"There are also two kinds of truths: truth of reasoning and truths of fact. Truths of reasoning are necessary and their opposite is impossible; those of fact are contingent and their opposite is possible"

In this quote, Gottfried Leibniz is comparing 2 kinds of truth. The first type is "reality of thinking," which refers to logical or mathematical realities that are based upon concepts of logic or reason. These truths are needed, implying they can not be incorrect or otherwise be false, and their opposite is difficult.

The second type of reality is described as "realities of truth," which are statements about the physical world that are contingent on empirical evidence. These facts are not required, indicating they can be false or untrue, and their opposite is possible. This difference is very important since it helps to clarify the different realms of truth that exist and the types of evidence and reasoning that are needed to establish their credibility.