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Can or Should God's Existence be Proven?

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  • Can or Should God's Existence be Proven?

    In a recent thread, robrecht made the following statement in Apologetics 301.

    Originally posted by robrecht View Post
    Any god whose existence can be proved, disproven, or definitively doubted is not God.
    Is this a statement that you agree with or disagree with? Why or why not?

  • #2
    I'm not sure why robrecht believes that if a God could be proven to exist, then that would somehow be unbelievable, or disqualify God from being.

    The Catholic Church has always held, which was defined infallibly in the First Vatican Council, that God's existence and Him being the first principle and end of all things, could be learned by natural reason. That is without any kind of supernatural revelation. We can know that God exists.

    The Church takes a more nuanced approach in regards to the doctrines about God specific to Christianity, as some of those require revelation, that is, the nature of the Trinity for instance. And the Church also recognises that the use of human reasoning has various limitations, so that God has graciously granted that we can also come to know of His being by supernatural inspiration.

    Source: Dei Filius, First Vatican Council

    1. The same Holy mother Church holds and teaches that God, the source and end of all things, can be known with certainty from the consideration of created things, by the natural power of human reason : ever since the creation of the world, his invisible nature has been clearly perceived in the things that have been made. [13] 2. It was, however, pleasing to his wisdom and goodness to reveal himself and the eternal laws of his will to the human race by another, and that a supernatural, way. This is how the Apostle puts it : In many and various ways God spoke of old to our fathers by the prophets; but in these last days he has spoken to us by a Son [14].

    © Copyright Original Source

    Comment


    • #3
      Disagree.

      Romans 1:19-21New International Version (NIV)

      19 since what may be known about God is plain to them, because God has made it plain to them. 20 For since the creation of the world God’s invisible qualities—his eternal power and divine nature—have been clearly seen, being understood from what has been made, so that people are without excuse.

      21 For although they knew God, they neither glorified him as God nor gave thanks to him, but their thinking became futile and their foolish hearts were darkened.

      It's been clear that God exists since the beginning of creation.

      I think that robrecht has gone too far into apophatic* theology, and has essentially denied that we can know anything about God, even His existence. This is unbiblical and IMO unchristian.

      robrecht's comment basically rules out the God of Christianity as God. I don't think that was his intent, because he never seems to follow through these ideas to their logical conclusion. When confronted about this in the past he immediately went on to denigrate logic as "pedestrian".

      *At least his version anyway.

      Comment


      • #4
        Originally posted by Cerebrum123 View Post
        Disagree.

        Romans 1:19-21New International Version (NIV)

        19 since what may be known about God is plain to them, because God has made it plain to them. 20 For since the creation of the world God’s invisible qualities—his eternal power and divine nature—have been clearly seen, being understood from what has been made, so that people are without excuse.

        21 For although they knew God, they neither glorified him as God nor gave thanks to him, but their thinking became futile and their foolish hearts were darkened.

        It's been clear that God exists since the beginning of creation.

        I think that robrecht has gone too far into apophatic* theology, and has essentially denied that we can know anything about God, even His existence. This is unbiblical and IMO unchristian.

        robrecht's comment basically rules out the God of Christianity as God. I don't think that was his intent, because he never seems to follow through these ideas to their logical conclusion. When confronted about this in the past he immediately went on to denigrate logic as "pedestrian".

        *At least his version anyway.
        No, my intent was certainly not to rule out the God of Christianity as God. I do believe we can have personal assurance of God's existence, and see his effects all around us, but have yet to see any rational deductive proofs of God's existence that were either universally accepted by all people or able to comprehend the nature of God. I think our weak and fallible human reason is too weak to fully comprehend the nature of God.
        βλέπομεν γὰρ ἄρτι δι᾿ ἐσόπτρου ἐν αἰνίγματι, τότε δὲ πρόσωπον πρὸς πρόσωπον·
        ἄρτι γινώσκω ἐκ μέρους, τότε δὲ ἐπιγνώσομαι καθὼς καὶ ἐπεγνώσθην.

        אָכֵ֕ן אַתָּ֖ה אֵ֣ל מִסְתַּתֵּ֑ר אֱלֹהֵ֥י יִשְׂרָאֵ֖ל מוֹשִֽׁיעַ׃

        Comment


        • #5
          Originally posted by robrecht View Post
          No, my intent was certainly not to rule out the God of Christianity as God. I do believe we can have personal assurance of God's existence, and see his effects all around us, but have yet to see any rational deductive proofs of God's existence that were either universally accepted by all people or able to comprehend the nature of God. I think our weak and fallible human reason is too weak to fully comprehend the nature of God.
          Nobody here said anything about anything being "universally accepted by all people", or anyone "fully comprehend"(ing) the nature of God. This is about whether or not He can be proven to exist. You didn't either in the post quoted in the OP. You will not find any topic that is "universally accepted by all people", and you don't need to "fully comprehend" the nature of God in order to know that He exists. Basically, you've moved the goal posts.

          You've made a very, very different claim in this thread as opposed to the quoted post.

          How about I give you an analogy. John Martin seems to even be disputing that planet earth is a globe, and is putting forth a flat earth model. Somehow I doubt you would say that the earth as a globe hasn't been sufficiently proved. He's without excuse on that issue, as are others when it comes to the existence of God. I'm guessing that most people would also accept that we can't exhaustively know the natural world, but they will certainly know that it has been sufficiently proved to exist.

          The claim in your quoted post however says that a God that could be proven is not God. This is a rejection of what Christianity explicitly teaches about God. I think you need to take a deep look at what you really believe.

          Comment


          • #6
            Originally posted by Cerebrum123 View Post
            Nobody here said anything about anything being "universally accepted by all people", or anyone "fully comprehend"(ing) the nature of God.
            I did.

            Originally posted by Cerebrum123 View Post
            This is about whether or not He can be proven to exist.
            And to whom he can be proven to exist. What good is a 'proof' if it fails to convince those to whom it is directed?

            Originally posted by Cerebrum123 View Post
            You didn't either in the post quoted in the OP.
            I reserve the right to explain my own remarks.

            Originally posted by Cerebrum123 View Post
            You will not find any topic that is "universally accepted by all people", and you don't need to "fully comprehend" the nature of God in order to know that He exists. Basically, you've moved the goal posts.
            Not really. My comment in the other thread was admittedly cryptic, but in context it was directly related to arguments employing a poorly defined idea of the supernatural. I do not agree that God can be defined. In the classical sense of a definition, the specific difference is comprehended by the genus and we do not have this type of comprehensive knowledge of the nature of God. If we think we do, our limited understanding of God is not God. As I've already said, I do think we can know that God exists, but I don't think we can prove it, at least not very well. Not sufficiently to convince others who do not share some of the same metaphysical presuppositions or intuitions.

            Originally posted by Cerebrum123 View Post
            You've made a very, very different claim in this thread as opposed to the quoted post.
            I've merely tried to clarify my perspective for you.

            Originally posted by Cerebrum123 View Post
            How about I give you an analogy. John Martin seems to even be disputing that planet earth is a globe, and is putting forth a flat earth model. Somehow I doubt you would say that the earth as a globe hasn't been sufficiently proved. He's without excuse on that issue, as are others when it comes to the existence of God. I'm guessing that most people would also accept that we can't exhaustively know the natural world, but they will certainly know that it has been sufficiently proved to exist.
            Ironically, JohnMartin's perspective is based on a false assumption that the nature of the universe has been better understood by revelation and that therefore our scientific methods and theories are misguided.

