A defense of moral skepticism

For my argument I will use a somewhat revised edition of Walter Sinnott-Armstrong's adaptation of the regress argument for general skepticism as applied to morality.P1: If any person T is justified in believing any moral claim, then T must be justified either inferentially or noninferentially.This is akin to saying that an apple will either be red or a color other than red. It is simply descriptive of the two logical options that arise when dealing with justification of knowledge.P2: No person T is ever noninferentially justified in believing any moral claim.To validate this premise, we only ought to look at the agreed upon definition of 'justified'. It says that a belief is justifiedwhen it is warranted or well grounded, that is if it is based on some reason(inferentially).C1: If any person T is justified in believing any moral claim, then T must be justified inferentially.To put it simpler, if the solution is not A than it must be B. I have shown why it is not A. Therefore it must be B.P3: If any person T is inferentially justified in believing any moral claim, then T must be justified either byinference with some moral premises or by inference without any moral premises.The reason for this principle is the same as my first premise. Since to be justified means needing to be inferentially justified and since to be inferentially justified one must derive logical consequences from some sort of premise, we areleft with the options of either a moral or a non-moral premise.P4: No person T is ever justified in believing any moral claim by an inference without any moral premise.This premise can be seen as coming from David Hume. It is better known as the is-ought problem. One cannot deriveprescriptive statements('ought') from descriptive statements('is') without comitting the naturalistic fallacy of assigningnon-natural properties to natural properties.C2: If any person T is justified in believing any moral claim, then T must be justified by an inference with some moral premise.Again, if the solution is not A, it must be B. I have shown that the solution is not A(is-ought problem) and so thereforeit must be B.P5: No person T is ever justified in believing a moral claim by an inference with a moral premise unless T is alsojustified in believing that moral premise itself.Simply put, you should not believe your five year old sister when she says the tooth fairy exists unless there is a reasonable reason to believe her.P6: If any person T is justified in believing any moral claim, then T must be justified by a chain of inferences that either goes on infinitely or includes T itself as an essential premise.This is simply a continuation of P5. Why should you believe your sister? Because she is a genius. How do you know sheis a genius? She took an IQ test. How do you know the IQ test is accurate.... and so on in an infinite regress. Hence thename of the argument.P7: No person T is ever justified in believing any moral claim by a chain of inferences that includes T as an essential premise.This commits the fallacy of begging the question. A smple example would be if I said I was a genius and you asked mehow I knew this. If I answer with 'Well I'm a genius so of course I'd know if I was a genius.' This assumes the conclusion as one of it's premises.P8: No person T is ever justified in believing any moral claim by a chain of inferences that goes on infinitely.This is probably the most self explanatory premise in this argument. If the chain of inferences goes on infinitely thenyou don't actually get an answer to the problem of whether we can know moral facts. C3: No person is ever justified in believing any moral claim.Again, if not A or B, then C. We cannot be justified in believing moral claims based on a chain of inferences with T as anessential premise or believe moral claims based on an infinite regress. Therefore we are left with only one option, thatwe cannot be justified in believing moral claims. I rest my case for now and very much look forward to my opponent's response.