There is a traditional divide between the sciences and the humanities. Philosophy has traditionally been included as a humanity, one of the classics to be studied alongside Latin and Greek. The scientist CP Snow wrote some books and started being invited to the sorts of parties literary people go to. He spent his time asserting the superior intelligence of the scientific mind. The defence was taken up by F.R. Leavis and the whole affair was dubbed the Snow-Leavis Controversy.
Being a mathematician, I am of course biased and believe that the best way of discriminating between intellectuals and non intellectuals is whether or not a person understands the principles of Calculus and can differentiate a few functions from first principles. Unfortunately, I suspect that in this age of rising standards, most university science graduates will fail this test.
Joking apart, science is an attempt to narrow the gap between subjective and objective reality and therefore should form the backbone of any body of knowledge posing under the title Philosophy. When people do not understand the way nature works, they are likely to invent irrational explanations and imagine that a volcano erupts because there is a god inside it who has been angered. Science is not always right and can in some cases be little more than a pseudo religion offering explanations which are just as untenable, but its methodology usually results in mistakes being identified and corrected. The volcano is a case in point. When I was a child, science described the processes of eruption, but apart from hypothesizing that the earth had a solid mantle surrounding a molten core, had no detailed understanding of why, where and when volcanoes occur. In the last forty years, we have seen the development of Geotectonic Plate Theory and our understanding of earthquakes and volcanic eruptions is more complete.
Those readers familiar with my Physics web-site will know that I believe modern physics to contain many conceptual errors simply because it has got its philosophy wrong and been contaminated by existentialist ideas. Science produces mathematical equations and formulae into which we can put numbers and get answers. Einstein's relativity attempts to derive the equations describing the effect of near light speed motion, but history records that the equations were derived earlier by others on based on entirely different philosophical assumptions about how nature works. The original derivation comes from the laws of electricity of magnetism and describes the way electromagnetic interactions affect matter. Einstein's derivation is based on the idea that God has made a world in which all observers see the same laws of physics. Consequently the equations are interpreted as describing artefacts of observation rather than real physical effects. Those readers who understand the principles of Calculus and can differentiate a few functions from first principles should be able to follow my explanations. I noted with interest that in the library of my local university, relativity spread over far more feet of shelf under philosophy than under mathematics or physics.
Science can get things wrong because the subjective reality of the scientist is limited. If we step back and take a wider perspective including history, philosophy and psychology, we see the scientist trying to fit the pieces of a jigsaw together before historical accident has produced all the pieces. Not realizing that their brains are designed to work with limited information, they are fooled into thinking their logical reasoning must be correct. When explanations seem illogical, they fall into the trap of believing accepted wisdom. Men like Einstein, Feynman and Hawking are almost deified by those unable to understand their theories.
Richard Dawkins's has made two outstanding contributions to our understanding of evolution enabling us to understand how complex organs like eyes can evolve and how the statistics of advantage and disadvantage control the spread of a genetic characteristic throughout a population. Other researchers have pieced together the effects of genetic mutation and sexual reproduction until our understanding of evolution as a biological process is fairly complete. Without a knowledge of this body of information, it is impossible to come to a reasonable understanding of our place in the universe.
Hubble enabled us to comprehend the vastness of the universe and Einstein, I cannot say bless his cotton socks, for he never wore any, stumbled across the effects of gravitational potential and laid the foundation for Hawking's attempts to explain away the creation of the universe. Without a knowledge of these ideas, we cannot begin to comprehend the universe in which we find ourselves.
Medicine would still be floundering in the dark without without the discovery of bacteria and viruses. Alchemists would still be trying to create gold without our understanding of chemistry and without physics, we would have no radio, televisions, power tools or kitchen appliances. These bodies of information have contributed to the prosperity of Western Society.
If we are to understand the world we live in; both the natural world and the technological world, then we need to have a broad overview of these bodies of information and a way of delving into them when the need arises.