Science, reason, and superstition - 3:
The church connection to reason

C. K. Raju

Earlier, I gave examples of how superstitions have crept into Western science. These is not limited to belief in “laws of nature”. There is a more systematic conduit through which Christian superstitions have crept into present-day science. Science is based on mathematics, and mathematics is based on reason—or so we are taught in school. And, today, we hear much about reason and rationality as a cure for superstition. But is it?

Now, as already noted, reason is not culturally alien to India, and all but one system of traditional Indian philosophies accepted proofs based on “reason” and inference. The exception was Lokayata (“people’s philosophy”) which rejected proofs based on inference (for good reason, as we will see). And reasoning was also used in Indian tradition to counter superstitions. For example, there is a superstitious belief that the earth is flat, a superstition found also in the Bible. Lalla contested this by reasoning: if the earth is flat, say why can’t tall trees be seen from afar?[1] In contrast, the Bible (Daniel 4:10-11) speaks of a tall tree that can be seen from the “ends” of the earth!

However, for rationalists, the really embarrassing fact is this: the church (“schoolmen”) adopted reason as part of its theology—the Christian theology of reason. This happened during the Crusades (and before the Protestant split).  I have dwelt elsewhere on the  political motives for this (desperation to grab the wealth of Muslims by converting them;  Muslims, then, could not be converted by military force, as the first Crusades proved, and Muslims rejected the Bible, but accepted reason, as in the aql-i-kalam, or Islamic theology of reason).[2]

The immediate question, however, is this: if rationality is an antidote to superstition, how could the church adopt reason as part of its official theology? Rationalists never raised this common-sense question nor answered it. 

Having raised the question, let us try to answer it. The first thing to understand is that reason is NOT universal: one word “reason” can mean two conflicting things. By “reason” most people understand what should properly be called “normal reason”, that is, reason + empirical facts. For example, Lalla’s reasoning starts with an empirical fact: far off trees cannot be seen. This is an easy observation: from a ship moving away from land, tree-tops are seen to disappear over the horizon, and vice versa. Hence, the inference that the earth is round.

Note that this example is also against the dirty caricature that because the non-West used observation it excluded reasoning. For Lalla, that the earth is round was NOT an observation made by travelling into space; it was an inference based on a common observation (that far off trees cannot be seen).

The second thing to understand is that the church did NOT use reason in this way. The church defanged reason by divorcing reason from empirical facts. Why? Because empirical facts are contrary to church superstitions, reason alone is not. The church understanding of “reason” was designed to make reason compatible with superstitions. This sort of reason may be called “formal reason” (reason MINUS empirical facts), for this is the reasoning used in formal mathematics which is taught today in our schools and universities. (In contrast, traditional normal mathematics used normal reasoning, since it accepted the use of empirical facts in math; e.g. Aryabhata says that the vertical is decided by a plumb line, as a mason still does.)

But, today, the official justification for rejecting the empirical in mathematics is that empirical proofs are fallible. Everyone accepts that. The classic example in Indian thought is that, in dim light, one may mistake a rope for a snake or vice versa. But all traditional Indian systems of philosophy nevertheless accepted empirical proof as the first means of proof, for the matter of erroneous observation can be quickly settled by inductively repeating the observation, and e.g. tapping the rope/snake with a stick. 

Is there anything better? The church claimed so, through the superstition that “deductive proofs are infallible”. Hence, it proclaimed that proofs based purely on reason (minus empirical facts) are “superior”.  As any colonised mind will today parrot, “deduction is superior to induction”. Hence, “infallible” deductive proofs are declared superior to empirical proofs.

But the belief that “deduction is infallible” is a pure church superstition. For,  how exactly do we know that deduction is infallible? We don’t. To the contrary, anyone who has ever done a complex mathematical proof, or engaged in a long chain of deductive reasoning, understands that deduction is very likely to involve errors.  Deduction is highly fallible.

It is amazing how the colonised mind goes by this superstition, and is supremely oblivious to the gross fact that innumerable students make innumerable errors in deductive proofs, hence get flunked in math.  Nor is mathematical authority immune to errors: the ostensive reason why TIFR sacked the (Marxist) mathematician D. D. Kosambi,[3] who (trained in Harvard with G. D. Birkhoff) was that he published an erroneous proof of the Riemann hypothesis. More recently, the world’s top-rated mathematician Michael Atiyah (the only mathematician to have got both the Fields medal and the Abel prize) claimed a proof of the Riemann hypothesis, which was almost certainly erroneous.  Atiyah certainly erred (in the content) when he brazenly plagiarised[4] my published correction to Einstein’s mistake[5] [6] during his Einstein centenary lecture.

So, regardless of the superstition, the fact is that deductive proofs are fallible, even top authorities can err.  It is no use saying that a valid deductive proof (like a valid observation) is infallible, for how do we know when a proof is valid except by rechecking it repeatedly? But a philosophical doubt can always persist about the validity of the proof, even after it has been checked ten times.  This is a much stronger doubt than that in imagining a dead snake might yet be a rope. That is, fallible deductive proofs, like fallible empirical proofs, can only be corrected inductively, and induction too is fallible. If the validity of deductive proof can be settled only by induction, it is very foolish to believe that deduction is infallible or “superior” to induction. This is an example of how a superstition can be widely believed.

