Permanently change symbol of itemize

Question

I am aware one can locally change the symbol of itemize by adding an option to \item, like:

\begin{itemize}
\item[$\uparrow$] some item
\end{itemize}

Is there a way to set permanently the symbol of itemize, for instance by redefining a command?

Something like

\setitemizesymbol{$\uparrow$]
\begin{itemize}
\item some item
\end{itemize}

Answer 1

It's easy if you load the enumitem package, adding this code in your preamble:

\setlist[itemize,1]{label=$\uparrow$}

The number 1 (second argument) denotes the level of the environment. Here, it is not nested in another itemize.

Answer 2

For the four supported levels of nesting, the labels output by the itemize environment of the LaTeX kernel are produced by \labelitemi, \labelitemii, \labelitemiii and \labelitemiv. You can redefine these macros:

\documentclass{article}
\renewcommand{\labelitemi}{\labelitemfont\textasteriskcentered}
\renewcommand{\labelitemii}{\labelitemfont\textendash}
\renewcommand{\labelitemiii}{\labelitemfont\textbf{\textdagger}}
\renewcommand{\labelitemiv}{%
  \labelitemfont\textbf{:\kern 1.5pt -\raisebox{-0.1ex}[0pt][0pt]{)}}%
}
\begin{document}
\begin{itemize}
\item foo1
  \begin{itemize}
  \item foo2
  \item bar2
    \begin{itemize}
    \item foo3
    \item bar3
    \item baz3
      \begin{itemize}
      \item foo4
      \item bar4
      \item baz4
      \end{itemize}
    \end{itemize}
  \end{itemize}
\item bar1
\item baz1
\end{itemize}
\end{document}