Beneke’s Neue Grundlegung zur Metaphysik is a programmatic declaration of the possibility of metaphysics. Beneke does not give a definite explanation of metaphysics, but he evidently contrasts it with a mere study of human consciousness - metaphysics, in comparison, deals with being and not mere thinking.
Problem of justifying the possibility metaphysics means then for Beneke a problem for showing that we can think of something we know to exist. Beneke’s not that original solution is to note that when we think of our very activities of thinking, we necessarily think of something that exists, because self-evidently our own activities of thinking must exist, whenever we happen to think them.
Beneke’s aim in pointing out this rather clear-looking fact is to argue against a position he calls strong idealism.This strong idealism is apparently supposed to endorse the notion that we can never connect thinking with being, but are always closed within the circle of mere representations of being. It is not at first clear why Beneke would call such a position idealism, but he is at least thinking about Kant’s notion of inner sense, which he explicitly denies.
It might be that Beneke and Kant are speaking of two different things. When talking about inner sense, Kant wants to emphasise that we cannot know even ourselves from a perspective reaching over our experience and that we therefore cannot know e.g. whether we are immortal and immaterial entities or material objects. Beneke accepts this, but insists that we still can know something about our mental life, namely, its existence as such, and even more, what this mental life feels to us. Of course, Kant might object that none of this is enough for knowledge, but we might well ask whether Kant just has a too tight definition of knowledge.
Although Beneke speaks against idealism, he is also willing to speak against a crude sort of realism that would state that we have as immediate connection with other things as with ourselves. Beneke still admits, against what he calls weak idealism, that we can know the existence of other things, although only mediately. The link between our immediate knowledge of ourselves and mediate knowledge of other things is, according to Beneke, our knowledge of our own bodies - we know our bodies just as we know our mental life, but our bodies are also causally connected to other bodies (Beneke deals here briefly with the Humean problem of how we recognise causality, and like in his earlier work, he insists that we can through an indefinite number of repeats become more and more certain of the existence of such a causal connection).
Although the lens of the body allows us to recognise the existence of other things, Beneke says, it also restricts our knowledge to a certain perspective. In other words, Beneke is of the opinion that we know other things more completely, if they happen to resemble ourselves. Even things quite removed from us, such as mere material objects with no life or consciousness, can be known only through the lens of our own bodily feelings - for instance, we can understand the physical movement of objects through our own experiences of moving through space.
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