Quentin Smith Contra Skepticism

I'm currently reading Quentin Smith's book Language and Time, in chapter 1 of which he has a nice argument against a certain kind of skepticism (pp. 14-18). His argument runs as follows.

Is it ever reasonable for you to believe something just because it seems true to you and, so far as you are aware, there are no good empirical, logical, or other relevant reasons to disbelieve it? Well, suppose there is a skeptic who says No, seeming is never sufficient grounds for believing. Such a skeptic proposes:

(1) Even if it seems to S that p and S has no reasons (empirical, logical, or other) to disbelieve p, S is not justified in believing p.

Now, asks Smith, what could possibly justify a belief in (1)? Suppose we grant the skeptic that there are no empirical, logical, or other reasons to disbelieve in (1). Obviously, the skeptic cannot justify (1) on the grounds that it seems right to him, since (1) disallows that move. So the skeptic needs to give positive empirical, logical, or other reasons to show that (1) is true. Call these reasons R.

Now, what justification could there be for thinking that R supports (1)? Again, given (1) it can't be that R seems to support (1). So we need further reasons, R', for believing that R supports (1). But now why should we think that R' supports the claim that R supports (1). Again, given (1) it can't be that R' seems to support that claim. So that claim has to be justified by appeal to still further reasons, R'', and so on. An infinite regress ensues. And the regress is vicious since, as a finite mind, the skeptic "cannot comprehend an infinite number of steps in a chain of alleged justifications" (p. 17). Even if he could, says Smith, the skeptic would still not be justified in believing (1) because he would have no justification for believing that the infinite chain justifies (1). A skeptic who appeals to a principle like (1) is, therefore, hoist on his own petard. If (1) is true, then no one (including the skeptic), could be justified in believing it to be true.

The moral of the story: (1) is false. It's seeming to S that p is, in the absence of S's possession of reasons for believing the contrary, sufficient to justify S's believing that p.