Can someone who rejects God as He has revealed Himself in Scripture be consistently rational? Cornelius Van Til, a 20th century Christian apologist and theologian, frequently demonstrated the inherent irrationalism of all non-Biblical worldviews. One of his students, John Frame, has applied this insight to many of the major philosophical thinkers and movements of western civilization, showing how at the heart of their attempts to be rational lies irrationalism (A History of Western Philosophy and Theology). If Christianity is right in claiming that God created the heavens and the earth and all that is in them, this makes sense: if this world is created, administrated, and interpreted by an all-knowing and ever-present Creator, every truth and correct interpretation of the world will have reference to Him. Without Yahweh as a reference point, consistency would be impossible, thus the irrationalism at the heart of all our attempts to be rational. Here I want to outline how this insight applies to the two forms of reasoning we all regularly use, inductive reasoning (concluding truths or hypothesis from observed data) and deductive reasoning (the use of deductive logic, e.g., all men are mortal, Socrates is a man, therefore Socrates is mortal).
Inductive reasoning can give no certainty within an open or unknown system: only exhaustive knowledge allows the possibility of true knowledge. In its pure form, it is inherently contradictory in this sense. To assert knowledge of anything, an inductivist must assume that he knows everything—that all the data is available to him. For example, any theory works from the known data and theorizes, giving predications, but can be contradicted by any fact. If I theorize the impossibility of a resurrection, the occurrence of a resurrection demands reconsideration of all the facts that led to that conclusion. If the universe is to a great extent unexplored, then there is a wealth of unknown data that could contradict any inductively based belief—it only takes one case of an effect not following a cause to cast doubt on all causality (tradition teaches that John the Revelator survived being placed in boiling oil: the effect should have been death, what other effects should we then doubt?). An inductivist (e.g., empiricist) desiring to live rationally must first, then, irrationally disregard all possibly contradictory data, such as miracles (which is to argue in a circle). Furthermore, to provide any knowledge, inductive reasoning must be built on a foundation, with deductive reasoning, of certainty. Only certain knowledge, a solid foundation, grounds the possibility of inductive reasoning or deductive logic. Inductive reasoning relies upon the certainty of extra mental existence, causality, individual existence, trustworthy senses, and the correspondence between mental impression and extra-mental being. All inductive reasoning relies on the certainty of these truths, yet cannot establish them.
Deductive reasoning requires the truth of at least initial premises (via either innate knowledge or inductive verification) and the validity of logic—which presumes a whole worldview necessary to support it (mind, rationality, consistency). The certainty of the initial premises, as with inductive reasoning, presumes upon exhaustive knowledge—that there is nothing that could possibly disprove or provide an exemption to the premise. Is unbiblical reasoning, therefore, really rational? To gain knowledge through reason, the unbiblical worldview first assumes without a reason a rational universe, causality, the existence of others, the existence of self, and the correspondence between thought and reality, and then it postulates a naturalistic open system—no one has exhaustive knowledge, there is no transcendent being—and thus destroys the very possibility of useable knowledge.
Consider two examples, David Hume and Descartes. The most consistent of empiricists, David Hume has had a profound influence lasting far beyond his death. Yet, even Hume could not provide a rationally satisfactory system of thought. To make his radical empiricism work, Hume had to postulate so-called ‘natural beliefs.’ Natural beliefs are those beliefs that man cannot deny and therefore he is not obligated to deny even if he is lacking any proof. These then become the foundational beliefs by which his empiricism functions. To qualify as such, a belief must be undeniable: examples are the existence of self and others and the reliability of perceptions. He defends these as ‘natural beliefs’ because they cannot be demonstrated in any way. So, those beliefs most foundational to Hume’s epistemology—to human experience—are rationally unfounded, without any support. The center, then, of Hume’s attempt at rational thought, his empiricism, is pure irrationalism—beliefs that must be assumed without any evidence. Even his criterion for natural beliefs is arbitrary: how does one know, on an empiricist system, that such beliefs are universal, undeniable? what sense impression supports this universal negative? what experience does Hume have of universal belief? Furthermore, what sense impression leads to the postulation of this criterion?
Descartes, on the other hand, attempts to establish all truth through deductive reasoning. Yet, he runs into very similar problems. His primary axiom, that belief from which he deduces all else is “I think therefore I am.” Here he finds certainty in the immediate, undeniable, impression of self-existence. He then attempts to prove from this starting point of self-existence the existence of God and, from there, everything else. Yet to move beyond the self, Descartes had to introduce irrationalism into his system. His reasoning for God rests upon deductive logic, presuming on the existence and validity of reason, and knowledge of all the terms within his syllogism (what does ‘god’ mean? where does he learn this meaning? what do ‘is,’ ‘exists,’ and ‘self’ mean?). These are unprovable assumptions: Descartes had to assume they were valid before he could engage in any reasoning, before he could come to any conclusion beyond his own self-existence. The irrationalism at the heart of his attempt is even clearer when one examines just what his famous cogito—“I think therefore I am”—achieves. “I” and “am” here have no definite value, and can have no definite value on Descartes epistemology. He claims to have established as a certain principle the existence of self, yet he is unable to explain what self is. There is the undeniable impression of thought, of self-awareness, but whether this is the self-awareness of a bee, a computer program, a robot, a human being, or a black hole is unknowable. The self he has proved is, without the knowledge of anything else, a hopeless postulate: what good does it do to know that ‘the self’ exists, with no knowledge of what that means or the ability to prove anything beyond “I am.” Rationalism, with Descartes, yields only hopeless irrationalism—the knowledge of bare self or the irrational assumption of reason and exhaustive knowledge necessary to deductively prove with certainty any other truth.
 Knowledge must be able to be traced back to sense impression: none of these ideas can be traced back to such impressions, so they cannot be knowledge.
 Thanks to James Hooks for a helpful discussion and clarification on Decartes argument.
Proposition 1: If God promises that all things are worked together for the good of those who believe
– This is seen in Romans 8:28
P1A: going to Hell is not good
P2: and someone who truly believes apostatizes forever from the faith
Then: P3; a promise of God has failed (which is in contradiction with His nature)
P3A: if God is all knowing so he knows everything that will happen and all powerful so that he can make things happen.
P3B: and a promise then fails
Then: P3C; God would be a liar for he would know that what he says will not come to pass.
P3Ci: if God is truthful and therefore cannot lie
P3Cii: and a worldview/argument leads to the conclusion that God lied
Then: P3Ciii: that worldview is false or a proposition in the argument is false.
If this all holds true, then proposition 2 must be false (for P1 is an exegetical truth of Scripture [see here] (presupposing the evangelical understanding of the inerrancy and authority of Scripture)) and this person has to either have temporarily backslidden or was in fact never truly a believer (and perseverance of the saints is proven to be true; see here for the an outline of the doctrine).
CP1: if it is impossible for someone who is a true believer to fall away
CP1A: an inability to choose to walk away means that a believer is only able to in the end choose A and not B. A (persevering to glorification) is ensured by God’s persevering power making B (apostatizing forever from the faith) impossible.
CP2: and libertarian free will requires freedom of contrary choice (ability to choose A or B)
Then: CP3; libertarian free will is necessarily false according to God’s infallible word (Romans 8:28) and the universe is partially determined; because Scripture teaches that humans are responsible for their actions Compatibilism is true (soft determinism is the reality of our world.)