Without facts,we cannot form a worthwhile opinion ,for we need to have factual knowledge (upon which to base) our thinking.Without facts,we cannot form a worthwhile opinion ,for we need to have factual knowledge (which to base on) our thinking.尤其

Without facts,we cannot form a worthwhile opinion ,for we need to have factual knowledge (upon which to base) our thinking.Without facts,we cannot form a worthwhile opinion ,for we need to have factual knowledge (which to base on) our thinking.尤其
Without facts,we cannot form a worthwhile opinion ,for we need to have factual knowledge (upon which to base) our thinking.
Without facts,we cannot form a worthwhile opinion ,for we need to have factual knowledge (which to base on) our thinking.尤其是括号中的.)

Without facts,we cannot form a worthwhile opinion ,for we need to have factual knowledge (upon which to base) our thinking.Without facts,we cannot form a worthwhile opinion ,for we need to have factual knowledge (which to base on) our thinking.尤其
此句考察对which引导的定语从句的掌握情况:
句意：没有事实依据我们无法形成有价值的见解,因为我们的思考需要建立在实际情况的基础之上.介词结构在which引导的定语从句中不能去掉.因此第二句是错误的.
factual knowledge 实际情况、事实性知识 For e.g.:
The act of reasoning from factual knowledge or evidence.
推断由实际情况或证据而作出推理的行为
base upon 以.为基础、根据 如：
In America law and custom alike is based upon the dream of spinster.在美国,法律与风俗习惯一样,是把基础置于老处女的梦想之上.
括号部分结构分析：
which 指代 factual knowledge,引导定语从句,介词短语结构base upon,介词前置,upon介词+关系代词which,关系代词在定语从句中作宾语.理解时可还原成：
We need to have which(which =our thinking to base upon factual knowledge)
参考更多：
介词+关系代词引导的定语从句关系代词在定语从句中做介词宾语时
从句常由介词+关系代词引导
(1) The school (that/which) he once studied in is very famous.
(2) The school in which he once studied is very famous.
(3) Tomorrow I will bring here a magazine (that/which) you asked for.
(4) Tomorrow I will bring here a magazine for which you asked.
(5) We’ll go to hear the famous singer (whom/that/who) we have often talked about.
(6) We’ll go to hear the famous singer about whom we have often talked.
注意：1.含有介词的动词短语一般不拆开使用,如：look for,look after,take care of等
(1) This is the watch which/that I am looking for.(T＝正确)
(2) This is the watch for which I am looking.(F＝错误)
2.若介词放在关系代词前,关系代词指人时用whom,不可用who或者that；指物时用which,不能用that；关系代词是所有格时用whose
(1) The man with whom you talked is my friend.(T)
(2) The man with that you talked is my friend.(F)
(3) The plane in which we flew to Canada is very comfortable.(T)
(4) The plane in that we flew in to Canada is very comfortable.(F)
3.“介词+关系代词”前可有some,any,none,both,all,neither,most,each,few等代词或者数词
(1) He loved his parents deeply,both of whom are very kind to him.
(2) In the basket there are quite many apples,some of which have gone bad.
(3) There are forty students in our class in all,most of whom are from big cities.

第一句话：缺乏事实依据，我们就无法形成有价值的想法，因为我们需要根据实际情况进行思考。
第二句话是错误的

这两句话都没错。
第一句是：由于我们需要用实实在在的知识来为我们的思维方式打基础；第二句是：由于我们需要以自己的思维方式去理解和接受现实的知识。简而言之：
第一句是强调以知识为基础，二句是以思维方式为基础。