Logic is circular therefore it is invalid

This is an argument I have encountered several times and I always find it difficult to respond to.

P1: Logic is required to justify logic

P2: Using logic to justify logic is circular reasoning

P3: Circular reasoning is invalid

C: Logic is invalid (or 'broken')

Usually, the person making the argument then goes on to claim that faith is no worse than logic since logic is invalid/broken. For example: "You can't justify logic, so why do I have to justify my belief in XYZ?"

The obvious rebuttal would be to point out that they already presupposed logic in order to refute logic. However, one counter argument is that the only reason they used logic is to show that it is a self-refuting system. 

Any advice on how to approach these sorts of arguments? Is it even worth arguing with someone that rejects logic from the start?

Thanks

Ironically they are using logic to try and invalidate logic. 

It's worth pointing out that circular reasoning is only problematic when the circles are insufficiently large to exchange meaningful information. This is because arguably, all arguments are circular, as they all converge on first principles or axioms. If the circle is big enough, though, it will attempt to adequately justify its conclusions with evidenced, supporting premises.

In addition, as Jason Mathias points out, anyone who says this is using logic to try and invalidate logic - this is the stolen concept fallacy.

Further, the argument itself can be made circular:

Logic is required to justify logic -> Using logic to justify logic is circular reasoning -> circular reasoning is invalid -> logic is invalid, because -> logic is required to justify logic...

When they say that logic is required to justify logic you could ask why it's required. I'm not sure what the answer to that question would be.

Yes, this is the Fallacy of the Stolen concept, which I define somewhat differently than Bo. I define a concept as “stolen” when one asserts a concept while denying or ignoring its epistemological or genetic roots. 

Can one posit a concept while denying the concept’s prior roots? Logically, of course, one cannot do this. For example, one cannot discuss the concept of an orphan while denying the concept of parents.

But there are other errors involved here. 

Understanding of an axiom and the definition of logic. For simplification, my definition of an axiom is a proposition that defeats its opponents because they have to use it in any attempt to deny it. 

Logic itself is the focus of the discussion. Therefore, it must be explicitly defined.  

The term “logic” is used quite often, but usually not in its technical sense. Logic, strictly speaking, is the science or study of how to evaluate arguments and reasoning. Logic is what allows us to distinguish correct reasoning from poor reasoning. Logic is important because it helps us reason correctly —  without correct reasoning, we don’t have a viable means for knowing the truth or arriving at sound beliefs. Restated, and as a good working definition, I say logic is the correct identification of the facts of reality.

So, applied here, to claim “Logic is required to justify logic” defeats itself because the proponent must use it in any attempt to deny it. 

While logic appears to be concerned solely with the process of reasoning, it is ultimately the result of that reasoning which is the purpose of reason. For example, logic allows you to learn that arsenic and soda is different from a soft drink, though both taste sweet.

I don't think that logic is required to justify logic. As somebody already said (what I remember they said), axioms are valid to use in systems. The branch of study is the system and the axioms. 

Example: The associative law of addition is needed to perform arithmetic. Would we really say that mathematics is required to justify the associative law of addition? 

I think that there's a play of words with premise 1. By requiring logic to justify logic, what we mean is that rules of inference are needed to perform deductions. Would we really say that logic is required to justify the rules of inference? 

Then there is a confusion between the name of the branch of study and the axioms they're used to perform the operations that the system is meant to allow. 

Example: Modus ponens is a rule of inference found in logic. Therefore, modus ponens is logic. 

This would be appeal to definition.

1. The dictionary definition of "logic" does not distinguish the branch of study with the rules of inference.

C. Therefore, there is no distinction between the name of the branch with the rules.

Notice how premise 2 depends on premise 1. The reasoning becomes circular only if we insist that the name of the branch is the same as the rules that we use. 

If it is circular reasoning to use logic to justify the logic then so is using faith to justify faith.

This negates both - which might be their intention.

If, however, they are using logic to justify faith, I assume they would be okay with using faith to justify logic.

It would be helpful to know whether, when they refer to logic, they mean,

1. a priori reasoning, independent of experience (deductive)
2. a posteriori reasoning, relying on experience/evidence (inductive)
3. both

If it is purely a priori reasoning then you can appeal to empirical evidence for the efficacy of deductive reasoning.

The problem is that it is impossible to make sense of evidence without using some deduction.

If they are denying the validity of any form of deduction then communication becomes impossible which makes the conversation (quite literally) meaningless.