            Originally posted by Cerebrum123 View Post
            The claim in your quoted post however says that a God that could be proven is not God. This is a rejection of what Christianity explicitly teaches about God. I think you need to take a deep look at what you really believe.
            Not quite. I claimed that a god (note the small g) whose existence can be proved, disproven, or definitively doubted is not God (note the big G). The existence of lots of gods can be proven, but they are not God. I believe such gods are based on a poorly defined sense of the supernatural. God himself, the true supernatural, is beyond our ability to fully comprehend or define. For me, God is certainly known, as I said, in the community, in the resurrected Christ who is at work in the community, in the Eucharist, and in history. He is real. But I am reluctant to offer a definition of God, and I have seen no rational, deductive proofs of his existence that effectively communicate this reality.
            βλέπομεν γὰρ ἄρτι δι᾿ ἐσόπτρου ἐν αἰνίγματι, τότε δὲ πρόσωπον πρὸς πρόσωπον·
            ἄρτι γινώσκω ἐκ μέρους, τότε δὲ ἐπιγνώσομαι καθὼς καὶ ἐπεγνώσθην.

            אָכֵ֕ן אַתָּ֖ה אֵ֣ל מִסְתַּתֵּ֑ר אֱלֹהֵ֥י יִשְׂרָאֵ֖ל מוֹשִֽׁיעַ׃

            Comment


            • #7
              Originally posted by Leonhard View Post
              I'm not sure why robrecht believes that if a God could be proven to exist, then that would somehow be unbelievable, or disqualify God from being.
              I'm not sure what this means. I do not believe we have the power or ability to disqualify God from being!

              Originally posted by Leonhard View Post
              The Catholic Church has always held, which was defined infallibly in the First Vatican Council, that God's existence and Him being the first principle and end of all things, could be learned by natural reason. That is without any kind of supernatural revelation. We can know that God exists.

              The Church takes a more nuanced approach in regards to the doctrines about God specific to Christianity, as some of those require revelation, that is, the nature of the Trinity for instance. And the Church also recognises that the use of human reasoning has various limitations, so that God has graciously granted that we can also come to know of His being by supernatural inspiration.

              Source: Dei Filius, First Vatican Council

              1. The same Holy mother Church holds and teaches that God, the source and end of all things, can be known with certainty from the consideration of created things, by the natural power of human reason : ever since the creation of the world, his invisible nature has been clearly perceived in the things that have been made. [13] 2. It was, however, pleasing to his wisdom and goodness to reveal himself and the eternal laws of his will to the human race by another, and that a supernatural, way. This is how the Apostle puts it : In many and various ways God spoke of old to our fathers by the prophets; but in these last days he has spoken to us by a Son [14].

              © Copyright Original Source

              I too believe that God can be known with human certainty. But our human knowledge of God is not God. And the God whose existence can be understood and proven to exist (to ourselves) by our limited human knowledge and reasoning falls infinitely short of the reality of God. We do not yet have the beatific vision of God that we will enjoy in heaven. Now we see as through a glass darkly, then we shall understand as we are ourselves understood by God.
              βλέπομεν γὰρ ἄρτι δι᾿ ἐσόπτρου ἐν αἰνίγματι, τότε δὲ πρόσωπον πρὸς πρόσωπον·
              ἄρτι γινώσκω ἐκ μέρους, τότε δὲ ἐπιγνώσομαι καθὼς καὶ ἐπεγνώσθην.

              אָכֵ֕ן אַתָּ֖ה אֵ֣ל מִסְתַּתֵּ֑ר אֱלֹהֵ֥י יִשְׂרָאֵ֖ל מוֹשִֽׁיעַ׃

              Comment


              • #8
                Originally posted by robrecht View Post
                I did.
                The context is those in the thread other than you.

                And to whom he can be proven to exist. What good is a 'proof' if it fails to convince those to whom it is directed?
                You neglected the part where there are people who willfully ignore the proof(ie "hearts are darkened"). That's on them, not on God.

                I reserve the right to explain my own remarks.
                When your remarks are at odds with one another it's not "clarification". People have the "right" to say that black is white, but it doesn't make it true.

                Not really. My comment in the other thread was admittedly cryptic, but in context it was directly related to arguments employing a poorly defined idea of the supernatural. I do not agree that God can be defined. In the classical sense of a definition, the specific difference is comprehended by the genus and we do not have this type of comprehensive knowledge of the nature of God.
                "Comprehensive knowledge" is not needed to prove that God exists. While God can't be exhaustively defined, there are certain things that define Him. He is truth, He is love, He is just, etc.

                If we think we do, our limited understanding of God is not God.
                Only if we say that understanding is exhaustive of who God is. This doesn't stop us from knowing things about Him, such as His "eternal power and divine nature".

                As I've already said, I do think we can know that God exists, but I don't think we can prove it, at least not very well. Not sufficiently to convince others who do not share some of the same metaphysical presuppositions or intuitions.
                This is directly against what the Bible claims, and as Leonhard has shown against what Catholicism claims.

                I've merely tried to clarify my perspective for you.
                Reversing a claim is not "clarifying" no matter how much you insist that black is white.

                Ironically, JohnMartin's perspective is based on a false assumption that the nature of the universe has been better understood by revelation and that therefore our scientific methods and theories are misguided.
                So? The analogy still holds. You will find someone somewhere who will deny anything know matter how basic.

                Not quite. I claimed that a god (note the small g) whose existence can be proved, disproven, or definitively doubted is not God (note the big G). The existence of lots of gods can be proven, but they are not God.
                This is special pleading. You are exempting God from your statement despite the fact that it clearly encompasses Him. You're still saying that God can't be proven. If this reasoning applies to the "gods" why not to "God"? Oh, let me guess, it's because logic is too "pedestrian" to be useful when speaking about God.

                I believe such gods are based on a poorly defined sense of the supernatural. God himself, the true supernatural, is beyond our ability to fully comprehend or define. For me, God is certainly known, as I said, in the community, in the resurrected Christ who is at work in the community, in the Eucharist, and in history. He is real. But I am reluctant to offer a definition of God, and I have seen no rational, deductive proofs of his existence that effectively communicate this reality.
                You don't need a full definition or comprehension to understand that He exists, or to prove that He exists. His claims through revelation are that the proof is in creation, and even more importantly in His Son.

                All I'm seeing, again, is that I show you how your words mean something that I know you do not agree with, but you insist that's just not true. This is what comes to mind when reading your posts lately.

                Source: Through the Looking Glass

                “When I use a word,” Humpty Dumpty said, in rather a scornful tone, “it means just what I choose it to mean—neither more nor less.” “The question is,” said Alice, “whether you can make words mean so many different things.” “The question is,” said Humpty Dumpty, “which is to be master—that’s all.”

                © Copyright Original Source



                You can't fault others for not understanding you when you're arbitrarily changing what your words mean like Humpty Dumpty.

                ETA: Without some basic definition for God you can't distinguish heretics from those who are truly Christian. There needs to be some level of definition for who God is otherwise anyone can come in and claim they believe in "God" while believing stuff completely contrary to the Christian faith.
                Last edited by Cerebrum123; 02-10-2016, 10:33 AM.

                Comment


                • #9
                  Originally posted by Cerebrum123 View Post
                  The context is those in the thread other than you.

                  You neglected the part where there are people who willfully ignore the proof(ie "hearts are darkened"). That's on them, not on God.
                  Are you under the impression that I have blamed God for something?

                  Originally posted by Cerebrum123 View Post
                  When your remarks are at odds with one another it's not "clarification". People have the "right" to say that black is white, but it doesn't make it true.
                  I don't agree, not when you understand the context and my perspective.

                  Originally posted by Cerebrum123 View Post
                  "Comprehensive knowledge" is not needed to prove that God exists. While God can't be exhaustively defined, there are certain things that define Him. He is truth, He is love, He is just, etc.
                  I am glad we agree on this.

                  Originally posted by Cerebrum123 View Post
                  Only if we say that understanding is exhaustive of who God is. This doesn't stop us from knowing things about Him, such as His "eternal power and divine nature".

