We can perceive mathematical abstractions (e.g. a perfect circle). But they are nonsensory perceptions..
1) You can
conceive of such abstractions only because you have
perceived physical instantiations. Without having seen circles you could not conceive of them.
2) Abstractions are rooted in sensorimotor experiences and require sensorimotor brain regions to process.
3) If you think you can actually conceive of mathematical abstractions that don't have ready physical analogues, try imagining the angle between two basis vectors in a complex, infinite-dimensional space (by "infinite-dimensional, I don't mean it extends infinitely as 1D space extends infinitely; I mean it extends infinitely along infinitely many "directions"). Or just picture how one can rotate a line segment in 10 dimensional space vs. 1000. When mathematics gets abstract, it really gets abstract. One cannot readily picture algebraic structures (and I mean real algebra not high school stuff), and to the extent one can it is by virtue of our ability to think about them in terms of geometrical structures that have physical analogues.
4) Nonsensory perception is an oxymoron. Perception is sensory.
Therefore, we have first-person evidence for the reality and existence of the nonphysical.
We have evidence that had you used "conceive" instead of "perceive" that we can conceive of things independently of specific instantations. Despite Hamlet's mind's eye, this hasn't persuaded really anybody that conception must be nonphysical in the sense that mental images or thoughts somehow must be distinct from physical processes.
Until you can measure consciousness, you have no evidence that it exists as physical energy or matter.
We do. My favorite example (which I think I mentioned to you before) is that of the "severed" corpus callosum or "split brain" phenomena. We've shown experimentally that, if we stop biochemical signals from crossing from one hemisphere to another, we can make participants process information such as visual commands (e.g., a screen with the command "Please stand up") and, by ensuring it only enters one eye that the individual will both obey the command and not be conscious of the reasons for doing so. When asked why they did what was commanded, they don't know the answer but because they are conscious of having done what was commanded they make-up reasons they believe to be true to explain why they consciously did something because of information processed unconsciously.
Simply put, by ensuring certain information is processed in only one part of the brain, we an make you consciously perform an action but prevent you from knowing why. When we enable full "communication", you will stop making up reasons for your conscious actions and simply state that you did what you did because you were asked to.
We can also stimulate conscious experiences, sensations, etc.,by sending electrical signals directly to the brain.
Now, while this and other findings are evidence that consciousness is physical (or that it is the property/product of the brain), it is true that we have not demonstrated either that non-physical things like a soul are necessarily involved in consciousness or that consciousness can be completely reduced to processes in the brain. That's not the same as saying we have "no evidence".