add-type fails to load an assembly, but why?

I am trying to call method Path.GetFileNameWithoutExtension ( ie - [Path]::GetFileNameWithoutExtension( ... ) ).

However, Powershell reports that the assembly containing the type is not loaded: 'Unable to find type [Path]: make sure that the assembly containing this type is loaded.'

So I try to load the assembly containing the Path class (according to msdn, the Path is in the System.IO namespace, but in the mscorlib.dll assembly). I attempt to load the assembly as follows:

add-type -AssemblyName "mscorlib"

Nothing is returned so I retry my method call again, but the same error is reported:

Unable to find type [Path]: make sure that the assembly containing this type is loaded.

So, what am I doing wrong? This is quite confusing because when you search for this error, the fix is to use add-type, but the examples quoted look like they've specified a namespace, not an assembly.

PS, I'm doing this all in a powershell console interactively.

Appreciate a fix to this silly problem, thanks.