Not intellectually. Whilst we seek an explanation for everything, human logic cannot prove anything absolutely. For absolute knowledge, you’ll have to find some other tool. In this case that tool is your Jewish soul.

The Askmoses Answer:

Absolute Proof

There is no absolute proof for anything at all. One of the conditions of intellect is that anything that can be intellectually proven can also be questioned. To put it another way, if it cannot be disproved, it is not an intellectual argument.

This “Principle of Falsification” was demonstrated by the great British philosopher, Karl Popper, and is generally accepted in scientific and philosophical circles today. It is also in consonance with the Talmudic position.

Furthermore, every intellectual argument requires axioms, which themselves cannot be proven. This was demonstrated in the 19th century by Karl F. Gauss, called by some the “greatest mathematician who ever lived,” who began to question the absoluteness of Euclid’s axioms. Later, in the 20th century, American mathematician Kurt Gödel demonstrated logically that no system can be proven without evidence from beyond that system. His paper was hailed universally as one of the most outstanding contributions to mathematics and philosophy in history.

In sum: Human logic cannot prove anything absolutely. For absolute knowledge, you’ll have to find some other tool.

Human logic cannot prove anything absolutely

Nevertheless, the human mind can come to some very educated conclusions. Such as concluding that it is raining outside by going outside and getting wet in the rain. The possibility remains that our senses are lying to us, but we will always need to make some assumptions, if just to survive.

Often, we can assure ourselves with almost absolute certainty without even seeing the thing for ourselves. For example, by looking out the window and seeing the trees swaying we can assume that it is windy. By observing the lights going on, we can assume there is electricity in the wires. Or by bouncing electrons off of sub-microscopic objects, we can construct a working model of their form.

So too, the fact that there is a Primal Source for all that exists is one of the most evident facts there is. So is the fact that this Primal Source generates this world with design/intelligence.

G-d by Scientific Principle 

The concept of a Primal Source relies on an axiom that all of science relies upon: the Principle of Explanation. This principle simply states that all phenomena must have an explanation. Science is the endeavor of discovering those explanations. Molecules are explained by the dynamics of atoms. Atoms are explained by the dynamics of their sub-particles. The sub-particles are explained by photons. Eventually, there must be an explanation for the existence of matter and energy.

Without this principle, not only would there be no science, there would be no human endeavor whatsoever. In everything we do, we rely on the assumption that each thing has an explanation, thereby providing us with a consistent universe to deal with. Imagine the confusion if everything just appeared as though it had suddenly arrived out of nowhere.

The Primal Source, then, is nothing more than the ultimate explanation for all that exists, the end of the chain.

G-d beyond Science

What then, you ask, is the explanation for this Primal Source? But that is just the concept of a Primal Source: That there is something (if it can be called a “thing”) that does not require an explanation. Because otherwise we are really stuck: Either we surrender and say that there are things that do not require an explanation. Or we just say that the explanations go on and on ad infinitum—which really is the equivalent of saying that the cosmos as a whole has no explanation.

We cannot imagine such a thing—or non-thing. How could we imagine something that has no defined boundaries? But that does not render it illogical. After all, can you imagine gravity? Or electricity? All we know of these things is their effects that we observe. But no human being can tell you he knows what they are. Similarly, we know the Primal Cause from its effects—the existence of the universe—yet we cannot say we know what it is.

The Creator Cares

As for the fact that this Primal Source cares about what we are doing down here and gave us the Torah, etc.—for all this we rely upon the revelation at Mt. Sinai. This is dealt with in other essays. In brief, it was a mass experience, not just a personal revelation transmitted by one or a handful of individuals. A mass experience is accepted as historical fact.

We can also point to the otherwise inexplicable survival of the Jewish people. Several other proofs are given by various authors.

We cannot imagine such a thing:or non-thing... But that does not render it illogical. After all, can you imagine gravity? Or electricity?

All the above are arguments based on standard logic. However, the real reason Jews believe is not for any of these reasons. It is simply because they inherently know these things to be true from within, a trait they have inherited from their ancestors for 3700 years. It is that inner conviction, not the weight of intellectual proof, that has brought them to be martyrs for their faith and withstand all challenge for all these millennia.

In fact, the classic Jewish philosophers explain that when the Torah commands us to have faith in G–d, it is not discussing this knowledge that there is a Primal Cause. That, they say, has nothing to do with faith, but knowledge. For example, you do not command someone to believe that at night it is dark outside. They go outside at night and know that it is dark. Similarly, knowing that there is a Primal Cause is an obvious conclusion from common human experience. Rather, when the Torah tells us to believe in G–d, as in the first of the Ten Commandments, it is telling us to connect with a G–d who is far beyond even the limitations of being a Primal Cause.

Yes, even the idea of a Primal Cause has its limitations. I know we said that it is infinite and indefinable, but that’s relative. After all, how did we come to the conclusion that there is a Primal Cause? Through our knowledge of this world. So there is one limitation already: the Primal Cause is the Primal Cause of our world—and that’s as far as we know. Furthermore, it is a cause. And it’s stuck in being primal. We could go into this at length, but I think that is for another essay. The matter is discussed at length in the classic Derech Mitzvosecha, beginning page 88.

The point here is that the G–d in which Jews believe and to whom we connect is far transcendent of anything human reason can fathom. Because the human soul contains faculties beyond reason. There is a place within the human soul for absolute knowledge, for a vision of reality that supercedes all other matters of life and perception. And that is the core of the Jew.