                  This is directly against what the Bible claims, and as Leonhard has shown against what Catholicism claims.
                  I think we may have somewhat differing interpretations of various texts of the Bible. I do not think St Paul was claiming that we can prove God's existence sufficiently to convince others who do not share some of the same metaphysical presuppositions or intuitions. The Bible also says that the fool says in his heart that there is no God.

                  Originally posted by Cerebrum123 View Post
                  Reversing a claim is not "clarifying" no matter how much you insist that black is white.
                  But I do not insist that black is white.

                  Originally posted by Cerebrum123 View Post
                  So? The analogy still holds. You will find someone somewhere who will deny anything know matter how basic.
                  So?

                  Originally posted by Cerebrum123 View Post
                  This is special pleading. You are exempting God from your statement despite the fact that it clearly encompasses Him. You're still saying that God can't be proven. If this reasoning applies to the "gods" why not to "God"? Oh, let me guess, it's because logic is too "pedestrian" to be useful when speaking about God.
                  Please stop trying to put words in my mouth. It is rude and will not help you to understand what I am saying. You once tried to use a syllogism to prove that my view of Genesis necessitated God being a liar. I called that syllogism pedestrian logic that was not appreciative of the poetic narrative. I apologized if you took the word 'pedestrian' as an insult, but I was insulted with your attempt to imply that I supposedly saw God as a liar. I never said that 'logic is too pedestrian to be useful when speaking about God'. I never said or implied that God is a liar. Please refrain from putting words in my mouth.

                  Do you really need me to explain why statements made about gods do not necessarily apply to God? Because gods are not the one true God. Everything said of gods certainly does not encompass the living God.

                  Originally posted by Cerebrum123 View Post
                  You don't need a full definition or comprehension to understand that He exists, or to prove that He exists. His claims through revelation are that the proof is in creation, and even more importantly in His Son.
                  But you do need such comprehension for a classical definition of God. Poor attempts to define the supernatural are the context of my remarks about proving the existence of God.

                  Originally posted by Cerebrum123 View Post
                  All I'm seeing, again, is that I show you how your words mean something that I know you do not agree with, but you insist that's just not true. This is what comes to mind when reading your posts lately.

                  Source: Through the Looking Glass

                  “When I use a word,” Humpty Dumpty said, in rather a scornful tone, “it means just what I choose it to mean—neither more nor less.” “The question is,” said Alice, “whether you can make words mean so many different things.” “The question is,” said Humpty Dumpty, “which is to be master—that’s all.”

                  © Copyright Original Source



                  You can't fault others for not understanding you when you're arbitrarily changing what your words mean like Humpty Dumpty.
                  I have not faulted anyone for not understanding what I've said. I have here asked you not to put words in my mouth. I do not arbitrarily change the meaning of words. I do not think that gods are the same as the living God, the one true God, the maker of heaven and earth.
                  βλέπομεν γὰρ ἄρτι δι᾿ ἐσόπτρου ἐν αἰνίγματι, τότε δὲ πρόσωπον πρὸς πρόσωπον·
                  ἄρτι γινώσκω ἐκ μέρους, τότε δὲ ἐπιγνώσομαι καθὼς καὶ ἐπεγνώσθην.

                  אָכֵ֕ן אַתָּ֖ה אֵ֣ל מִסְתַּתֵּ֑ר אֱלֹהֵ֥י יִשְׂרָאֵ֖ל מוֹשִֽׁיעַ׃

                  Comment


                  • #10
                    Originally posted by Cerebrum123 View Post
                    ETA: Without some basic definition for God you can't distinguish heretics from those who are truly Christian. There needs to be some level of definition for who God is otherwise anyone can come in and claim they believe in "God" while believing stuff completely contrary to the Christian faith.
                    I agree with Thomas Aquinas about our inability to define God in the classical sense. Perhaps you could offer us your classical definition of God and show us why Thomas was wrong.
                    βλέπομεν γὰρ ἄρτι δι᾿ ἐσόπτρου ἐν αἰνίγματι, τότε δὲ πρόσωπον πρὸς πρόσωπον·
                    ἄρτι γινώσκω ἐκ μέρους, τότε δὲ ἐπιγνώσομαι καθὼς καὶ ἐπεγνώσθην.

                    אָכֵ֕ן אַתָּ֖ה אֵ֣ל מִסְתַּתֵּ֑ר אֱלֹהֵ֥י יִשְׂרָאֵ֖ל מוֹשִֽׁיעַ׃

                    Comment


                    • #11
                      On the contrary. There are numerous logical proofs for God's existence.

                      Anselmian Ontological Argument:

                      Dx =df x is a definite description
                      d =df the definite description "(⎫x) ~(∃y)Gyx"
                      g =df (⎫x)~(∃y)Gyx
                      P(Y) =df Y is a great-making property
                      … =df it is conceivable that…

                      A1 The definite description "that than which it is not conceivable for something to be greater" is understood. (Premise)
                      (Dd & Ud)
                      A2 "That than which it is not conceivable for something to be greater" refers to that than which it is not conceivable for something to be greater. (Premise)
                      Fdg
                      A3 The concept of whatever a definite description that is understood refers to has existence-in-the-understanding. (Premise)
                      (x)(y)((Dx & Fxy & Ux) ⊃ Sy)
                      A4 It is conceivable that something is greater than anything that lacks a great-making property that it conceivably has. (Premise)
                      (x1)(Y)[(P(Y)&~Yx1&Yx1)⊃(∃X2)Gx2x1]
                      A5 Existence-in-reality is a great making property. (Premise)
                      P(E)
                      A6 Anything the concept of which has existence-in-the-understanding conceivably has existence-in-reality. (Premise)
                      (x)(Sx ⊃ Ex)
                      A7 It is not conceivable that something is greater than that than which it is not conceivable for something to be greater. (Premise)
                      ~(∃y)Gyg
                      Therefore,
                      A8 That than which it is not conceivable for something to be greater exists-in-reality.
                      Eg

                      Deduction:
                      1. Dd & Ud pr
                      2. Fdg pr
                      3. (x)(y)((Dx &Fxy & Ux) ⊃ Sy) pr
                      4. (x1)(Y)[(P(Y) & ~Yx1 & Yx1) ⊃ (∃x2)Gx2x1) pr
                      5. P(E) pr
                      6. (x)(Sx ⊃ Ex) pr
                      7. ~(∃y)Gyg pr
                      8. Fdg & ~(∃y)gyg 2, 7 Conj
                      9. (∃x)[ ~(∃y)Gyx & (z)(~(∃y)Gyx ⊃ z=x) & (Fdx & ~(∃y)Gyx)] 8, theory of descriptions
                      10. ~(∃y)Gyv & (z)(~(∃y)Gyz ⊃ z=v & (Fdv & ~(∃y)Gyv) 9, EI
                      11. ~(∃y)Gyv 10, Simp
                      12. Fdv 10, Simp
                      13. (P(E) & ~Ev & Ev) ⊃ (∃x2)Gx2v 4 UI
                      14. (Dd & Fdv & Ud) ⊃ Sv 3, UI
                      15. (Dd & Fdv & Ud) 1, 12, Simp, Conj
                      16. Sv 14, 15 MP
                      17. Sv ⊃ Ev 6, UI
                      18. Ev 16, 17 MP
                      19. ~(P(E) & ~Ev & Ev) 13, 11 MT
                      20. ~((P(E) & Ev) & ~Ev) 19 Com, Assoc
                      21. ~(P(E) & Ev) ∨ ~~Ev) 20, DeM
                      22. P(E) & Ev 5, 18 Conj
                      23. Ev 21, 22, DS, DN
                      24. ~(∃y)Gyv & (z)(~(∃y)Gyx) ⊃ z=v) 10 Simp
                      25. ~(∃y)Gyv & (z)(~(∃y)Gyx) ⊃ z=v) & Ev 23, 24 Conj
                      26. (∃x)[~(∃y)Gyx & (z)(~(∃y)Gyx) ⊃ z=x) & Ex] 25 EG
                      27. Eg 26, theory of descriptions

