every true statement that could possibly be said about something—for instance, the location of my laptop—I must have access to every available perspective: it is in front of me, beside my lamp, beneath the roof, at a certain longitude and latitude, a certain distance from Alpha Centauri, etc. You may respond: it is true that I need to know all things to exhaustively describe something, but practically I do not need to know every way a laptop’s location could be described to know where it is. This is true enough, but what if one of those unknown details is vital to the use you want to make of the laptop, yet you don’t know that it is? If so, you will fail when you try to use it. Entertain a thought experiment with me: we are aliens visiting Adam and Eve on the 7th day of creation, we want to use our knowledge of human growth to determine when the world began. We could analyze Adam perfectly and arrive at the conclusion that the world began 41 years, 2 months, and 9 days ago; yet we would be wrong. The problem, in this case, is not that we don’t properly understand human growth; our problem is that we are unaware that God created Adam only a day ago in a fully mature adult state. That one piece of data could ruin all our otherwise perfect calculations.
Do you see the problem? When we try to understand anything within our universe, how can we know that some unknown piece of data will prove all our data wrong? We cannot! What is needed make a proper induction (i.e., empirical science: gather a set of data and reach a conclusion from it) or deduction (concluding truths from other truths via logic) is certain truths from which to begin. Yet, if certainty only comes through knowledge of the whole system of truth, we need these truths revealed to us from one who knows the whole system completely. Only God knows this “system” completely; only He knows everything that is properly false and true. Therefore, we need His input to begin any reasoning that hopes to rightly describe the universe (e.g., I need to know my reason can be trusted, something only he can tell me—cf. this post).
This is where limiting concepts come in: in the Christian worldview, we trust that God has told us enough to properly understand His world (to reach appropriate inductive and deductive conclusions). Yet, He has not told us everything: He has given us a good foundation from which to reason from, but also knowledge that hedges in our reason—that constrains it—and guards us from going too far in our logic. What God has told us about Himself, us, and the world serves both to guide us in interpreting and to prevent us from over-interpreting: it functions as a limiting concept. This brings us to examples of why limiting concepts matter [continued here].