In the "real world", the relation "is indistinguishable from" is a non-transitive relation. This fallacy arises from assuming that it is a transitive relation.
Why do I say it is non-transitive in the "real world"? Because the theory of evolution implies that it is.
From the point of view of species, I am indistinguishable from my mother (we are both human). My mother is indistinguishable from her mother. Etc.. However, if you follow this chain back enough, you find a monkey, which is obviously not a human.
I would therefore say that this is a formal fallacy; i.e., logical fallacy. Unlike informal fallacy, I don't think it would be given a name.
EDIT Nov 2 Thanks for your additional comments.
Re-reading my answer, I admit that I haven’t been entirely clear - in fact, it’s a bit muddled. Although my comments about intransitivity are correct, they do not really hit at the heart of Russell’s view. In my subsequent comments, I have not clearly distinguished between Russell and the Lawyer, which is slightly ironic given the context, and this makes it difficult to understand.
First, I realise that I have not answered the question of naming this fallacy. I now think this is what is called a Naturalistic Fallacy -
[3.] that which arises by inferring evaluative conclusions from purely factual premises in violation of fact-value distinction.
Here is what I mean by [3.]: My reading is that Russell is saying that the lawyer's conclusions are drawn by "evaluating" objective facts/data which are beyond the normal everyday meaning of the word distinction. So when I say "...that which arises by inferring evaluative conclusions from purely factual premises in violation of fact-value distinction", I am saying that the lawyer is evaluating facts of a scientific nature that do not relate directly to our everyday world and our everyday use of the word "distinction", and this is in violation of the fact-value distinction.
A fact-value distinction is the distinction between what “is” in a scientific sense, and what “is” by way of common consensus. The name “Naturalistic Fallacy” may relate to the role of natural language here.
Here’s my understanding of Russell’s objection :
The lawyer’s argument is using the word “distinction” in a way that is intended to encompass all aspects of objectivity and subjectivity - i.e fact-value distinction. The fallacy Russell is highlighting arises because in the real world the meaning of the word “distinction” does not encompass all possible aspects of objectivity. It is used in the context of our senses and in this limited context we are clearly able to distinguish things. Our senses have limits, and we understand this when we use the word “distinction”.
For example, if I buy a set of six spoons, then in the everyday-world, from a legal point of view, it is correct for me to say that one spoon is indistinguishable from another. However, I could get out a microscope and identify a small variation in the surface scratching, thus enabling me to distinguish between any two spoons. So the lawyer is saying that because I can make such a distinction, this renders all indistinctions worthless or incoherent - it undermines our claim to be able to clearly distinguish.
With a natural language such as English, the scope of our objectivity and subjectivity is limited by our ability to sense the world around us. We understand the meaning of words such as “distinction” in this limited context. This is the correct legal context, not the more restrictive and formal usage implied by the lawyer’s argument which uses fact-value distinction.
So ignore my previous answer and comments, and treat this edit as a new answer. If you have any further questions, I’m happy to try to answer them.
See this excellent wiki page here for the fact-value distinction. It i critical here, and is related to the Naturalistic Fallacy, though some applications in social sciences have weakened this link.
Are you saying that contrary to Russell's argument, the lawyers infer too much from facts?
I'm saying something slightly different. That Russell argues the lawyers are using too many (scientific) facts to make their implication. These scientific facts are not relevant to everyday use of the word distinction and that using them to undermine it is fallacious because it is changing the everyday meaning of distinction.
What are evaluative conclusions?
Those conclusions drawn by evaluating the facts - in this case the irrelevant, scientific facts that undermine and change our meaning of distinction.