The achievements of ancient Greek science were amongst the finest in antiquity. Building on Egyptian and Babylonian knowledge, figures such as Thales of Miletus, Pythagoras, and Aristotle developed ideas in mathematics, astronomy, and logic that would influence Western thought, science, and philosophy for centuries to come. Aristotle was the first philosopher who developed a systematic study of logic, an early form of evolution was taught by such figures of Greek philosophy as Anaximander and Empedocles, and Pythagoras' mathematical theorem is still used today.

However, besides its great achievements, Greek science had its flaws. Observation was undervalued by the Greeks in favour of the deductive process, where knowledge is built by means of pure thought. This method is key in mathematics, and the Greeks put such an emphasis on it that they falsely believed that deduction was the way to obtain the highest knowledge.

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Early Achievements

During the 26th Dynasty of Egypt (c. 685–525 BCE), the ports of the Nile were opened for the first time to Greek trade. Important Greek figures such as Thales and Pythagoras visited Egypt, and brought with them new skills and knowledge. Ionia, in addition to Egyptian influence, was exposed to the culture and ideas of Mesopotamia through its neighbour, the kingdom of Lydia.

The astronomical knowledge that Thales got from the Egyptians & Babylonians likely allowed him to predict a solar eclipse on 28 May 585 BCE.

According to Greek tradition, the process of replacing the notion of supernatural explanation with the concept of a universe that is governed by laws of nature begins in Ionia. Thales of Miletus, c. 600 BCE first developed the idea that the world can be explained without resorting to supernatural explanations. It is likely that the astronomical knowledge that Thales got from Egyptian and Babylonian astronomy allowed him to predict a solar eclipse which took place on 28 May 585 BCE.

Anaximander, another Ionian, argued that since human infants are helpless at birth, if the first human had somehow appeared on earth as an infant, it would not have survived. Anaximander reasoned that people must, therefore, have evolved from other animals whose young are hardier. It was Empedocles who first taught an early form of evolution and survival of the fittest. He believed that originally “countless tribes of mortal creatures were scattered abroad endowed with all manner of forms, a wonder to behold”, but in the end, only certain forms were able to survive.

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The Influence of Mathematics

The Greek achievements in mathematics and astronomy were one of the finest in antiquity. Mathematics developed first, aided by the influence of Egyptian mathematics; astronomy flourished later during the Hellenistic Period after Alexander the Great (356 BCE - 323 BCE) conquered the East, aided by the influence of Babylon.

A powerful aspect of science is that it aims to detach itself from notions with specific use and looks for general principles with broad applications. The more general science becomes the more abstract it is and has more applications. What the Greeks derived from Egyptian mathematics were mainly rules of thumbs with specific applications. Egyptians knew, for example, that a triangle whose sides are in a 3:4:5 ratio is a right triangle. Pythagoras took this concept and stretched it to its limit by deducting a mathematical theorem that bears his name: that, in a right triangle, the square on the opposite side of the right angle (the hypotenuse) is equal to the sum of the squares on the other two sides. This was true not only for the 3:4:5 triangle, but it was a principle applicable to any other right triangle, regardless of its dimensions.

Bust of Pythagoras by Skies (CC BY-SA)

Pythagoras was the founder and leader of a sect where Greek philosophy, religion, art, and mysticism were all fused together. In ancient times, Greeks did not make a clear distinction between science and non-scientific disciplines. There is a widespread argument which states that the coexistence of Greek art, philosophy, mysticism, and other non-scientific disciplines interacting together with science has interfered with the development of scientific ideas. This seems to show a misconception of how the human spirit works. It is true that in the past moral and mystic bias has either delayed or led some knowledge up a blind alley and that the sharp limits of scientific knowledge were not clear. However, it is equally true that non-scientific disciplines have enhanced the imagination of the human mind, provided inspiration to approach problems that seemed impossible to solve and triggered human creativity to consider counterintuitive possibilities (such as a spherical earth in motion) that time proved to be true. The human spirit has found plenty of motivation for scientific progress in non-scientific disciplines and it is likely that without the driving force of art, mysticism and philosophy, scientific progress would have lacked much of its impetus.

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The Deductive Process

By discovering mathematical theorems, the Greeks came across the art of deductive reasoning. In order to build their mathematical knowledge they came to conclusions by reasoning deductively from what appeared to be self-evident. This approach proved to be powerful, and its success in mathematics encouraged its application in many other disciplines. The Greeks eventually came to believe that the only acceptable way of obtaining knowledge was the use of deduction.

However, this way of doing science had serious limitations when it was applied to other areas of knowledge, but from the standpoint of the Greeks, it was hard to notice. In antiquity, the starting point to discover principles was always an idea in the mind of the philosopher: sometimes observations were undervalued and some other times the Greeks were not able to make a sharp distinction between empirical observations and logical arguments. Modern scientific method no longer relies on this technique; today science seeks to discover principles based on observations as a starting point. Likewise, the logical method of science today favours induction over deduction: instead of building conclusions on an assumed set of self-evident generalizations, induction starts with observations of particular facts and derives generalizations from them.

Ancient Greek science used experimentation to help theoretical understanding while modern science uses theory to pursue practical results.

Deduction did not work for some kind of knowledge. “What is the distance from Athens to Chios?” In this case, the answer cannot be derived from abstract principles; we have to actually measure it. The Greeks, when necessary, looked at nature to get the answers they were looking for, but they still considered that the highest type of knowledge was the one derived directly from the intellect. It is interesting to note that when observations were taken in consideration, it tended to be subordinated to the theoretical knowledge. An example of this could be one of the surviving works of Archimedes, The Method, which explains how mechanical experiments can help the understanding of geometry. In general, ancient science used experimentation to help theoretical understanding while modern science uses theory to pursue practical results.

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The undervaluing of empirical observation and the emphasis on pure thought as a reliable starting point for building knowledge can also be reflected in the famous account (in all probability apocryphal) of the Greek philosopher Democritus who removed his own eyes so the sight would not distract him from his speculations. There is also a story about a student of Plato who asked with irritation during a mathematics class “But what is the use of all this?” Plato called a slave, ordered him to give the student a coin, and said, “Now you need not feel your instruction has been entirely to no purpose” With these words, the student was expelled.

Aristotelian Logic

Aristotle was the first philosopher who developed a systematic study of logic. His framework would become an authority in deductive reasoning for over two thousand years. Although he repeatedly admitted the importance of induction, he prioritized the use of deduction to build knowledge. It eventually turned out that his influence strengthened the overestimation of deduction in science and of syllogisms in logic.

The doctrine of syllogism is his most influential contribution to logic. He defined the syllogism as a discourse in which certain things having been stated, something else follows of necesity from their being so. A well-known example is:

All men are mortal. (major premise) Socrates is a man. (minor premise) Socrates is mortal. (conclusion)

This argument cannot be logically challenged, nor can we challenge its conclusion. However, this way of doing science has, at least, two failures. In the first place, the way the major premise works. Why should we accept the major premise without question? The only way that a major premise can be accepted is to present an obvious statement, such as “all men are mortal”, which is considered self-evident. This means that the conclusion of this argument is not a new insight but rather, something that was already implied either directly or indirectly within the major premise. Secondly, it does not seem to be necessary to go through all this in order to prove logically that Socrates is mortal.

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Aristotle Bust by Lisippo by Mark Cartwright (CC BY-NC-SA)

Another problem of this way of building knowledge is that if we want to deal with areas of knowledge beyond the ordinary everyday life, there is a great risk of choosing wrong self-evident generalizations as a starting point of reasoning. An example could be two of the axioms upon which all Greek astronomy was built:

The earth is resting motionless at the centre of the universe. The earth is corrupt and imperfect, while the heavens are eternal, changeless, and perfect.

These two axioms appear to be self-evident and they are supported by our intuitive experience. However, scientific ideas can be counterintuitive. Today we know that intuition alone should never be the guide for knowledge and that all intuition should be sceptically tested. The errors in the way of reasoning are sometimes hard to detect, and the Greeks were not able to notice anything wrong with their way of doing science. There is a very lucid example of this by Isaac Asimov:

...if brandy and water, whiskey and water, vodka and water, and rum and water are all intoxicating beverages, one may jump to the conclusion that the intoxicating factor must be the ingredient these drinks hold in common-namely, water. There is something wrong with this reasoning, but the fault in the logic is not immediately obvious; and in more subtle cases, the error may be hard indeed to discover. (Asimov, 7)

Aristotle’s logic system was recorded in five treatises known as the Organon, and although it does not exhaust all logic, it was a pioneering one, revered for centuries and regarded as the ultimate solution to logic and reference for science.

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Legacy

Aristotle’s contribution to logic and science became an authority and remained unchallenged as late as the modern age. It took many centuries to notice the flaws of Aristotle’s approach to science. Platonic influence also contributed to undervalue inference and experimentation: Plato’s philosophy considered the world to be only an imperfect representation of the ideal truth sitting in the world of ideas.

Another obstacle for Greek science was the notion of an 'ultimate truth'. After the Greeks worked out all the implications of their axioms, further progress seemed impossible. Some aspects of knowledge seemed to them 'complete' and some of their notions were turned into dogmas not open to further analysis. Today we understand that there are never enough observations that could turn a notion into 'ultimate'. No amount of inductive testing can tell us that a generalization is completely and absolutely valid. A single observation that contradicts a theory forces the theory to be reviewed.

Many important scholars have blamed Plato and Aristotle for delaying scientific progress, since their ideas were turned into dogmas and, especially during medieval times, nobody could challenge their work while keeping their reputation intact. It is highly likely that science would have reached its modern state a lot earlier if these ideas had been open to review, but this by no means questions the genius of these two talented Greeks. The mistakes of a gifted mind can appear to be legitimate and remain accepted for centuries. The errors of a fool become evident sooner rather than later.