Wednesday, October 16, 2013

THE MISPLACED COMMA


There is a seemingly unassuming verse in the Bible that creates all kinds of problems for a number of Christian faith traditions.  The text is Luke 23:43.  The setting is the crucifixion scene where Jesus is flanked on either side by so-called thieves, who are also being crucified.  One thief remains unrepentant, while the other has had a change of heart and recognizes Jesus’s righteousness.  He asks Jesus to remember him when Jesus sets up his kingdom.  According to the King James version, Jesus responds, “Verily I say unto thee, To day shalt thou be with me in paradise.”  The problem is with the placement of the comma in that verse, and a great deal has been written about it.


I have always had a great deal of affection for the King James Version of the Bible.  It is the version I grew up with, and for the longest time I simply thought that was how the Bible was written, with “thees” and “thous.”  Moreover, it has great poetic qualities.  It is the version of the Bible that I got for my 8th birthday and that I still have.  Even so, I do have two other versions of the New Testament, The New Testament in Modern English, by J.B. Phillips, and the New English Bible.  The Phillips (no relation) translation reads, “I tell you truly, this very day you will be with me in paradise.”  And the New English Bible reads, “I tell you this: today you shall be with me in Paradise.” Thus both agree with the King James Version, the New English Bible substituting a more emphatic colon in place of the comma.  Other versions and translations that I have consulted generally agree with the King James also.  It seems clear that most scholars have concluded that the meaning of the verse is that Jesus assured the thief that they would be together in paradise that same day.

Some faith traditions teach the idea that no one goes to heaven directly after death.  Either there is a mandatory intermediate stage, e.g., purgatory, or, as Seventh-day Adventists believe, the individual remains in the grave until Christ’s second coming at some later date.  In addition, there is the problem that, never mind the thief, Jesus didn’t go directly to heaven either.  Instead, he remained in the tomb until the following Sunday morning.  So how could he assure the thief that they would both be in paradise that very day?

What to do?  What to do?  The solution for many of these faiths has been to move the comma, so that the verse reads, “Verily I say unto thee to day, Shalt thou be with me in paradise.”  Awkward, I know.  Or they might reword the verse slightly to read, “Verily, I say unto thee this day, Thou shalt be with me in paradise.”

Having said all this, it should be pointed out that commas didn’t even come into use until the end of the 15th century.  They simply weren’t around at the time the gospel was written in Greek.  Moreover, Jesus was communicating orally, not in writing, and we simply don’t use punctuation in oral speech.  (Except for the comic/pianist Victor Borge, who had a routine where he assigned a different sound to each punctuation mark.  It was funny when I heard it the first time when I was in grade school, but it got old fast.)  Commas initially came into use to indicate a place for the reader to pause (and perhaps to catch their breath).  Eventually, they came to play a role in clarifying meaning, as in the verse in question.  (A fun book to read along these lines is Eats Shoots and Leaves, by Lynne Truss, which deals with the history of punctuation and which includes a discussion of Luke 23:43.)  

I majored in English literature in college, and one of the courses required for an English major at Andrews University, the SDA college I attended, was entitled, “The Bible as Literature.”  There’s no way that the course should have been required for majors, but the class itself wasn’t a terrible idea: There are a number of portions of the Bible that have literary merit, including Psalms, Ecclesiastes, and Song of Solomon, among others.  But the thing I most recall about the class was a remark that the professor made one day in class that really had little to do with the Bible’s literary qualities.  He reported that a committee of SDA Biblical scholars had recently reviewed the proper interpretation/translation of the gospels and had paid special attention to Luke 23:43.  He literally beamed as he informed us that the committee had concluded that the verse should be interpreted with the comma following rather than preceding the word “today.”  Really.

