I would like to do something like this:
- First premise.
- second premise.
- Third premise.
C. Conclusion
(I can't even do it in this comment box)
As Werner said (two minutes ago) in the comment:

\documentclass{article}
\usepackage{enumitem}
\begin{document}
\begin{enumerate}
\item First premise.
\item second premise.
\item Third premise.
\item[C.] Conclusion
\end{enumerate}
\end{document}
Two patterns for presenting arguments in standard form. The first is the one I tend to use, where the conclusion is also numbered. The second uses the 'C.' marker shown in your example. Both use the infer environment, defined in the preamble.
\documentclass{article}
\usepackage{enumitem,expdlist,setspace}
\newlist{inferenum}{enumerate}{10}
\setlist[inferenum]{label={\arabic*.},ref={\arabic*},partopsep=0pt,topsep=0pt}
\makeatletter
% %:infer (standard form)
\let\premise\item
\let\conc\item
\def\conclusion{\item[C.]}
\newlength{\trythis}
\setlength{\trythis}{\parindent}
\newcommand{\inferline}{}
\newenvironment{infer}%
{%
\pagebreak[3]%
\begin{singlespacing}%
\vspace{0pt\@plus\baselineskip}%
\renewcommand{\listpartsep}{-.5\baselineskip}%
\begin{inferenum}%
\setlength{\itemsep}{.25\baselineskip}%
\setlength{\parsep}{0pt}%
\renewcommand{\inferline}{\listpart{\hspace{\trythis}\rule{25mm}{0.5pt}}}%
}{%
\end{inferenum}%
\vspace{1\baselineskip\@plus\baselineskip}%
\end{singlespacing}%
}
\makeatother
\begin{document}
\begin{infer}
\premise First premise.
\premise Second premise.
\premise Third premise.
\inferline
\conc Conclusion.
\end{infer}
\begin{infer}
\premise First premise.
\premise Second premise.
\premise Third premise.
\conclusion Conclusion.
\end{infer}
\end{document}

enumicounter? If so, yes, this is possible. Or do you mean the label? – Nov 27 '14 at 20:43\item[C.]. – Werner Nov 27 '14 at 20:45enumeratecounter which contains both letters and numbers? and Something likeenumerate, but with custom numbers at each\item. – Werner Nov 27 '14 at 20:46