[11] Philodemus, περὶ σημείων, ed. Gomperz, 1865, with additional readings from the papyrus by Philippson in _Rhein, Mus._ (1909). See Weltring, _Das σημεῖον in der Aristotelischen, Stoischen und Epikureischen Philosophie_ (Bonn, 1910). Philodemus anticipated some of the difficulties that later troubled Mill, noticing that in some inductive problems a single observation provided valid conclusions, whereas in others very many were required (Gomperz, 19, 13); he knew that many fallacies were due to the use of insufficient instances (Gomp. 30, 2; 35, 15), that it was well not only to observe nature but to conduct systematic research and to employ the observations of others (Philippson, _loc. cit._, 13), that the observer must choose essential similarities in using the mode of “agreement” and must exclude conclusions as soon as a refuting instance appeared (Gomp. 13, 1; 17, 30; 20, 32), and he emphasized the need of employing the principle of difference (Gomp. 18, 15; Phil. p. 28). This treatise which probably draws lavishly on Zeno, has not yet been fully restored, and being a defense against Stoic attack it is not to be considered a formal and complete exposition of inductive logic. But in germ it contains most of the essential observations of J. S. Mill. [12] _Trans._ W. E. Leonard. [13] iii. 290 ff. [14] ii. 23; iii. 57; v. 1105.