Simonb That's the thing ... you must demonstrate with the popular major/minor system only - that a diminished third interval is third degree .... with either the major or minor system only.
Go ahead and show how a dim 3 interval is third degree in our popular major/minor scale system.
And no ... you're not allowed to go outside the boundaries ... such as to introduce another scale system that isn't our major/minor scale system ... such as a minor version of our minor scale system.
If all of you cannot show it (third degree) ... then you will know that I'm right ... and you folks ... or the ones that are disagreeing ..... are wrong.
And I did mention it ... it's ok to be wrong. You will just learn from this.
I'm not going to give anyone the 'third degree' if they didn't understand or realise that a dim 3 interval is not a type of third in our major/minor system.