Madilog

History

Madilog was written by Tan Malaka in Radjawati, near a shoe factory in Kalibata, Pantjoran, Batavia. Malaka stayed there between 1942 and 1943 as a tailor, while inspecting the condition of the city and kampungs in Batavia, from where he left over 20 years before. He spent 720 hours writing Madilog, over 8 months from July 1942 to March 1943, spending approximately 3 hours a day on the book and Gabungan Aslia (Aslia Merged), which was written at the same time. Publication had to be postponed due to lack of money and being under strict supervision of the Japanese Keibodan during World War II, from 1942 to 1945, when Indonesian independence was declared.

While writing Madilog, Malaka served as Chairman of the Agency to Aid Defense (Indonesian old-spelling: Badan Pembantoe Pembelaan, BPP) and as Chairman of the Agency to Help Worker Soldiers (Indonesian old-spelling: Badan Pembantoe Pradjoerit Pekerdja, BP3), to help forced laborers (Romusha). He was eventually elected as representative for Bantam to the Young Generation Congress (Indonesian old-spelling: Congres Angkatan Moeda, Dutch: Congres van de Jonge Generatie), but his swearing-in was cancelled. In Bantam, he met some Indonesian nationalist youth activists such as Sukarni, Chaerul Saleh, and Wikana, who would be known as members of Persatuan Perdjuangan in Surakarta in 1948.

Madilog introduced the Madilog idea. It was first self-published in 1943, using the pen name Iljas Hussein, and 568 pages in length. In the post-independence era, Madilog was published by Widjaya Publisher, in 1951, in Jakarta. Madilog was translated into Dutch by Ted Sprague and was published in 1962 in The Hague.

Epistemology

Madilog introduced a way of thinking of evidence and fact in a way that fit into Indonesian demographics and culture, in line with Indonesian thinking on fundamentals. Evidence is fact and fact is founded on scientific evidence. There are two main ways of thinking in Western philosophy. The first is idea (mind), unity of thinking, and sense. The second is matter as tangible reality, objective in nature as existence. Those two concepts were combined in the same way of thinking for human beings, who are the subject living things. In Madilog, the main field is evidence. Although evidence can't be described rationally, scientifically—as to what, why, and how—evidence should be considered as a true way of thinking, the consequence of not thinking evidentially being logical fallacies and myth-making. This is the focus of the epistemology of Madilog, concerning truth, the validity of science, and the correlation of human knowledge to life. The epistemology is divided into three parts: definition, testing, and mathematical thinking.

Definition

A proper definition limits the kind of reasoning undertaken in the processing of an idea, expressed in natural language, with the object of limiting the impact of optimistic thinking that tends to result in an ideal-final explanation as the truth. One requirement of a definition is that if we define that A is equal to B, then the reverse (B is equal to A) must also be true, or it is necessary to modify the original definition (A = B). In addition, a proper definition should have the following components: (1) it should be as simple as possible; (2) it should not involve circular reasoning; (3) it must be general or common; (4) metaphor, analogy, figurative language, description, obscure words, ghaib (occult words), abstractions, and vagueness are forbidden; and (5) a definition should not contain any negative statement.

Examples of poor definition are the statements a human is an animal, combined with the statement that apes and reptiles are animals. If those statements are reversed, then animal is human, and so it is that the syllogism apes and reptiles are human results in a logical fallacy. A further example: if a human is a two-eyed animal, then a syllogism can result in the fallacy a buffalo is also human.

Arithmetic

Using algebra does not increase human intelligence, when mankind encounters mathematics for the first time, even it is going to be limitation of thinking in the human brain. It can make a mankind as a mechanical creature as a programmed robot, which does not need to investigate something first. This was a phenomenon of the Indonesian people under the Dutch Ethical Policy (Dutch: Ethische Politiek, Indonesian: Politik Etis), from 1901 to 1942.

Algebra is more abstract than arithmetic or calculus. With arithmetic, we know 2 + 2 = 4 as a model of addition, and we don't mind that "two" might not only be a number, but also a thing that has attributes such as "one pen and one pen equals two pens" even though "two" is only a number, not a thing. Similarly with black as an attribute of color; the number is describing more than just a number in human thinking.

A specific number is apart from something that represents all things. "two" can be two buffaloes or two eggs, although we know that two buffaloes added to two eggs are not equal to four buffaloes or four eggs. This is based on a logical fallacy, even though a human equates attributes to the numbers (2 and 4).

2 or 4 is only a number that sorts to mere symbol, only a mind abstraction. Yet algebra is more apart from reality, more abstract. For example, given the following equation:

(a+b) (b-a) = a² - b²

Suppose that a = 3 and b = 2, so the equation becomes: (3 + 2)(3 - 2) = 3² - 2². To the left of the symbol "be equal to" (=) we have 5 x 1 = 5, to the right, 9 - 4 = 5. So that we find the left part is equal to the right part. Malaka described it as the meaning of algebra in the Arabic lexicon (Arabic: الجبر al-jabr) which literally means “reunion of broken parts”. It also works for other numbers: if a = 5 and b = 3, then we have (5 + 3) (5 - 3) = 5² - 3². On the left we have 8 x 2 = 16 and on the right 25 - 9 = 16.

