‘In any case, even those who profess to deny the validity or the objective reality of the true-false distinction continue to maintain, without apparent embarrassment, that this denial is a position that they do truly endorse. The statement that they reject the distinction between true and false is, they insist, an unqualified true statement about their beliefs, not a false one.
This prima facie incoherence in the articulation of their doctrine makes it uncertain precisely how to construe what it is that they propose to deny. It is also enough to make us wonder just how seriously we need to take their claim that there is no objectively meaningful or worthwhile distinction to be made between what is true and what is false.’
Reference
Frankfurt, Harry G. (2006) On Truth. Alfred A.Knopf, New York.
The Logical Place 
Both those positions are incorrect; this little post reveals less an indication of some ‘actually truth’ and more that taken together they reveal a contradiction.
The idea that humanity might discern a truth is itself only a mandate of function, and at what level any argument is supposing to offer a truth for.
This arguement (your post quote) is based, as Paul said, in a categorical error. But both positions are involved in this error. Not just the author of the book.
The truth is that there is two, and only two, irreconcilable routes to what is real. The quote itself shows the two routes, but the positions, in as much as they might argue one better than the other, the argue only one route that contains all possibility for truth, which is the categorical error.
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I’m not suggesting anything. The quote is from Emeritus Prof. Harry Frankfurt, of Princeton. I will give a reference to his book. I suggest that you read it.
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Fallacy; specifically, category mistake. It is perfectly possible to distinguish between statements about things, and statements about statements about things. Thus the statement “All statements about things describe an arbitrary consensus, rather than reality”, while utter bollocks, is not self-refuting in the way that you suggest
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