Why am I dwelling on the kerfuffle over this verse?  After all, I don’t believe either the thief or Jesus ever made it to paradise, either that day or any other day.  I am pointing out this little controversy because it nicely illustrates what happens when so-called scholarship is driven by a need to support a particular point of view rather than being driven simply by a open-minded analysis of the available evidence.  If there are passages of the Bible that seem to be in contradiction, a person intent on supporting a particular religious perspective is required either to ignore the contradiction or to rationalize the difference.  For example, the great discrepancy between the blood-and-thunder, vindictive Old Testament God and the Pauline God of love and forgiveness of the New Testament is rationalized by saying that Christ’s life, death, and sacrifice transformed man’s view of God. We all have biases, of course, but the goal is to recognize those biases and to make every effort to ensure that we do not let them dominate our view on things.  

This account also points out, I believe, the problems with treating the Bible as inerrant authority.  When a passage appears inconsistent with one’s point of view, if the Bible is the authority, then one has to scramble to make sense of things.  That just doesn’t happen if the Bible is treated like any other writing.

This concern applies not just to Biblical scholarship but also to investigations in other areas, such as evolutionary science, geology, and paleontology.  If scientific facts are inconsistent with scripture, then either the scripture must only be metaphorical, as in the creation story--not so bad--or the scientific facts have to be ignored, distorted, or twisted to fit one’s views--much worse.

© 2013 John M. Phillips

14 comments:

  1. Hi John,

    I just came across your blog today. I also went to BCA, 1968 grad. However, in about the 9th grade I bought a used copy of "The Story of Philosophy" by Will Durant at the Goodwill store near the Tabernacle (or was it a Salvation Army store?). I was interested in math and my hero became the mathematician/philosopher, atheist/agnostic Bertrand Russell. By the age of 20 I had no faith, was estranged from my family, and was on probation at Andrews University for not attending the required worship services.

    I was dropping out of college, and more than that, with absolutely no hope for the future, I was dropping out of life. However, fall of 1970 there was a major revival at the school that was quite surprising. I kept my distance, but could not help notice the prayer bands and Bible study groups that sprang up in Meier Hall. Anyway, I was on my way out and only taking one class that last quarter, so would soon be gone.

    Not too long before the end of the quarter, I think it was in November, another student from BCA who had been really down on religion, Bob Maehre, came by my dorm room, and said "God loves you!" Bob had had a sudden and unexpected born-again conversion experience.

    I said, "Bob, I don't believe in God, but if you want to play games with your mind to make yourself happy that's fine with me. I just don't want to believe something to make myself happy." Bob didn’t argue with me, but came back a time or two. I started to avoid him.

    However, one night about midnight I was lying in bed not able to go to sleep. This was unusual for me because I worked in construction on the new science building and played a lot of tennis. Anyway, I suddenly heard singing in my mind that I did not know the words to. It was such a real experience that I knew in an instant that there is a God, that He did care about me, and He was trying to get through to me. I got out of bed and began to wrestle with the greatest decision of my life. I knew I had personal, although subjective, but very real evidence for the existence of God. What was I going to do with it? I knew if I became a Christian my lifestyle would radically change. I almost got back in bed, but I knew the consequences were eternal. Finally, I said, “God, I’m yours.”

    I leaned later that two young men were praying for me right at about that time. That subjective experience completely changed the direction of my life. Without it, I believe I would have been dead long ago based on the direction my life was taking.

    So, my subjective evidence that led me to become a Christian led me to search for objective evidence as well. I even became a statistician out of my desire to have better tools to search for objective evidence. I ended up working for two national laboratories. I have had remarkable answers to prayer and was even given a software idea in my personal devotions in 1997 that has become a standard for statistical environmental sampling design. The program that resulted, Visual Sample Plan, is still available at http://vsp.pnnl.gov/.

    I briefly discuss evidences in a recent talk I gave with my wife Virginia at the Kennewick, Washington Seventh-day Adventist church:
    http://www.uccsda.org/files/audio/Churches/Kennewick/2015-02-21-More_to_This_Life_Spirituality-Jim_and_Virginia_Davidson-24.mp3

    I believe that even mathematics, the language of science, is based on faith. See “Mathematics the Loss of Certainty” by Morris Kline. Naturalistic science is also based on faith. The belief that life arose by natural processes in a finite amount of time is definitely based on faith, not observation, or even evidence.

