Jean-Paul Sartre, answered from the texts and cited to the page.
Nothingness is not a thing. This must be said at the outset, because the grammar of the question already misleads: to ask what nothingness is invites the answer in the form of a substance, a property, a region — some positive content that nothingness could never possess. Nothingness has no being of its own. It arises, and it arises only through the pour-soi (for-itself; consciousness), which is the being that is not what it is and is what it is not.
The structure is this: the pour-soi can arise only in connection with the totality of the en-soi (in-itself; the massive, undifferentiated plenitude of being) that encloses it, retaining that being before and around it as what it is not.1 It needs being in order not to be. This is not a paradox but a description of the ontological situation: consciousness is absence, and absence can only exist before a presence.
Nothingness, then, is not the void that precedes being; it is the nihilation that consciousness accomplishes with respect to the totality of the in-itself — and this nihilation is what we call being-in-the-world.2 To be conscious is to make oneself into non-world in the world's presence, concretely and precisely into what is not that particular world.
One must not read this as withdrawal. If nihilation were accompanied by a retreat from the world, it would be nihilation of nothing and would collapse back into the in-itself — which is perhaps how death must be understood.3 Consciousness is not a substance that withdraws behind a wall of representations; it adheres to the world immediately, without distance, separated from the world by nothing save that it is itself a nothing.
This presence — the world vesting consciousness in order to be surpassed by it in nothingness — is transcendence. From the side of knowledge, the same structure appears. A thing must be present to consciousness as not being consciousness before any comparison, any construction, any combination of representations can occur.4 The original relation of presence, as the foundation of all knowledge, is negative.
But since the thing is what it is in the absolute indifference of identity, the negation cannot come from the thing; it comes from the pour-soi itself, which constitutes itself, through original negation, as not being the thing.5 Knowledge is therefore not a relation subsequently established between two beings; it is the for-itself's very being insofar as it is presence to something — insofar as it has its being to be, in making itself not be a specific being to which it is present.6
The Hegelian formula — every determination is a negation — gestures toward this but misses it, because Hegel conceives the determination as imposed from outside, as if consciousness always received its status from an exterior.7 The truth is that the pour-soi is the internalization of its own finitude; its limits are existed in the deep freedom of its being.
To exist its own finitude is to make itself as not being the Whole of Being.8 The for-itself grasps itself simultaneously as that vanishing contexture which is not the totality of being, and as denying to itself that it is this totality — and this negation is its relation to itself.9 Consciousness cannot draw from itself alone either the concept or the project of being.
It draws it from its comprehension of a being borne upon the Being of the world.10 It is its being besieged by Being that allows it to be conscious of the Being that it has to be. Nothingness, then, is not prior to being, not a rival substance, not a Heideggerian void that retains the world within it. It is what consciousness is — the permanent, structural, non-thetic absence that makes the world appear as world, the this appear against its ground, the tree appear as a tree rather than as an undifferentiated lump of the in-itself. That is what nothingness is: the being of consciousness, which is no being at all.
The for-itself can arise only in connection with the totality of the in-itself that encloses it. The for-itself retains the in-itself before and around it, as what it is not. It needs being in order not to be.War Diaries, p. 193
Being-in-the-world is making oneself into absence from the world. The unity between consciousness and the world pre-exists both consciousness and the world. To be consciousness is to make onself into non-world in the world's presence; it's to make onself, precisely and concretely, into what is not that particular world.War Diaries, p. 193
If nihilation were accompanied by withdrawal, it would be nihilation of nothing and would relapse back into the in-itself. This, perhaps, is how death must be understood.War Diaries, p. 193
In advance of any comparison, or any construction, a thing has to be present to consciousness as not being consciousness. The original relation of presence, as the foundation of knowledge, is negative.Being and Nothingness, pp. 285–286
As it is through the for-itself that negation comes into the world, and as a thing is what it is in the absolute indifference of identity, what posits itself as not being the for-itself cannot be a thing. The negation comes from the for-itself itself.Being and Nothingness, pp. 285–286
Knowledge appears therefore as a mode of being... It is the for-itself's very being insofar as it is presence to..., i.e., insofar as the for-itself has its being to be, in making itself not be a specific being to which it is present.Being and Nothingness, pp. 285–286
The reason why we say every determination is a negation is that we see this determination as imposed from the outside (Hegel's sophism). For Hegel, consciousness is for itself, but it always gets its status from the outside.Notebooks for an Ethics, pp. 555–556
In truth the For-itself is the internalization of its own finitude. Its limits are existed in the deep freedom of its being. And to exist its own finitude is to make itself as not being the Whole of Being.Notebooks for an Ethics, pp. 555–556
The For-itself denies to itself that it is the Whole and this negation is its relation to itself.Notebooks for an Ethics, pp. 555–556
Consciousness cannot draw from itself alone either the concept or the project of being. It draws it from its comprehension of a being borne upon the Being of the world or the Whole of Being.Notebooks for an Ethics, pp. 555–556