You have to keep in mind that Law is a philosopher, not a professional historian. So, in order to evaluate some of Law's premises in his argument, you will have to compare Law's knowledge of ancient history with the knowledge of history of contemporary professional historians.

Law's argument is this:

1. Extraordinary claims require extraordinary evidence. In the absence of extraordinary evidence there's excellent reason to be skeptical about the claims.

2. There is not extraordinary evidence for any of the divine/miraculous stuff in the NT documents.

3. Therefore (from 1 and 2), there's excellent reason to be skeptical about those extraordinary claims.

4. Where testimony/documents combine both mundane and extraordinary claims, and there's excellent reason to be skeptical about the extraordinary claims, then there's pretty good reason to be skeptical even about the mundane claims, at least until we possess some pretty good independent evidence of their truth.

5. The NT docs combine extraordinary and mundane claims about Jesus.

6. There's no pretty good independent evidence for even the mundane claims about Jesus (such as that he existed)

7. Therefore (from 3, 4, 5, and 6), there's pretty good reason to be skeptical about whether Jesus existed.

Let's to comment briefly on some of the premises of this argument:

Regarding premise 1 (Extraordinary claims require extraordinary evidence. In the absence of extraordinary evidence there's excellent reason to be skeptical about the claims.), we can reply, quoting this author: "Skeptics, both of the genuine and the pseudo variety, have elevated this double standard to a principle of science: extraordinary claims require extraordinary evidence! But this principle does not hold up to logical scrutiny, because a claim is only ordinary or extraordinary in relation to a theory. For the sake of making this point, let us assume a scenario in a hypothetical new science in which there are two pieces of evidence to be discovered, A and B, each equally credible, each one suggesting an obvious, but incorrect explanation (call them (1) and (2)). (1) and (2) are mutually incompatible, and a third, highly non obvious explanation (3) that accounts for both A and B is actually correct.

As chance would have it, one of the two pieces of evidence A,B will be discovered first. Let A be that piece of evidence, and further suppose that the scientists working in that hypothetical field all subscribe to the principle of the double standard. After the discovery of A, they will adopt explanation (1) as the accepted theory of their field. At a later time, when B is discovered, it will be dismissed because it contradicts (1), and because A and B are equally credible, but A is ordinary relative to (1) and B is extraordinary.

The end result is that our hypothetical science has failed to self-correct. The incorrect explanation (1) has been accepted, and the correct explanation (3) was never found, because B was rejected. I therefore submit that extraordinary claims require extraordinary evidence is not suitable as a guiding principle for sound scientific research. All evidence, whether it supports accepted theories or not, should be given the same level of critical scrutiny. "

Ordinary or extraordinary are relational properties of claims relative to a theory or a body of knowledge. In the case of New Testament documents referring to Jesus, they contain extraordinary claims relative to the naturalistic, atheistic worldview, but not relative to a theistic worldview in which God, whenever he wanted and for purposes which only he fully knows, could intervene selectively in certain events (and a theistic worldview was essential in Jesus' teachings and hence is part of the religious context to understand Jesus' putative miracles).

If you assume a body of knowledge or theory or worldview which excludes a given X phenomenon, then whatever claim for the existence of X is intrinsically and by definition considered extraordinary. For example, if you assume atheistic materialism, then phenomena like miracles, survival of consciousness or paranormal phenomena are antecedently improbable (in fact, impossible). This is why a materialist like Richard Wiseman concede the evidence for remote viewing but remains skeptical of its existence appealing to is putative "extraordinary" nature: "I think that they meet the usual standards for a normal claim, but are not convincing enough for an extraordinary claim."

Hence, it is not the intrinsic qualitity of the evidence, but the putative extraordinary nature of the claim (considered in the context of a assumed materialistic worldview) which precludes Wiseman's belief in the evidence.

In case of Law, since his naturalism precludes the miraculous as "normal" phenomena, whatever claim of supernatural events is, by definition, extraordinary, and give us a reason to be skeptical of such claims.

Premise 6 is simply false. An example of a mundane claim related to Jesus is his death by crucifixion. It was a common method of execution employed by Romans and more importantly, this fact is attested in independent non-Christian sources of the same period. For example, historian Josephus comments "When Pilate, upon hearing him accused by men of highest standing amongst us, had condemmed him to be crucified" (Antiquities, 18.64).

As consequence of this independent evidence (plus other credible Christian and non-Christian sources), virtually all historians and scholars agree that Jesus died by crucifixion (which implies Jesus' existence). This is why, even a revisionist and radical skeptical and atheist scholar like John Dominic Crossan of the Jesus Seminar has conceded "That he [Jesus] was crucified is as sure as anything historical can ever be" (Jesus: A Revolutionary Biography, p. 145).

Again, Law is not a professional historian and probably this is the reason why he claims a premise like the number 6, a premise which any major (atheist) professional historian and New Testament scholar would consider simply ignorant, incompetent, agenda-driven and ridiculous. (The only "scholars" who assert this are an extremely tiny minority of atheist fanatics, like for example online atheist apologist Richard Carrier, or Jesus Seminar "scholar" Robert Price, who have not much weight or influence in the academic community with their idiosyncratic ideas. These individuals have as their main purpose in life to destroy Christianity and the best way to do it, they believe, is to deny Jesus' existence).

Finally, in response to people skeptical of Jesus' existence, agnostic scholar and historian Bart Ehrman comments: