Depending on who you ask mathematics is or isn't a science.
I get the feeling that all this turns on how reliable it needs to be to count as reliable. As reliable as science in the long run? Not much if anything in my opinion.
Mathematical truth isn't a scientific truth in that it doesn't require observation for verification/falsification. It's a good example of a non-scientific field of inquiry into reliable truths about inferences regarding purely intellectual constructs. Some science relies on mathematics as a tool but this fact doesn't equate mathematics with science.
To recap, the epistemologically untrained (skeptic or not) often fail to realize that our consciousness experiencing and understanding profound mathematical, philosophical, political, ethical and even aesthetic ideas are abstract 'observations', sometimes compelling sensations of what is real similar to physical observations except for their abstraction. They can be consistent
, inter-subjective (objective)
observations in much the same way physical scientific observations are. Sometimes even more so. One such abstract observation is us being aware that this is an epistemological discussion. Another one is us being aware that there's a world outside my imagination that is independent from it despite the fact that theoretically it could be just an amazingly persistent and consistent dream.
A sane and rational investigator may justifiably accept them as truths but only after examining them carefully and after they meet the foregoing epistemological standards. These abstract experiences are so real and so mundane in our everyday life that sometimes we forget they are actually 'meta
physical' in the sense that they haven't been successfully reduced to known physical properties. Scientifically we may say that they may
not be successfully reduced to neuroscientific properties in the future. But that's another debate and speculation.
Which brings us back to the Skeptic's Paradox or the Materialist's Paradox, depending on which of these theories it's applied to. The paradox does not really concern the ‘moderate skeptic/agnostic/materialist’ who simply honestly acknowledges not consciously knowing things beyond the ken of physical science or immediate observations to exist while not ruling out the possibility of knowing in the future. The 'strong' skeptic, however, is usually either an unwitting or a conscious proponent (a swankier word for 'believer') of a positive philosophical claim, better known as empiricism
. That is, the belief that only what is scientifically provable or physically observable is reliably knowable.
Which is simply not true as demonstrated earlier.
Logically, to make a positive claim on reliable knowledge being restricted to the domain of science, is to pronounce a blind metaphysical belief in a universe where any other possible domain of inquiry outside science and physical observation is forever bound to be inaccessible to reliable knowledge. Scientifically, however, there is no possible way to know such a sweeping truth about all reality. It's purely speculative. Such a notion resides principally in the realm of philosophy, unapproachable by science.
Scientism is just another scientifically unfalsifiable and unverifiable philosophical theory, often motivated by an understandable historical yet emotional aversion to the intrusive preachiness of fanatics and superstitious believers, insisting that you blindly swallow evidently absurd, and even harmful, ideas as truth, while judging you fiercely for their rejection.
Against this backdrop scientism is understandable and a logical counter-reaction. But in so doing it allows the pendulum to swing to another epistemological extreme and ending up becoming another belief-system.