这句话归纳公职人员的选拔及晋升。从专业训练中的人员选出,晋升是靠一步步走出来,由低到高来,做好了低级的才能晋升,而非年龄到了就行,也非关系搞好了就行(后面自己补充的)。
Nor shall any man hold office without specific training, nor hold high office till he has first filled a lower office well(Gorgias, 514-5).
任何未经专业训练的人不能担任公职;任何人唯有先胜任低级公职,方可担任高级公职(《高尔吉亚篇》,第514-515节)。
细节解析
1、fill: to perform the work of (an office, position, etc.)充任,担任;发挥【熟词生义】
Dena was filling the role of diplomat's wife with the skill she had learned over the years.德娜利用她多年来学到的处事技巧扮演着外交家妻子的角色。
段总结
这段主要关注民主中的公职问题。前段描述执政的人是怎么产生的。这段则从民主这方面看公职人员,民主是在于实质的竞争的绝对公平,而非在于形式上的公平。

所在段落
The Story of Philosophy《哲学的故事》第1章Plato第7节VI. The Political Solution第1段第5句:
Automatically — without any hypocrisy of voting. Democracy means perfect equality of opportunity, especially in education; not the rotation of every Tom, Dick and Harry in public office. Every man shall have an equal chance to make himself fit for the complex tasks of administration; but only those who have proved their mettle (or, in our myth, their metal), and have emerged from all tests with the insignia of skill, shall be eligible to rule. Public officials shall be chosen not by votes, not by secret cliques pulling the unseen wires of democratic pretense, but by their own ability as demonstrated in the fundamental democracy of an equal race. Nor shall any man hold office without specific training, nor hold high office till he has first filled a lower office well(Gorgias, 514-5).
浙江大学译本: 没接受过专业培训的人不能担任公共职务;只有将基础职位干好的人才能升至更高的职位。(《高尔吉亚篇》,第514-515节)
上句见:Day434