Shabbat Parashat Tzav | 5768

Religion and Science- part IV (from Perakim B’Machshevet Yisrael, ch. 30)

Moreshet Shaul

Rav Yisraeli gathered classical and more contemporary rabbinic views on the interaction between religion/belief and science. We present his sources in an abridged, free translation form.

6. Contradictions Between Torah and Exact Sciences Are Impossible

 Hamadah V’Hadat, ch. 2 (Dr. Y. R. Holtzberg)

The concept of “proof” is known, but not everyone recognizes the simple definition of the concept and the conclusions that emanate from it. Proof is affirming a statement by means of other statements accepted as truths. In order to prove the other statements, yet other statements are needed and so on. At the end of the chain are statements whose truth we accept as givens without proof; we call these axioms. From a certain set of axioms, for example, the scientific basis of geometry is set, and such a set of axioms is necessary for every field of exact science.

Once upon a time, people viewed axioms with respect, as a truth upon which one may not cast aspersions, and this is also the case nowadays. However, more than a century ago, an event fundamentally changed scholars’ outlook on axioms, as one was “publicly disgraced,” uncovering the weakness of all of the world’s axioms. This is what happened. A famous axiom regarding parallel lines, set by Euclid, 360 years before the Common Era, can be described as follows. Through a point that is outside a straight line only one straight line traverses the point and is parallel to the first line. For 2,000 years people tried to prove the axiom, in other words, to base it on other axioms without having to replace it with another axiom, but no one succeeded. Then three scholars tried to prove it by means of the negative. They assumed that the axiom was incorrect, an assumption from which followed far-reaching conclusions, and looked for contradictions between the conclusions and other axioms. Surprisingly, not only were there no contradictions, but it was proven that there could not be such contradictions. Based on their assumption, which contradicts the axioms of parallel lines, they built a new field of geometry without internal contradictions.

What is the basis of the choice of an axiom? Science’s surprising answer is that it is not on the basis of its truth but on its convenience for us. Normally, Euclid’s axiom is more convenient because it allows for shorter calculations.

This event brought into question the outlook on exact sciences, as the source and wellspring of absolute truth. All conclusions of science, even exact sciences, are conditional on axioms that the science accepts and relies on as if they were absolute truth. The event demonstrated that this was necessary of any systematic work of human logic. Furthermore, the acceptance of something as an axiom is arbitrary, and not based on some logical necessity in the recognition of truth. Science is unable to contradict conclusions that flow from other basic assumptions that are based on different axioms than the ones it accepts.

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