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Theory of Knowledge by Henri Poincare.


It can be said that science is a form of knowledge but one must add that it is a higher form of knowledge. This is because we can easily equate knowledge to facts and facts need not necessarily be scientific. For instance I love chocolate ice cream and that my favorite food is a mozzarella laden pizza. I know these things for a fact. My built-in knowledge about myself includes this list of favorite foods but on the other hand others may simply dismiss this knowledge as mere opinion and therefore does not belong to the category ascribed to scientific know how.

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Before going any further it is imperative to first have a concrete definition of science. Doing so will lead to a much better understanding of Poincare’s quote. But according to Charles Singer it is almost impossible to provide that answer and he wrote:

Science is often conceived as a body of knowledge. Reflection, however, will lead to the conclusion that this cannot be its true nature. History has repeatedly shown that a body of scientific knowledge that ceases to develop ceases to be science at all. The science of one age has often become the nonsense of the next (Singer, 1997).

At the early stage of the discussion we have encountered a major problem. This does not mean that there is no way to understand the intricacies of science but it must be understood that there is no simple definition that can be had when dealing with this branch of knowledge. It is understandable why modern intellectuals will gravitate towards science – the scientific method offers a more rational explanation of the world but an honest assessment will reveal that science does not always offer absolute answers to life’s questions. This led Singer to conclude, “Science, then, is no static body of knowledge but rather an active process that can be followed through the ages” (1997). This is a good starting point in analyzing what scientific knowledge is all about in light of Henri Poincare’s statement.

At first glance the famous quote made by the mathematician and philosopher extraordinaire Henri Poincare alludes to a systematic presentation of facts before the random accumulation of data can be considered as scientific fact. There is no problem with this assessment because it is common knowledge that there is a need, say for an author to organize data in order for the reader to make sense of what he is trying to convey to them.

But not only that it must be pointed out also that there seems to be a two-way process that will result in following Poincare’s standard of knowledge acquisition. First of all facts becomes science based on how the speaker or author systematically organizes data. Secondly, facts become science the moment the receiver or the audience makes sense of the system used by the communicator. There are many examples that can demonstrate this dynamic.

A good example that will demonstrate the truthfulness of this view can be seen in linguistics. Language, before it can be called as such, starts as a random grouping of sounds. The human vocal chords emit the sound but for the visiting foreigner hearing the local dialect for the first time, everything sounded as gobbledygook. A Frenchman will no doubt be greatly troubled if left in a room with two Chinese nationals chattering constantly and unable to comprehend and unable to join in the conversation.

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The dialogue between the Chinese couple was achieved through the use of sophisticated language developed through more than a thousand years of Chinese civilization. Without a doubt the Chinese language used was as sophisticated as the French language but the Frenchman knows nothing about Mandarin and therefore for him everything is rubbish. Applying Poincare’s idea, the foreign sounds reaching the ears of the Frenchman are coming from fluent Chinese speakers and these are standard Mandarin words – these are facts. But the Frenchman did not have the capability to organize these sounds to make it comprehensible.

In the area of mathematics, Poincare’s theory can be tested and affirmed. Just as easily as the above-mentioned example mathematical formulas and mathematical rules must be understood first before a civil engineer use numbers to explain that the bridge they are building will not collapse once ten-wheeler trucks begin moving over it. In linguistics emphasis is placed on makings sense of the sound and creating a system that will help the person understand what the words mean. In mathematics the idea of being systematic in terms of organizing knowledge reaches a new level.

When it comes to words, there can be a margin for error. Two people can have two different ideas when it comes to the word “beauty” but in math 1 + 2 = 3 and there is no other interpretation when one uses the plus sign and placing numbers 1 and 2 on either side. The same is true when using the multiplication sign, placing numbers 4 and 3 in an equation: (4 X 3) will give the answer 12 and there is no other possible interpretation.

When it comes to natural sciences and sociology, Poincare’s theory is difficult to apply. In linguistics and mathematics one can argue that we are dealing with symbols. The letter “A” is a symbol and through association and growing up in a particular community we learned that there is a definite way to pronounce this symbol. The same way with numbers through studying we are made to understand the significance of the number line as well as the various operators used in arithmetic expressions.

But when it comes to natural sciences and sociology something can be part of the whole but even without knowing the taxonomy of the animal and plant kingdom it is still possible to appreciate the beauty of a 100 year old oak tree. Even without knowing the genealogy of the pretty girl in front of a man, he can still easily fall in love. A tree can be a part of the forest but it also stands on its own. Furthermore, human behavior is more complex than mathematical symbols. In mathematics one can predict what will happen if a particular function is used, in human relationships no one can claim to be an expert.

Problems Encountered

Going back to Charles Singer’s definition of science reminds us that knowledge acquisition and making sense of the world around us is an ongoing process. Poincare will no doubt agree with this assessment but when it comes to his analogy of using bricks and building houses there is one problem that needs a resolution – how can we discover the ultimate process that will lead to true knowledge? Furthermore, one could also ask if there is a formula that can be used that can help organize facts into a useful piece of information in the same way that a builder can expertly use bricks to create a home.

Aside form the problem of looking for a universal formula that will help in communicating as well as understanding true knowledge there is also a problem when it comes to information that can be had without a complicated system of analyzing facts. As mentioned earlier I know without a doubt that I love chocolate ice cream and that from time to time I will crave for a mozzarella laden pizza but I cannot explain how I know these things. Furthermore, I cannot find a way to show other people how I truly love these types of food.

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In the aforementioned case scenario where a Frenchman was described as drowning from a sea of unintelligible words, no fault can be attributed to the Chinese couple making conversation in their native tongue. Poincare’s assertion does not work in this situation. The Chinese nationals had an efficient way of systematizing their thought patterns and were very much capable of organizing facts. They may have been discussing scientific data for all we know but the Frenchman was unable to realize that they were indeed passing along scientific knowledge. Here we see a scenario where Poincare’s theory does not work as expected.


One way of understanding Poincare’s analogy of using bricks as the material for building houses is to acknowledge that data or scientific facts must undergo a process of organization, a particular system of rearranging facts so that we can make sense of it and consider it as scientific knowledge. By doing so Poincare created a higher standard when it comes to knowledge acquisition. This could be bad or good depending on the perspective of the person. If one is dealing in pure mathematics and other branches of pure science such as physics and chemistry this idea is laudable. But if one is dealing with social science this idea is problematic.

Based on the preceding discussion it seems that Poincare’s theory of knowledge acquisition is limited to data that can be understood in mathematical terms. It is therefore not an accident that mathematics is considered as the language of science. This also leads to another implication which is that true knowledge is limited to scientific pursuits. And finally there is also the added implication that scientific knowledge is limited to what can fit inside a prescribed system. This system must be pre-approved by the scientific community as an acceptable system to filter out error.

These pre-approved systems are the scientific laws and principles that are considered as infallible as far as scientists are concerned. Examples are the Law of Gravity, the Law of Thermodynamics and other scientific laws that govern the physical world. If we go this way then we can also conclude that Poincare’s statement encourages us to believe that absolute truth is possible. And this may indeed be true in the world of pure mathematics but when it comes to the other branches of knowledge it would be impossible to maintain this view.


Helmholtz, Hermann. (1995). Science and Culture: Popular and Philosophical Essays. Illinois: University of Chicago Press.

Singer, Charles. (1997). A Short History of Science to the Nineteenth Century. New York: Dove Publications.

Stehr, Nico & Volker Meja. (2005). Society and Knowledge. 2nd ed. New Jersey: Transaction Publishers.

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