In GNU’s parse-datetime.y, or as it used to be called, getdate.y, the second ordinal is commented out. I guess for English ambiguity reasons.
{ "THIS", tORDINAL, 0 },
{ "NEXT", tORDINAL, 1 },
{ "FIRST", tORDINAL, 1 },
/*{ "SECOND", tORDINAL, 2 }, */
{ "THIRD", tORDINAL, 3 },
{ "FOURTH", tORDINAL, 4 },
{ "FIFTH", tORDINAL, 5 },
This leads to weird things.
ellen% date --date "first day"
date --date "first day"
Sat 04 Jun 2022 10:29:20 AM CEST
ellen% date --date "second day"
date --date "second day"
Sat 04 Jun 2022 10:29:33 AM CEST
ellen% date --date "third day"
date --date "third day"
Mon 06 Jun 2022 10:29:40 AM CEST
ellen% date --date "fourth day"
date --date "fourth day"
Tue 07 Jun 2022 10:29:48 AM CEST