Logic is a broad field, and there is lots of discussion around it. If the Wiki article was too long, then going to Princeton was a good idea.
IMHO my explanations have been very clear, with clear examples.
Why do I get the sense I am being addressed by the
Black Knight? I suggest you look up "coward"... I dont think it applies.
It is telling that you take what is the fifth definition for logic from the Princeton dictionary.
First off, you do understand that dictionaries concern themselves with common usage?
People use the term this way, rarely, which is why it is the fifth definition.
The first four definitions given at your Princeton link are:

logic (the branch of philosophy that analyzes inference)

logic (reasoned and reasonable judgment) "it made a certain kind of logic"

logic (the principles that guide reasoning within a given field or situation) "economic logic requires it"; "by the logic of war"

logic, logical system, system of logic (a system of reasoning)
I submit that the fifth definition involves precisely the anthropomorphism which is the subject of this entire argument. Yes people use the term that way... rarely... and they are being anthropomorphic about machines when they do that.
See how definitions can be twisted and get you in hot water?
Exactly my point. You have failed to supply the precise definition of 'logic' which you prefer to use for this conversation (or was your link to the Wikipedia entry, a source known for contraversial and often incorrect information, meant to indicate the definition you require?).
My demonstration was simply to show that the facts change depending on the definitions used. In common parlance, logic is a process of manipulating data according to strict principles (for example, no true statement can be false, two opposing statements cannot both be true, etc.). If you are, in fact, indicating that no machine is capable of philosophy, that would be a different argument. My rebuttal to said argument would be considerably weaker, something along the lines of, 'not yet' or 'brains are meat machines, ergo you are wrong'. But the indicated question was whether or not logic and materialism were incompatible. If we are using a version of 'logic' that relates it directly to 'philosophy', I submit that there is not as yet sufficient data to answer such a question. We have not yet constructed sufficiently complex machines to mirror the complexity of the human brain, nor yet come to understand the brain sufficiently.
What you are essentially positing is that the human brain is not 'merely a machine' - this indicates an unspoken premise that materialism is already false. Hence, your argument becomes circular.
In fact, the statement which apparently started this thread is, simply, "You claim you are interested in logic, but if materialism is true then there is no such thing as logic. The thought that ends all thought... "
Since this statement includes no definition for logic, but an all-inclusive predicator (no such thing as), I submit that, through careless wording, you have spoken erroneously.
Aside from that, though, there is no reason why, under materialism, that modes of data processing are impossible; the comments about transistors and computers is simply to demonstrate that data processing IS possible, and that logic is nothing more than another mode of data processing - one which machines are, in fact, capable of (Or, to extend this into the philosophical definition you prefer, logic is a mode of data processing machines may one day be capable of, and that some (not all) human minds are also capable of).
I further submit that the use of 'logic' in the other definitions is not as rare among the common populace as you would suggest; in fact, the 'common man' would more likely consider logic to be a process of thought, not a philosophical branch involving inference.
(Too many Trekkers out there, you know...)
Now, if you'd care to state your premise, definitions, and arguments, we can probably get somewhere. However, at this point, I see a shoddy statement made off-handedly by someone who won't even apply logic as he prefers it defined.
Let's start with your initial statement:
1) IF materialism is true,
2) THEN there is no such thing as 'logic'.
As stated, this argument is completely vacuous and lacking in detail. How about we flush it out? Start with premise a) Materialism is true. Then give us the chain of arguments that leads to z) Logic does not exist.