Quentin Smith’s Argument for Moral Realism

I am summarizing Smith’s argument here, without comment pro or con, for interested readers. Feel free to debate in the combox.
In his history of 20th century moral philosophy, Ethical and Religious Thought, Quentin Smith draws the following distinction between first-level and second-level ethical beliefs:

A first-level ethical belief is that something is good or evil or that something is of equal or greater value than something else, for example, that philosophical understanding is at least as valuable as aesthetic enjoyment. A second-level ethic belief is about some or all first-level ethical beliefs. The belief that “the intuition the proposition that philosophical understanding is at least as valuable as aesthetic enjoyment is true does not absolutely justify belief in this proposition” is an example of a particular second-level ethical belief, and the belief that “life is meaningful but absurd” is an example of a general second-level ethical belief. (p. 18)

Smith defends the following argument for moral realism.

(1)  Ordinary ethical sentences and commonsense first-level moral beliefs imply moral realism (or “Moral realism tacitly seems to be true in ordinary commonsense moral attitudes”).
(2)  There are no empirical or a priori reasons to believe that first-level moral beliefs are all false.
(3)  It is more reasonable to believe moral realism that not to believe this.
(4)  There is no reason to believe that the conjunction of (1) and (2) is a defective reason to believe moral realism.
(5)  The belief in moral realism is indefeasibly justified.