                      Cartesian/Leibnizian Ontological Argument:

                      Rx =df x is supremely perfect
                      Nx =df (Ex ⊃ Ex)
                      C(Y, X) =df Y is included in the concept or essence of x

                      D1 For every X and Y, if the property of being a Y is contained in the concept or essence of being an X, then necessarily everything that is an X is a Y. (Premise)
                      (X)(Y)(C(y˛[Yy], y˛[Xy]) ⊃ (z)(Xz ⊃ Yz)
                      D2 The property of necessarily existing if existing at all is contained in the concept or essence of a supremely perfect being. (Premise)
                      C(y˛[Ny], y˛[Ry])
                      D3 It is possible that a supremely perfect being exists. (Premise)
                      ◊(∃x)(Rx&Ex)
                      D4 Necessarily, supremely perfect beings are necessarily supremely perfect. (Premise)
                      (x)(Rx⊃Rx)
                      Therefore,
                      D5 A supremely perfect being exists.
                      (∃x)(Rx&Ex)

                      Deduction:
                      1. (X)(Y)(C(ŷ[Yy]‚ ŷ[Xy]) ⊃ (z)(Xz  Yz) pr
                      2. C(ŷ[Ny]‚ ŷ[Ry]) pr
                      3. ◊(∃x)(Rx & Ex) pr
                      4. (x)(Rx ⊃ Rx) pr
                      5. C(ŷ[Yy]‚ ŷ[Ry]) ⊃ (x)(Rx ⊃ Nx) 1 UI
                      6. (x)(Rx ⊃ Nx) 2, 5 MP
                      7. (x)(Rx ⊃ (Ex ⊃ Ex)) 6, df “N”
                      8. ((x)(Rx ⊃ (Ex ⊃ Ex)) & (x)(Rx ⊃ Rx)) ⊃ (x)((Rx & Ex) ⊃ (Rx & Ex)) theorem16
                      9. (x)(Rx ⊃ (Ex ⊃ Ex)) & (x)(Rx ⊃ Rx) 4, 7 Conj
                      10. (x)((Rx & Ex) ⊃ (Rx & Ex)) 8, 9 MP
                      11. (x)((Rx & Ex) ⊃ (Rx & Ex)) ⊃ (◊(∃x)(Rx & Ex) ⊃ ◊(∃x)(Rx & Ex)) theorem
                      12. ◊(∃x)(Rx & Ex) ⊃ ◊(∃x)(Rx & Ex) 10, 11 MP
                      13. ◊(∃x)(Rx & Ex) 3, 12 MP
                      14. ◊(∃x)(Rx & Ex) ◊(∃x)(Rx & Ex) theorem
                      15. ◊(∃x)(Rx & Ex) 13, 14 MP
                      16. ◊(∃x)(Rx & Ex) ⊃ (∃x)(Rx & Ex) theorem
                      17. (∃x)(Rx & Ex) 15, 16 MP

                      Malcolm’s Ontological Argument:

                      U1x =df x is unlimited
                      D1x =df x depends on something else for its existence or nonexistence
                      Hx =df x happens to exist
                      Jx =df x happens not to exist
                      B1x =df x is caused to begin to exist by some other being
                      C1x =df x is caused to cease to exist by some other being
                      M1x =df x begins to exist
                      N1x =df x ceases to exist

                      C1 It is possible that the greatest conceivable being exists. (Premise)
                      ◊Eg
                      C2 The greatest conceivable being is unlimited. (Premise)
                      U1g
                      C3 Everything that is unlimited is so if and only if it does not depend on anything else for its existence or nonexistence and it neither just happens to exist nor just happens not to exist. (Premise)
                      (X)(U1x ≡ (~D1x & ~Hx & ~Jx))
                      C4 Everything that does not depend on anything for its existence or nonexistence is such if and only if no other beings causes it to begin to exist and no other being causes it to cease to exist. (Premise)
                      (x)(~D1x ≡ (~B1x & ~C1x))
                      C5 Anything that begins to exist is caused to begin to exist by some other being , or it just happens to begin to exist. (Premise)
                      (x)(M1x ⊃ (B1x Hx ∨ Hx))
                      C6 anything that ceases to exist is caused to cease to exist by some other being, or it just happens to cease to exist. (Premise)
                      (x)(N1x ⊃ (C1x ∨ Jx))
                      C7 Anything that neither beings nor ceases to exist exists necessarily if it exists at all, and fails to exist necessarily if it exists at all.
                      (x)((~M1x & N1x) ⊃ ((Ex ⊃ Ex) & (~Ex ⊃ ~Ex)))
                      Therefore,
                      C8 The greatest conceivable being exists.
                      Eg

                      Deduction:
                      1. ◊Eg pr41
                      2. U1g pr
                      3. (X)(U1x ≡ (~D1x & ~Hx & ~Jx)) pr
                      4. (x)(~D1x ≡ (~B1x & ~C1x)) pr
                      5. (x)(M1x ⊃ (B1x Hx ∨ Hx)) pr
                      6. (x)(N1x ⊃ (C1x ∨ Jx)) pr
                      7. (x)((~M1x & N1x) ⊃ ((Ex ⊃ Ex) & (~Ex ⊃ ~Ex))) pr
                      8. U1g ≡ (~D1g & ~Hg & ~Jg) 3, UI
                      9. (~D1g & ~Hg & ~Jg) 2, 8 Equiv, Simp, MP
                      10. ~D1g ≡ (B1g & ~C1g) 4UI
                      11. ~D1g 9 Simp
                      12. (~B1g & ~C1g) 10, 11 Equiv, Simp, MP
                      13. ~Hg 9 Assoc, Simp
                      14. ~B1g 12 Simp
                      15. ~(B1g ∨ Hg) 13, 14 Conj, DeM
                      16. ~Jg 9 Assoc, Simp
                      17. ~C1g 12 Simp
                      18. ~(C1g ∨ Jg)16, 17 Conj, DeM
                      19. M1g ⊃ (B1g ∨ Hg) 5 UI
                      20. ~M1g 15, 19 MT
                      21. N1g ⊃ (C1g ∨ Jg) 6 UI
                      22. ~N1g 18, 21 MT
                      23. (~M1g & ~N1g) ⊃ ((Eg ⊃ Eg) & (~Eg ⊃ ~Eg)) 7 UI
                      24. (~M1g & N1g) 20, 22 Conj
                      25. ((Eg ⊃ Eg) & & (~Eg ⊃ ~Eg)) 23, 24 MP
                      26. (~Eg ⊃ ~Eg) 25 Simp
                      27. ~~Eg ⊃ Eg 26 Trans
                      28. ◊Eg ⊃ Eg 27 ME
                      29. Eg 1, 28 MP

                      Hartshorne’s Ontological Argument:

                      q =df There is a perfect being

                      H1 It is possible that a perfect being exists. (Premise)
                      ◊q
                      H2 Necessarily, if a perfect being exists, then a perfect being necessarily exists.) (Premise) (Anselm’s Principle)
                      (q ⊃ q)
                      Therefore,
                      H3 A perfect being exists.
                      q

                      Deduction:
                      1. ◊q pr
                      2. (q ⊃ q) pr
                      3. (q ⊃ q) ⊃ (q ⊃ ◊q) theorem
                      4. (◊q ⊃ ◊q) 1, 3 MP
                      5. ◊q 2, 4 MP
                      6. ◊q ⊃ q theorem
                      7. q 5, 6 MP
                      8. q 7, NE

                      Plantinga’s Ontological Argument:

