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More on the trinity

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  • More on the trinity

    For more discussion about the Trinity, an interesting debate is occurring in a thread here --->
    "The exact sciences also start from the assumption that in the end it will always be possible to understand nature, even in every new field of experience, but that we make no a priori assumptions about the meaning of the word "understand"."

    Heisenberg
    .....................

    " It is the glory of God to conceal a matter, and it is the glory of a king to search out a matter. " ( Proverbs 25:2 )

  • #2
    Here is his argument for those curious. Trinitarians seem as capable of attacking an argument in that thread as they do anywhere else,...... i.e. badly. That may be a function of the untenable position rather than the capabilities of the individual Trinitarian.

    Originally posted by HillyBilly View Post
    The trinity literally violates the Laws of Logic.

    Like isomorphisms, identity is an equivalence relation. For any equivalence relation ~, the following properties hold for all objects a, b, and c in the domain of discourse:

    (0) a~a [Reflexivity]
    (1) (a~b)⇒(b~a) [Symmetry]
    (2) ((a~b)&(b~c))⇒(a~c) [Transitivity]

    Now, identity, being an equivalence relation, has all of the above properties. It does, however, have another special property that usually goes by either "Leibniz's Law" or "Indiscernability of Identity" (not to be confused with its controversial converse, the Identity of Indiscernibles):

    (3) (a=b)⇒(φ(a)=φ(b)) [Substitutivity]

    This says that if something is identical with itself, then it has all of the same properties as itself. This allows us to replace any instance of a with an instance of b in any formula containing a once we find out that a=b.
    Comment from the peanut gallery......i.e. me.

    Trinitarians don't believe that "God" is an identity when saying Jesus is God, but rather God is a "quality" or "nature" or some other nonsense when saying Jesus is God.

    For example, Jesus is God, but God is not Jesus, and the Father is God, but God is not the Father (this leads to other logical problems that the trinitarian will ignore)



    The rest of the argument.......... which is sound with the exception noted above.

    Originally posted by HillyBilly View Post
    Leibniz's Law is actually a "Law of Logic", in that it is a necessary presumption (axiom) for identity in first order logic. In fact, from reflexivity and Leibniz's Law alone, you can prove both symmetry and transitivity for identity, which means those two are the only assumptions that must be added to predicate logic to be able to use identity in a Boolean way.

    Unfortunately for the doctrine of the Trinity, it violates both Leibniz's Law and Transitivity.

    From the Hypostatic Union, since Jesus *is* God, we can infer via Leibniz's Law that God is entirely human and entirely Divine. From God being entirely human and entirely Divine, via conjunction elimination, we can infer that God is entirely human. Using Leibniz's Law again along with the Holy Spirit being God and God being entirely human, we can infer that the Holy Spirit is entirely human. But, we know that the Holy Spirit is not human, so we have a contradiction.

    More straightforwardly, we can appeal to transitivity and both that Jesus is God and God is the Holy Spirit to infer that Jesus is the Holy Spirit, which is explicitly denied by the doctrine of the Trinity. So, another contradiction.


    So, the doctrine of the Trinity is literally inconsistent with the Laws of Logic.

    So, a syllogism follows:
    (0) If God exists, then God is a trinity. [Premise from mainstream Christianity]
    (1) God is not a Trinity [see arguments above]
    (2) Therefore, God does not exist [MT: 0, 1]
    Therefore, if anyone is in Christ, he is a new creation. The old has passed away; behold, the new has come.

    Comment


    • #3
      Originally posted by StephenC View Post



      The trinity literally violates the Laws of Logic.

      Like isomorphisms, identity is an equivalence relation. For any equivalence relation ~, the following properties hold for all objects a, b, and c in the domain of discourse:

      (0) a~a [Reflexivity]
      (1) (a~b)(b~a) [Symmetry]
      (2) ((a~b)&(b~c))(a~c) [Transitivity]

      Now, identity, being an equivalence relation, has all of the above properties. It does, however, have another special property that usually goes by either "Leibniz's Law" or "Indiscernability of Identity" (not to be confused with its controversial converse, the Identity of Indiscernibles):

      (3) (a=b)((a)=(b)) [Substitutivity]

      This says that if something is identical with itself, then it has all of the same properties as itself. This allows us to replace any instance of a with an instance of b in any formula containing a once we find out that a=b.
      Hello StephenC,

      The poster doesn't even come close in refuting the Trinity. If anything, the poster refuted Modalism i.e. Neo-Oneness. However, in logic, the logical condition "if" is a pragmatically presupposes. When using the logical negation we used the word "unless" being equivalent to "if not" and for logical biconditional "if and only if not". The Oneness logic If A is B, and B is C, then C is A, which would be harder to interpret this in light of Scriptures, since the Biblical account does not affirm such position.

