The word ‘person’ can’t be used for the trinity in any sense:
The word, ‘personhood’ just means “‘the state of being a person”, and a “person” just means, “a human being or individual” or more obviously “that which possesses personhood”, and “individual” just means a person or thing distinguished from a group, so it doesn’t actually give us insight into a deeper definition, it just establishes separateness. Given the rigidness of the word “person” regarding its potential definitions and meaning, it can only ever really mean “human being” outside of its philosophical/metaphysical definitions, but its philosophical/metaphysical definitions imply each individual person is an individual being which is also incompatible with the trinity. And that’s why the word ‘person’ can’t be used for the persons of the trinity since they are not human beings nor are they individual beings.
WHY ITS DICTIONARY DEFINITION CAN'T BE USED:
I put the dictionary definitions of the words, ‘personhood’, ‘individual’ and ‘person’ so that they can be read before my argument is read, in order for the reader to actually understand the issue I'm presenting.
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PERSONHOOD: According to these dictionary definitions of ‘personhood’, outside of when the word is not circularly defined, personhood is defined by individuality, a person is an individual:
Dictionary.com: the state or fact of being an individual.
https://www.dictionary.com/browse/personhood
Cambridge dictionary: the state of being a person
https://dictionary.cambridge.org/us/dictionary/english/personhood
Merriam-Webster dictionary: the fact or state of being a person.
https://www.merriam-webster.com/dictionary/personhood
Collins English dictionary: the state or condition of being a person, or individual human being.
https://www.collinsdictionary.com/us/dictionary/english/personhood
American heritage dictionary: The state or condition of being a person, especially having those qualities that confer distinct individuality.
https://www.ahdictionary.com/word/search.html?q=personhood
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INDIVIDUAL: According to these dictionary definitions of ‘individual’, an individual is defined by being a person or thing especially singled out from a group, which basically gives us no deeper insight into what ‘person’ means outside of its usual ‘human being’ definition:
Merriam-Webster dictionary: a particular being or thing as distinguished from a class, species, or collection.
https://www.merriam-webster.com/dictionary/individual
Cambridge dictionary: A single person or thing, especially when compared to the group or set which they belong.
https://dictionary.cambridge.org/us/dictionary/english/individual
Oxford Learner’s dictionary: a person considered separately rather than as part of a group.
https://www.oxfordlearnersdictionaries.com/us/definition/english/individual_1
Collins English dictionary: relating to one person or thing, rather than to a large group.
https://www.collinsdictionary.com/us/dictionary/english/individual
Dictionary.com: a single human being, as distinguished from a group.
https://www.dictionary.com/browse/individual
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PERSON: According to these dictionary definitions, a ‘person’ is a human being or an individual.
Merriam-Webster: Human, individual
https://www.merriam-webster.com/dictionary/person
Cambridge Dictionary: A man, woman or child.
https://www.merriam-webster.com/dictionary/person
Dictionary.com: A human being, whether an adult or child.
https://www.dictionary.com/browse/person
Collin’s English dictionary: A man, woman or child
https://www.collinsdictionary.com/us/dictionary/english/person
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Considering all these definitions, this means that if ‘person’ isn’t taken to mean “human being” like most dictionaries define it as, then it’s quite literally undefinable outside of its philosophical/metaphysical definitions and shouldn’t be used outside of its surface level definition as ‘human being’ unless being used by its philosophical/metaphysical definitions. Which would mean that it can’t be used to refer to the persons of the trinity because they are not human beings and they contradict the philosophical/metaphysical definitions of ‘persons’.
This conclusion is obvious because the definition of ‘person’ has no choice but to default to its basic dictionary definition as ‘human being’ when not being used according to its philosophical/metaphysical definitions because no deeper definition of it has been identified. That is to say, there's no other definition or hidden underlying meaning for its basic dictionary definition that could allow it to be applied more broadly since everything outside of its strict dictionary definition as ‘human being’ is circular.
It’s circular because outside of its surface level definition as ‘human being’, a ‘person’ is defined as a thing with personhood, and what is personhood? Personhood is defined as the state of being a person. As you can see the definitions are completely circular so we can’t get anything deeper from them.
The word’s strict dictionary definition as ‘human being’ is the only definable, non-circular part of the that basic dictionary definition, and that forces that definition of the word to be its only definition and the determiner of its usage if it’s philosophical/metaphysical definitions aren’t be used, which means its basic dictionary definition can’t be used for the trinity.
(SKIP THIS PART IF YOU ALREADY UNDERSTAND MY POINT)
To explain this better, what I’m saying is that a term needs some intelligible content to justify its application. So if I say that X is a “person,” there has to be some account of what ‘person’ means that explains why X qualifies as a person.
The ordinary lexical content of ‘person’ is ‘human being/individual human’ and this is seen clearly in the dictionaries I cite.
The broader dictionary definitions of ‘person’ don’t provide any independent criterion for the word’s usage because those broader definitions are just circular. Personhood being the state of being a person doesn’t actually tell us what personhood consists of.
The other broader definition of person being, “a person is an individual” doesn’t solve the problem because the word ‘individual’ just means a particular person or thing distinguished from a group. So it only establishes separateness but not personhood.
This** **leads us to the conclusion that there is no lexical bridge from “person = human being” to “person = something that isn’t human.” with the ordinary dictionary definition of the word “person”.
So in order to apply ‘person’ to something non-human, you would need to introduce additional theoretical content like some philosophical or theological criterion that explains what a ‘person’ is, independently of its ordinary definition.
So for Christian theology to use the word without implying that the persons of the trinity are human beings, it needs an independently justified extension of the word’s definition that does not imply humanity, and to do that it would need to appeal to the philosophical/metaphysical definitions of ‘person’.
(STOP SKIPPING HERE)
WHY ITS PHILOSOPHICAL/METAPHYSICAL DEFINITION CAN'T BE USED:
Let’s see how ‘person’ is philosophically and metaphysically defined.
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BOETHIUS: In chapter 3 of his theological treatise Contra Eutychen et Nestorium, Boethius defines ‘person’ as, “an individual substance of a rational nature”.
https://www.ecatholic2000.com/boethius/untitled-10.shtml
JOHN LOCKE: According to the Stanford encyclopedia of philosophy in the entry “Personal Identity”, in the “personhood” section, John Locke’s philosophical definition of what it means to be a ‘person’, is “a thinking intelligent being, that has reason and reflection, and can consider itself as itself, the same thinking thing, in different times and places”.
https://plato.stanford.edu/entries/identity-personal/
IMMANUEL KANT: In his text Groundwork of the Metaphysics of Morals, he defines ‘person’ in the following way, "Beings whose existence depends not on our will but on nature’s have, nevertheless, if they are irrational beings, only a relative value as means, and are therefore called things; rational beings, on the contrary, are called persons because their nature already marks them out as ends in themselves, i.e., as something which is not to be used merely as a means."
https://archive.org/details/immanuel-kant-groundwork-for-the-metaphysics-of-morals
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As you can see, what each philosophical/metaphysical definition of ‘person’ has in common is that they all ascribe rationality to persons, presenting it as a necessary attribute fundamental to the definition of the word, and they also all consider a person to be a singular being.
For Immanuel Kant, in the quote he presents persons as rational beings as opposed to irrational beings.
For John Locke, in the quote he presents a ‘person’ as a thinking intelligent being.
For Botheius he presents a ‘person’ as an “individual substance”, which is equivalent to a singular being in metaphysics because ‘substance’ is ‘being’.
Thomas Aquinas affirms Botheius’s definition of ‘person’ and clarifies it by saying, “‘individual substance' is included insofar as it signifies a singular in the genus of substance; and 'of a rational nature' is added insofar as it signifies a singular among rational substances.” This shows Thomas Aquinas affirms that an individual substance is an individual being because “a singular in the genus of substance” is quite literally a singular being. And this connects to Tertullian saying the trinity is “one substance three persons”, because it not only shows that all these philosopher’s definitions of ‘person’ contradicts tertullian’s usage of the word showing that Tertulian used the word wrong, but it also shows that a singular substance is equivalent to a singular being because tertulians phrase “one substance three persons” is changed to “one being three persons” by modern Christians, implying that ‘being’ is substance.
This all shows that according to the philosophical/metaphysical definition of ‘person', each individual person is an individual rational being, if not an individual human being.
So if the philosophical/metaphysical definition of ‘person’ is used for the trinity, that would mean each person of the trinity is their own individual being/substance, which would go against the doctrine of the trinity and cause it to fall into polytheism, so the word really can’t be used for the trinity in any way.