                      Ax =df is maximally great
                      Bx =df is maximally excellent
                      W(Y) =df Y is a universal property
                      Ox =df is omniscient, omnipotent, and morally perfect

                      P1 The property of being maximally great is exemplified in some possible world. (Premise)
                      ◊(∃x)Ax
                      P2 The property of being maximally great is equivalent, by definition, to the property of being maximally excellent in every possible world. (Premise)
                      (x)(Ax ≡ Bx)
                      P3 The property of being maximally excellent entails the properties of omniscience, omnipotence, and moral perfection. (Premise)
                      (x)(Bx ⊃ Ox)
                      P4 A universal property is one that is exemplified in every possible world or none. (Premise)
                      (Y)[W(Y) ≡ ((∃x)Yx ∨ (~(∃x)Yx)]
                      P5 Any property that is equivalent to some property that holds in every possible world is a universal property. (Premise)
                      (Y)[∃Z)(x)(Yx ≡ Zx)
                      Therefore,
                      P6 There exists a being that is essentially omniscient, omnipotent, and morally perfect (God.)
                      (∃x)Ox

                      Deduction:
                      1. ◊(∃x)Ax pr
                      2. (x)(Ax ≡ Bx) pr
                      3. (x)(Bx ⊃ Ox) pr
                      4. (Y)[W(Y) ≡ ((∃x)Yx ∨ (~(∃x)Yx)] pr
                      5. (Y)[∃Z)(x)(Yx ≡ Zx) ⊃ W(Y)] pr
                      6. (∃Z)(x)(Ax ≡ Zx) 2, EG
                      7. [(∃Z)(x)(Ax ≡ Zx) ⊃ W(A)] 5, UI
                      8. W(A) ≡ ((∃x)Ax ∨ (~(∃x)Ax) 4, UI
                      9. W(A) 6, 7 mp
                      10. W(A) ⊃ ((∃x)Ax ∨ (~(∃x)Ax) 8, Equiv, Simp
                      11. (∃x)Ax (~(∃x)Ax) 9, 10 MP
                      12. ~◊~~(∃x)Ax ∨ ((∃x)Ax) 11, Com, ME
                      13. ◊(∃x)Ax ⊃ (∃x)Ax DN, Impl
                      14. (∃x)Ax 1, 13 MP
                      15. (x)(Ax ≡ Bx) ⊃ ((∃x)Ax ⊃ (∃x)Bx) theorem
                      16. (∃x)Bx) 14, 15 MP (twice)
                      17. (x)(Bx ⊃ Ox) ⊃ ((∃x)Bx ⊃ (∃x)Ox) theorem
                      18. (∃x)Ox 16, 17 MP (twice)
                      19. (∃x)Ox 18, NE

                      Godel’s Ontological Theorems:

                      Primitive:
                      P1(Y) =df Property Y is positive

                      Definitions:
                      Df 1 A being has the property of being God-like (G1) if and only if it has every positive property.
                      G1x=df(Y)(P1(Y)⊃Yx)
                      Df 2 A property is an essence (E1) of something if and only if it has the property, and the property entails each of its properties.
                      E1(Y,x)=dfYx&(Z)(Zx⊃(y)(Yz⊃Zy))
                      Df 3 Something has the property of being a necessary being (N2) if and only if every essence it has is necessarily instatiated.
                      N2x=df(Y)(E1(Y,x)⊃(∃z)Yz)

                      Axioms:
                      Ax 1 A property is positive if and only if its negation is not positive.
                      (Z)(P1(Z)≡~P1(y˛[~Zy]))
                      Ax 2 Positive properties entail only positive properties.
                      (Y)(Z)(P1(Y)&(x)(Yx⊃Zx))⊃P1(Z))
                      Ax 3 God-likeness is positive
                      P1(G1)
                      Ax 4 Positive properties are necessarily positive.
                      (Y)(P1(Y)⊃P1(Y))
                      Ax 5 The property of being a necessary being is a positive.
                      P1(N2)

                      Theorems:
                      Tm 1 It is possible that something is God-like
                      ◊(∃y)G1y
                      Tm 2 God-likeness is an essence of whatever is God-like.
                      (x)(G1x⊃E1(G1,x))
                      Tm 3 Something is God-like
                      (∃y)G1y

                      Proof of Tm 1:
                      1. ~◊(∃y)G1y AIP
                      2. ~◊(∃y)G1y ⊃ (x)(G1x ⊃ ~G1x) theorem
                      3. (x)(G1x ⊃ ~G1x) 1, 2 MP
                      4. (x)ŷ[~G1y]x ≡ ~G1x) Abs, NI42
                      5. ((x)(G1x ⊃ ~G1x) & (x)(ŷ[~G1y]x ≡ ~G1x)) ⊃ (x)(G1x ⊃ ŷ[~G1y]x) theorem
                      6. (x)(G1x ⊃ ŷ[~G1y]x) 3, 4, 5, Conj, MP
                      7. P1(G1) Ax 343
                      8. (P1(G1) & (x)(G1x ⊃ ŷ[~G1y]x)) ⊃ P1ŷ[~G1y]) Ax 2, UI
                      9. P1ŷ[~G1y]) 6, 7, 8, Conj, MP
                      10. P1(G1) ⊃ ~P1(ŷ[~G1y[) Ax 1, UI, Equiv, Simp
                      11. ~P1(ŷ[~G1y]) 9, 10 MP
                      12. ◊(∃y)G1y

                      Proof of Tm 2:
                      1. G1μ & Θμ ACP
                      2. ~P1(Θ) AIP
                      3. ~P1(ŷ[~Θy]) ⊃ P1(Θ) Ax 1, UI, Equiv, Simp
                      4. P1(ŷ[~Θy]) 2, 3, DN, MT
                      5. P1(ŷ[~Θy]) ⊃ ŷ[~Θy]μ 1, Simp, df “G1,” UI
                      6. ŷ[~Θy]μ 4, 5 MP
                      7. ŷ[~Θy]μ ≡ ~Θμ Abs, UI
                      8. ~Θμ 6, 7 Equiv, Simp, MP
                      9. Θμ & ~Θμ 1, 8 Simp, Conj
                      10. P1(Θ) 2-7 IP
                      11. (x)(G1x ⊃ (Y)(P1(Y) ⊃ Yx)) theorem, df “G1
                      12. (x)(G1x ⊃ (Y)(P1(Y) ⊃ Yx)) ⊃ (x)(Y)(P1(Y) ⊃ (x)(G1x ⊃ Yx)) theorem
                      13. (x)(Y)(P1(Y) ⊃ (x)(G1x ⊃ Yx)) 11, 12 MP
                      14. P1(Θ) ⊃ (x)(G1x ⊃ Θx) 13 UI
                      15. P1(Θ) ⊃ P1(Θ) Ax 4, UI
                      16. P1(Θ) 10, 15 MP
                      17. (x)(G1x ⊃ Θx) 14, 16 MP
                      18. (G1μ & Θμ) ⊃ (x)(G1x ⊃ Θx)) 1-17 CP
                      19. (x)(Z)((G1x & Zx) ⊃ (x)(G1x ⊃ Zx)) 18, UG
                      20. (x)(Z)((G1x & Zx) ⊃ (x)(G1x ⊃ Zx)) ⊃ (x)(G1x & (Z)(Zx ⊃ (x)(G1x ⊃ Zx)))) theorem
                      21. (x)(G1x & (Z)(Zx ⊃ (x)(G1x ⊃ Zx)))) 19, 20 MP
                      22. (x)(G1x ⊃ E1(G1, x)) 21, df “E1