    One of the best statements for me regarding faith is “Our faith must rest upon evidence, not demonstration.”

    I testify that there is wonderful evidence available to the reality and character of God.

    With great respect for your search for truth, your fellow BCA alumnus,

    Jim Davidson

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    1. Jim,

      Sorry it has taken me so long to reply to your comment. I’m not sure how you would know that I am responding, but if you do please feel free to reply. Let me reply briefly to several of the points that you have raised.

      Though it is apparent that you have related your faith journey before, I’m sure that both your comments and your faith are sincere.

      Many, if not most of my Christian friends have stated that, like me, they had a period in their life when they had become atheists or at least doubters. But in nearly all of those cases there were differences between their experience and mine. Some simply stated that they had gotten angry with God but admitted that they never fully lost their faith. Others, perhaps similarly to you, stated that they had lost their belief for a time. The difference that I noted, though, was the following. When I lost my faith it was based on a massive discrepancy between what I was being taught and what I had been reading on my own—astronomy, evolutionary biology, geology. Moreover, while my friends’ experiment with doubt was a time of personal difficulty and crisis, mine was accompanied by a great sense of relief and, frankly, joy. The tension between what I had learned and what I was being taught was broken. And that has been the experience of most of my atheist friends as well. From your comments, it appears that your crisis of faith was more typical of those who have returned to the Christian faith.

      If I heard “singing in my mind that I did not know the words to,” my reaction would be one of curiosity, but it would not occur to me that this was confirmation of the existence of God. This brings up the question of what constitutes “evidence.” Generally, internal feelings and thoughts do not represent good evidence because they are notoriously difficult to test. I have a standing offer to accept belief in a deity if I am provided with objective, testable evidence. This needs to be evidence that is not subject to natural interpretation. It’s never happened. And I believe that has been the experience of other atheists as well. Why do I insist on such evidence? Because that is the kind of evidence that we ordinarily require for other beliefs about the nature of the world. From my point of view, it shouldn’t be any different for beliefs relating to the existence of God.

      You mention searching for “objective evidence” as well. But the only evidence you provide relates to belief in answered prayer and to having come up with software ideas during (?) personal devotions. The well-designed and run studies of the efficacy of prayer have failed to provide any objective evidence. There are literally millions of stories about answered prayer, of course, but as I’m sure you understand, there is no way to distinguish those instances from mere coincidence or other natural, mundane causes for the prayed for event. It is only natural for humans to remember those instances when prayer was seemingly answered and not to remember those instances when it was not. To me the most telling point is that no one ever prays for the regeneration of lost limbs. Why is that? Because that really would be a miracle.

      Interesting that you mention “Mathematics: the Loss of Certainty.” That’s a book that I read over 30 years ago. I still have it and plan to reread it. My take-away from reading the book was different from yours. I don’t believe that a logic system, which is another way of describing math, is a matter of faith. Nor do I believe that “naturalistic science” is based on faith. The understanding of the world that we have gained through science is based on objective evidence, just the opposite of faith, which is belief despite a lack of evidence.

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    2. Hi John,

      I just noticed your reply. I will reply when I get some time to share my thoughts. In a nutshell, I believe it is demonstrable that mathematics, the language of science, and "naturalistic science" are both based on faith. This will take some time, because any discussion such as this requires careful definitions of terms.

      Later,
      Jim

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  2. Hi John,

    I’m glad that you read Morris Kline’s “Mathematics, the Loss of Certainty,” and are planning to read it again. Some points from that book that lead me to believe that mathematics involves faith follow.

    First, for me, personally, faith is personal belief based on evidence, not demonstration. I sincerely want to base my faith on the best evidence available, not just my personal wishes and desires.

    I believe the last two words of Kline’s book, p. 354, require faith, whether you accept them or reject them. They are the words “surely divine.” The context is: “Alfred North Whitehead once wrote, ‘Let us grant that the pursuit of mathematics is a divine madness of the human spirit.’ Madness, perhaps, but surely divine.”

    Earlier in the book, Kline points out how deeply linked faith and mathematics were in the studies of some of the most influential mathematicians of all time.

