This is not a mathematical question. Nevertheless, I can attempt to answer it from personal observation and my own rather limited understanding of philosophy.
Plato's metaphysics was based on two concepts of reality: the physical and the spiritual (divine or intellectual). Technology and scientific knowledge was apparently not as advanced or progressed in Plato's time as it is now, so even some of his physical premises and conclusions could be classed as idealistic and based on observation rather than from scientific findings of his predecessors. Because spiritual, divine and mental premises and conclusions cannot, by definition, be based on physical observations, they have to be classed as wholly idealistic, unless their realism is demonstrable in physical terms.
Aristotle's metaphysics deals primarily with the physical world, and attempts to explain all phenomena solely as having a material basis, although he introduces the concept of "essence", rather than matter, as being the fundamental substance. Hence, his philosophy is classed as realistic, based on the evidence of physical observation. But science or scientific knowledge (as an explanation of reality) was limited in Aristotle's day just as it was in Plato's. So some of his conclusions could be classed as idealistic. He based much of his philosophy on information derived directly from the senses (sight, hearing, touch, taste, smell). He focussed on the "why" things existed rather than simply the fact that they existed. That's the metaphysics behind and beyond physics.
For example, to explain the phenomenon of consciousness in Aristotle's terms, it may be treated as a secondary effect of electrical or chemical (or alchemical) activity in the brain, and this would be the basis for neurosurgery, psychology, psychiatry and the like. Behaviour (good and bad) would be driven by chemical and electrical stimuli. In other words, we think and act because of this physical neural activity.
The physical is fundamentally the generally accepted world view of reality. The spiritual, mental or intellectual deals with mental perceptions, and is largely ignored, except perhaps by theologians or those of religious faiths, because spiritual attributes are non-physical. However, as human beings (and perhaps other sentient beings), non-physical feelings (thought, reasoning, intelligence, love, anger, hate, mercy, altruism, philanthropy, etc.) are very much in the human consciousness, but can be expressed in physical terms.
Gradually, more attention is being given these days to the phenomenon of consciousness. In quantum physics, for example, the observer plays a fundamental role which is counterintuitive (defies "common sense"). Isaac Newton was probably one of the greatest physicists and mathematicians of his time, but he did have an interest in other-worldly things. And, of course, he was interested in the "why" of things. By and large, Newton's Laws of motion are utilised today as being a fair representation of "reality" in the macro-world; and only since the early 20th century, through Einstein, Planck and others, has attention be drawn to the micro-world of the atom and subatomic particles. Hence the development of practical quantum physics which has given rise to enigmatic interpretations regarding what is really real.
Parapsychology, which deals with so-called supernatural and paranormal phenomena, also raises puzzling questions because "normal" physical laws do not appear to operate. Consequently, many such phenomena are, and have been, simply ignored or explained as delusion or superstition.
Hypnotism is used extensively and effectively in the medical and psychiatric fields today, but no concrete physically-based explanation has been given for how it works, but clearly it has a mental basis.
The Holy Bible gives many accounts of "miracles" that defy physical explanation. Christ Jesus in particular performed many such acts in apparent defiance of material laws, as did his disciples, apostles and other Christians later. "Explaining" everything in terms of lies, coincidence, delusion, superstition, etc., is in itself a form of madness, given the extensive documentation over thousands of years. And many would claim and provide indisputable evidence that so-called miracles still take place. The very existence of the immense variety of life and expressed intelligence on this planet are regarded by many as miracles in themselves, despite the evolutionary and revolutionary findings of Darwin, Wallace, Lamarck and others.
Philosophers from ancient times have puzzled over what constitutes reality. For example, the existence of the electron and atom were postulated millennia ago. Near death experiences (NDE's) have also raised some puzzling questions regarding what constitutes reality (see the talks by neurosurgeon Dr Eben Alexander).
Technology, particularly modern technology, is clearly physically based, yet the laws of quantum physics are utilised within it.
As society progresses (or retrogresses) as a result of developing technologies, Plato's view of reality has faded in favour of Aristotle's view. People readily and enthusiastically welcome technological advances, because of the materialistic advantages and the physical comfort that comes with those advantages, and the world is becoming rapidly more secular as a result. However, even thinkers with no religious faith can see the downside of some of these modern advances, and many have adopted a more spiritual outlook, which inevitably affects their view of true reality.
Plato and Aristotle were great thinkers. And the world (and the universe) needs thinkers!