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Making factual inferences depend on general words presumes the factual inference can't be based on the nature of particular instances and the facts found in them. On the contrary generality comes about becsuse we understand particular instances on a realists basis, the contents of a particilar situation themselves bring about what jappens in it, so anything apparently indistinguishable should behave and be understood on the same basis; otherwise there should be a difference between the situations after all.
Archimedes puts the postulate that in a liquid the part pushed more travels to the part push less. This is hypothetical; and does not seem to need to be a law. If, in a liquid the part pushed more did move to the part pushed less, then what would happen is as he shows in proposition 4, lighter objects than the liquid would not be in equilibrium, but will rise to the surface (lighter objects are ones that push less. So a continuation of an object with the property of being lighter than the fluid (which can be demonstrated objectively by comparing them on a balance, and seeing which pushes more) which continues with the property of being heavier than, will mean that that object floats. This seems an objectively possible state of affairs, so the objectively observable effect would be adequately explained if the matters of fact do continue with these properties. But all matters of fact, externally distinguishable from one another are logically distinct and from the idea of any such fact nothing logically follows about any other such fact. A liquid with a lighter object in it, and both objects continuing, are or may be analysed into a series of such logically distinct facts. Nevertheless Archimedes demonstrates, as is accepted by everyone what will happen on the continuation of objects with the properties he specifies, and it seems possible objects could continue like this, which would adequately and objectively explain the said effect.