Is McGee's counterexample to Modus Ponens accepted by the mathematical community? In the mid 1980's Vann McGee proposed a counterexample to Modus Ponens:

(a) If a Republicans will win the election, then if Reagan will not
win, Anderson will win. (b) A Republican will win the election. (c)
So, if Reagan will not win, Anderson will win.

Christian Piller describes it here: "[McGee's] attempt to show that modus ponens is not a valid form of inference - and to show this by the help of a counterexample and not by envisaging an evil demon confusing us - is proof of the ingenuity of a philosopher's ability to doubt."
John MacFarlane here lists two additional statements of the same type:

(a) If that creature is a ﬁsh, then if it has lungs, it is a lungﬁsh.
(b) That creature is a ﬁsh. (c) So, if it has lungs, it is a lungﬁsh.
(a) If Uncle Otto doesn’t ﬁnd gold, then if he strikes it rich, he
will strike it rich by ﬁnding silver. (b) Uncle Otto won’t ﬁnd gold.
(c) So, if Uncle Otto strikes it rich, he will strike it rich by
ﬁnding silver.

Modus Ponens permeates all of mathematics yet the counterexample seems primarily discussed in the philosophical literature. Is it accepted in the mathematical community? Is there a precise, mathematical restatement (eg, in terms of set theory or categorical) - free of subject-matter - that everyone can agree on? Or does it lead to a no-mans land of disputed interpretations?
Recall, proof of the conditional A --> B doesn't require A to be true. But the detachment of B as a true consequence the only follows via Modus Ponens, which requires the antecedent of a conditional to be true.
Lawvere & Rosebrugh write in Sets for Mathematics that substitution, correctly objectified, is composition.
If McGee's counterexample is valid, it would seem that substitutions of the form A --> (B --> C) are a "transitivity trap" so to speak.
 A: Mc Gee's counterexample points one problematic application of classical propositionnal logic to natural language. In general mathematicians are not interested with it because they are happy with classical logic and consider that it gives a correct model of their way to reason. As far as I know, it is not possible to produce the same counterexample applied to mathematical objects. Perhaps it is due to the necessary relations between objects in mathematical sentences.
For those who do not see any interest in this kind of counterexample, I just want to point that the problematic application of classical logic to reasoning in natural language does not interest only philosophers but also computer scientists and many other researchers. This question concerns non-classical logics, a field perhaps not useful for mathematics but important to other areas as Artificial Intelligence.
A: In the first example, it seems like the problem is with an intuition of truth being "high likelihood."  You can't start from 

(a') If a Republican wins, then if Ronald Reagan doesn't win, Anderson will win
  (b') It is highly likely that a Republican will win

and deduce:

(c') If Reagan doesn't win it is highly likely that Anderson will win

That certainly is not a valid statement, even if (a') and (b') are true.  But it also isn't an application of Modus Ponens.
(For those not old enough to remember, in 1980, the US presidential election was between Reagan, a Republican, Carter, a Democrat, and Anderson, a Republican running as an independent.  Anderson was not very likely to win - if Reagan did not win, then it was highly likely that Carter would be the winner.  But, given that a Republican was going to win, if Reagan did not win, it was most likely that Anderson would have won.)
Vann McGee, then, appears to be unaware of the fact (or just playing qwith it) that the truths used in logic are absolute.  Modus Ponens only works if you are careful about your language.  If you are lazy about your language, as in all things, logical deduction is useless.
If you want to deal with degrees of likelihood, you want probability. If you want degrees of truth other than pure "true" and pure "false," you want fuzzy logic.  Modus Ponens fails in these variants of logic, and it is worth exploring how it fails and what sorts of deductions you can do in these spaces, but it is hardly a failure of modus ponens - it is more a failure of imprecise colloquial language.
The lungfish example is actually a different sort of error, fundamentally related to the difference between Propositional Logic, in which the only types are propositions, and First Order Logic, in which you can make propositions about "all" things. In first order logic, you would write:

(a) For any thing, if the thing is a fish, then if the thing has lungs, then the thing is a lungfish.
  (b) This thing is a fish
  (c) Therefore, if this thing has lungs, then this thing is a lungfish.

