Final answer:
The believability of a syllogism does influence your judgment if you're using system 2 thinking.
Step-by-step explanation:
The statement that the believability of a syllogism does not influence your judgment if you're using system 2 thinking is False.
In system 2 thinking, individuals use conscious, analytical, and logical reasoning to make judgments. When using system 2 thinking, the believability of a syllogism does influence your judgment. A syllogism consists of two premises and a conclusion, and if any of the premises are false or questionable, it can lead to an inaccurate or unreliable conclusion.
For example, if a syllogism has a false premise, the conclusion drawn from that syllogism would be invalid. So, in system 2 thinking, it is important to critically evaluate the believability and validity of a syllogism to make accurate judgments.