Modus Ponens: why it should not work The scenario I'm analyzing is the following:
I have the set of clauses
$${ ( \neg A \Rightarrow B ),\, ( B \Rightarrow A ),\, ( A \Rightarrow ( C \wedge D ) )  }$$
and I have to prove the proposition 
$$(A \wedge C \wedge D)$$
 using only Modus Ponens if possible. Well, the solution says me that just using MP the proposition is not possible to be proved. I wonder why it is not possible. I mean are there precise conditions or it is just because I have no "facts" (for example as $A$ or $\neg A$ that would mean having propositions with an exact value) in my set of clauses and so I cannot infer anything?
 A: Basically, yes.
Modus Ponens is the rule of inference $\{X, X\to Y\} \vdash Y$ .   Without anything pairs of the form $X$ and $X\to Y$ you have nothing on which to use the rule.
Note: it is possible to infer the conclusion from those clauses; just not with only modus ponens to work with.

If you assume $\lnot A$ then using modus ponens on that and the first clause, and modus tollens with it and the second clause, will provide contradictory conclusions.   Hence inferring $\lnot\lnot A$, which will infer $A$ (unless you are restricted to intuitionalistic or constructive proofs).   If you prove $A$ then using modus ponens with that and the third clause proves the rest.
A: I think because you need a proof from contradiction: 
Suppose $\lnot A$. Then MP gives $B$ by the first clause. Then MP again gives $A$ by the second clause. But we assume $\lnot A$, so we have a contradiction.
So $\lnot \lnot A$ holds, and then if we have the rule of Tertium non datur (excluded third), we have that $A$ holds, and then the third clause by MP gives $C \land D$, so in total (but this uses the a rule to introduce $\land$!) we know that $A \land C \land D$.
But we need at least two extra rules as well, and the excluded third. So in an intuitionistic logic (which does have MP, and the intro $\land$ rule) we could never prove $A \land C \land D$, but only $\lnot \lnot A$, using a $\lnot$-introduction rule. 
