Answering the question posed by Heidegger's title is no simple matter, and any proposed definition will meet with a few passionate supporters, but probably more passionate opponents. Philosophers who offer definitions of 'metaphysics' sometimes even equivocate on their own terms. Immanuel Kant initially flirts with a definition of 'metaphysics' as that branch of philosophy which deals with God, with the immortality of the soul, and with the freedom of the will. He then goes on to offer his more widely-known definition of 'metaphysics' as the a priori synthetic.
Let's examine three possible definitions:
First, metaphysics might be that branch of philosophy - that science in the sense of Wissenschaft - which deals with things composed of neither matter nor energy.
Second, metaphysics might be that science which deals with things that cannot be perceived by the five senses.
Third, metaphysics might be that science which deals with things located outside of time and space.
Each of these definitions has some intuitive appeal, but also some problems. The word 'things' might require sharpening: it might include persons, ideas, or objects. To explain what an 'object' is, if it is outside of time and space, not detectable by the five senses, and not composed of matter or energy, could be a challenge. An opponent might say that this is not an object at all, or at most an object by analogy.
Another problem is the use of the preposition 'outside' - it is a spatial preposition, and so to be 'outside of space and time' might be judged to be either nonsense or senseless.
Beyond these two problems - and other problems which might be raised - a question might be posed about these three potential definitions: are they equivalent? Again there seems to be some intuitive appeal to the notion that these three are in fact synonymous expressions.
If we understand our five senses to operate on a basis explainable by garden-variety physics, then it would seem that the objects of our senses are composed of matter or energy or some mixture of the two. The processes described by physics take place in time and space.
Although these three definitions are far from trouble-free, it does seem that there is a strong argument to be made for their equivalence.
