The proposition "All golden mountains are mountains" is tautologous, since the predicate are mountains is already given in the subject all golden mountains. Similarly, with regard to "all golden mountains are golden". The conclusion "therefore, some mountains are golden" is the apparent result of a third-figure syllogism AAI; but in fact it is already given in the subject - the compound term "golden mountains" implying that the two elements golden and mountains are compatible, i.e. that "some mountains are golden" (and vice-versa, some golden things are mountains).
All this said, just to point out that the example used here is very artificial!
But to return to the central issue - this is the issue of EXISTENTIAL IMPORT. In this regard, I invite you to read my essay "The triviality of the existential import doctrine" in my website: http://www.thelogician.net/A-FORTIORI-LOGIC/Some-Logic-Topics-of-General-Interest-Appendix7.htm#_Toc370306065
There you will see that this issue is a bit made up by modern logicians like Russell to give themselves importance.
Much more serious is the mega-error made by Russell and his ilk in the (mis)understanding of class logic, which gave rise to the RUSSELL PARADOX - and that you can find out about on the same webpage, further down, at:
I hope this answers your questions at a deep enough level.
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Hi Avi, Thanks. I will look at the links you posted and get back to you if I have any questions.