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"once the general happiness is recognised as the ethical standard
Yes this is exactly what is in contention and is not self- evident. Many people do not recognize "the general happiness" as the ethical standard, and if he is simply asserting it without some kind of proof then he is without foundation.
As to truth that applies to all places, times, and circumstances and it truly universal (throughout the infinite and eternal universe) I think we are far from being able to establish anything in those terms, especially in the field of ethics. The life of the "gods" is different from the life of "men" because of their circumstances, not because there is a universal force which makes it so. It is certainly possible to generalize within a certain set of facts, such as "all humans eventually die" and "death is nothing to us" but those general observations are based on experience rather than a force which would allow us to say that such and such "always must" be the case. That is the difference between reasoning by observation, while keeping in mind the limits of observation, vs attempting to call into existence "universal principles" which exist only in our minds and have no true existence outside our minds.
Diogenes Laertius: "They [Epicureans] affirm that .... there are two kinds of inquiry, the one concerned with things, the other with nothing but words."
Letter to Herodotus: "In the first place, Herodotus, you must understand what it is that words denote, in order that by reference to this we may be in a position to test opinions, inquiries, or problems, so that our proofs may not run on untested ad infinitum, nor the terms we use be empty of meaning. For the primary signification of every term employed must be clearly seen, and ought to need no proving; this being necessary, if we are to have something to which the point at issue or the problem or the opinion before us can be referred.
Someone wanting to research into this question could refer to Philodemus' "On Methods of Inference" for a part of the Epicurean argument on this.