Here we have an example of the fact that, if the definitions of angle are inde ed Epicurean and if these are really related to the internal structure of atoms and to the clinamen motion, geometry is strictly connected to the science of nature: through the definitions of angle that explicitly use the Epicurean notion of minimal part, geometry succeeds in explaining why the atom declines only at a minimum degree cf.
Geometry, 5 therefore, is used to support a crucial physical doctrine which, in turn, helps to justify a decisive ethical doctrine: the existence of libera voluntas Lucret. II Some passages from Plutarch, in addition, are especially valuable because they bear witness to the existence of an Epicurean geometer named Boethus, not mentioned by any other ancient source.
The purpose of this article, therefore, is quite straightforward: to reconstruct the views of this philosopher, and in particular his attitude towards geometry, on the basis of the little information provided by Plutarch who, as is well known, is a rather problematic source, given his clear loathing for Epicureanism. At this point Boethus the geometer entered into the conversation. You know that the man is already changing his allegiance in the direction of Epicureanism. While the Epicurean interlocutors are convinced that the imitator can communicate pleasure and delight because he does not personally experience the suffering he portrays , Plutarch believes that this view is inadequate.
He maintains that we possess an affinity for any performance that exhibits reason or artistry, and admire its success. According to Plutarch, people require no instruction in order to be attracted to subtlety and cleverness; as a matter of fact, if a person shows to a child a shapeless lump of silver, while another brings him a little silver animal or cup, it is certain that the child will prefer and be drawn to the latter.
To criticize the position of the Epicureans, at the end of his argument Plutarch points out that his position is really good evidence in favour of the Cyrenaics with whom the followers of Epicurus polemicize : for according to the Cyrenaics we receive pleasure from sights and sounds not through our sight or hearing, but in our minds. In citing the position of the Cyrenaics Plutarch seems to suggest, moreover, that the problem of poetics is related to the theory of knowledge and indirectly also to physics : it is not possible to rule out that Boethus may have been interested in poetics chiefly because of its epistemological implications.
When silence fell, Boethus said that when he was still young and occupied with sophistic pursuits, he had been accustomed to using postulates from geometry and adopting unproved hypotheses, but that he would now employ some of the demonstrated doctrines of Epicurus. Ammonius recalls that this issue has already been solved by Aristotle: 20 the voice coming from inside weakens and dissipates when it goes outside in the open air, whereas the voice that goes from the outside to the inside remains clear.
Given that the problem has already been treated by Aristotle, the discussion moves on to the reasons why voices at night are more sonorous and clear. VII, c, for the task of dialectics to ground and justify the hypotheses about the unproved hypotheses of geometry, arithmetic, and similar sciences.
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For the same reason, empty bodies transmit sound more effectively than full bodies: gold and stones, being solid and dense bodies, retain sounds, while bronze, being less dense, is a much more sonorous material. For this reason, it seems to me that the argument is not at all confused, but rather that it connects in an orthodox manner these issues of acoustic physics to atoms and void: when there is more void according to Boethus, at night, when the heat thins out and gives way to the cold , sound or, more correctly, the atoms of sound propagate better. This is perhaps the reason why, according to Cicero, Polyaenus totam geometriam falsam esse credidit : of course, it is necessary to understand which geometry this is.
From some of the fragments of this work we learn that the Epicurean Philonides was interested in geometry and also wrote possibly exegetical works on the Epicurean notion of minimum from a geometrical perspective fr. What is more complex is the presentation of Boethus in Book 8 of Table-Talk. Boethus states that in his youth he behaved in the manner of the sophists and, above all, that he used the postulates of geometry and accepted unproved hypotheses, while now, as an Epicurean, he accepts principles demonstrated by Epicurus. What Zeno refutes — in turn being disproved by Posidonius — is the adequacy and completeness of geometric principles.
One must also bear in mind that the question of the principles of science seems to be precisely the point that the Epicureans criticize in their rebuttal of the sciences. A passage from Cicero Fin.
Boethus once accepted the postulates of geometry and used unproved hypotheses, but now, having understood that this methodology is probably fallacious and unproductive, has thought to adopt the principles demonstrated by Epicurus. Both Zeno and Boethus criticize from the Epicurean side the accuracy and completeness of the postulates especially from the epistemological point of view. Boethus, in particular, seems to reject the idea that geometry should be based on unproved hypotheses: that is why he assumes the principles demonstrated by Epicurus.
An analysis of the little evidence from Plutarch in the light of surviving Epicurean texts could suggest at first glance not only that Boethus may not have rejected geometry completely, but even that he is perhaps to be counted among those Epicureans who were interested in geometry and possibly applied it to the science of nature in order to give certain doctrines a more articulate explanation. In his explanation of acoustic physics, Boethus does not explicitly refer to geometric doctrines but we cannot exclude that he may have done so in other circumstances.
One ought to bear in mind that, all in all, Plutarch is a very hostile source on the Epicureans, and that he therefore may have misrepresented or consciously ignored certain points. On this matter, I find interesting a suggestion that I received per litteras by Jean-Baptiste Gourinat:. In Plutarch we have a text saying that Boethus used to practice geometry, and that he then replaced it with Epicurean philosophy.
One can weaken or qualify what Plutarch says by comparing Boethus to Philonides or Demetrius , but one can also use what Plutarch says about Boethus to strengthen the idea that Epicureans were strictly hostile to geometry. Nevertheless, despite the great scarcity and the rather limited clarity of sources, I would like to reaffirm that Boethus is an interesting figure, since his depiction in Plutarch who remains a hostile source for Epicureanism does not seem to support the idea that the Epicureans did not at all reject their possible education as geometers.
Angeli , A. Citti eds. Babbitt, F. Babut , D.
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