(c) Is not the same as saying, "For any thing, if the thing has lungs, then the thing is a lungfish," but rather, a statement about a specific thing about which we have some (possibly incomplete) information.
If you start with the statements:

(u) For all X, If X won the election, then X is a Republican.
  (v) Y won the election

You can conclude:

(w) Y is a Republican

But that doesn't mean that (w) is true for all Y, it only means it is true given the statement (v).
One of the frequent flaws in elementary logic is that people think "implication" actually implicitly means "for all cases." (Often it also is taken to imply causality.)  It doesn't.  Implication is always about individual instances.  The only way you get a "for all" added to implication is by explicitly adding that phrase to the sentence. In common language, it often doesn't need to be there.  But the meaning in hard logic of the "P implies Q" is always about an individual instance, and the only way to make it general is by adding a "for all" explicitly to the sentence and adding a variable to the expression.
Modus ponens is a purely Propositional Logic statement.
The symbol $\forall$ is used to represent "For all" in First Order Logic.  What you are trying to do is start with the statements:

(a) $\forall X: P(X)\implies Q(X)$
  (b) $P(Y)$

and conclude:

(c) $\forall Y: Q(Y)$

But that is not how modus ponens of First Order Logic works.  You cannot add back the $\forall$ part of the sentence.  What you can do, from (a), and (b) is conclude:

(a') $P(Y)\implies Q(Y)$ (by the substitution rule for $\forall$)
  (d) $Q(Y)$ (By modus ponens)

$Q(Y)$ is not the same statement as $\forall Y: Q(Y)$. $Q(Y)$ is a conclusion given that you've already stated that you know $P(Y)$ is true.
A: To put it briefly, McGee's "counterexample" is not accepted by the mathematical community because it is not, per se, a statement about mathematics.  Modus ponens certainly holds in the context of logic, with its absolute interpretations of "true" and "false", and the references you give acknowledge that.  But those authors (who are philosophers, not mathematicians) appear to be considering other possible notions of truth, different from those of logic, which they believe may better describe the way humans routinely think, and noting that modus ponens can fail to hold for those.  
Some of those models make sense to describe mathematically, but mathematicians would not confuse those models with plain logical truth, and indeed would probably avoid using the words "true" and "false" to describe anything else.
A: McGee isn't very explicit in his article, but I do not believe he was proposing counterexamples to Modus Ponens as a rule of inference (contra the title of his article).  If that were what we was proposing, he'd have to show that (c) is false when both (a) and (b) are true.  But nowhere in his article is that shown.  Rather, I think his article shows that knowledge/justification is not closed under modus ponens.  This means that we can be justified in believing (a) and (b) and not be justfied in believing (c).  This is certainly an odd feature of Modus Ponens and worth discussing, but it doesn't show it to be formally invalid.  In fact, he so much as says this in his article but he uses 'good grounds for believing' instead of 'justifies'.  Again, even if Modus Ponens does not preserve knowledge or justification, it does not follow that it does not preserve truth (i.e. is invalid).  There is distinction between what is true and what we are justified in believing.  
To answer the question explicity, having studied both math and philosophy, I don't know any academics in either field that reject the validity of Modus Ponens as a rule of inference.  But it is a point of contention as to whether or not knowledge/justification is closed under implication, and McGee seems to provide reasons for thinking that it is not. 
Aside: to the interpretations of McGee that imply philosophers do not know how to use logic, this is definitely mistaken.  Logic is as much a branch of philosophy as it is of mathematics.  
A: It looks to me like McGee is making the following error.
Suppose, for a moment, that $A \to (B \to C)$ is a tautology.
Because of this, we know
$$ A \vdash B \to C$$
which means, among other things, that
$$\mathcal{M} \models A  \quad \text{implies} \quad \mathcal{M} \models B \to C$$
However, McGee seems to have fallen into a trap of some sort, and is concluding
$$ \vdash B \to C$$
which is incorrect.
(the other answer does say this too, but in a more verbose language)
A: The comments here seem to be a bit confused about what McGee was arguing. He's arguing that modus ponens is invalid for the ordinary language conditional (if, then statement). I mean, it's obviously valid for the material conditional (horseshoe statement) in logic and math: that's true by stipulation. (We've stipulated that horseshoe statements have the truth table they have, and modus ponens is obviously truth-preserving for horseshoe statements given those stipulations.)
I think that it's hard to deny that McGee's examples show that modus ponens isn't a universally good "rule of thought" for ordinary language conditionals: that there are cases where we shouldn't reason with ordinary language conditionals using modus ponens. His Republican argument is an instance of ordinary language modus ponens, and it seems very clear that while it was rational to believe the premises, it would have been irrational to accept the conclusion. Hence, ordinary language indicative conditionals are not material conditionals, as is commonly thought, since while modus ponens is a good rule of thought for material conditionals, it is not a good rule of thought for indicative conditionals.
It doesn't immediately follow that modus ponens is invalid (in the sense of being non-truth-preserving), but that does follow given some fairly plausible bridge principles about rationality and truth. Maybe we should give up on those principles rather than the validity of (ordinary language) modus ponens, but that's still an interesting result.
