Parameterized methods are more specific than non-parameterized ones:

julia> g(x) = 1
g (generic function with 1 method)

julia> g{X}(x::X) = 2
g (generic function with 2 methods)

julia> g(4)
2

I don't think there is any way to call the first method of g.

Similarly for several arguments:

julia> h(x,y) = 1
h (generic function with 1 method)

julia> h{X}(x::X,y) = 2
h (generic function with 2 methods)

julia> h{X,Y}(x::X,y::Y) = 3
h (generic function with 3 methods)

julia> h{Y}(x,y::Y) = 4
h (generic function with 4 methods)

julia> h(4,5)
2

One solution is to consider above methods ambiguous and throw MethodError ... is ambiguous. on call. Another solution is to make those method definitions overwrite the previous one. Probably should be in sync with #8974.

X-ref: https://groups.google.com/d/msg/julia-users/-ldkZlbg76Q/pYRNT4eIBAAJ