Meaning: Gottfried Wilhelm Leibniz was a prominent German philosopher, mathematician, and logician of the 17th century. He made significant contributions to various fields, including metaphysics, epistemology, and the philosophy of language. The quote in question captures one of the central distinctions in Leibniz's philosophy, namely the categorization of truths into two types: truths of reasoning and truths of fact.

Firstly, Leibniz's distinction between truths of reasoning and truths of fact reflects his broader philosophical framework, which was heavily influenced by his work in mathematics and logic. Truths of reasoning, according to Leibniz, are necessary truths that are derived from reason and are not contingent on empirical observation. These truths are grounded in logical principles and are necessary in the sense that their opposite is impossible. For example, the statement "2+2=4" is a truth of reasoning because it is necessarily true based on the principles of arithmetic and cannot be contradicted without violating those principles.

On the other hand, truths of fact, as Leibniz describes them, are contingent truths that are based on empirical observations and are not necessarily true. Their opposite is possible because they are dependent on the particular state of affairs in the world. For instance, the statement "It is raining outside" is a truth of fact because its truth value is contingent on the current weather conditions, and it could be false in different circumstances.

Leibniz's distinction between these two types of truths is crucial to his broader philosophical project, particularly his philosophy of metaphysics and his concept of possible worlds. According to Leibniz, necessary truths are grounded in the nature of reality itself and are true in all possible worlds, while contingent truths are specific to the actual world we inhabit and may not hold in other possible worlds. This distinction plays a central role in Leibniz's argument for the existence of a perfect, necessary being (God) and his theory of monads, which are the ultimate constituents of reality.

Moreover, Leibniz's distinction has implications for his views on the nature of knowledge and the relationship between the human mind and the external world. By delineating between truths of reasoning and truths of fact, Leibniz emphasizes the role of reason and logical principles in establishing certain knowledge, while also acknowledging the importance of sensory experience and empirical investigation in ascertaining contingent truths about the world.

In conclusion, Gottfried Leibniz's distinction between truths of reasoning and truths of fact reflects his commitment to a comprehensive and systematic philosophical framework that incorporates insights from mathematics, logic, and metaphysics. This distinction serves as a foundational element of his broader philosophy, shaping his views on the nature of truth, the structure of reality, and the foundations of human knowledge. By recognizing the different types of truths and their respective characteristics, Leibniz provides a nuanced account of the relationship between reason and experience, necessity and contingency, and the nature of reality itself.