Meaning: The quote "And for mathematical science, he that doubts their certainty hath need of a dose of hellebore" by Joseph Glanvill reflects the author's strong belief in the certainty and reliability of mathematical science. Joseph Glanvill was a philosopher, clergyman, and writer who lived in the 17th century. He is best known for his works on natural philosophy and his defense of the existence of witches and witchcraft. The quote in question is taken from his book "The Vanity of Dogmatizing," which was published in 1661.

In this quote, Glanvill uses the term "mathematical science" to refer to the field of mathematics and its applications in the natural sciences. He asserts that anyone who doubts the certainty of mathematical science is in need of a "dose of hellebore," a reference to a medicinal plant that was historically used as a treatment for madness or irrational behavior. By invoking this metaphor, Glanvill emphasizes the idea that skepticism towards the certainty of mathematical science is akin to a kind of intellectual illness or delusion.

Glanvill's assertion about the certainty of mathematical science reflects a common view held during the 17th century, a period often referred to as the Scientific Revolution. This era saw significant advancements in the understanding of mathematics and its role in describing and explaining the natural world. Figures such as Galileo Galilei, Johannes Kepler, and Isaac Newton made groundbreaking discoveries in physics and astronomy, using mathematical principles to formulate laws and theories that transformed scientific knowledge.

The confidence in the certainty of mathematical science expressed by Glanvill and his contemporaries was rooted in the belief that mathematics provided a universal language for describing the laws of nature. Unlike other forms of knowledge, which were often subject to interpretation and debate, mathematics was seen as a realm of absolute truth and certainty. The use of mathematical reasoning and methods was regarded as a powerful tool for unlocking the secrets of the natural world and explaining phenomena that had previously been mysterious or inexplicable.

Glanvill's assertion also reflects the broader cultural and intellectual context of the 17th century, characterized by a growing emphasis on the importance of empirical observation, experimentation, and rational inquiry. The rise of new scientific methodologies, such as the use of controlled experiments and the development of mathematical models, contributed to a sense of confidence in the ability of science to uncover objective truths about the world.

However, it is important to note that Glanvill's perspective on the certainty of mathematical science was not without its critics. In subsequent centuries, the nature of mathematical truth and the relationship between mathematics and the natural world have been subjects of intense debate among philosophers, mathematicians, and scientists. The emergence of non-Euclidean geometries, the development of quantum mechanics, and the challenges posed by complex systems have all raised questions about the limits of mathematical certainty and the extent to which mathematical models can fully capture the complexities of the physical universe.

In conclusion, Joseph Glanvill's quote "And for mathematical science, he that doubts their certainty hath need of a dose of hellebore" reflects a historical perspective on the certainty and reliability of mathematical science prevalent during the 17th century. It highlights the confidence in the universal applicability of mathematical principles to the understanding of natural phenomena. While Glanvill's assertion captures a specific moment in the history of scientific thought, it also invites reflection on the ongoing dialogue about the nature of mathematical truth and its relationship to our evolving understanding of the natural world.