      Do you agree that A ~A negation for Unitarianism?

      I would assume that our Unitarian friends agree with this aspect --
      1). A is not B, and A is not C
      2). B is not A, and B is not C
      3). C is not A, and C is not B

      But our Unitarians friends have issues with this aspect --
      1). A is X
      2). B is X
      3). C is X
      Not three Xs, but one X.

      For example, Jesus is God, but God is not Jesus, and the Father is God, but God is not the Father (this leads to other logical problems that the trinitarian will ignore)
      As for your argument, an informed Trinitarian wouldn't make that mistake. The immediate inference is a good argument against Modalism i.e. Neo-Oneness, especially the Jesus Only concept. Because the immediate inference switches the subject and predicate of a statement called the converse. The converse is only valid for E and I statements. A and O do not have a valid converse. Such as: All S is P does not imply that All P is S, like "All women are people" converse "All people are women".

      Do you agree "All the Father is God converse All God is the Father" for Unitarianism?

      From the Hypostatic Union, since Jesus *is* God, we can infer via Leibniz's Law that God is entirely human and entirely Divine. From God being entirely human and entirely Divine, via conjunction elimination, we can infer that God is entirely human. Using Leibniz's Law again along with the Holy Spirit being God and God being entirely human, we can infer that the Holy Spirit is entirely human. But, we know that the Holy Spirit is not human, so we have a contradiction.
      The poster starts off with a false statement for the Hypostatic Union. So, Conjunction Elimination: ^E as H ^ D |- H would be a straw man, and refuting the straw man with Modus Ponendo Tollens: MPT as ~ H ^ D |- D, ~ H. The HU doctrine doesn't teach "God" himself is "entirely human and entirely Divine". Nor does the two natures share each other properties. But again, the poster seem to be addressing Neo-Oneness that teaches Physical Union called "Dual Nature" or somekind of Neo-version of Eutychianism. Conflating Trinitarian doctrines with Neo-Oneness doctrines is not a valid argument.

      So, a syllogism follows:
      Not a syllogism
      (0) If God exists, then God is a trinity. [Premise from mainstream Christianity]
      P ---> Q
      (1) God is not a Trinity [see arguments above]
      ~Q
      (2) Therefore, God does not exist [MT: 0, 1]
      |- ~P
      At first look, the logical conditional "God's existence" does not imply "God is a trinity". In Predicate Logic, this is invalid and not even a Categorical Syllogism, but a Modus Tollen P ---> Q , ~Q |- ~P. No universal and existential quantifiers too.
      Last edited by Binyawmene; 01-15-19, 01:18 AM.
      Interdenominational (Respecting all Churches by demonstrating the power of Biblical unity).

      Comment


      • #4

        Originally posted by Binyawmene View Post
        Hello StephenC,

        The poster doesn't even come close in refuting the Trinity. If anything, the poster refuted Modalism i.e. Neo-Oneness. However, in logic, the logical condition "if" is a pragmatically presupposes. When using the logical negation we used the word "unless" being equivalent to "if not" and for logical biconditional "if and only if not". The Oneness logic If A is B, and B is C, then C is A, which would be harder to interpret this in light of Scriptures, since the Biblical account does not affirm such position.
        That is the logical conclusion of my observation.

        Originally posted by Binyawmene View Post
        Do you agree that A ~A negation for Unitarianism?

        I would assume that our Unitarian friends agree with this aspect --
        1). A is not B, and A is not C
        2). B is not A, and B is not C
        3). C is not A, and C is not B

        But our Unitarians friends have issues with this aspect --
        1). A is X
        2). B is X
        3). C is X
        Not three Xs, but one X.
        I assume that you are speaking of X being the God, with A being the Father, B being the Son, and C being the Holy Spirit.

        If my assumption is correct, then you are correct with the caveats that
        C is a property of A
        A is X
        X is A.


        Originally posted by Binyawmene View Post
        As for your argument, an informed Trinitarian wouldn't make that mistake. The immediate inference is a good argument against Modalism i.e. Neo-Oneness, especially the Jesus Only concept. Because the immediate inference switches the subject and predicate of a statement called the converse. The converse is only valid for E and I statements. A and O do not have a valid converse. Such as: All S is P does not imply that All P is S, like "All women are people" converse "All people are women".
        I didn't make an argument. Instead, I made an observation. The observation is that HiillyBilly mis-stated the trinitarian position. The logical conclusion to my observation is that HillyBilly is arguing against the modalist position and not the trinitarian position.

        Originally posted by Binyawmene View Post
        Do you agree "All the Father is God converse All God is the Father" for Unitarianism?
        Yes.