    Kline, pp. 34, 35, “The search for the mathematical laws of nature was an act of devotion which would reveal the glory and grandeur of His handiwork. Mathematical knowledge, the truth about God’s design of the universe, was as sacrosanct as any line of Scripture.”

    Kline, p. 35, “Perhaps the most impressive evidence that the Greek doctrine of the mathematical design of nature coupled with the Renaissance belief in God’s authorship of that design had taken hold in Europe is furnished by the work of Nicolaus Copernicus and Johannes Kepler.”

    Kline, pp. 38, 39, “After stating his third law Kepler broke forth into a paean to God: ‘Sun, moon, and planets glorify Him in our ineffable language! Celestial harmonies, all ye who comprehend His marvelous works, praise Him. And thou, my soul, praise thy Creator! It is by Him, and in Him that all exists. That which we know best is comprised in Him, as well as our vain science.’”

    Kline, p. 46, “For Pascal, science is the study of God’s world. The pursuit of science for mere enjoyment is wrong. To make enjoyment the chief end of science is to corrupt research, for then one acquires ‘a greed or lust for learning, a profligate appetite for knowledge.’ ‘Such as study of science springs from a priori concern for self as the center of things rather than a concern for seeking out, amid all surrounding natural phenomena, the presence of God and His glory.’”

    Kline, p. 46, “Of the seminal thinkers who forged modern mathematics and science, Galileo Galilei (1564-1642) ranks with Descartes….Divine reason is the source of the rational in nature. God put into the world that rigorous mathematical necessity which men reach only laboriously….Moreover, the study of nature is as devout as the study of the Bible. ‘Nor does God less admirably reveal himself to us in Nature’s actions than in the Scriptures’ sacred dictions.’”

    Kline, p. 50, “If the conviction that the mathematical laws of science were truths incorporated by God in His design of the universe needed any reinforcement, it was superbly provided by Sir Isaac Newton (1642-1727).”

    Kline, p. 59, “In the third edition of his Mathematical Principles of Natural Philosophy, Newton answers his own questions: ‘This most beautiful system of sun, planets, and comets could only proceed from the counsel and dominion of an intelligent and powerful Being….This Being governs all things, not as the Soul of the world, but as Lord over all….’ Newton was convinced, too, that God was a skilled mathematician and physicist….Science should uncover God’s glorious designs. Newton began the same letter to Bentley with the thought: ‘When I wrote my treatise about our system [The Mathematical Principles of Natural Philosophy], I had an eye on such principles as might work with considering men for the belief in a Deity; and nothing can rejoice me more than to find it useful for that purpose.’ There are many other such letters in Newton’s correspondence.”

    The blog is stopping by on number of characters. Will try to add more in next post.

    Jim

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  3. Kline, p. 60, “Like Newton, Leibniz, regarded science as a religious mission which scientists were duty bound to undertake. In and undated letter of 1699 or 1700 he wrote, ‘It seems to me that the principal goal of the whole mankind must be the knowledge and development of the wonders of God, and that this is the reason that God gave him the empire of the globe.”

    Kline, p. 66, “Leonhard Euler, the greatest of the 18th-century mathematicians…agreed with Maupertius that God must have constructed the universe in accordance with some basic principle and that the existence of the principle evidenced the hand of God.”

    Kline, p. 71, “Unintentionally, even the most faithful began to make distinctions that led gradually to the elimination of God’s role in the design of the universe.”

    Kline, pp. 71, 72, “Though many a mathematician after Euler continued to believe in God’s presence, His design of the world, and mathematics whose main function was to provide the tools to decipher God’s design, the further the development of mathematics proceeded in the 18th century and the more numerous it successes, the more the religious inspiration for mathematical work receded and God’s presence became dim.”

    Kline, p. 72, “Laplace completely rejected any belief in God as the mathematical designer of the universe.”

