Philosophy, as many human sciences fields, tends to be said to be separated from science. In my opinion is it not nuanced than that. Philosophy has always been linked to science, and can play a role, even limited, to scientific innovation.
Philosophy touches to sciences, through analysis. It is not a technical field and doesn’t pretend to solve problems. Anyway many thinkers have analyzed theorems, demonstrations… For instance Plato wrote at the entrance of the academy that « no one can enter here if he is not a geometre » Aristotle wrote second analytics, which is an analysis about demonstrations. Descartes and Leibniz were great mathematicians and philosophers. Hegel had an excellent biological and mathematical culture. Moreover thinkers like Russell made logics at the core of mathematics, to explain axioms. This approach has been contested, anyway it is necessary to build new approaches about science.
As said Badiou, philosophers always had a reverence towards mathematicians. One of the reasons it mathematics achieves the best the human species can do the philosophical quest for truth. Philosophy of science is one of the oldest field of thinking for this reason. Even if, during the Middle Ages, science was not independant from theology. But the modernization of science, its emancipation from theology, matched to the development of Western power. But philosophy has always been linked to science. Kant, for instance, wrote many books about this field before writing critic of pure reason. Marx considered that the progress of civilization was often linked to productive forces, which means science. To that extend we can say that philosophy touches to the intellectual part of science. Many thinkers explored theorems or demonstrations, without pretending to solve problems, which is at the core of the purely scientifical activity (except the logic resolution).
The current philosopher Markus Gabriel was telling about giving back to philosophy a role it lost in minds. An the context can give opportunities to philosophy, in my opinion, to contribute to innovation. Today scientific innovation is more and more moving : the creation of the 5G, the development of artificial intelligence, the creation of new kind of planes in a context of more acute international competition, especially linked to competition between the Western world and China, can give more place to human sciences. This approach from the speech of Emmanuel Macron in his 2030 investment plan. Investing in more environmental friendly energy will be more and more detrimental in the future. That is the reason why philosophy can contribute to building these new technologies. That is the reason why, in my opinion, there can be a link between philosophy and scientific innovation, and philosophy can contribute to those innovations.
The observer 