        Originally posted by Binyawmene View Post
        The poster starts off with a false statement for the Hypostatic Union. So, Conjunction Elimination: ^E as H ^ D |- H would be a straw man, and refuting the straw man with Modus Ponendo Tollens: MPT as ~ H ^ D |- D, ~ H. The HU doctrine doesn't teach "God" himself is "entirely human and entirely Divine". Nor does the two natures share each other properties. But again, the poster seem to be addressing Neo-Oneness that teaches Physical Union called "Dual Nature" or somekind of Neo-version of Eutychianism. Conflating Trinitarian doctrines with Neo-Oneness doctrines is not a valid argument.
        The poster does not make a false statement about the hypostatic union. He misapplies "God" as an identity (i.e. reflexivity, symmetry, Add to dictionary, substitutivity) within the context of "Jesus is God", and then arrives at a false conclusion regarding the hypostatic union.


        Originally posted by Binyawmene View Post
        At first look, the logical conditional "God's existence" does not imply "God is a trinity". In Predicate Logic, this is invalid and not even a Categorical Syllogism, but a Modus Tollen P ---> Q , ~Q |- ~P. No universal and existential quantifiers too.
        You are correct that "God's existence does not imply that God is a trinity.". However, in his proof, he makes the ASSUMPTION that if God exists, then God is a trinity. Trinitarians agree with this assumption. Making assumptions is perfectly acceptable if your opponent agrees with the assumption, and in the context of that thread, his opponents agree with the assumption.

        In the three or four pages I read, Trinitarians weren't smart enough to figure out that he slipped in a false assumption and then articulate it back to him.



        (-- Please note, my comments weren't directed at attacking or defending a doctrine, but rather to point out that defenders of the Trinity do not know how to engage HillyBilly's argument in the arena and style of which is was presented, and it makes trinitarians look foolish when threads get cluttered up by a bunch of commenters not knowing what they are doing and tossing out one liners and meaningless comments unrelated to the argument --)


        Therefore, if anyone is in Christ, he is a new creation. The old has passed away; behold, the new has come.

        Comment


        • #5
          Originally posted by StephenC View Post

          ..<snip>...

          The rest of the argument.......... which is sound with the exception noted above.

          Well, the usual suspects in the debate are not providing the same ideas. The mix is different.

          "The exact sciences also start from the assumption that in the end it will always be possible to understand nature, even in every new field of experience, but that we make no a priori assumptions about the meaning of the word "understand"."

          Heisenberg
          .....................

          " It is the glory of God to conceal a matter, and it is the glory of a king to search out a matter. " ( Proverbs 25:2 )

          Comment


          • #6
            Originally posted by StephenC View Post

            ..<snip>..

            I didn't make an argument. Instead, I made an observation. The observation is that HiillyBilly mis-stated the trinitarian position.

            ..<snip>..
            His conclusion was incorrect.
            "The exact sciences also start from the assumption that in the end it will always be possible to understand nature, even in every new field of experience, but that we make no a priori assumptions about the meaning of the word "understand"."

            Heisenberg
            .....................

            " It is the glory of God to conceal a matter, and it is the glory of a king to search out a matter. " ( Proverbs 25:2 )

            Comment


            • #7
              Originally posted by StephenC View Post

              I assume that you are speaking of X being the God, with A being the Father, B being the Son, and C being the Holy Spirit.
              Hello StephenC,

              Yes. The constant X is God.

              If my assumption is correct, then you are correct with the caveats that

              C is a property of A
              A is X
              X is A
              No need to further addressing the atheist poster since his OP is a straw man and he has already been refuted. Anyways, do you know First Order of Logic (Predicate Logic)? If not, then we will go through it step-by-step first. But I am not sure that your logic (in the above quote) is making any logical sense to me. If possible maybe can clarify the logic of your Unitarianism assumption? After that, I would like to see you interpret that logic in light of Scriptures Biblically.

              So, according to you.
              "All of the Father is the Holy Spirit".

              Ɐx = All
              Fx = Father
              Sx = Holy Spirit
              Therefore, Ɐx [Fx ---> Sx]

              "For all x, if x is the Father, then x is the Holy Spirit" <--- Predicate Logic
              And "A is X" and "X is A" (or "All Father is God" converse "All God is Father") is invalid. Because the immediate inference switches the subject and predicate of a statement called the converse. The converse is only valid for E and I statements. A and O statements do not have a valid converse. Such as: All S is P does not imply that All P is S, like "All women are people" converse "All people are women".


              Btw: We don't have to use the constant 'standard form' but simply roll with it.
              All S is P
              S = subject
              P = predicate
              Interdenominational (Respecting all Churches by demonstrating the power of Biblical unity).

              Comment

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