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This is answered on the wikipedia page for "infinite regress":

Our own doctrine is that not all knowledge is demonstrative: on the contrary, knowledge of the immediate premises is independent of demonstration. (The necessity of this is obvious; for since we must know the prior premises from which the demonstration is drawn, and since the regress must end in immediate truths, those truths must be indemonstrable.) Such, then, is our doctrine, and in addition we maintain that besides scientific knowledge there is its original source which enables us to recognize the definitions. (Aristotle)
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A snarky response would be that a truly radical skeptic should doubt that it is possible to justify anything at all, including the necessity of justification.

Taking the position more seriously, Objectivism identifies that the primacy of existence is axiomatic and the radical skeptic position violates the axiom. The very idea of justifying single concepts or propositions is not innate automatic knowledge but arises from the possibility of the failure of correspondence between what exists and what one believes.

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To deny the accuracy of the senses is to deny the law of causality and subsequently to deny all natural laws. Our senses simply cannot sense something which is not there.

Skeptics also tend to ignore the role of the mind in arriving at knowledge. Sensory information on it's own is meaningless before our minds make something of it.

For example, the image reflected onto the retina is upside down. The mind turns it right side up.

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Proof or justification "is the process of deriving a conclusion step by step from the evidence of the senses, each step being taken in accordance with the laws of logic" ( Peikoff). If one cannot rely on one's senses, then justification becomes a stolen concept, that is-a concept which denies its genetic roots..

Edited by Leonid
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What do you think of the radical skeptical argument, that you cannot rely on your own senses, because the only way to justify your senses would be via an appeal to senses, which is infinite regress?

One way to justify your senses is by the fact that you're alive -- an infinite regress is not required. If you could not rely on your own senses, staying alive would be impossible.

Having valid senses is also a requirement for consciousness; to be conscious is to be conscious of something.

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