So, "a" represents an unlimited range of numbers, 2, or 3, 4, 5 …, as constanta. And "b" also represents an unlimited. Algebra classifies "a" and "b" as variables. Notation "a" does not need to be greater than notation "b", for example this supposition:

(3+6) (3-6) = 3² - 6² is reduced to 9 x (-3) = 9 – 12 = -3

or

(½+⅔) (½-⅔) = (½)² - (⅔)² is reduced to 1/4 x (-4/9) = 1/4 - 4/9

The number symbols in the equation above can represent things: 2 buffaloes or 2 eggs, as well as simply numbers, which are abstractions apart from things. The abstract number, "a" and "b" in algebra, makes algebra is more abstract than arithmetic, because algebra can signify abstractions not things.

This does not mean that if mathematics is separate from material concerns, it is useless; or that algebra, which is more abstract, is more useless. After all, algebraic abstraction is based on arithmetic, which is inherently material. This concerns the main idea of Madilog, of thinking on the right path.

Geometry

Geometry is not about the weight, heat, or energy of an object. Geometry defines four main attributes: (1) volume is a part of natural space which is contiguous to all parts of spheres; (2) a sphere is a mass border; (3) a line is a sphere border; and (4) a dot is a line border.

Volume is a part of natural space. So, volume is classified in a more general class than that of being a "part of nature", which does not include all the parts of space in nature. 1 m³ of air as a "part of nature", like buffalo, egg, human, does not fit into 1 m³ toward being a "part of natural space". We must define unambiguously. The borders are differences among the things in the same classification. So, "volume" means being in accord with the definition above. Science defines the organization of facts by generalizations such as geometry. This is the last step in thinking "madilogically".

Theory testing

There are twenty nine pages in Madilog which describe theorems and scientific theory testing. A theory is a tested hypothesis (h ≠ 0), in order to be truth. The hypothesis itself is a notion, presumption, or belief, not necessarily truth at all. A theory is a result of testing, and testing in many ways. Theory testing in science uses "triple methods", which were adapted in Madilog into three methods, as follows.

Synthetic method

The synthetic method is an application of Hegelian dialectic: thesis → antithesis → synthesis). It is an integration the two or more elements that produce a new resulting idea. However, the practice is not synthetic dialectic, but synthetic epistemology.

For instance, the synthesis of the limit of a function and an simplified algebraic operation, to prove that the derivative of x² is 2x.

First, the hypotheses, or givens:
f(x) = y = x²
dy/dx = 2x
dy/dx is the derivative f’(x)

Then, dy/dx is forbidden to be limited by aggregate constanta, which means ∆x has a limit of nil (0). We can replace dy/dx with the zero limit of a function.

Based on limit of function theory on derivation (f’(x)), f’x is ((f(x+y) - f(x)) / y) for the zero limit of a function, limit x→0, we have the formula:

f’x = lim (f(x+∆x) - f(x)) / ∆x
      ∆x→0

Shortly after applying limit of a function, it can be tested by substituting the equation y = x²:

Based on f’x = lim (f(x+∆x) - f(x)) / ∆x
                       ∆x→0

dy/dx = lim ((x+∆x)²-x²) / ∆x
            ∆x→0

Algebraically, the formula (a+b)ⁿ = aⁿ + n.a + bⁿ can be replaced by (x+∆x)²-x², which becomes x² + 2x.∆x + ∆x².

So: dy/dx = lim (x² + 2x.∆x + ∆x² - x²) / ∆x
                  ∆x→0

The result is (2x + ∆x) = 2x.

So, it is proven that the derivative of x² is 2x. And the verification fuses two principles: the limit of a function and simplified algebraic operation.

Analytic method

The analytical method is the second method used to verify a theory. Take the supposition: "I wish this theory was right". This is what we call analytical thinking. For instance, we want to prove 2x is the derivative of x².

First, we give the hypothoses: y = x² dy/dx = 2x dy/dx is the derivative function f’(x)

If we want to prove that the derivative of y = x² is dy/dx = 2x, we have a supposition of "I wish it was true". From the supposition we have a logical formula:

x² → 2x
x² = 1x² → 2x

otherwise,
2x = (1+1)x²ˉ¹ ← x²
2x = 2x¹ ← x²
2x ← x²

So, it has been proven that x² is derivation of 2x. The analytical method is simpler than the synthetic method. Yet, both are still more complicated than the third method below: reductio ad absurdum.

Reductio ad absurdum

Reductio ad absurdum is a Latin phrase that means "reduction to absurdity". It is actually a common term for an argument that seeks to demonstrate that a statement is true by showing that a false, untenable, or absurd result is the consequence of its not being true, or, in turn, to demonstrate that a statement is false by showing that a false, untenable, or absurd result follows from its being true. For instance, "if A then both B and not-B, so not-A" and "if not-A then both B and not-B, so A". In Madilog, every single theory can be proven this way. Reductio ad absurdum in Madilog is the simplest way to verify a theory.

For instance, using the same case as above, we want to prove 2x is the derivative of x². We need to know the principles of derivation, and make sure that y = f(x), so dy/dx = f’(x) or y’. If a small addition of x, equal to ∆x, results in increasing y by ∆y, so that y = f(x) becomes y + ∆y = f(x+∆x), the value of dy/dx = 2x is f(x) = x² (proven after simplifying to y + ∆y), which means that a small a addition of x, ∆x, has reduced dy/dx.