The fundamental laws of rationality are also the fundamental laws of the Biblical worldview.
The two laws of Non-Contradiction & Sufficient Cause (sometimes misleadingly call the law of Sufficient Reason) are the rock bottom foundation of logical and empirical evidence. It was the unique combination of those two laws during the late middle ages which led to first a freemarket of ideas which then led to the rise of science.
The Law of Non-Contradiction states that “nothing can both be and not be at the same time, place, and respect.” A light can be red at one moment and green or yellow at another moment, but it cannot be both red and green at the same time and place. The color is the “respect” in this case.
This is the fundamental law of the Cosmological Argument for God (see Personality, Empiricism, & God) God is the differentiator between the possible and the existing. He who Is absolutely gives existence to that which is contingently. So the difference between being and non-being, between existence and non-existence, must be clear and precise. The very nature of God as Creator ex-nihilo itself ensures that. Only so can the cosmos be rational, thus providing a basis for science.
The law of sufficient cause states that every event must have a sufficient cause, that is, the law of nature, given by God, specifies that the cosmos is rational, not random chance and thus unpredictable. The “sufficiency” is rationally set by natural law as given by God. No one would think that a large dump truck being overturned and smashed could be caused by a 3-year old riding carelessly on his tricycle. The alleged cause would not measure up to the effect.
It was often first called the law of sufficient reason because Western philosophy was dominated by the rationalist oriented Greek philosophical tradition. Abstractions (such as reason) were treated as though they could cause events. But the principle of sufficient reason tended to spurn the empirical world and to exalt the logical, intellectual world as the more real than the physical world. That error was a major hangup in the development of Western philosophy and science (see Nancy Pearcey’s Total Truth. It is the sufficient cause, not sufficient reason, which gives the empirical world its rational character.
The Hebrew focus on the empirical world of time and space, insisting that God Himself quite naturally and easily invested Himself in that world of His own creating, was for centuries in Christian thinking overshadowed by that Hellenic preference for the logical and abstract as the more real — as with Plato’s Ideas. So, despite the Biblical influence, the empirical world for centuries got short shrift.
But that began to change in the late Middle Ages when there developed the floating free-market of ideas, which then was institutionalized into the great universities of Europe, at Oxford, Cambridge, Paris, Rome, etc. From those universities developed Western science. The budding scientists threw off the Hellenic/pagan worldview but kept the Greek tools of abstract reasoning, importing those tools into the Biblical worldview of the particular, personal, temporal, spatial, and material.
For the first time in human history, there was a sophisticated intellectual mechanism for studying the world in which human relationships took place, planned by God for the Kingdom. Those Greek tools of the intellect, it is beginning to be discovered, work far better in the Biblical worldview than in the pagan/secular worldview.
But Christians lost the initiative, early on rejecting reason, and pitting it against revelation. Other than using force to convert people, that was the worst mistake the Church of God ever made. The anti-intellectual (and unBiblical) stance aided and abetted the rise of secularism and rejection of Biblical faith.
Christians are beginning to discover the power of science for explaining, not trashing, the Biblical view. The 21st century thus bids fair (if we do not first self-destruct) to be a powerful renewal of Biblical civilization. The wedding of reason to revelation creates the Biblical 2-edged Sword of the Spirit, an invincible weapon — reason and revelation welded back to back.
Both fundamental laws of rational thinking are foundational to the Biblical worldview.