Copernicus's Argument Against Ptolemy

Introduction

Thomas Kuhn (1957, p.181) claims that the "harmony" of Copernicus’ system appeals to an "aesthetic sense, and that alone." Here is how he puts it:

The sum of evidence drawn from harmony is nothing if not impressive. But it may well be nothing. "Harmony" seems a strange basis on which to argue for the Earth’s motion, particularly since the harmony is so obscured by the complex multitude of circles that make up the full Copernican system. Copernicus’ arguments are not pragmatic. They appeal, if at all, not to the utilitarian sense of the practicing astronomer but to his aesthetic sense and to that alone. (Kuhn, 1957, p.181)

Copernicus himself explained his project in these terms (De Revolutionibus, Book 1, Chapter 10): "We thus follow Nature, who producing nothing in vain or superfluous often prefers to endow one cause with many effects." (My emphasis) Repeatedly, Copernicus boasted that his theory of planetary motion was more harmonious than Ptolemy’s.

The phenomena to be explained:

  1. An inferior planet will never stray far from the sun. In particular, inferior planets are always seen in conjunction with the sun.
  2. The retrograde motion of superior planets occurs when and only when the planet is in opposition to the sun. (Retrograde motion of the superior planets occurs if, and only if, the moon is a full moon when it is near the planet.)

Copernicus's Explanation

(Multimedia presentation)

Ptolemy's Alternative 'Explanation'

(Multimedia presentation)

Important Concepts Introduced in this Example

observed quantity: A quantity, like position against the fixed stars, which is determined, at least approximately, by past observations, without using theoretical assumptions. (Note: 'Observation' is a hard concept to define—so this is postponed until later.) In antiquity, the distance of a planet from us was not an observed quantity. The angular position of planets against the fixed stars at a specific time was.

phenonemon: A generalization of an observed regularity amongst observed quantities—usually uncontroversial. E. g., phenomena (a) and (b) above.

(skip) cosmic coincidence: A pattern repeated many times, or a long coincidence of occurrences, that has arisen by chance. There is a sense in which cosmic coincidences are improbably. It is widely considered a basic principle of science that one should believe in as few cosmic coincidences as possible.

period of motion: The time it takes for one revolution around a circle.

Question: Is the period an observed quantity?

theory: A general set of laws and principles of broad scope, from which different models are derived from various auxiliary assumptions. For example, Ptolemy's theory is that all celestial bodies move around the earth on circles on circles without any change in the motion.

auxiliary assumptions: The assumptions made about particular systems, like the number of planets, the number of epicycles in Ptolemaic or Copernican astronomy. When combined with a theory, they lead to a model. The assumptions are often known to be false, in which case the model is called an idealization.

adjustable parameters: Parameters, like the radius of circles, or the period of their motion, whose values are estimated from the observed data. A statement of their values are not referred to as an auxiliary assumption.

model: A theoretical statement, usually in the form of an equation, usually deduced from a theory with the aid a auxiliary assumptions.

Discussion: What is a model in Ptolemaic or Copernican astronomy? It assigns a fixed number of circles to each planet, but does not assign values to adjustable parameters, like the radii of those circles, or their relative sizes, or to the periods of motion on those circles. These values are determined by fitting the model to the observed data.

idealization: A model obtained from a theory using auxiliary assumptions that are known to be false, such as "there is no friction." Another example is the assumption that the mass of the universe is spread evenly in all directions in space originally used in 'big-bang' models of how the universe evolved.

prediction: A statement deduced from a theory or a model stating the value, or approximate value, of an quantity, which can be checked by observation. Predictions need not always be of the future. For example, the assertion that there was a lunar eclipse of the sun in 350 B.C. counts as a prediction in our sense.

  1. Fit the model to observed data, choosing the values of the radii and periods of motion that produce the closest fit with past observations.
  2. Plug those values into the model (that is adjust the parameters), and deduce new values of observable quantities, like planetary positions relative to the fixed stars.

accommodation: When a model succeeds in fitting, or conforming, to a phenomenon without predicting it.

simplicity: Is usually considered to have many aspects. The simplicity of a model is usually taken to be the paucity, or fewness of number, of adjustable parameters.

(skip) predictively equivalent models: Also, observationally equivalent models. Two models that, when combined with the same observed data, make the same predictions.

Note 1: It is very rare that two models are predictively equivalent, although it is common that two models are predictively equivalent with respect to a restricted set of quantities. E. g., for every Ptolemaic model (without equants) there is a Copernican model that is predictively equivalent with respect to the angular positions of the planets.

Note 2: In planetary astronomy, predictions are made from a model of the solar system as a whole. This important because the Ptolemaic and Copernican models of the whole solar system makes different predictions about the phases of Venus, for example, even if they made the same predictions about the angular positions of the planets. Therefore, Ptolemaic and Copernican models are not predictively equivalent in any unrestricted sense.

(skip) logically equivalent models: Also, equivalent models. Two models that make all the same assertions, including theoretical assertions.

Note: Ptolemaic and Copernican models of a single planets make different assertions about absolute motions. Absolute motions are not observed (they are inferred with the aid of background theory), but this difference is sufficient to ensure that they are not logically equivalent even if they are predictively equivalent.

Four Virtues of Copernicus's Explanation

  1. Copernicus explains why there are many epicycles in the Ptolemaic system that replicate the relative motion of the earth and the Sun. Ptolemy has to dismiss this a cosmic coincidence.
  2. Copernicus’s account explains many effects (the apparent motions of many planets) using the Earth’s motion around the sun as a common component, or cause. Ptolemy’s posits separate causes here because he has to replicate the Earth’s motion relative to the sun separately for each planet. This is the sense that Copernicus’s system is simpler (even if it is not very simple).
  3. Copernicus's theory seems to predict the phenomena, whereas Ptolemy's theory merely accommodates the phenomena. On Copernicus’s account the phenomena (a) and (b) follow from the fact that the Sun is near the center of every planetary orbit, which is a central claim of the theory built into every model. In contrast, the phenomena are not deduced from Ptolemy’s theory, because it is possible that the theory is true while the phenomena are false.
  4. Copernicus’s account is simpler and more harmonious than Ptolemy's.

The is a vagueness is a problem here. What is simplicity? What is being compared?

4a. Copernicus's theory is simpler than Ptolemy's theory. False. There is no sense in which the general principles used by Copernicus are simpler (except possibly is abandonment of the equant).

4b. Copernicus's model is simpler than Ptolemy's model. False. The Copernican model published in De Revolutionibus is a least as complicated as the one published by Ptolemy in the Amagest.

4.c. For every Copernican model, there exists a Ptolemaic model that can make the same assertions about the angular positions of the planets. Given any such pair of models, the Copernican model is simpler (has fewer circles) than the corresponding Ptolemaic model. Correct!

Open Philosophical Problems: