The concept of “person” has to be massaged a lot by Trinitarians; Latter-day Saints are in an enviable position of being able to use the term “person” to each member of the Godhead and use the term in the proper sense of the word; many Trinitarians, especially those who are not “Social Trinitarians” like Richard Swinburne, have to engage in linguistic gymnastics (similar to the biblical and mental gymnastics they are forced to engage in to prop up their man-made doctrine). As one apologist wrote in response to Socinianism:
Trinitarian theologians have regularly stipulated that they are using the term person analogically. That is, Trinitarian theology refers to the Father, Son, and Holy Spirit as "three persons" in a special, limited use of the term person to denote what distinguishes one from the other two. To put the matter another way, to say that the Father and the Son are two persons is a way of saying that the Father is not the Son.
To support this utter nonsense, he appeals to allegedly similar “mysteries” or “paradoxes” in the Bible:
An obvious retort is that there is no need for such difficulties if the Bible does not teach such paradoxical claims in the first place. This is precisely where the issue must be decided. If the Bible teaches that God is love and yet not subject to changeable emotions, or that God has all knowledge but never learns anything, or that God is omnipresent but physically located nowhere, we must change our assumptions about what is metaphysically possible to fit what God has revealed about himself. The same principle applies to the doctrine of the Trinity: If it teaches that there is one God, that the Father, Son, and Holy Spirit are each this God, and yet distinguishes among these three in a personal way, then we must abandon the assumption that a single divine being (God) could only be a unitarian (one-person) being.
Let us focus on issues relating to God's knowledge. Examples of God’s contingent foreknowledge are part and parcel of the biblical text. For instance, 1 Sam 23:1-4 records one of the clearest instances: David’s free-will decision, based on the contingencies that God gives him, prevents the occurrence of a harmful event foreseen by God.
Many critics will appeal to texts such as Mal 3:6 to the effect that God does not change his mind, and, furthermore, such texts that speak of God changing His mind (e.g., Gen 6:6) are to be relegated as mere “anthropomorphisms.” Notwithstanding, such an approach is based on eisegesis. The context of Mal 3:6 specifies that God’s unchangeability refers only to His unchanging character to forgive if the sinner repents, not that God cannot change His mind about previous decisions or about contingencies that arise in accordance with man’s free-will decisions (cf. Jer 18:7-10).
Other passages which indicate that God “does not change” (e.g., Num 23:19; 1 Sam 15:29; Psa 110:4; Jas 1:17) refer only to God’s inability to lie, take back an oath He made, tempt one to sin, or reverse decisions based on a capricious whim, since these would be adverse to His divine character (see passages where God promises to change His mind if the future free-will actions of man resulting in their repentance--Zech 1:3; Mal 3:7; 1 Tim 2:4; 2 Pet 3:9).
Exo 32-33 is a very potent example of (1) God changing his mind and (2) God’s personal nature. Let us look at it in point by point format:
1. God determines to destroy all of Israel for worshipping the golden calf.
2. Moses pleads with God to relent, reiterating the promise to Abraham and the potential mockery from Egypt.
3. God rescinds His threat to destroy all of Israel, yet punishes the leading perpetrators.
4. Moses spends 40 days prostrate and fasting to appease God for Israel’s sin.
5. Although temporarily appeased, God refuses to go with the Israelites through the desert, because they are so “stiff-necked” he “might destroy them on the way.”
6. Moses pleads again with God to change His mind.
7. God changes His mind and decides to go with them.
8. God then remarks on the intimate relationship He has with Moses as the basis of His decision to change His mind.
9. God confirms this intimate relationship by showing Moses part of His actual appearance.
For a book-length treatment of the concept of "person," including papers from Trinitarians (e.g., Brian Leftow), see Persons: Human and Divine (Oxford University Press, 2007), eds. Peter Van Inwagen and Dean Zimmerman.