Chong Ho Yu, Ph.D.


cientific methodologies are often stereotypically equated with experiments and observations. Based on this premise, positivist Mach (1976) credited Galileo as the father of modern physics for his observational research. In a similar vein, Koszarvez (2000) argued that the confrontation between Galileo and the Catholic Church was a clash of methodologies. To be specific, science is concerned with explaining natural phenomena by empirical methods such as observations and experimentations. One the other hand, religion is concerned with divine revelation and received wisdom. However, these views neither accurately represent the mistrial of Galileo nor capture the essence of modern sciences. The thesis of this article is to argue that idealization and thought experiments play an important role in Galileo's research as well as modern scientific methodology.

Experimentation and observations

It is important to note that experimentation in the modern sense did not exist in the 17th century at all. Modern experiments are characterized by random sampling, randomization, and controlled conditions. It was hard for scholars in the 17th century to think about control group, treatment group, and hypothesis testing. Thus, whether experimentation plays a significant role in Copernicus and Galileo's research is out of the question. The only empirical research that could be employed by Copernicus and Galileo was observation. While discussing experiments regarding motion in a vacuum, Press and Tanur (2001) questioned whether it was possible, in terms of laboratory equipment and techniques, for Galileo to have carried out the experiments he described and that are sometimes credited to him.

Today observation is equipped with precise instruments, rigorous procedures and standardized protocols. However, the definition of empirical observation was very vague in that era. If empirical research meant collecting sensory data and interpreting the data using common sense, we might say that empirical research had been employed for a long time. Actually, it was exactly this type of "empirical observation" that was questioned by Copernicus and Galileo. In their view, senses do not contribute in the slightest to the understanding of facts. It was Copernicus who put reason into the framework of methodology, which forced people to withdraw their trust in the appearance meaning of sensory data (Nowak, 1994).

Even if we put empirical observation into a modern framework, its significance of constructing the heliocentric system is doubtful. The procedure of observation could be defined in a hypothetical-deductive fashion as the following:

  • If theory A is true, then after conducting observation the data should reveal phenomenon B.
  • If B occurs, then A is confirmed.

Put simply, the logical flow is: If A then B; if B then A. Anyone who has received training in logics could point out that this approach commits the fallacy of affirming the consequent (Kelley, 1998). Moreover, different theories, say Theory C and Theory D, may also be used to predict B with small residuals. Thus, the following two sets of inferences are equally valid.

Ptolemaic model:

  • If the geocentric theory (A) is true, then after conducting astronomical observations, we should expect to see daily, yearly, and retrograde motions of various heavenly bodies (Bs).
  • If Bs are observed, then A is confirmed.

Copernican model:

  • If the heliocentric theory (C) is true, then after conducting astronomical observations, we should expect to see daily, yearly, and retrograde motions of various heavenly bodies (Bs).
  • If Bs are observed, then C is confirmed.

It is a well-known fact that in terms of explanation and prediction, the Ptolemaic model is as powerful as the Copernican model. In this case, empirical evidence does not appear to be a good judge. No wonder Kesareva (1999) argued that the heliocentric theory's popularity and rapid dissemination could not be explained by its scientific advantages (in terms of empirical evidence) over the geocentric system. Indeed, for a long time no direct experiments were carried out to validate the new theory. While Kesareva attributes the success of the heliocentric theory to cultural changes in Europe, I consider idealization and thought experiments conducted by Galileo to be a major factor to the rise of the heliocentric model and even modern sciences.


Idealization is a method of distorting the empirical reality for research purposes. Since some required scenarios for the an experiment are too unrealistic to occur in this physical world, simplified assumptions must be imposed on the imagined world. Galileo is one of the masters of idealization because he emphasized mathematization of the universe. In a way, idealizing conditions are necessary to deform the phenomena to the effect that the idealized counterparts of those phenomena fall under the mathematical functions (Nowak, 1994). Galileo's argument against Aristotelian physics utilized idealization. Aristotle maintained that in the universe there are two types of motions, namely, natural motion and violent motion. The latter requires an external force because it is unnatural. In order to challenge the Aristotelian notion, Galileo "idealized" the following assumptions:
  • There is a rolling ball which is perfectly round.
  • There is a plane which is perfectly smooth and spherical.
  • The resistance of the environment is completely absent.

Given this ideal situation, Galileo asked how this ball would move on the plane, and the logical conclusion is that the ball would keep moving without an external mover if space were infinite.

