You can't build your arguments on very shaky prmises.
你不能把论点建立在不可靠的前提下。
shaky premise直译过来就是：“摇摇晃晃的前提”，既然“摇摇晃晃”那必定就是“不可靠、可疑的”了，由此我们可以猜测出这个短语的正确意思是：“不可靠的前提”。因此，当美国人说"You can't build your arguments on very shaky premises."时，他/她要表达的意思就是:"You can't build your arguments on unreliable preconditions."、"Your arguments should be dependable."
情景对白：
Colleague: We should center on R&D of new energy now. Its application is promising for certain.
同事：我们应当以新能源的研发为重心，新能源的应用绝对有前景。
Boss: You can't build your arguments on very shaky premises. We can't foretell on which day new energy will replace traditional energy.
老板：你不能把论点建立在不可靠的前提下，我们无法预测哪一天新能源彻底取代传统能源。
搭配句积累：
①The more we lower the price, the higher the sales will be.
价格下调幅度越大，销量就会越高。
②Your point lacks theory foundation.
你的观点缺乏理论依据。
③Apparently you lost this debate.
显然，你输了这场辩论。
④We can't say it for certain still. The information isn't rock-solid.
我们对此还不是很肯定，这个信息并不绝对可靠。
单词：
1. shaky adj. 不可靠的
They invested in a shaky business venture.
他们投资了一个不可靠的商业项目。
Otherwise, his "intuition" rests on a shaky foundation.
否则，他的“直观”就没有可靠的基础。
The evidence is very shaky.
这证据相当靠不住。
2. premise n. 前提
The premise is that schools will work harder to improve if they must compete.
前提是，如果各学校必须参与竞争的话，就会更加努力。
The programme started from the premise that men and women are on equal terms in this society.
这个项目是以这个社会男女平等为前提的。
Development is our driving force, equality the premise, and mutual benefit our goal.
发展是动力，平等是前提，互利是目的。
