  We first study the properties of the Fuchsian ordinary differential equations
for the three and four-particle contributions $ \chi^{(3)}$ and $ \chi^{(4)}$
of the square lattice Ising model susceptibility. An analysis of some
mathematical properties of these Fuchsian differential equations is sketched.
For instance, we study the factorization properties of the corresponding linear
differential operators, and consider the singularities of the three and
four-particle contributions $ \chi^{(3)}$ and $ \chi^{(4)}$, versus the
singularities of the associated Fuchsian ordinary differential equations, which
actually exhibit new ``Landau-like'' singularities. We sketch the analysis of
the corresponding differential Galois groups. In particular we provide a
simple, but efficient, method to calculate the so-called ``connection
matrices'' (between two neighboring singularities) and deduce the singular
behaviors of $ \chi^{(3)}$ and $ \chi^{(4)}$. We provide a set of comments and
speculations on the Fuchsian ordinary differential equations associated with
the $ n$-particle contributions $ \chi^{(n)}$ and address the problem of the
apparent discrepancy between such a holonomic approach and some scaling results
deduced from a Painlev\'e oriented approach.
