Recently I have been working on getting a handle on 'nothing' in order to to more fully appreciate Heidegger's question in Introduction to Metaphysics: Why is there something rather than nothing? I wish to understand this question not simply to understand Heidegger - he can speak for himself well enough - but to help understand some of the history of philosophy where Heidegger drew the question from. And this goal itself is only a stop along the way to unlocking the significance of 'nothing' for continued genuine questioning.
So far I have considered Leibniz and Kant. The reason for considering Leibniz is that he asks and answers our guiding question in a manner that Heidegger is aware of and reflective about. My reason for selecting Kant was my familiarity with him, and that his passage on nothing has a straightforward introduction to some difficulties of the subject; a secondary consideration was that the section that Kant's discussion of 'nothing' appears in - the Amphiboly - is one which Heidegger calls decisive, even if he does not (to my knowledge) directly reference the discussion of 'nothing'.
I also plan to consider 'nothing' in Parmenides, but before I do I want to take an opportunity to reflect on the considerations so far and to add some remarks and refinements.
One thing that has come up in the interpretation so far has been different kinds of nothing. For Leibniz, I attempted to understand nothing as the simple negation of the actual, as well as nothing as a privation (of goodness); in Kant, there was also nothing as a negation of the different ways of being judged objectively, as well as a nothing that was indistinguishable from being: the problematic object, theoretically indeterminable whether it 'is' something or nothing. To help to understand these different types of nothing I will consider the negation of a specific thing (any thing, say, a cup).
For Leibniz, the denial of the actuality of a specific thing means that it is contradictory with whatever is actual and better (more good). The negated object is still a possible object, but it has specific reasons relative to what is actual for not being actual (even if we do not know them). Simply not being actual still allows us to consider why this is so, and so blurs the difference between nothing as not-actual and as privation. If an object is self-contradictory, however, then we get a different sense of nothing for Leibniz which we should consider.
For Kant, the negation of a specific object reveals no other determination about it, but this also does not mean an object is nothing, but simply that we think it as an object of possible experience. A cup is not impossible, and so is not properly nothing, just as in Leibniz we can say that the negation of the actuality of the cup is not nothing.
For Kant, 'nothing' is determined by impossibility of the object being given in any possible experience, and there are four ways of being such an impossible object. However, the impossibility of the object is ultimately determined by its inability of being temporalized. So, for Kant, 'nothing' is relative to the constitution of our experience. On the other hand, the problematic is the positive expression of the limits of our cognition, and reveals some new options.
If something is problematic for us, and intelligible, then it is at least not self-contradictory, but we still cannot say that it is possible or impossible, since it does not relate to a possible experience. Freedom is such a concept as this, which we can think without contradiction, but also cannot be made an object of a possible experience. We can also consider the problematic in stronger terms, according to what is not even intelligible; here, even self-contradictory concepts, such as square circles, are considered problematically. Perhaps there is a being which 'experiences' square circles, and for whom a round circle is a contradiction. This is meaningless for us apart from the recognition that our form of experience is not itself necessary.
In Kant, then, we have, first, the negation of a thing, which still leaves it as possible - the imaginable; second, the nothing, which means something impossible - inability to temporalize; third, the problematic intelligible object, which is also atemporal, and is thought without contradiction - the positive expression of the limits of theoretical reason; fourth, the unintelligible problematic object which is atemporal and self-contradictory, which we can think as possible for some being constituted differently than us - the positive expression of the limits of all human reason.
We may be tempted to consider a fifth: the absolute problematic - a positive expression of the limits of any kind of reason (not only human). But the only reason that this cannot really be considered, is that it is actually just an instance of something unintelligible problematic. The contradiction of absolute limitation is that limitation is always of something, and so a non-relative limitation cannot be thought by us. However, just because it is unintelligible to us, does not discount it absolutely, since it is still unintelligible problematically.
Leibniz considers the self-contradictory to be exactly the absolute problematic (the unconditioned limit), but because this absolute limit is intelligible, it must be different from our determination above. For Leibniz, the absolute limit is self-contradiction, which is even a limit for the absolute being - God. In Kant's terms, Leibniz only goes as far as the intelligible problematic, but this intelligible problematic is determined to exist by Leibniz, and not just as intelligible. From Kant, we see that practical reason is what first gives the (intelligible) problematic determinations beyond self-consistency, such as existence, and on such practical foundations we make further determinations within the problematic. This shows more clearly the moral outlook already unconsidered in Leibniz' position.
Since Leibniz determines the absolute being as existing, and so as having a (theoretical) thingly character, we can see a choice had to be made between how we think God and objects: either the objectivity of objects must be expanded to be moral, or the nature of God must be reduced to conditions of appearance so that he can be determined theoretically. (Perhaps we can see a glimpse of Spinoza's pantheism here.) We know that Leibniz expands on the objectivity of the object, making goodness the determining factor of the actual. But, in order to have real possibilities - actual possibilities - these also must be good, and so a consideration of degrees is employed.