σῴζειν τὰ φαινόμενα, sozein ta phainomena

For all those, who like myself, can’t actually speak or read ancient Greek the title of this post is a phrase well known in the history of astronomy ‘saving the phenomena’, also sometimes rendered as ‘saving the appearances’. This post is in response to a request that I received from a reader asking me to explain what exactly this expressions means.

The phrase saving the phenomena was first introduced into the history of astronomy discourse by the late nineteenth-century and early twentieth-century French physicist and historian of science, Pierre Duhem. Duhem used the expression in the title of his work on physical theory Sauver les Phénomènes. Essai sur la Notion de Théorie Physique de Platon à Galilée, (1908), which was translated into English in 1969, as To Save the Phenomena, an Essay on the Idea of Physical Theory from Plato to Galileo. In this work Duhem argued that all mathematical astronomy from Plato up to Copernicus consisted of mathematical models designed to save the phenomena and were not considered to represent reality. The phenomena that needed to be saved were the so-called Platonic axioms, i.e. that the seven planets (Mercury, Venus, Moon, Sun, Mars, Jupiter and Saturn) move in circles at a constant speed. It is fairly obvious that the planets do not move in circles or at a constant speed thus posing a difficult problem for the mathematical astronomers, in order to save the phenomena they have to present a mathematical model, which can account for the apparent irregularity of planetary motions in the form of a more fundamental real regularity.

Duhem’s thesis suffers from several historical problems. He bases his argument on a quote from Simplicius’ On Aristotle, On the Heavens, which dates from the sixth century CE. According to Simplicius Plato challenged the astronomers to solve the following problem:

“…by hypothesizing what uniform and ordered motions is it possible to save the phenomena relating to planetary motions.”[1]

Simplicius goes on to say:

“In the true account the planets do not stop or retrogress nor is there any increase or decrease in their speeds, even if they appear to move in such ways … the heavenly motions are shown to be simple and circular and uniform and ordered from the evidence of their own substance.”

Simplicius attribution of the concept of saving the phenomena to Plato is made more than nine hundred years after Plato lived. In fact there is no mention in the work of Plato of the principle of uniform circular motion, the earliest known example being in Aristotle. The earliest example of the phrase ‘saving the phenomena’ occurs in Plutarch’s On the Face in the Orb of the Moon, from the first century CE and does not refer to planetary motions but to Aristarchus’ attempt to explain the revolution of the sphere of the fixed stars and the movement of the Sun through heliocentricity.

We find some support for the view of Simplicius in the introduction to astronomy of Geminus of Rhodes in the first century BCE, although he doesn’t use the explicit phrase to save or saving the phenomena, he writes:

“For the hypothesis, which underlies (hupokeitai) the whole of astronomy, is that the Sun, the Moon, and the five planets move circularly and at constant speed (isotachôs) in the direction opposite to that of the cosmos. The Pythagoreans, who first approached such investigations, hypothesized that the movements of the Sun, Moon, and the five wandering stars are circular and uniform … For this reason, they put forward the question: how would the phenomena be accounted for (apodotheiê) by means of uniform (homalôn) and circular motions.”

As we can see Geminus attributes the concept of uniform circular motion to the Pythagoreans and not Plato. It should be pointed out that neither Simplicius nor Geminus was a mathematical astronomer.

Duhem also claimed that the most significant of all Greek astronomers, Ptolemaeus, adhered to the principle of saving the phenomena in his Syntaxis Mathematiké, the only substantial work of Greek mathematical astronomy to survive. However a careful reading of Ptolemaeus clearly shows that he regarded his models as representing reality and not just as saving the phenomena.

The most famous case of saving the phenomena can be found in Andreas Osiander’s Ad lectorum (to the reader) appended to the front of Copernicus’ De revolutionibus. In this infamous piece Osiander, who had seen the book through the press writes:

For it is the duty of an astronomer to compose the history of the celestial motions through careful and expert study. Then he must conceive and devise the causes of these motions or hypotheses about them. Since he cannot in any way attain the true causes, he will adopt whatever suppositions enable the motions to be computed correctly from the principles of geometry for the future as well as the past. The present author has preformed both these duties excellently. For these hypotheses need not to be true nor even probable. On the contrary, if they provide a calculus consistent with the observations that is enough. [2]

As can be clearly seen here Osiander is suggesting to the reader that Copernicus’ work is just a mathematical hypothesis and thus need not be regarded as mirroring reality. It is clear from the rest of his text that Osiander is trying to defuse any objections, religious or otherwise, that Copernicus’ heliocentricity might provoke. Of course his claims stand in contradiction to Copernicus’ text where it is obvious that Copernicus believes his system to reflect reality. Because Osiander’s Ad lectorum was published anonymously, it was assumed by many people that it was written by Copernicus himself a confusion that was only cleared up at the beginning of the seventeenth century.

