A negative concept identifies the negation of another concept, its object, on which it logically depends. Negative concepts refer only to an absence of the specific object, not to the presence of anything else - they are merely the logical negation of the object, not the assertion of the existence of some other object. To assert the existence of a negative thing, as a different kind of existent, is a fallacy of the Reification of the Zero, a variant of the fallacy of the Stolen Concept.
The concept "nothing" does not assert the existence of something called "nothing" - there is no such thing as "nothing" in and of itself, only the absence of a thing (the word literally means no-thing). The concept "non-existence" does not assert the existence of a "non-thing" - there is no such thing as "non-existence" in and of itself, only the absence of a thing in existence.
In the same way, the concept "evil" depends on the concept "good". Evil is a negative concept indicating the logical negation of the good. The concept "evil" does not assert the existence of a "non-good", there is no such thing as an "evil" in and of itself, only the absence or contradiction of a good.1
Pain and fear are innate capacities to alert us that something is wrong, that there is a potential threat to our life and our pursuit of the good, but they do not by themselves offer us any positive value to seek. Pleasure tells us what is good, what is right, but pain can only tell us that something is wrong - it cannot tell us what is good or right.2 Rationally we can identify pain and suffering as a contradiction to the good, as a negative and an impediment, but innately pain simply does not offer us any pleasure, that is, it is a zero. It do not offer us the presence of any incentive to seek, so it cannot logically be the source of any conceptual values, nor can it be the fuel that makes us function.3
Man is by nature faced with a fundamental alternative: identity or non-identity, existence or non-existence – life or death. The concept of value, of "good or evil", is not an arbitrary human invention, but rather is based on a metaphysical fact, on an unalterable condition of man's existence: his life. The ultimate value, the final goal or end to which all lesser goals are means, is man's life. His life is his standard of value: that which furthers his life is the good, and that which threatens it is the evil.4 The choice to live is therefore the most basic moral choice that one faces.5
Only in life do we have any possibility of acting to seek the good or to enjoy happiness. Death offers no possibility of action or enjoyment. Moral action means to act for one's own rational self-interest, but there are no interests to seek in death. Only life can offer us a positive incentive. Death, like pain, cannot offer any positive incentive, but rather it is a zero.
Suicide is the act of sacrificing life for death. Suicide is the sacrifice of the good for the sake of a zero. But it cannot be in one's self-interest to destroy one's self. One cannot rationally or morally act to end their life.
Observe the contradiction present in Piekoff's "Objectivism: The Philosophy of Ayn Rand" (aka. OPAR):
On the one hand he says the commitment to life is essentially axiomatic, and that there's no basis for questioning it, and on the other hand that suicide is justified if you're suffering and your condition seems hopeless. This is an apparent contradiction. But Peikoff is not the pope, OPAR is not the Bible, and Ayn Rand is not God. It's possible that this is merely a contradiction. OPAR is not inerrant.
Finding such a contradiction does not fundamentally break the philosophy of Objectivism, either. On the contrary, the fundamental moral conviction of the Objectivist philosophy is that life is the ultimate standard. This defense of suicide is inconsistent with the basic moral premises of the philosophy. The mistake here is derivative, not fundamental. The philosophy as a whole is sound; only the position on suicide is not.
I submit to you that this position on suicide is a contradiction to the fundamental moral philosophy of Objectivism.
If you disagree, let's hear your arguments.
I'll start by responding to Peikoff's argument for suicide: can suicide be an "affirmation" of life if it's impossible to achieve happiness?
Suicide cannot be an affirmation of life - it's the deliberate choice to destroy life. You cannot affirm your life by destroying it.
As long as you are alive, and you are conscious to think and act, then you can either choose to act in the best interest of your life and happiness, no matter how tragically hopeless the situation may seem, or you can choose to sacrifice your best interest for something lesser. Suicide is the sacrifice of all possible interest. Death is non-existence, it knowably has no value at all - it is a zero. You cannot seek values in death. To act on the assumption that happiness is impossible would not be an affirmation of a happy life - that would be in fact be the most damning denial you could make.
In such a tragic situation where happiness seems impossible, the way to affirm your life is to continue to seek your happiness despite the tragedy and hopelessness of the situation. In Peikoff's own words:
That is an affirmation of life.
- The Objectivist Ethics, Ayn Rand
Howard Roark and Dominique Francon
See "The Objectivist Ethics", in "The Virtue of Selfishness" by Ayn Rand