The Trinity is not three gods
Objection: If the Father, Son and Spirit are distinct, why are they not three gods?
Orthodoxy confesses one undivided divine essence in three distinct Persons: Father, Son and Holy Spirit. The distinction is personal, not a division into three beings with separate divine natures or competing wills. Neither are the Persons temporary roles of a single Person. Begin by distinguishing person from nature rather than using an analogy that silently changes the confession.
Evidence, distinctions and limits
Key distinction
One essence does not mean one Person. Three Persons does not mean three independent gods.
Scripture in context
Matthew 28:18–20 · King James Version
Read the full Bible chapter18 And Jesus came and spake unto them, saying, All power is given unto me in heaven and in earth.
19 ¶ Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost:
20 Teaching them to observe all things whatsoever I have commanded you: and, lo, I am with you alway, [even] unto the end of the world. Amen.
Patristic evidence
Concerning the Holy Trinity.
one essence, one divinity, one power, one will, one energy, one beginning, one authority, one dominion, one sovereignty, made known in three perfect subsistences and adored with one adoration, believed in and ministered to by all rational creation, united without confusion and divided without separation (which indeed transcends thought).
Read the complete source paragraph
We believe, then, in One God, one beginning, having no beginning, uncreate, unbegotten, imperishable and immortal, everlasting, infinite, uncircumscribed, boundless, of infinite power, simple, uncompound, incorporeal, without flux, passionless, unchangeable, unalterable, unseen, the fountain of goodness and justice, the light of the mind, inaccessible; a power known by no measure, measurable only by His own will alone (for all things that He wills He can), creator of all created things, seen or unseen, of all the maintainer and preserver, for all the provider, master and lord and king over all, with an endless and immortal kingdom: having no contrary, filling all, by nothing encompassed, but rather Himself the encompasser and maintainer and original possessor of the universe, occupying all essences intact and extending beyond all things, and being separate from all essence as being super-essential and above all things and absolute God, absolute goodness, and absolute fulness: determining all sovereignties and ranks, being placed above all sovereignty and rank, above essence and life and word and thought: being Himself very light and goodness and life and essence, inasmuch as He does not derive His being from another, that is to say, of those things that exist: but being Himself the fountain of being to all that is, of life to the living, of reason to those that have reason; to all the cause of all good: perceiving all things even before they have become: one essence, one divinity, one power, one will, one energy, one beginning, one authority, one dominion, one sovereignty, made known in three perfect subsistences and adored with one adoration, believed in and ministered to by all rational creation, united without confusion and divided without separation (which indeed transcends thought). (We believe) in Father and Son and Holy Spirit whereinto also we have been baptized. For so our Lord commanded the Apostles to baptize, saying, Baptizing them in the name of the Father, Son, and Holy Spirit.
Do not overclaim
No physical analogy explains divine life exactly. John of Damascus is a later patristic expositor, not an eyewitness to Nicaea.
Clarifying question
Are you objecting to three independent gods, or to personal distinction within the one divine nature?