                      Proof of Tm 3:
                      1. G1μ ACP
                      2. P1(N2) Ax 5
                      3. P1(N2) ⊃ N2μ 1, UI, df “G1
                      4. N2μ 2, 3 MP
                      5. E1(G1, μ) ⊃ (∃z)G1z 4, UI, df “N2
                      6. G1μ ⊃ (G1μ & (Z)(Zx ⊃ (x)(G1μ ⊃ Zμ))) Tm 2, df “E1,” UI
                      7. (G1μ ⊃ (G1μ & (Z)(Zx ⊃ (x)(G1μ ⊃ Zμ)))) ⊃ (G1μ & (Z)(Zx ⊃ (x)(G1μ ⊃ Zμ))) theorem
                      8. E1(G1, μ) 6, 7 MP, df “E1
                      9. (∃z)G1z 5, 8 MP
                      10. G1μ ⊃ (∃z)G1z 1-9 CP
                      11. (x)(G1x ⊃ (∃z)G1z) 10 UG, NI
                      12. (x)(G1x ⊃ (∃z)G1z) ⊃ (◊(∃y)G1y ⊃ ◊(∃z)G1z) theorem
                      13. ◊(∃y)G1y ⊃ ◊(∃z)G1z 11, 12 MP
                      14. ◊(∃z)G1z 13 Tm 1, MP
                      15. ◊(∃z)G1z ⊃ (∃z)G1z theorem
                      16. (∃z)G1z 14, 15 MP
                      17. (∃z)G1z 16 NE

                      Modal Perfection Argument:

                      S1x =df (~◊(∃y)Gyx & ~◊(∃y)(x≠y & ~Gyx))

                      M1 A property is a perfection only if its negation is not a perfection.
                      M2 Perfection entails only perfections.
                      M3 The property of being supreme is a perfection.

                      Deduction:
                      1. ◊(∃x)S1x pr
                      2. ◊(∃x)S1x ⊃ (∃x)◊S1x theorem35
                      3. (∃x)◊S1x 1, 2 MP
                      4. ◊S1v 3, EI
                      5. ◊(~◊(∃y)Gyv & ~◊(∃y)(v≠y & ~Gyv)) 4, df “S1
                      6. ◊(~◊(∃y)Gyv & ~◊(∃y)(v≠y & ~Gyv)) ⊃ (◊~◊(∃y)Gyv & ◊~◊(∃y)(v≠y & ~Gyv)) theorem
                      7. (◊~◊(∃y)Gyv & ◊~◊(∃y)(v≠y & ~Gyv)) 4, 5 MP
                      8. ◊~◊(∃y)Gyv 7 Simp
                      9. ◊~◊(∃y)(v≠y & ~Gyv) 7 Com, Simp
                      10. ◊~◊(∃y)Gyv ⊃ ~◊(∃y)Gyv theorem
                      11. ◊~◊(∃y)(v≠y & ~Gvy) ⊃ ~◊(∃y)(v≠y & ~Gvy) theorem
                      12. ~◊(∃y)Gyv 8, 10 MP
                      13. ~◊(∃y)(v≠y & ~Gvy) 9, 11 MP
                      14. ~◊(∃y)Gyv & ~◊(∃y)(v≠y & ~Gvy) 12, 13 Conj
                      15. S1v 14, df “S1
                      16. (∃x)S1x 15 EG

                      The Temporal-Contingency Argument

                      B2x =df x begins to exist at some time and ceases to exist at some time
                      T2x =df x is temporally necessary
                      C2x =df x is temporally contingent
                      F2x =df x exists for a finite period of time
                      M2 =df Only finitely many things have existed to date
                      P3 =df Something presently exists
                      N2 =df There was a time when nothing existed
                      S2xy =df x is a sufficient reason for y for the existence of y
                      W2x =df x is without limitations

                      T1 Something presently exists.
                      T2 Only finitely many things have existed to date.
                      T3 Every temporally contingent being begins to exist at some time and ceases to exist at some time.
                      T4 Everything that begins to exist at some time and ceases to exist at some time exists for a finite period of time.
                      T5 If everything exists for only a finite period of time, and there have only been finitely many beings to date, then there was a time when nothing existed.
                      T6 If there was a time when nothing existed, then nothing presently exists.
                      T7 A being is temporally necessary if and only if it is not temporally contingent.
                      T8 Everything has a sufficient reason for its existence.
                      T9 Anything that has a sufficient reason for its existence also has a sufficient reason for its own existence.
                      T10 No temporally contingent being is a sufficient reason for the existence of a temporally necessary being.
                      T11 Every temporally necessary being that is a sufficient reason for its own existence is a being without any limitations.
                      T12 A being without any limitations is necessarily greater than any other being.
                      T13 It is not possible for anything to be greater than itself.
                      T14 It is necessarily the case that “greater than” is asymmetric.
                      Therefore,
                      T15 There exists a supreme being.

                      Deduction:

