Archive for April, 2022

The church origins of (axiomatic) math

Friday, April 15th, 2022

Formal math is like the emperor’s new clothes, a metaphysical (=unreal) cloak over useful normal math. Formal math itself is neither useful not beautiful.
Axiomatic or formal math is like a metaphysical (=unreal, invisible) cloak over useful normal math. This metaphysics is neither useful for any applications of math, nor beautiful. Modern math is NOT “rigorous”; just resurrects the con-trickery of medieval church theology by injecting a metaphysics (fantasy) of infinity/eternity into math. It has the political value of giving Westerners control over mathematical knowledge.

The previous article[1] explained why the terminology of the “Pythagorean theorem” is racist. That terminology is defended by appealing to the two myths of “Euclid”, used to assert that White Greeks did “superior” geometry compared to Black Egyptians. But both myths of “Euclid” (the myth of the person “Euclid”, and the myth about the book “Euclid” that it has axiomatic proofs in it) are false.

It is a completely bogus claim that “Greeks used axiomatic proofs which originated with Euclid”. There are no axiomatic proofs in the actual “Euclid” book, whoever wrote it. This fact was publicly admitted by Bertrand Russell[2] and David Hilbert[3] over a century ago.

How then did axiomatic proofs actually originate? Who FIRST advocated axiomatic proofs? These questions are important, for axiomatic proofs are what are used in the math taught in universities and schools today. But Western mathematicians (and historians) never asked this question about the real origin of axiomatic proofs. All Westerners gullibly believed for centuries in the myth of axiomatic proofs in the “Euclid” book. Today they just carry on believing in the Greek-birth myth of axiomatic math (like the virgin-birth myth, underlying church ethics), using myth jumping, or the tactic of defending one myth by invoking another myth as evidence.

But if the “Euclid” book as the origin of axiomatic proofs is just a false creation myth, one has to ask this question about the real origins of axiomatic proof, and answer it.

Why the Crusading Church adopted reason

The fact is that the earliest recorded case of actually (not mythically) using the axiomatic method of proof is its use by the church. An influential priest of the Crusading church, Thomas Aquinas,[4] used axiomatic reasoning to prove his “angel theorem” that many angels can fit on a pin. That is, axiomatic proofs originated during the Crusades, shortly after the “Euclid” book arrived in Europe as a crusading trophy. This correlation was later confounded with a causal relation, that “axiomatic proofs originated with Euclid”!

But why did Aquinas want to use reason? The context of the Crusades is critically important. Crusading spies like Adelard of Bath (who first brought the “Euclid” book from Muslim lands to Christian Europe) explained that Muslims accepted reason, unlike Christians who went by authority.[5] Indeed, there was a whole Islamic theology of reason, called the aql-i-kalam.[6]

This observation by the Crusading spy Adelard, that Muslims used reason, was very important for the real aim of the Crusades, which was to grab Muslim wealth, by trying to convert Muslims by the sword. But force failed against Muslims for centuries (after the first Crusade). The then military inadequacy of all the squabbling nations of Europe, combined under a religious flag, was amply manifest by the time of Aquinas. So, it was evident that Muslims could not be converted to Christianity by the sword, which method had earlier succeeded with pagans in Europe. This method (the sword) did not work even in the then Muslim parts of Europe (al Andalus, Spain etc.). These were the wealthiest parts of Europe then, hence a prime target of church greed.

Muslims obviously rejected the authority of the church. They also regarded the Bible as corrupted by the church, as even the scientist Isaac Newton did.[7] Force, church authority, and Bible all three were ineffective. But what else could work to convert Muslims? That is, the church had no option but to turn to reason to try to persuade Muslims to convert by reasoning. For this purpose, the church first erected a Christian theology of reason, parallel to the Islamic theology of reason. But how? The word “reason” occurs less than 100 times in the Bible, depending on the translation. So what were the church sources for this transformation? The church could hardly acknowledge that it was mimicking its religious enemy.

Therefore, the first step the church took was to appropriate reason and claim it as a Christian inheritance: this was achieved by its traditional secular method[8] of fooling opponents by concocting false history, since Orosius. False Crusading history simply attributed all “useful” knowledge in Arabic books (captured from Muslims) to early Greeks.[9] It was asserted that key Arabic books (incorporating world knowledge) were of Greek origin. The thought did not cross the minds of gullible Westerners that this tale of the sudden recovery of a long-lost heritage, during a religious war, might by a political stratagem.

Asserting the myth of the Greek origins of “reason”, in “Aristotle” and “Euclid”, enabled reason to be appropriated as a Christian inheritance, on the belief (since Eusebius) that the early Greeks were the sole “friends of Christians” (since they were before Christianity). So strong was the grip of the Crusading church on the minds of Westerners, that gullible Westerners are still sold on those Crusading myths of the Greek origins of reason. We have already examined, in the first part of the article, the falsehood of the myths about Euclid. (“Aristotle” will not concern us here.)

How and why the church invented axiomatic reasoning

However, even if reason came to be regarded as a Christian inheritance, it could still be dangerous to church dogmas. This danger was recognized, before reason was accepted into the church fold. Hence the Inquisition placed a number of reason-related books, translated from Arabic, on its notorious “Index”, and persecuted those engaging with these books.

This was the problem (resolving the danger of reason to church dogma) to which Aquinas and his schoolmen found a simple solution. The solution was to subtly twist reason to turn it into a church tool, so that “reason” could be used to support church dogma, and prove exactly what the church wanted: neither more nor less. How? By inventing axiomatic reasoning!

To understand how the church twisted reason, let us review the difference between normal reasoning and formal reasoning (or axiomatic reasoning). Normal reasoning begins with facts or observations. We see smoke, and reason that there must be fire. This is a good way of reasoning, and is very ancient;[10] its use in India is documented from long before any fictitious Greeks, such as Aristotle (of Toledo[11]) or “Euclid”. This is the kind of reasoning used also in science: for facts and observations are a key part of science.

However, Aquinas could not reason in this normal (or scientific) manner, for facts or observations are contrary to church dogmas about the nature of God [theology=God-knowledge]). Therefore, the church invented axiomatic reasoning, or reasoning which excludes facts. (more…)