Identity Transitivity & Trinitarian Distinction
Question #13: Does the transitive nature of identity, as applied in classical metaphysics, imply (if the Father is God and the Son is God) that Father = Son, undermining the Church’s dogmatic insistence on Trinitarian distinction (DS 804)?
The concern about the transitive nature of identity–“if A = B and B = C, then A = C”–often arises when comparing statements like “The Father is God” and “The Son is God,” which might suggest “The Father = The Son.” At face value, this inference appears to conflict with the Church’s Trinitarian doctrine (DS 804) that the Father and Son are truly distinct Persons. However, classical Catholic theology clarifies why these claims do not yield a contradiction, and why applying modern, post-Leibniz identity theory can sometimes be anachronistic when interpreting historical theology.
1. Different Senses of Identity
In classical metaphysics, identity is indeed transitive when every term refers univocally to the same reality in the same respect. But in Trinitarian theology, the statement “The Father is God” (likewise “The Son is God”) operates differently. It is shorthand for:
• “The Father fully possesses the one divine essence,” and
• “The Son fully possesses the same one divine essence,”
yet the Father and the Son remain distinct in relational identity. Being “God” refers to possessing the divine nature wholly, whereas being “Father” or “Son” refers to a particular relational mode. Thus, “Father is God” does not automatically imply “Father is numerically identical to the Son.”
2. Distinguishing Person from Essence
Church teaching maintains that God’s essence is one and indivisible, yet Father, Son, and Holy Spirit are distinguished by relationships of origin (the Father begets, the Son is begotten, the Spirit proceeds). From a Thomistic viewpoint, each Person is the divine essence–without partition–and is distinct by virtue of how that one essence is “expressed” or “possessed.” Hence:
• Father is God means “The Person we call Father is fully the divine essence in the Father’s relational mode (unbegotten).”
• Son is God means “The Person we call Son is fully the divine essence in the Son’s relational mode (begotten).”
Because these modes are different, it does not follow that “Father = Son.” Their distinction remains personal and relational, not a division of the essence.
3. Non-Univocal Identity Statements
In classical logic, the transitive property applies if “A = B” and “B = C” refer to exactly the same sense of “=.” Here, we have two distinct levels:
• Person–Essence identity: “The Father is the divine essence” and “The Son is the divine essence.”
• Person–Person distinction: “Father ≠ Son.”
The Church carefully qualifies these identity statements so that they do not collapse into “Father = Son.” Instead, we end up with:
1. Father = God (as essence),
2. Son = God (as essence),
3. Father ≠ Son (relational distinction).
No logical contradiction arises because (1) and (2) are about person-to-essence identity, while (3) describes how each Person relates distinctly to that one essence.
4. Preserving Church Dogma–and Addressing Modern Identity Theory
Thus, Catholic teaching upholds DS 804 on the real distinction of Persons. Each Person is truly God; each wholly is the divine nature. Yet the Father is not the Son. This is not an evasion of logic but a clarification of what exactly is meant by “being God” vs. “being the Father” or “being the Son.”
Moreover, modern identity theory–often rooted in Leibniz’s Law (the Indiscernibility of Identicals)–emerged long after the early Church Fathers and Scholastics formulated Trinitarian doctrine. Interpreting patristic or medieval sources through strictly post-Leibniz lenses can be anachronistic. The Fathers and Aquinas never equated “sharing the divine essence” with “numerical identity” in the strict modern sense. They worked with Aristotelian/relational categories, focusing on how one essence can be “possessed” differently by subsistent relations. Furthermore, contemporary developments in logic, physics, and the philosophy of mind have cast doubt on whether identity laws must always be applied in a simplistic, univocal manner–suggesting a more nuanced approach might actually better reflect classical Trinitarian distinctions.
(As a side note, some interpreters suggest that over-reliance on Leibniz’s principle of the Identity of Indiscernibles can appear dated and passé when viewed through contemporary philosophical lenses like I have. In particular, strictly modern concepts of identity are anachronistic if retroactively applied to ancient or historic Christian theological contexts. For instance, Jean-Luc Marion, a phenomenologist I’m influenced by, does not appear to engage Leibniz’s framework directly; his approach focuses on how phenomena themselves confer identity in a way that can transcend purely analytical treatments. In my opinion, the broader philosophical and theological landscape has evolved in such a way that most now adopt methodologies and concepts of identity less bound by Leibniz’s classical formulations. I actually did a survey of the metaphysics literature on this subject once. As far as I can tell the field is pluralistic and not dogmatically committed to Leibniz anymore, not by a long shot. For what it’s worth (zero, I know).)
Hence, from the-Catholic-Church’s vantage point, as far as I understand it, the transitive property does not force “Father = Son” because the statement “Father is God” and “Son is God” is not an assertion of strict numeric identity in the modern sense. Rather, it confesses that both Persons fully share the one divine essence, while remaining distinct as Persons by eternal relational modes.
(see questions #11, #14 for more)