It is not clear whether Osiander was appealing to a two thousand year old tradition of saving the phenomena, as Duhem would have us believe, or whether he, and possibly Petreius the publisher, had devised a strategy to avoid censure of the book and Copernicus’ radical idea.

Although many people continue to quote it as a historical fact it is highly doubtful that Duhem’s thesis of the saving of the phenomena ruling mathematical astronomy for the two thousand years from Plato to Galileo is true and it is fairly certain that most if not all mathematical astronomers, like Ptolemaeus, believed the models that they devised to be true representations of reality.


[1] This and all other quote from the Greek are taken from Mark Schiefsky, “To save the phenomena” and curve fitting” (pdf)

[2] On The Revolutions, translation and commentary by Edward Rosen, The Johns Hopkins University Press, Baltimore and London, pb., 1992, p. XX


Filed under History of Astronomy

19 responses to “σῴζειν τὰ φαινόμενα, sozein ta phainomena

  1. Will Thomas

    Thanks for this Thony. I’m pretty sure I asked you about this ages ago, as well. This is a concept that, as someone familiar with but not expert in this history, I am eager to get right. So, I have two questions:

    1) I’m curious about the connotations of the verb “to save” here. Should this be interpreted in the vein of “rescue,” i.e., “observation appears to contradict what we know to be true, therefore we must labor to show that we can save the appearances” (connoting a defusing of a possible intellectual crisis); or merely in the vein of “recover” or “reconstruct,” i.e. “we have a set of observations, and our ability to describe their regularities is limited to the geometry of circles (which also conveniently conforms to philosophical desiderata), but fortunately we can actually use that geometry to describe (save) the phenomenon pretty well” (connoting merely calculative lingo)?

    2) Did Copernicus believe only in the reality of his ordering of the cosmos, or does he appear to have believed in the reality of his epicycles as well (or did he view them as only the accepted means of refining astronomical calculations)?

    Thanks for this post!

  2. There is a wonderful account of “saving the phenomena” in Pierre Hadot’s “The Veil of Isis” beginning on pp. 164, described as “to propose explanations that enable us to account for what appears before us”.

  3. It is interesting though how Ptolemy divided up his astronomical works, with the “phenomenon saving” parts in the Almagest, the astrology in the Tetrabiblios, and the cosmological speculations in the Planetary Hypotheses (and the tables in the Handy Tables). Not that this validates Duhem’s thesis. Indeed, the greater certainty Ptolemy ascribed to the Almagest models seems to cut against it.

    The phenomena that needed to be saved were the so-called Platonic axioms, i.e. that the seven planets (Mercury, Venus, Moon, Sun, Mars, Jupiter and Saturn) move in circles at a constant speed.

    It’s also curious that Ptolemy pays lip service to uniform circular motion throughout the Almagest, while silently departing from it (because of the introduction of the equant) in all his planetary models.

    By the way, did Duhem say that the phenomena were the Platonic axioms, as the sentence above seems to suggest?

  4. Seb Falk

    Thanks, this is useful. Like Michael, in my reading in medieval astronomy I’m mostly struck by how the cosmological implications of the astronomical models are simply ignored. I’m sure astronomers had a view on their realism (particularly in the context of the devotional motivation of understanding Creation), but the overwhelming impression is that it doesn’t really matter, as long as the models account for observations.

    That’s what I always understood saving the phenomena to mean: accounting for observations – using the axioms of uniform circular motion of course. So I’d go for the latter of Will’s interpretations above – reconstructing rather than rescuing. (This may be splitting hairs, but by equating the phenomena with the axioms you make the astronomers sound rather desperate!)

    • I assumed that it was a slip of phrasing, and that Thony did not mean to equate the phenomena with the axioms.

      The Tetrabiblios was, during the Middle Ages, the best known of Ptolemy’s works (at least according to Olaf Pedersen, who specialized in medieval astronomy). By contrast, the original Greek of parts of the Planetary Hypotheses were lost, and the latter part of the first Book were lost completely until recovered in Arabic translation in 1967.

      Ptolemy was not per se skeptical of astrology, but he regarded it as less certain than the measurable celestial phenomena. Kepler had a similar attitude, come to think of it.

  5. Saving the phenomena seems like an inaccurate description of what Copernicus or Kepler were doing, but there’s a bit of a problem in claiming that modern astronomers are trying to determine what’s really going on in the heavens. You can complain about Osiander’s evasiveness, but how does the alternative jive with the skeptical epistemology of the natural sciences? Scientists may not agree about much, but everybody repeats the mantra that all results are provisional. Your fingers are supposed to be permanently crossed in what amounts to the contemporary version of what the ancients called suspension of judgement (epoche). Which is why the positivists took the notion of saving the phenomena to the point where the scientific view of the world is just an economical summary of observations. The stoned hippie supposedly exclaimed “Reality, what a concept!” but are natural scientists entitled to any concept of reality? A Platonist with his eternal ideas or a theist with his transcendent God can understanding science as an asymptotic approach to the Truth through a succession of likely stories, but a modern naturalist doesn’t have it so easy. I’m not stumping for a return to a dogmatic metaphysics—like Pyrrho, Narjaruna, and Hume I believe in the emptiness of the dharma—but it does seem to me that proposing that there is an obvious coherent alternative to saving the phenomena is not as easy as it seems.