At first glance the validity of idealization is questionable. How could one make an inference from something that does not exist to the physical world? As a matter of fact, the idealization approach has been adopted by modern scholars in various disciplines under different names. For example, economists study market behaviors with certain unrealistic assumptions such as perfect competition. Social and physical scientists employ statistical methods to smooth the data in order to fit mathematical functions. To be specific, when the raw data, which are full of noise, hinder the researcher from detecting a pattern, the researcher imposes a mathematical function on the dataset to suppress the noise. This type of mathematical function represents an ideal relationship among variables for the convenience of research (Yu & Behrens, 1995). By extending this notion, statistics in general could be viewed as a type of idealization. For instance, many statistical tests require certain assumptions on the data structure such as a normal distribution. Actually, there is no perfect normality in the reality. Normality is assumed for its mathematical efficiency instead of its empirical equivalence (Yu & Ohlund, 2000; Yu, Ohlund, DiGangi, & Jannasch-Pennell, 2000). In short, normality is an idealized condition for convenience.

Thought experiments

Thought experiments are device of the imagination used to investigate nature. Nonetheless, thought experiments are different from idealization in two aspects. First, thought experimenters do not have to construct ideal or unrealistic conditions. In other words, an idealization must be a thought experiment, but a thought experiment is not necessarily an idealization. Second, while the primary purpose of idealization is to draw a logically consistent conclusion, the goal of thought experiment is to purge us of bias, circularity, and cognitive inefficiencies (Sorensen, 1992).

Again, Galileo is one of the masters of thought experiments. His falling ball experiment is considered by Brown (1991) to be the best thought experiment. The falling ball experiment is in response to the faulty Aristotelian notion that heavy bodies fall faster than lighter objects. Unfortunately, this misconception is reinforced by naive empirical observations (e.g., leaf, paper), in which sensory data are interpreted by common sense. Galileo debunked this myth by asking this hypothetical question: "What would happen if a heavy cannon ball is tied to a light musket ball and they are dropped at the same time?" Following Aristotelian physics, the conclusion is inevitably contradictory. On one hand, the lighter ball will slow down the heavy one and thus the combined speed would be slower than that of the heavy one alone. On the other hand, the combined objects are heavier than the heavy one alone and thus they should fall faster. In short, this thought experiment exposes the logical inconsistency of Aristotelian physics.

Thought experiments are prevalent in both science and philosophy. Well-known examples of thought experiments are Stevin's inclined plane, Newton's bucket and absolute space, Poincare and Reichenbach's geometry, Heisenberg's gamma-ray microscope, Schrodinger's cat, Thomson's violinist, Searle's Chinese room, and Williams' mind swapping machine. Again, many of these thought experiments were used to illuminate logical fallacies. In recent years, more and more scholars have endorsed thought experiments as a valid research methodology (e.g., Brown, 1991; Horowitz & Massey, 1991; Sorensen, 1992). Sorensen asserted that thought experiments are experiments, and therefore lessons learned about experimentation carry over to thought experiments, and vice versa.


Precise instruments and well-developed experimental methods were not available in the time of Galileo. To Galileo, observations contaminated by common sense were also questionable. As a mathematician, Galileo found that idealization and thought experiments were better research tools. Today empirical methods are pre-dominant in the scientific community. This mindset makes modern scholars such as positivists project their own views onto Galileo, and as a result, the role of observation is greatly exaggerated. On the other hand, people who are submerged in the ocean of empirical methods may be skeptical of Galileo's idealization and thought experiments. As a matter of fact, idealization and thought experiments are employed by many famous scholars. In addition, the nature of idealization is in alignment with that of statistical methods, which frequently impose idealized functions on data and adopt idealized assumptions for mathematical convenience.



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Horowitz, T., & Massey G. J. (Eds.). (1991). Thought experiments in science and philosophy. Savage, MD: Rowman and Littlefield

Kelley, D. (1998). The art of reasoning (3rd ed.). New York: W. W. Norton & Company.

Kesareva, L. M. (1990). On the edge of the universe cognition. Annual Collection of Articles/Historical-Astronomical Studies, 22, 74-109.

Koszarycz, Y. (2000). The 17th to the 20th centuries: The church in the modern era. [On-line] Available: URL:

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Novak, L. (1994). Remarks on the nature of Galileo's methodological revolution. In M. Kuokkanen (Ed.), Idealization VII: Structuralism, idealization, and approximation (pp. 111-126). Altanta, GA: Rodopi.

Press, S. J., & Tanur, J. M. (2001). The subjectivity of scientists and the Bayesian approach. New York: John Wiley & Sons.

Sorensen, R. A. (1992). Thought experiments. New York: Oxford University Press.

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Yu, C. H., & Ohlund, B. (2000). Mathematical Reality: An Inquiry into the existence of theoretical distributions and its implication to psychological researchers. [On-line] Available: URL:

Yu, C. H., Ohlund, S., DiGangi, S., & Jannasch-Pennell, A. (2000). Incoherence and the parametric test framework: Misconceived relationships among sample, sampling distribution, and population. American Statistical Association 1999 Proceedings of the Section on Statistical Education, 225-230.



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