Meaning: The quote "There is no philosophy which is not founded upon knowledge of the phenomena, but to get any profit from this knowledge it is absolutely necessary to be a mathematician" by Daniel Bernoulli, a prominent mathematician, highlights the essential role of mathematics in understanding and deriving practical benefits from the phenomena observed in the world. This quote encapsulates the intersection of philosophy, knowledge of the natural world, and the indispensable role of mathematics in making sense of this knowledge.

In the context of this quote, "philosophy" refers to the broader pursuit of understanding the fundamental nature of existence, knowledge, reality, and values. It encompasses the study of the world and our place in it, often involving deep contemplation and critical analysis of various phenomena. Bernoulli's assertion that philosophy is founded upon knowledge of the phenomena reflects the idea that philosophical inquiries are rooted in observations and experiences of the world around us.

The term "phenomena" refers to observable events, occurrences, or facts that are perceived through the senses or through scientific instrumentation. These phenomena form the basis of empirical knowledge, providing the raw material for philosophical inquiry and scientific investigation. Whether in the realms of natural philosophy, metaphysics, or epistemology, an understanding of the phenomena is crucial for developing coherent theories and interpretations about the nature of reality.

However, the quote also emphasizes the vital role of mathematics in extracting value from this knowledge. Bernoulli's assertion that "it is absolutely necessary to be a mathematician" to derive profit from knowledge of the phenomena underscores the idea that mathematics is not only a useful tool but a prerequisite for fully grasping and leveraging the insights gained from empirical observations.

Mathematics plays a fundamental role in quantifying and modeling the phenomena, allowing for precise descriptions, predictions, and analyses of natural and abstract phenomena. From the laws of motion and the equations of thermodynamics to the principles of probability and statistics, mathematics provides the language and framework for understanding and manipulating the data derived from empirical observations.

Bernoulli's statement resonates with the historical and contemporary significance of mathematics in various fields, including natural sciences, engineering, economics, and philosophy. In the natural sciences, mathematical models and theories have been essential for explaining physical phenomena, from the motion of celestial bodies to the behavior of subatomic particles. In economics and finance, mathematical tools such as calculus, differential equations, and optimization theory are indispensable for analyzing and predicting complex phenomena like market behavior and economic systems.

Moreover, in the realm of philosophy, mathematics has played a critical role in shaping philosophical discourse and inquiry. The application of formal logic, set theory, and symbolic reasoning has enriched philosophical debates and contributed to the development of philosophical systems. Additionally, the use of mathematical methods in areas such as ethics, decision theory, and philosophy of science has led to new insights and approaches to longstanding philosophical questions.

In conclusion, Daniel Bernoulli's quote underscores the intertwined relationship between philosophy, knowledge of the phenomena, and mathematics. It highlights the essential role of mathematics in extracting meaningful and practical insights from empirical knowledge, and it emphasizes the interdisciplinary nature of these pursuits. By acknowledging the foundational importance of phenomena and the indispensable nature of mathematics, the quote captures the essence of the symbiotic relationship between philosophy and mathematics in the pursuit of understanding and utilizing the world around us.