  6. We have accumulated a number of questions to which I will give my opinions.

    In answer to Will’s first question, irrespective of what Duhem thought, the few sources that we have don’t really make it clear if rescue or reconstruction is the intended meaning. Basically you pays your money and you takes your choice. I, for one,as opposed to Seb, read both Simplicius and Geminus to mean rescue rather then reconstruct, but I don’t really think that the matter can be decided definitively either way.

    No Duhem doesn’t use the term Platonic axioms as far as I know but yes they are exactly the phenomena that have to be saved. Astronomers please demonstrate that planetary motion is uniform and circular.

    Seb: I think that medieval astronomers are genuinely more concerned with accurate observations for use in astrology than in cosmology and therefore the lack of literature on the subject. The first real cosmological text as far as I know is Peuerbach’s New Planetary Theory, which is, as we now know, Ptolemaeus’ Planetary Hypothesis, which very definitely tries to show how epicycles and deferents fit into planetary spheres. Very obviously a realist cosmology that includes the whole complex Ptolemaic baggage.

    This brings us to Will’s second question concerning Copernicus. Simple answer, we don’t know. However Copernicus learnt his astronomy and cosmology from the books of Peuerbach and Regiomontanus so it is more than possible that he like Peuerbach thought that the whole wheels within wheels system was real.

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  8. It had occurred to me that Duhem might have been looking at the history of astronomy with 20th century eyes and not thinking in terms of what the various astronomers would have known at the time. The reason why I thought that this could be the case was that in his ‘Aim and Structure of Physical Theory’ (1906) he argued that Newton could not have deduced his law of gravitation from Kepler’s Laws (I am relying on Wikipedia here as i have not seen Duhem’s book). Duhem argued that Newton’s Law contradicted Kepler because mutual gravitational perturbations meant that the planetary orbits were not ellipses. However, Newton’s positional data was not much better than Kepler’s; the big improvement in positional accuracy starts with Ole Roemer’s invention of the transit circle in 1690; and it is unlikely that Newton would have been able to test his theory of gravitation by measuring the small departures from ellipticity caused by gravitational perturbations.

    In contrast, Duhem was writing just over half a century after Neptune had been discovered by its perturbations of Uranus’ orbit (a classic case of saving the appearance) and there was still a belief in the existence of a planet inside Mercury (Vulcan) which was needed to explain part of the precession of Mercury’s orbit under Newtonian gravitation, finally successfully explained by Einstein’s general relativity.

  9. I have personally always understood saving the phenomena to mean preserving the appearances, that is, whatever explanation we come up with must leave the appearances invariant.

    I remember reading somewhere that sozein could mean either save or solve. I thought it was Ian Hacking but not sure. Any substance to that?

  10. Renato

    I think you can find a very good explanation in:

    Lucio Russo. The Forgotten Revolution: How Science Was Born in 300 BC and Why it Had to Be Reborn

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  13. Thank you for the brief and helpful history on the phase. It was delightful. I thought I’d also mention something in response to your statement: “Geminus attributes the concept of uniform circular motion to the Pythagoreans and not Plato.” Of note regarding this point is that while modern scholarship (which obviously employs a different method of analysis than the ancients) debates the legitimacy of classifying Plato as a Pythagorean, in classical thought he was typically viewed as a Pythagorean (as was Aristotle). Just thought that might be a helpful bit given that Simplicius probably uses the term Pythagorean more broadly—to include Plato and Aristotle—rather than in the more limited sense. Thanks again.

  14. Grant Sheppard

    An excellent book concerning the outlook of ancient to modern people, and the ways in which that outlook has changed. is Owen Barfield’s ‘Saving the Appearances: A Study in Idolatry’ (1957). As to the meaning of sozein, he quotes Milton’s use of, “To save appearances…”, then states “…in order to ‘save’ (in the sense of rescuing) the Ptolemaic system…” I hope this can be of some help. But I want to emphasize that reading Barfield’s book has been of much interest and benefit to me. I recommend it to everyone who has an interest in such matters.

  15. An excellent book concerning the outlook of ancient to modern people, and the ways in which that outlook has changed. is Owen Barfield’s ‘Saving the Appearances: A Study in Idolatry’ (1957). As to the meaning of sozein, he quotes Milton’s use of, “To save appearances…”, then states “…in order to ‘save’ (in the sense of rescuing) the Ptolemaic system…” I hope this can be of some help. But I want to emphasize that reading Barfield’s book has been of much interest and benefit to me. I recommend it to everyone who has an interest in such matters.

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