Both of you reduce everything to subjective terms, licensed by assumptions of authenticity driven by figures of personal experience.

In Zack Doctor’s case, it isn’t that you don’t objectify, but you are objectifying in out of context and mistaken ways. Your interpretations are stuck in the hypostatic fixations of some sorts of conventional reception.

You’re not looking at the ‘logical’ form(s) of the metaphysics of both ‘presence’ and ‘nihilism’.
Straightaway, you import concerns of subjectivity and meaning, considerably and unnecessarily complicating the issue.
Very simply, the concept of ‘presence’ inhabits a differential and binary structure of application, together with ‘absence’. Whatever ‘presence’ and ‘absence’ are predicated of and whatever or whichever such predications occur from the perspective of, vary according to the case of application.
But the differential and binary structure of ‘presence’ and ‘absence’ remain constant.

The metaphysics of nihilism can take different forms, but all these forms revolve around the concept of ‘nothing’ or ‘nothingness’, said concept instanced as semantic function in the transactions and operations of nihilism.
The metaphysics of nihilism; its transactions and operations; the ‘nothing’ or ‘nothingness’ which such transactions and operations shuttle around; all of these constitute nihilism and the metaphysics of nihilism, as a ‘presence’.
Nihilism, as a logic of negation is contingent on ‘there being’ something to negate. If nihilism obtains, then there is nothing to negate, which can be interpreted in two ways, lol.
That there are no positive ‘things’ (or assertions), to negate; or that, hypostatically, ‘there is nothing’ (there actually is ‘nothing’, as a positive term or thing), to negate.
The first interpretation removes all positivity thus causing nihilist negation to be redundant, there is nothing left to negate.
The second interpretation positivises or positively asserts nothing or nothingness in order to negate it.

So negating the negation; negating the negative; which sounds suspiciously like Hegel?
It could well be what Heidegger means by “the Nothing nothings”, that phrase which Rudolf Carnap so eagerly ridiculed when critiquing existentialism and Heidegger? Not sure, though, would have to check it.

Anyway, the seemingly self-reflexive application of negation to negation, it would seem can only apply in conditions of positivised negation, the negative considered as positive instance.
Because, if the negative is seen as pure negation, with no positivity whatsoever, then it could not self-reflexively negate itself, because it is not an ‘itself’; an ‘itself’, at least within the context of consideration, would ‘automatically’ constitute a posit, position, and positivity.*  

Notions of presence and absence hinge on these considerations.
But what can be straightaway seen, is a mutual and necessary contingency of the positive and negative, reflected in the oscillation of positivist consideration between the two interpretations of the obtaining of nihilism and the logic of nihilism.
That, in the absence of positivity, nihilist negativity cannot obtain; nihilism cannot absolutise itself, at least not without recourse to the very positivity vitiating its self-absolution.

Zack Doctor brings up nihilism in the context of conventional, US, psychology-speak; existential psychology-speak; et cetera. This is why he instantly imports irrelevant subjective considerations and even solipsism, all of which imports indicate only his own preoccupations and not those of the text he is interpreting. 
A cautionary note, though.
One has to be careful to retain awareness of multiple levels of pertinence and not get lost or led astray.
So, in this case, it was entirely unnecessary that ‘Zack Doctor’ repeat his own preoccupations when the text he is attempting to address doesn’t licence those preoccupations.

It might be that ‘Zack Doctor’ brings up solipsism as an indirect and shifted, metonymic response, to Brian Barr’s staging and valorisation of self-interiority? Who knows?

*This can, however, be recontextualised and reversed, à la Schopenhauer.

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