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The Piano Handbook by Carl Humphries is a great book for amateur piano-lovers. It consists of an introduction and 18 units that are arranged from easy to hard. However, can someone learn how to play the piano by reading The Piano Handbook, a systematically organized (from easy to hard) string of facts, without ever touching a real piano?
When the greatest pianists of history from Chopin to Rubinstein are studied, it is evident that they acquired their knowledge by practice. Therefore it would be rather absurd to claim that one can know how to play the piano by reading a book. In this case, playing the piano represents a special kind of knowledge called tacit knowledge or know-how. It is a type of knowledge that philosopher Michael Polanyi notes as “One can know more than one can tell” (Polanyi, 8).
As facts are things that cannot travel without being symbolically encoded, such knowledge as riding a bike, driving a car or swimming cannot be represented by a system of facts (Howlett and Morgan, 1). A similar argument can also be built for knowledge by acquaintance; therefore it is evident that the given statement does not capture the whole reality of knowledge but only propositional knowledge, one which can be transferred by language. In this essay, I will argue why the given statement should be rectified as follows: “Propositional a posteriori knowledge is the synthesis of the systemic organization of facts”.
Even though the terms such as “facts”, “systematic organization” and “nothing more than” are used loosely in the introductory paragraph, for a deeper understanding of the given statement, those terms should be clearly defined. Principally it should be acknowledged that the given statement is a definition of knowledge, thus a competing definition will not be used; rather I will explore the lexical and stipulative implications of using this definition. In the theory of definitions, the lexical definition is one that reports how a term is already used in a language community. On the other hand, a stipulative definition freely assigns a meaning to a term.
According to this theory, a definition should include both lexical and stipulative elements; while it should correspond to the reality, it should also have a stipulative component to reduce any vagueness in the definition. For the other terms, there are copious amounts of definitions; nonetheless, we need to choose one, as it isn’t possible to explore the consequences of using each different definition in the scope of this essay. David Hume in An Enquiry Concerning Human Understanding defines a fact as a correspondence to the reality that is acquired by experience (Mulligan, Kevin and Correia, Fabrice, “Facts”).
For example, the proposition that “the cat is in the hat” is considered factual if and only if the statement corresponds to the reality, i.e. if the cat is really in the hat. This approach assumes that sensual perception is the only way of knowing.
However can’t one acquire knowledge by reason, emotion or intuition? Another important part is “nothing more than”, this part represents a reductionist argument that knowledge can be reduced in to facts; however there can be a synergistic effect of facts as Kurt Koffka once famously said: “The whole is greater than the sum of its parts” (Dewey, “The Whole is Other than the Sum of the Parts”). Lastly, the systematic organization represents an arrangement according to a formal procedure. Hume’s definition of facts implies that propositional knowledge must be a posteriori, one that is gained by experience. However, this approach poses a problem in the field of mathematics since the mathematical knowledge is considered to be a priori, one that is independent of experience.
Consider the following proposition “2+2=4”: it is not a Humean fact, (Hume would define it as a relation of ideas) because it does not correspond to an experience, as numbers are abstract concepts. According to the given definition, we should reject mathematics as an area of knowledge since it is not empirical. This poses a lexical problem since mathematics is regarded as an area of knowledge in the real world. In reality, people claim that they know mathematical concepts. On the other hand, one can claim that mathematics is a posteriori; in order to include mathematics to the given definition of knowledge. Proponents of this approach may argue that every mathematical concept corresponds to an experience. For example, the abstract idea of “2+2=4” corresponds to the experience that “two apples and two oranges make four fruits”. This view that mathematics is a posteriori gets more plausible as one thinks how small children learn arithmetic.
They initially learn by visualization like adding two apples and two oranges to get four fruits. However, we know that some mathematical ideas don’t have any correspondence to the real life. Pure mathematics is an ideal example of this phenomenon as there is no experience that can correspond to the concepts in pure mathematics. Even in the field of applied mathematics, most of the ideas had discovered before they were applied to the real world. Complex numbers have been invented in the 16th century. They were studied diligently by mathematicians such as Descartes, Euler, and Gauss only as a mental endeavor. Only in the 19th century, complex numbers have started to be used in the electrical engineering; for 300 years they were just an abstract idea (Merino, A Short History of Complex Numbers).
Therefore, it is logical to conclude that building of mathematical knowledge is independent of experience; hence it is a posteriori. One can solve this lexical contradiction by amending the given statement as follows: “Propositional a posteriori knowledge is nothing more than the systematic organization of facts”. As all the knowledge is not empirical, the given statement should be refined to include only a posteriori knowledge. Contrary to mathematics, evidence in natural sciences is assumed to be purely factual. However, a systematic organization is not sufficient for the formation of scientific knowledge; one needs the synthesis of facts. A simple physics experiment testifies that knowledge is more than a systematic organization of facts. Recently, we have conducted an experiment to determine the gravitational acceleration in Istanbul. We have recorded a ball falling against a ruler. The ruler is used for determining the displacement and the camera for the time taken. In the end, there were two sets of data; time and displacement. They are called raw data and correspond to the idea of facts. We arranged the data in a systematic organization: Independent variable, time, was plotted on the horizontal axis and dependent variable, displacement, to the vertical axis of a graph. If the given definition was right, we would be done with the experiment; nonetheless, in reality, the acceleration was not evident from the initial graph. For finding the acceleration, we drew the best fit line and several tangents to it and gained a new set of processed data, which was no longer a set of fact as it was not gained directly by experience. This new table was synthesized by reason.
While the first step was the systematic organization of sensory inputs (facts), the other steps didn’t require any sensory perception. This testifies that plotting the raw data doesn’t yield the knowledge of gravitational acceleration, as one needs further evaluation. Furthermore, the knowledge of gravitational acceleration in Istanbul is a number value that cannot be reduced back to the facts. One cannot reduce the result, 9.805 m/s2, back to the raw measurements; hence systematic organization should be replaced with the word “synthesis”. Synthesis is chosen on purpose to refer to the analytic-synthetic distinction of Kant. The statement that “Gravitational acceleration in Istanbul is 9.805 m/s2” is not true by definition therefore it is a synthetic claim from a Kantian perspective; hence for the formation of knowledge of this claim synthesis is required (Rey, “The Analytic/Synthetic Distinction”)On the other hand this experiment may be seen redundant for some as there are sensors that can readily measure acceleration. This idea supports that the technology can convert synthesized knowledge into raw data. Yet, this would be a fallacious argument.
Physicists can only measure the world only in seven ways or in seven SI units; mass, kilogram, second, ampere, Kelvin, mole, and candela. All the other units are derived using those fundamental units. The machines that we assume to give raw data of derived units, in reality, replicate the explained process of synthesis; since the only way of measuring the acceleration is through displacement and time. It is evident from the provided experiment that knower needs more than a systematic organization of facts. While the systematic organization is vital, facts should be connected coherently to form an empirical knowledge that is greater than its parts. Therefore the initial statement should be amended to: “Propositional a posteriori knowledge is the synthesis of systematically organized facts”.
Defining knowledge is essential in the knower’s pursuit of knowledge, as one needs to know what one is looking for. A good definition of knowledge should be similar to achieve; it should be wide enough to permit each area of knowledge and way of knowing while eliminating elements such as pseudo-science. The nature of the given definition is on the narrow side of the continuum: it only allows empirical knowledge and sensory perception.
Consequently, it fails to capture the lexical definition of knowledge. Nonetheless, it should be acknowledged that the chosen definition fact determines the quality of this sieve. It shouldn’t be surprising that this sieve was biased towards empiricism since Hume is known as a founding father of this school.
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