Lucretius presents two arguments to support the view that ‘death means nothing to us’. The first is a standard Epicurean conception of the soul, based on their physics; the second is his asymmetry argument.
The first argument states that ‘death is nothing to us’ because at death, the soul is dispersed, and hence we ‘are’ no longer. This argument relies upon their notion of the soul, and their physics.
Their physics tells them that all things are material, and all composed of atoms, in much the same doctrine as Democritus (*Differences not important for the purpose of this essay*). Death is the end of life, nothing more. It is simply the point where the body begins its decay process after the loss of its life-force, its ‘soul’.
The Epicurean notion of soul is that of the self, and lifeforce of an entity (person). The soul is composed of atoms, just as their physics tells of the body. It cannot be destroyed through the loss of body parts, except for the head.
Essentially, Lucretius is claiming that this ‘soul’, this life-force, and the essential material for our conception of our ‘self’ is destroyed, dispersed through our death. Since this is, for Lucretius, the truth – death cannot mean anything for us, because at this point, there is no ‘us’ to have a meaning for. We are simply ‘not’.
Lucretius’ second argument hinges on our understanding of non-existence. Perhaps the response to his first argument has been that “it is not the ‘death’ part that I’m concerned about… I don’t like the idea of not existing anymore”. Lucretius responds by asking if ‘we’ are concerned about the period of time we were non-existent before our conception/birth. Lucretius argues that we were not concerned about the vast expanse of time before our birth (in which we were non-existent), so we should not be concerned about our future non-existence. We, like before, will not be ‘there’ to experience it, so anticipatory concern is baseless.