I meant; I'm not sure how you can circumvent this behaviour ;)

I'm not sure if that is really necessary in the Wolfram Language;

if you just have a function definitions like:

f[x_] := x^2

and you try to evaluate f[2,3] or f[1,2,3] or f[], it will just remain unevaluated; i.e. it automatically checks if the number of arguments matches...

A more in-depth version would be something like:

ClearAll[Arities]
Arities[g_]:=Module[{dv,bl,blns,bls,opts,num},
    dv=DownValues[g];
    dv=dv[[All,1]];
    bl=Count[#,Verbatim[Blank[]],\[Infinity]]&/@dv;
    bls=Count[#,Verbatim[BlankSequence[]],\[Infinity]]&/@dv;
    blns=Count[#,Verbatim[BlankNullSequence[]],\[Infinity]]&/@dv;
    opts=Count[#,Verbatim[Optional][_,_],\[Infinity]]&/@dv;
    num=MapThread[#1+If[#2>0,#2 {1,\[Infinity]},0]+If[#3>0, #3{0,\[Infinity]},0]-#4{1,0}&,{bl,bls,blns,opts}];
    {dv,bl,bls,blns,opts,num}
]

ClearAll[F]
F[x_, y_, z_, f_, g_: 2, x2_: 3] := 14
F[x_, y_, z_, f_, g_: 2] := 14
F[x_, z_, f_, y___] := 14
F[x_, z_, y__] := 14
F[x_, y_] := 14
F[x_] := 23
F[] := 12

Arities[F] // Transpose // Grid

returns:

Which is a list of Definition, # of Blanks, # of BlankSequences, # of BlankNullSequenced, # of optional arguments, and range of number of arguments.

May I ask why you need the arities of the function? I can't really think of a use in 'normal' calculations...

Thank you so much Sanders, for your much appreciated help. Being quite new to the language, I am not that familiar with the notion of DownValues... or UpValues for that matter. I will have check the documentations.

Again, thank you.