I think it's worthwhile to provide the beginning of Part 2 in Book X from Aristotle's 'Nicomachean Ethics' (EN X, 2, 1172b) to show Eudoxus' views on pleasure. It's chronologically interesting taking into consideration that Eudoxus had died a year before Epicurus was born.
That pleasure is the Good was held by Eudoxus, on the following grounds. He saw that all creatures, rational and irrational alike, seek to obtain it; but in every case (he argued) that which is desirable is good, and that which is most desirable is the best; therefore the fact that all creatures ‘move in the direction of’ 1) the same thing indicates that this thing is the Supreme Good for all (since everything finds its own particular good, just as it finds its own proper food); but that which is good for all, and which all seek to obtain, is the Good.
His arguments owed their acceptance however more to the excellence of his character than to their own merit. He had the reputation of being a man of exceptional temperance, and hence he was not suspected of upholding this view because he was a lover of pleasure, but people thought it must really be true.
He also held that the goodness of pleasure was equally manifest from the converse: pain is intrinsically an object of avoidance to all, therefore its opposite must be intrinsically an object of desire to all.
Again, he argued that that thing is most desirable which we choose not as a means to or for the sake of something else; but such admittedly is pleasure: we never ask a man for what purpose he indulges in pleasure - we assume it to be desirable in itself.
He also said that the addition of pleasure to any good - for instance, just or temperate conduct - makes that good more desirable; but only the good can enhance the good.
1) As we should say, ‘gravitate towards.’ Eudoxus, an unorthodox pupil of Plato, was a astronomer, and seems to have imported physical terminology into Ethics.
