[A.J.Armitage]

So I ask again: who determined the Canon? And on what basis?

God did, on the basis of which writtings He had inspired.

Could the Church put Thomas in the Canon? Why or why not? If it does, would Thomas gain in authority, or would it always have had this authority?

[Mrs. Don-o]

So I ask again: who determined the Canon? And on what basis?
--"God did, on the basis of which writtings He had inspired."

Absolutely. But when was it decided that the "Gospel of Thomas," for instance, didn't make the cut? When, where, and by whom?

Could the Church put Thomas in the Canon?

No.

Why or why not?

Because it was never used Liturgically: Lex orandi, lex credendi. Nor was it referenced as authoritative by the Ante-Nicene Fathers, or received as Scripture in Orthodox/Catholic Churches. That's the basis the Ecumenical Councils used, to determine the authenticity of Scriptures: liturgical, patristic, and ecclesial Tradition. The spurious texts were not in the Tradition.

If it does, would Thomas gain in authority, or would it always have had this authority?

No other books can be added to or subtracted from the Canon of Scripture. This is on the authority of the Church, "the Pillar and the Foundation of Truth." 1 Timothy 3:15.

P.S. to Kolokotronis: from an Orthodox point of view, what say ye?