Trinity: Logical Proof or Contradiction

Some of my Evangelical Christian friends have tried to use the following argument to support their belief that God the Father is only a spiritual reality and has not physicality or physical reality. They used the following New Testament scriptures as a kind of logical expression that they solved to say that God the Father was spirit only in favor of the Trinity doctrine put forth in the Nicene Creed. Here are the three scriptures:

1. John 4: 24 God is a Spirit: and they that worship him must worship him in spirit and in truth.
2. Luke 24: 39 Behold my hands and my feet, that it is I myself: handle me, and see; for a spirit hath not flesh and bones, as ye see me have.
3. John 10: 30 I and my Father are one.

Using these three scriptures, I asked my wife's cousin who is currently working on a PhD in Methematical Logic if he could express these statements as logical mathematical arguments, and what would be the result? He responded with the following in an email.

Your scripture/logic question is interesting. Here is how I would formalize the argument, and the result is a contradiction.

Definitions:
Sx: x is a spirit
Bx: x is/has a body
g: God
j: Jesus

Logical symbols:
^: conjunction (AND)
~: negation (NOT)
->: implication (IF/THEN)
<->: iff (IF-AND-ONLY-IF)(x)(p(x)): for all x, p is true of x (where p is some logical formula);the overall formula is said to be universally quantified
=: equality

Premises:
John 4:24 (ignoring the part about worshiping God in spirit and truth): Sg
Luke 24:39: Bj^[(x)(Sx -> ~Bx)]
John 10:30: g = j

The most natural deduction (to me, anyway) is the following:
1. Sg Given
2. Bj^[(x)(Sx -> ~Bx)] Given
3. g = j Given
4. (x)(y)(x=y <-> [(F)(Fx <-> Fy)])

Leibniz's law:
Any x and y are equal/identical iff for every property F, F holds of x iff F holds of y (i.e., equality means having all identical properties)

5. g=j <-> [(F)(Fg <-> Fj)] from 4 by axiom for universal specialization
6. (F)(Fg <-> Fj) from 3 and 5 by Modus Ponens
7. Sg <-> Sj from 6 by axiom for universal specialization
8. Sj from 1 and 7 by Modus Ponens
9. (x)(Sx -> ~Bx) from 2 by axiom for eliminating conjunction
10. Sj -> ~Bj from 9 by axiom for universal specialization
11. ~Bj from 8 and 10 by Modus Ponens
12. Bj from 2 by axiom for eliminating conjunction
13. ~Bj^Bj (a contradiction) from 11 and 12 by axiom for introducing conjunction.

Most logicians, including me, prefer to avoid contradictions (though there is a branch of logic that studies "paraconsistent" systems), so I would disagree if your friend claims that these verses, taken together,constitute an obvious, meaningful argument. I think that when logic breaks down in the real world, it is usually because there are some hidden axiomsa nd subtleties of definition. Probably both you and your friend would be reluctant to say that one or more of these verses is false, so resolution of the contradiction hinges on the interpretation of key phrases. The verse from Luke seems entirely straightforward, so in a Bill Clinton-esque way the matter depends on what "is" (or "are") means. Again, "God is a Spirit" seems straight forward (even if we don't know exactly what a spirit is, from Luke we know that it doesn't have flesh and bones), so I would conclude that "I and my Father are one" does not mean equality in the sense of Leibniz. Whether that is consistent with the doctrine of the Trinity would be something your friend would have to (try to) answer.

Take care, William

I also had a mathematical and logic computer science professional try the same experiment letting him interpret and convert the 3 verses into logical arguments in computer language and he came up with the same result.

What can we conclude from this exercise? The point here is that it is not logical for logical Evangelicals to use these 3 verses of scripture as logical arguments to somehow prove the doctrine of the Trinity and that God the Father is only a spiritual reality and only a spirit.

The truth is that the nature of God is the unification and harmonization of both the spiritual and physical and that God is both a spiritual and physical reality. This may seem trivial, but it happens to be the number one misunderstanding concerning the nature of God and leads many Christians to infer and interpret other scriptural truths as only spiritual realities. Many Evangelicals extrapolate this misunderstanding and apply it to their understanding of the Church not being an organization or hierarchy but only a spiritual body of believers. They extrapolate this misunderstanding to believe that their exists a general priesthood of all believers but ignore that there also is order and an actual priesthood authority. Evangelicals see the temple as the body of the believer only, and salvation is by grace without the need for any type of works, repentance, or ordinances. All these spiritual points are true, and the correct spiritual reality, but they are not correct apart from the associated physical reality. LDS doctrine recognizes both the physical and the spiritual reality of all these truths.

When you consider the historical context of John 4: 24, the verse stresses the spiritual nature of God. That is because the Jews being spoken too had swung the pendulum, with regard to their understanding of the nature of God, too far towards the physical. They knew God spoke to Moses face to face, and they were looking for the Messiah who would come and physically and politically redeem Israel from the oppression of Rome. And the Jews misunderstood the physical and outward requirements of the Law of Moses thinking they resulted in salvation alone. John 4:24 was spoken to remind the Jews that God was also a spirit and those that worship Him must worship Him in spirit and truth, word and deed, outward ordinances, and inward commitment and devotion. grace and works.

Now Satan has deceived many Christians by getting the pendulum of belief to swing too far to the spiritual side of things to the exclusion of any physical reality to Scripture and Religion. John warned of this in the Bible saying that the spirit of the Anti-Christ would deny that Christ came in the flesh, and that the mouth of the Beast would blaspheme the tabernacle (physicality) of God. This kind of things started with the Gnostic's but is perpetuated thanks to the Nicene and other non-Biblical Creeds that were contentiously debated, politicked, voted upon and ratified by slim majorities and split decisions resulting in later schizms and not a promised unity of the faith. Unfortunately, voting on doctrine doesn't make that doctrine true and voting does not represent the pattern God has set forth to reveal truth to man.

I hope that accepting the physical and spiritual nature of God and God the Father will lead all Christians to a proper understanding of the physical and spiritual realities of all doctrine and all truth. While my Evangelical friends were trying to use these 3 verses to make a logical argument to say that the Father is spirit only. Another scripture, Matt. 5: 48 says:

Matt 5:48 Be ye therefore perfect, even as your Father which is in heaven is perfect.

Therefore, with this understanding I would reject a recent statement by Ravi Zarcharias that only the Father, Son, and Holy Ghost together constitute the perfect expression of deity. Matt 5 says that God is perfect and complete alone. Christ came to perfect man and not the Father.

Also, Justin Martyr to Trypho used the creation story in Genesis which says: "Let us make man in our image" and "Now man has become as one of us" to disprove the "Royal We" argument and to prove that the Father and the Son are seperate, distinct, rational and intelligent individuals, persons, personages, and beings present. Even Pastor Ken Clause on the Luthern Hour radio program recently taught that the Father and the Son were separate and distinct "individuals".Therefore the word "homoousios" in the Nicene Creed saying that God the Father and the Son Jesus Christ are "One Substance." is incorrect and Stephen in the New Testament and Joseph Smith really did see God the Son standing on the right hand of God the Father.