                      1. P3 pr 1
                      2. M2 pr 2
                      3. (x)(C2x ⊃ B2x) pr 3
                      4. (x)(B2x ⊃ F2x) pr 4
                      5. ((x)F2x & M2 ) ⊃ N2 pr 5
                      6. N2 ⊃ ~P3 pr 6
                      7. (x)(T2x ≡ ~C2x) pr 7
                      8. (x)C2x AIP
                      9. C2μ ⊃ B2μ 3 UI
                      10. C2μ 8 UI
                      11. B2μ 9, 11 MP
                      12. B2μ ⊃ F2μ 4 UI
                      13. F2μ 11, 12 MP
                      14. (x)F2x 13 UG
                      15. (x)F2x & M2 2, 14 Conj
                      16. N2 5, 15 MP
                      17. ~P2 6, 16 MP
                      18. P2 & ~P2 1, 17 Conj
                      19. ~(x)C2x 8-19 IP
                      20. (∃x)~C2x 19 QN
                      21. ~C2v1 20 EI
                      22. T2v1 ≡ ~C2v1 7 UI
                      23. (T2v1 ⊃ ~C2v1) & (~C2v1 ⊃ T2v1) 22 Equiv
                      24. (~C2v1 ⊃ T2v1) 23 Com, Simp
                      25. T2v1 21, 24 MP
                      26. (∃x)T2x 25 EG
                      27. (x)(∃y)S2yx pr 8
                      28. (x)[(∃y)S2yx ⊃ (∃z)(S2zx & S2zz)] pr 9
                      29. (x)(y)[T2x & S2yx) ⊃ ~C2y] pr 10
                      30. (y)[T2y & S2yy) ⊃ W2y] pr 11
                      31. (y)[W2y ⊃ (z)z≠y ⊃ Gyz)] pr 12
                      32. ~◊(∃y)Gyy pr 13
                      33. (x)(y)(Gxy ⊃ ~Gyx) pr 14
                      34. (∃y)S2yv1 27, UI
                      35. (∃y)S2yv1 ⊃ (∃z)(S2zv1 & S2zz) 28, UI
                      36. (∃z)(S2zv1 & S2zz) 34, 35 MP
                      37. S2vv1 & S2vv 36, EI
                      38. (T2v1 & S2vv1) ⊃ ~C2v 29, UI twice
                      39. S2vv1 37 Simp
                      40. T2v1 & S2vv1 25, 39 Comp
                      41. ~C2v 38, 40 MP
                      42. T2v ≡ ~C2v 7, UI
                      43. (T2v ⊃ ~C2v) & (~C2v ⊃ T2v) 42 Equiv
                      44. ~C2v ⊃ T2v 43 Com, Simp
                      45. T2v 44, 41 MP
                      46. S2vv 37 Com, Simp
                      47. T2v & S2vv 45, 46 Conj
                      48. (T2v & S2vv) ⊃ W2v 30 UI
                      49. W2v ⊃ (z)(z≠v ⊃ Gvz) 31 UI
                      50. (z)(z≠v ⊃ Gvz) 47, 48, 49 MP
                      51. (z)(~z≠v ∨ Gvz) 50 Impl
                      52. (z)(~z≠v ∨ ~~Gvz) 51 DN
                      53. (z)~(z≠v & ~Gvz) 52 DeM
                      54. ~(∃z)(z≠v & ~Gvz) 53 QN
                      55. ~◊(∃z)(z≠v & ~Gvz) 54 ME
                      56. ~(∃y)Gyy 32 ME
                      57. (y)~Gyy 56 QN
                      58. (y)~Gyy ACP
                      59. ~Gμμ 58 UI
                      60. ~Gμμ ∨ v≠μ 59 Add
                      61. v≠μ ∨ ~Gμμ 60 Com
                      62. v=μ ⊃ ~Gμμ 61 Impl
                      63. μ=v ⊃ v=μ theorem
                      64. μ=v ⊃ ~Gμv 62, 63 HS
                      65. (y)~Gyy ⊃ (μ=v ⊃ ~Gμv) 58-64 CP
                      66. [(y)~Gyy ⊃ (μ=v ⊃ ~Gμv)] 65 (theorem) NI
                      67. (μ=v ⊃ ~Guv) 57, 66 MMP
                      68. (x)(y)(Gxy ⊃ ~Gyx) & (z)(z≠v ⊃ Gvz) 33, 50 Conj
                      69.  [(x)(y)(Gxy ⊃ ~Gyx) & (z)(z≠v ⊃ Gvz)] ⊃ [(x)(y)(Gxy ⊃ ~Gyx) & (z)(z≠v ⊃ Gvz)] theorem
                      70. [(x)(y)(Gxy ⊃ ~Gyx) & (z)(z≠v ⊃ Gvz)] 68, 69 MP
                      71.  {[(x)(y)(Gxy ⊃ ~Gyx) & (z)(z≠v ⊃ Gvz)] ⊃ (μ≠v ⊃ ~Gμv)} theorem
                      72. (μ≠v ⊃ ~Gμv) 70, 71 MMP
                      73. [(μ=v ⊃ ~Gμv) & (μ≠v ⊃ ~Gμv)] ⊃ [(μ=v ∨ μ≠v) ⊃ (~Gμv ∨ ~Gμv)] theorem
                      74. (μ=v ⊃ ~Gμv) & (μ=v ⊃ Gμv) 67, 72 Conj
                      75. [(μ=v ∨ μ≠v) ⊃ (~Gμv ∨ ~Gμv)] 73, 74 MP
                      76. (μ=v ∨ μ≠v) theorem
                      77. (~Gμv ∨ ~Gμv) 75, 76 MMP
                      78. (~Gμv ∨ ~Gμv) ⊃ ~Gμv theorem
                      79. ~Gμv 77, 78 MP
                      80. (z)~Gzv 79, UG
                      81. (z)~Gzv ⊃ (z)~Gzv theorem38
                      82. (z)~Gzv 80, 81 MP
                      83. ~(∃z)Gzv 82, QN
                      84. ~◊(∃z)Gzv 83, ME
                      85. ~◊(∃z)Gzv & ~◊(∃z)(z≠v & ~Gvz) 84, 55 Conj
                      86. S1v 85, def “S1
                      87. (∃x)S1x 86 EG

                      Logical Syntax:
                      The strongest logic used is a standard natural deduction system of second-order quantificational modal logic with identity (2QS5.) It is equivalent to a standard second-order extension of Kripke’s 1959 system of first-order modal logic. A weaker subsystem of 2QS5 is frequently used. The language of 2QS5 includes first-(lowercase) and second-order (uppercase) variables, constants and pseudo-names, property abstracts, and the standard array of quantifiers, connectives, punctuation marks, and so on.

                      The nonmodal propositional and quantificational inference rules of 2QS5 are from Gustason and Ulrich: Conjunction (Conj,) Addition (Add,) Simplification (Simp,) Disjunctive Syllogism (DS,) Excluded Middle Introduction (E-M I,) Modus Ponens (MP,) Modus Tollens (MT,) Hypothetical Syllogism (HS,) Constructive Dilemma (CD,) Commutation (Comm,) Distribution (Dist,) Association (Assoc,) Double Negation (DN,) DeMorgan (DeM,) Transposition (Trans,) Exportation (Exp,) Equivalence (Equiv,) Existential Instantiation (EI,) Existential Generalisation (EG,) Universal Instantiation (UI,) Universal Generalisation (UG,) Quantifier Negation (QF,) Identity Introduction (II,) Conditional Proof (CP,) and Indirect Proof (IP.)

                      The five Modal Inference Rules of 2QS5 are as follows:
                      For every substitution instance of ‘p’ and ‘q’
                      NE (necessity elimination) p /∴ p
                      MMP (modal modus ponens) (p ⊃ q), p /∴ q
                      NI (necessity introduction ) If ⎡p⎤ is a theorem, then ⎡p⎤ is a theorem
                      ME (modal equivalence) ⎡◊p⎤ for ⎡~~p⎤ and p for ⎡~◊~p⎤
                      PN (possibility necessity) ◊p /∴ ◊p

                      2QS5 also includes the Principle of Abstraction (Abs) as an axiom schema: (x)(y˛[Ψy]x ≡ Ψx), where ⎡y˛[Ψy] ⎤ denotes the property of being a Ψ.
                      Last edited by Rational Gaze; 02-10-2016, 10:59 AM.
                      My Amazon Author page: https://www.amazon.com/-/e/B0719RS8BK

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                      • #12
                        Originally posted by robrecht View Post
                        And to whom he can be proven to exist. What good is a 'proof' if it fails to convince those to whom it is directed?
                        Unless you have something broader in mind, like everyone already knows that God exists, but their hearts are darkened (as per Cerebrum's quote of Romans), God's existence is and has been proven countless times to people for thousands of years. This is how new converts are made. This is why we study theology, evangelize, and prepare apologetics.

                        My comment in the other thread was admittedly cryptic, but in context it was directly related to arguments employing a poorly defined idea of the supernatural. I do not agree that God can be defined. In the classical sense of a definition, the specific difference is comprehended by the genus and we do not have this type of comprehensive knowledge of the nature of God. If we think we do, our limited understanding of God is not God.
                        Again, as Cerebrum has pointed out, there's likely little we can say we have complete and comprehensive knowledge of. That just has to do with human limitations, and I think everyone is aware of that (with the exception of maybe radical materialist who might claim that we can have comprehensive knowledge given enough time). Again, most people seem to realize this as a sort of basic and unspoken truism when they're discussing whether or not someone like God can be known, proven, and the like. In most conversations I'm familiar with the parties don't have to stop every few minutes to explain that they're not referring to comprehensive knowledge. I mean, this is even true when discussing other persons. A man may know his wife, may be able to prove she exists, but no matter how long he lives with her, he'll never have comprehensive knowledge about her. There are some things that only she can know about her self. Heck, we don't have comprehensive knowledge of our own selves. There are events that have happened in my life that have shaped who I am today that I have long since forgotten. There are physical goings ons in my body and brain that I am not at all aware of. So, yeah, telling people that we can't have comprehensive knowledge of God is a given. It's not something that needs to be mentioned in every conversation about knowledge of God.

                        As I've already said, I do think we can know that God exists, but I don't think we can prove it, at least not very well. Not sufficiently to convince others who do not share some of the same metaphysical presuppositions or intuitions.
                        So, what's happening to all of those agnostic and atheist converts to Christianity? Is it purely through the will of the Holy Spirit that they move towards their faith in Christ? Do you take a sort of Reformed position on the subject? Does the intellect have anything at all to do with one's conversion? Is evangelism necessary? Are apologetics completely and utterly pointless?

                        Ironically, JohnMartin's perspective is based on a false assumption that the nature of the universe has been better understood by revelation and that therefore our scientific methods and theories are misguided.
                        How is that ironic? That seems to be analogous to your view of God. Probably we're missing something here, or miscommunicating somehow.