    After discussing non-Euclidean geometry and its implications (and a non-commutative algebra, i.e., the product AB does not always equal BA, based on quaternions), Kline states the following:

    Kline, p. 95, “Thus the sad conclusion which mathematicians were obliged to draw is that there is no truth in mathematics, that is, truth in the sense of laws about the real world. The axioms of the basic structures of arithmetic and geometry are suggested by experience, and the structures as a consequence have a limited applicability. Just where they are applicable can be determined only by experience. The Greeks’ attempt to guarantee the truth of mathematics by starting with self-evident truths and by using only deductive proof proved futile.”

    Kline, p. 97, “The relationship of mathematics to the physical world was well expressed by Einstein in1921, ‘Insofar as the propositions of mathematics give an account of reality they are not certain: and insofar as they are certain they do not describe reality….But it is, on the other hand, certain that mathematics in general and geometry in particular owe their existence tour need to learn something about the properties of real objects.’ Mathematicians had given up God and so it behooved them to accept man. And this is what they did.”

    I will finish with next post...

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  4. Moving on to more modern times, a development in mathematics that requires faith, which some mathematicians accept and others reject, is Cantor’s (1845-1918) notion of infinite sets.

    Kline, p. 203, “However, Cantor’s theory of infinite sets provoked a host of protests. Despite the fact that, as already noted, the theory was being used in many areas of mathematics, some mathematicians still refused to accept actually infinite sets and their applications….Cantor defended his work. He said he was a Platonist and believed in ideas that exist in an objective world independent of man. Man had but to think of these ideas to recognize their reality. To meet criticisms from philosophers, Cantor invoked metaphysics and even God.”

    The Wikipedia bio says Cantor “was a German mathematician, best known as the inventor of set theory, which has become a fundamental theory in mathematics.” “To Cantor, his mathematical views were intrinsically linked to their philosophical and theological implications – he identified the Absolute Infinite with God, and he considered his work on transfinite numbers to have been directly communicated to him by God, who had chosen Cantor to reveal them to the world.”

    A recent debate, “Infinity: does it exist?? A debate with James Franklin and N J Wildberger,” by two mathematicians regarding the existence or non-existence of the infinite in mathematics can be found at: https://www.youtube.com/watch?v=5CiiGdaYEPU

    Kline, p. 257, “Thus by 1930, four separate, distinct, and more or less conflicting approaches to mathematics and been expounded, and the proponents of the several views were, it is no exaggeration to say, were at war with each other.”

    I could also mention the work of Gödel and its implications. See Kline, p. 263.

    Whether we accept or reject Kline’s contention that mathematics is “surely divine,” I think we must exercise faith to reach our conclusion. Kline is certainly in influential company.

    I have much more I could say, but will stop there for now. If you would like my reasons for suggesting that faith is involved with science, as well, please let me know.

    With respect,

    Jim

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    1. Some of my comments get posted twice for some reason. That is the cause of the deletes. Jim

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    1. Jim,

      First, let me suggest that it might make more sense to continue this discussion either on email or on Facebook. I think that would avoid problems with length of response that the blog imposes. Also, you would know when I responded. Facebook would have the added advantage that it would allow others to comment as well, though that may not be your interest here. If you want to "move this discussion, just let me know. For now, here is my response to your latest comments:

      Because our world views are so different, I think we will need to come to an agreement on terminology if we are to have a fruitful dialog. In my experience in many cases disagreements have stemmed not so much from a difference in actual points of view as in the meaning of the terms being used. “Faith” is one of those words that has multiple meanings each of which can carry different connotations. Your understanding of the word is very different from mine, and I’m not sure I even understand it. I generally use faith to refer to a belief held despite a lack of objective evidence. It really doesn’t have any necessary relationship to religious belief or the supernatural. One can have faith, for example, in the value of homeopathy or in UFOs or even, I suppose, in string theory.

      You state that faith “is personal belief based on evidence, not demonstration.” First, I don’t know what you mean by “not demonstration.” Second, my sense is that you are using “faith” specifically in a religious context, perhaps as a synonym for belief in God, but I am not sure of that. I would ask you to clarify your meaning.

