Modalism denies the distinctions between the three Persons of the Trinity, so that God is presented as, not a Trinity at all, but rather a monad with three names. Modalism can be expressed chronologically (the Father became incarnate as the Son) or functionally (the names describe activities like Creator, Redeemer, Sustainer), but either way, in modalism the Son IS the Father in disguise, which ultimately denies the real humanity of Jesus Christ and the reality of his passion.
Links
For more information on Irenaeus of Lyons, listen to Mike Aquilina's Episode 10: https://www.catholicculture.org/commentary/irenaeus-lyon-putting-smack-down-on-heresy/
To read Irenaeus of Lyons' Demonstration of the Apostolic Teaching: https://www.tertullian.org/fathers/irenaeus_02_proof.htm
For more information on Tertullian, listen to Mike Aquilina's Episode 13: https://www.catholicculture.org/commentary/tertullian-and-theology-sarcasm/
and Episode 14: https://www.catholicculture.org/commentary/tertullian-man-who-forged-words-and-invented-freedoms/
To read Tertullian's Against Praxeas: https://www.catholicculture.org/culture/library/fathers/view.cfm?recnum=1670&repos=8&subrepos=0&searchid=2368544
For more information on Hippolytus, listen to Mike Aquilina's Episode 17: https://www.catholicculture.org/commentary/ep-17the-long-strange-trip-hippolytus-rome/
To read Hippolytus' Refutation of All Heresies: https://www.catholicculture.org/culture/library/fathers/view.cfm?recnum=1706&repos=8&subrepos=0&searchid=2371969
For more detail on the heresy of modalism, and an introduction to Irenaeus, Tertullian, Hippolytus, and Novatian, see the books:
Reading the Church Fathers: A History of the Early Church and the Development of Doctrine: https://sophiainstitute.com/product/reading-the-church-fathers/
and Trinity 101: Father, Son, Holy Spirit: https://www.liguori.org/trinity-101.html
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Dr. Papandrea's Homepage: http://www.jimpapandrea.com
Theme Music: Gaudeamus (Introit for the Feast of All Saints), sung by Jeff Ostrowski. Courtesy of Corpus Christi Watershed: https://www.ccwatershed.org/