                        Not quite. I claimed that a god (note the small g) whose existence can be proved, disproven, or definitively doubted is not God (note the big G). The existence of lots of gods can be proven, but they are not God. I believe such gods are based on a poorly defined sense of the supernatural. God himself, the true supernatural, is beyond our ability to fully comprehend or define.
                        I've mentioned this before, but generally speaking, most people are going to miss this peculiar distinction you make between God and god. Most people believe that the Christian God, or Yahweh, or Elohim, or whatever you want to call him, most people believe he is a god. Not necessarily a god among gods, but that he is characterized by those properties that most people think of when they hear or use the word "god". I doubt Gary is familiar with this distinction of yours, so just dropping "god" into a conversation and expecting him to realize that you have a nuanced concept of that particular word is, well, it's pointless. It doesn't benefit him any, and it just confuses the rest of us.

                        You know, this sort of reminds me how Mormons sometimes use common Christian words and phrases, yet have radically different definitions or ideas about what those words mean.

                        For me, God is certainly known, as I said, in the community, in the resurrected Christ who is at work in the community, in the Eucharist, and in history.
                        Since you believe that God can be known via the resurrection and history, I'm interested in your thoughts about the efficacy of apologetics that rely on historical evidence to demonstrate God's existence.

                        He is real. But I am reluctant to offer a definition of God, and I have seen no rational, deductive proofs of his existence that effectively communicate this reality.
                        I'm glad that's not a view shared by all. There are a number of Christians on this very forum who've come to their faith via rational, deductive reasoning (though certainly the Holy Spirit had as much to do with it as did logical arguments). I believe it was Leonhard himself who came to faith, or at least, came back to faith (and to the Roman Church) via rational arguments for God's existence (the Kalam Cosmological Argument, wasn't it?)

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                        • #13
                          Originally posted by Rational Gaze View Post
                          On the contrary. There are numerous logical proofs for God's existence. ...
                          Of course there are, but not all are convinced by them, not even all Christians of good will. For example, Thomas Aquinas did not accept the ontological proof for God's existence. I think they all have some value, but they all fall short of the glory of God in his reality. I think those who accept the epistemological presuppositions of neo-Platonism were especially inclined to accept the ontological proof. There have been more recent attempts to update it, but I don't like those that attempt to define, describe, or discuss a maximally great being. I think the more profound impulse of Anselm's thought is to accept that there is a being greater than which one cannot be thought, ie, not maximally great, but infinitely great, greater than anything which can be described.
                          Last edited by robrecht; 02-10-2016, 11:55 AM.
                          βλέπομεν γὰρ ἄρτι δι᾿ ἐσόπτρου ἐν αἰνίγματι, τότε δὲ πρόσωπον πρὸς πρόσωπον·
                          ἄρτι γινώσκω ἐκ μέρους, τότε δὲ ἐπιγνώσομαι καθὼς καὶ ἐπεγνώσθην.

                          אָכֵ֕ן אַתָּ֖ה אֵ֣ל מִסְתַּתֵּ֑ר אֱלֹהֵ֥י יִשְׂרָאֵ֖ל מוֹשִֽׁיעַ׃

                          Comment


                          • #14
                            Originally posted by Adrift View Post
                            Unless you have something broader in mind, like everyone already knows that God exists, but their hearts are darkened (as per Cerebrum's quote of Romans), God's existence is and has been proven countless times to people for thousands of years. This is how new converts are made. This is why we study theology, evangelize, and prepare apologetics.

                            Again, as Cerebrum has pointed out, there's likely little we can say we have complete and comprehensive knowledge of. That just has to do with human limitations, and I think everyone is aware of that (with the exception of maybe radical materialist who might claim that we can have comprehensive knowledge given enough time). Again, most people seem to realize this as a sort of basic and unspoken truism when they're discussing whether or not someone like God can be known, proven, and the like. In most conversations I'm familiar with the parties don't have to stop every few minutes to explain that they're not referring to comprehensive knowledge. I mean, this is even true when discussing other persons. A man may know his wife, may be able to prove she exists, but no matter how long he lives with her, he'll never have comprehensive knowledge about her. There are some things that only she can know about her self. Heck, we don't have comprehensive knowledge of our own selves. There are events that have happened in my life that have shaped who I am today that I have long since forgotten. There are physical goings ons in my body and brain that I am not at all aware of. So, yeah, telling people that we can't have comprehensive knowledge of God is a given. It's not something that needs to be mentioned in every conversation about knowledge of God.

                            So, what's happening to all of those agnostic and atheist converts to Christianity? Is it purely through the will of the Holy Spirit that they move towards their faith in Christ? Do you take a sort of Reformed position on the subject? Does the intellect have anything at all to do with one's conversion? Is evangelism necessary? Are apologetics completely and utterly pointless?

                            How is that ironic? That seems to be analogous to your view of God. Probably we're missing something here, or miscommunicating somehow.

                            I've mentioned this before, but generally speaking, most people are going to miss this peculiar distinction you make between God and god. Most people believe that the Christian God, or Yahweh, or Elohim, or whatever you want to call him, most people believe he is a god. Not necessarily a god among gods, but that he is characterized by those properties that most people think of when they hear or use the word "god". I doubt Gary is familiar with this distinction of yours, so just dropping "god" into a conversation and expecting him to realize that you have a nuanced concept of that particular word is, well, it's pointless. It doesn't benefit him any, and it just confuses the rest of us.

                            You know, this sort of reminds me how Mormons sometimes use common Christian words and phrases, yet have radically different definitions or ideas about what those words mean.

                            Since you believe that God can be known via the resurrection and history, I'm interested in your thoughts about the efficacy of apologetics that rely on historical evidence to demonstrate God's existence.

                            I'm glad that's not a view shared by all. There are a number of Christians on this very forum who've come to their faith via rational, deductive reasoning (though certainly the Holy Spirit had as much to do with it as did logical arguments). I believe it was Leonhard himself who came to faith, or at least, came back to faith (and to the Roman Church) via rational arguments for God's existence (the Kalam Cosmological Argument, wasn't it?)
                            Yes, God's existence can be proven to many people, and I do not object to this in any way. But the same presuppositions accepted by some cannot be proven to others, and I think that anyone who claims that God's existence can be definitively proven or disproven has not actually proven or disproven the actual existence of God as he actually exists. I think God's actual existence is quite simply beyond our comprehension. All that we can sometimes prove to some people is a much lesser reality than God himself. I certainly don't think apologetics are useless, but I do think they are of limited value. Our intellect is of great value indeed and will always be challenged to come to a fuller knowledge of all reality and God. If apologetics are to be useful to someone like Gary, they should try to engage him on the basis of the presuppositions he does accept. I think it can be worthwhile to point out to those who do not accept some particular proof that they have not necessarily rejected the one true God as he actually exists. Let me know if I left something out.
                            βλέπομεν γὰρ ἄρτι δι᾿ ἐσόπτρου ἐν αἰνίγματι, τότε δὲ πρόσωπον πρὸς πρόσωπον·
                            ἄρτι γινώσκω ἐκ μέρους, τότε δὲ ἐπιγνώσομαι καθὼς καὶ ἐπεγνώσθην.

                            אָכֵ֕ן אַתָּ֖ה אֵ֣ל מִסְתַּתֵּ֑ר אֱלֹהֵ֥י יִשְׂרָאֵ֖ל מוֹשִֽׁיעַ׃

                            Comment


                            • #15
                              I'm not familiar with some of the history of all this, but it seems to me that you guys aren't actually disagreeing much, if at all. Maybe I'm misreading things, though....
                              I DENOUNCE DONALD J. TRUMP AND ALL HIS IMMORAL ACTS.

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