I spent a good part of one summer trying to convince my 15-year-old brother (who was, at the time, decidedly unenthusiastic about philosophy) that it’s impossible to prove everything.
It was something I’d become convinced of after reading C. S. Lewis’ “The Abolition of Man,” in which Lewis explained that accepting what was unprovable was necessary to proving anything. Together with several philosophical concepts I’d been learning, Lewis’ argument convinced me that our understanding of reality rests, ultimately, on things that we cannot prove.
For Lewis’ argument, I would highly recommend reading “The Abolition of Man.” It’s quite a short book, and Lewis lays out some incisive critiques against our modern society’s subjectivist turn. But here, I’ll explain how, in philosophy, one of logic’s core principles cannot be deductively proven.
The Necessary Ground of Logic
Ultimately, all of logic rests on what philosophers like to call the LNC, or the Law of Non-Contradiction. The Law of Non-Contradiction refers to the impossibility of a statement being both true and not true at the same time in the same way. For instance, it is impossible for the statement, “Martin Luther died on Feb. 18, 1546,” to be both true and false. It must be one or the other.
Now, the LNC is necessary for any sort of reasonable argument. If I tell you, “I ate an avocado on July 14, 2026, for lunch,” the assumption is that either my statement is true (that I did indeed eat an avocado on that day for lunch) or that it is false (that I did not eat an avocado on that day for lunch).
With that, for someone to argue against my statement, they must assume that I am not both positing that I ate an avocado on July 14 and that I did not eat an avocado on July 14. The reasonableness of any back-and-forth about my avocado-eating, or anything else, depends on the LNC!
But here’s the kicker. Because the LNC is the ground of all logic, any effort we make to prove the LNC must involve the LNC itself. It’s essential to our philosophizing, and we must, at least initially, take it on trust.
Other Unprovables
Several years ago, a fellow student and I spent several weeks debating the ever-fertile topic of free will. One of us was a Calvinist; the other was Arminian. For several weeks, we exchanged emails on the nature of freedom, the meaning of divine will, and the significance of certain passages in Exodus.
One of my main takeaways from that conversation was that sometimes, in some ways, logic demands a resignation to mystery. Calvinism, at its heart, seems to demand an enigma: How do divine determination and free will coexist? The philosophical libertarians have their own problem: if creatures are completely free, without constraints on their action, what moves them to take one course of action over another? Again, our minds run into the problem of mystery. Yes, philosophers are working to answer such questions, but the answers are not always clear. Indeed, for some things, the answers might always lay in obscurity.
Conclusion
By pointing out what seems impossible to prove, I’m not saying that all the things we label “mysteries” are unable to be solved. Nor am I saying that, given the necessary trust involved with some issues and the apparent opaqueness of others, we must therefore throw up our intellectual arms and surrender to the lure of not thinking at all.
I am, though, pointing out the limits of our minds. The “unprovables” or mysteries we find, even if temporary, direct us to our finitude. We are not God. We will not know as Him. And if, when appropriate, we embrace that rather than chaffing against it, the inevitable mysteries of the world become far less of a catalyst for frustration and far more of a catalyst for praise.
Aletheia Hitz is an editor/writer by vocation, philosopher by training, and poet at heart. She’s currently working toward her Master's in theology, and she aspires to spend her life in pursuit of the infinite beauty of God.
This culture article was made possible by The Fred & Rheta Skelton Center for Cultural Renewal, a project of 1819 News. To comment on this article, please email [email protected]. The views and opinions expressed here are those of the author and do not necessarily reflect the policy or position of 1819 News.
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