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Broad Definition: It is the investigation of philosophical questions that arise from reflecting on science.
Historical Context: Scientists were originally referred to as "Natural Philosophers" from Ancient Greece up until the 18th century. This legacy lives on today; regardless of the field you study, obtaining a PhD makes you a "Doctor of Philosophy" in that subject.
Rise to Prominence: While the Philosophy of Science dates back to before Aristotle, it rose to distinct prominence in the 20th century alongside monumental scientific strides in quantum mechanics and general and special relativity.
Philosophical questions are defined by their resistance to being solved by empirical methods or disciplines. They cannot be answered merely by finding out what happened in the past, determining what most people believe, or even by using the sciences themselves. These questions are about science, but they do not belong to science.
To understand the distinction, consider the following types of questions:
Historical: “When was Neptune discovered?”
Sociological / Psychological: “Why did Soviet biologists under Stalin reject Mendelian genetics?” or “Why did Crick and Watson underestimate the contributions of Rosalind Franklin in the discovery of the double helix structure of DNA?”
Philosophical: “What is a law of nature?”, “When can we say that a theory is confirmed?”, and “What should our attitude be towards entities that cannot be seen by the naked eye?”
Ultimately, the Philosophy of Science is not a branch of science, but rather a part of philosophy that intersects with other areas like epistemology, metaphysics, and ethics.