As a non-mathematical example, the game of chess is based purely on deduction: if played correctly, it should always end in a draw. But EVERY human being almost ALWAYS makes an error, hence loses to a computer. That is, deduction is far, far MORE fallible than empirical proof.  The human mind is far more susceptible to errors than the senses.

The possible errors in deduction, like those in an empirical proof, can only be corrected inductively, by re-checking the proof. But, because the human mind is easily misled, errors in a deductive proof may persist for a long time, unlike the observational error about rope/snake which can be corrected in a jiffy.  As a concrete example, for over five CENTURIES, all Western scholars collectively failed to spot the error in the proof of the very first proposition of “Euclid’s” Elements,[7] regarded as a deductive proof. Recall that this was a compulsory church text, falsely asserted to be a text about deductive proofs. 

The third thing to understand is that the foolish superstition about the infallibility of deduction was tied to another church superstition about logic: that “God is bound by logic”. That is, the Christian priests superstitiously asserted: God cannot create an illogical world, but can create the facts of his choice. Hence, proofs in formal mathematics today are based on two-valued logic (which supposedly binds the Christian God). But if we were to use a different logic, the theorems of formal mathematics would change. And, in this country, at least, we should know that there are  many other systems of logic (Buddhist logic, Jain logic) etc. and these have existed from even before the historical Aristotle of Stagira (different from the mythical Aristotle of Toledo to whom logic is falsely attributed in the West).[8] For those who go by science, quantum logic is not 2-valued[9] (an electron can be both “here” and “not-here” at one instant of time).

Given a multitude of logics, which logic binds God? If we abandon the church superstition about logic, the nature of logic in the real world must be decided empirically. If deduction is based on logic, and the nature of logic is decided by empirical observations, it is downright foolish to assert that deductive proofs are less fallible than empirical proofs.  But it is an extremely widespread superstition, among the educated elite, and this superstition is used to justify the teaching of formal math in our schools and universities today.

Unlike normal reasoning which begins with facts, formal reasoning begins with axioms or (equivalently) postulates. The fourth thing to understand is that these axioms/postulates are also divorced from the empirical. As a specific example, unlike Lalla who begins with an observation, Aquinas simply postulated that angels occupy no space.[10] Hence, his conclusion (“Aquinas’ theorem”) that more than one angel can fit on the head of pin. Note that Aquinas’ axiom about angels is pure metaphysics in the sense of Popper: there is no conceivable way to refute or test the axiom against empirical facts, for angels don’t exist in reality.  This metaphysical way of reasoning is 100% compatible with ALL church superstitions, but our rationalists never understood this tric, and continue to believe reason is the cure for superstition!

References:
1. लल्ल, शिष्यधीव्र्द्धिद, chp. 20 मिथ्याज्ञाननिराकरणम्
2. Though the West learnt about reason from translated Arabic texts, the church misled people into believing these were of Greek origin, and the colonised mind not only believes that, but stubbornly refuses to check the facts about “Euclid” and “Aristotle”.
3. C. K. Raju, “Kosambi the Mathematician,” Economic and Political Weekly 44, no. 20 (May 16, 2009): 33–45, https://www.epw.in/journal/2009/20/special-articles/kosambi-mathematician.html.
4. C. K. Raju, “Plagiarism by Ex-President of the Royal Society. 1: The Facts.,” n.d., http://ckraju.net/blog/?p=183.
5. For a popular-level account, see C. K. Raju, “Acceptance Speech for the TGA Award,” 2010, http://ckraju.net/News/ckr-TGA-acceptance-speech.pdf.
6. For an expository account, see C. K. Raju, “Functional Differential Equations. 1: A New Paradigm in Physics,” Physics Education (India) 29, no. 3 (September 2013): Article 1, http://physedu.in/uploads/publication/11/200/29.3.1FDEs-in-physics-part-1.pdf; C. K. Raju, “Functional Differential Equations. 2: The Classical Hydrogen Atom.,” Physics Education (India) 29, no. 3 (September 2013).
7. B. Russell, “The Teaching of Euclid,” The Mathematical Gazette 2, no. 33 (1902): 165–67, http://ckraju.net/geometry/Bertrand%20Russell%20on%20Euclid.htm (accessed 21 May 2020).
8. C. K. Raju, “Logic,” in Encyclopedia of Non-Western Science, Technology and Medicine (Springer, 2016 2008).
9. For an account of quantum logic, see C. K. Raju, Time: Towards a Consistent Theory, chp. 6. “Quantum mechanical time”, Kluwer Academic, Dordrecht, 1994.
10. Thomas Aquinas, Sumnma Theologica, n.d., http://www.newadvent.org/summa/1052.htm#article3 First part, q. 52, article 3.

(To be continued)

Prof. C. K. Raju, TGA Laureate, Honorary Professor, Indian Institute of Education Tagore Fellow, Indian Institute of Advanced Study

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Jun 9, 2020