Critical rationalism is the view propagated by Popper.

Popper does not give up the concept of truth.

His first point is, that we cannot prove general theorems in science, because we always have only finitely many observations. The next observation could refute the statement. Hence Popper gives up proving general theorems in science.

According to Popper our scientific theorems are hypotheses. One should create hypotheses which are testable. A test can confirm or refute a hypothesis. In the latter case, the hypothesis is false and we need a better hypothesis. But even a confirmed hypothesis is not proved. We do not know whether it is true.
Hence Popper replaces **proof** by **falsifcation**.

By eliminating false hypotheses we hope to approach **truth**, which is considered a limit term. Pointedly formulated by Gerhard Vollmer: "We err upwards."

**Certainty** is the personal feeling to have true knowledge. It is a subjectice term and does not guarantee truth.

A simple google search for "critical rationalism stanford" gave the answer within seconds. I cannot see any effort answering the question yourself. – Philip Klöcking – 2015-11-30T08:30:19.317

6I vote for "Leave open". The question asks more than just to pigeonhole criticial rationlism. The issues truth, certainty, and proof are legitime philosophical points. – Jo Wehler – 2015-11-30T08:58:31.243