Moreover, I’m not sure how your definition of faith relates to your statements regarding the notion that mathematics requires “faith.” If you define faith as belief based on the best evidence available, does that mean that mathematics is based on the best evidence available? There seems to be a discrepancy between your initial definition of faith and your use of the term in the context of mathematics.

      Further, I am particular about the nature and quality of evidence. For me a distinction needs to be made between subjective evidence and objective evidence. By “subjective” I include evidence that is internal or personal to the individual and not being experienced by others. Objective evidence is evidence that can be tested, that is, supported or disconfirmed. Hearing unfamiliar music in one’s mind is subjective; conducting well designed experiments to establish a connection between the administration of certain drugs and the curing of specific diseases is objective. Of course, the subjectivity or objectivity of evidence is not always either/or but can be said to fall along a continuum. However, in general the value of evidence in advancing an understanding of the world is based on the extent to which it is objective.

      Continued below . . .

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    2. I do recall Kline’s book focusing my attention on the fact that mathematics is not so much about truth as about the development of formal systems of logic—playing with symbols on a piece of paper, if you will. What especially brought this home for me was the development of non-Euclidean geometries. That’s not to say that mathematics doesn’t describe the physical world. It’s just that specific mathematical systems may be very good or not so good in helping us to understand that world. After all, non-Euclidean geometries have done a better job of describing some of the ideas regarding the nature of space than Euclidean geometry has.

      Many of your quotes from the Kline book concern the fact that earlier mathematicians had a belief in God. And they saw mathematics as an expression of God’s grandeur and power. Of course, religious belief, at least in the western world, was nearly universal until at least the 18th century. The fact that these mathematicians had faith in God and saw a connection between the beauties of math and their understanding of God doesn’t mean that mathematics “requires” faith (or at least the religious faith to which I think you are referring). As you point out, Kline states that religious belief among more recent mathematicians has declined just as it has in the population generally. In short, the fact that many, generally earlier, mathematicians believed in God along with nearly everyone else is scant support at best for the proposition that God exists. And, indeed, the idea that mathematics may in some sense simply be a human invention, a development and exercise in logic systems, would seem to undercut the notion that mathematics requires a faith in the existence of God.

      Kline’s book discusses one of the fundamental philosophical questions in mathematics, a debate that goes back at least as far as Plato: Are mathematical concepts created or discovered? Plato, of course, argued that there are mathematical ideals, and under that analysis mathematics has been about the discovery of those already existing ideals. Euler’s equation, e^i(pi) + 1 = 0, the proof of the infinitude of primes, or even the Pythagorean Theorem are so beautiful and so elegant that they seem surely to have existed prior to their development by mathematicians.

      It is true that mathematics has its problems, and Kline lays these out very well. His basic thesis is that these problems go to the very heart of mathematics: Does mathematics represent truth or is it fundamentally flawed. Perhaps it is flawed. After all, we are only organisms that evolved to survive and create progeny. Evolutionary forces did not design us specifically to resolve philosophical questions. So perhaps we simply aren’t capable of resolving these issues or perhaps our logic is imperfect. On the other hand, mathematics has worked brilliantly in helping us to understand and manipulate our world. So perhaps we should treat math like we treat basic chemistry or physics—those disciplines almost certainly do not reflect precisely the actual nature of the world but for most practical purposes they do a terrific job.

      I had a different understanding of Kline’s use of the term “divine.” I think he, as well as Whitehead, were using it in the sense of wonderful, not in a sense relating to a divinity. In sum, I don’t see how the uncertainty regarding mathematics relates to religious belief, which I think is your basic premise. If there is something else or if I am missing your point, please let me know.

      John

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  7. Hi John,

    Thanks much for your thoughtful response. You make your points well, and I can heartily agree with some of what you say. Yes, it would be easier to carry on this discussion, if you wish, by email. I had a Facebook account, but canceled it due to time concerns. If you send your response to davidson@owt.com we could discuss by way of email.

    First, where we agree.

    “I think we will need to come to an agreement on terminology if we are to have a fruitful dialog.” [John]

    Yes, well said! [Jim]

    “Further, I am particular about the nature and quality of evidence. For me a distinction needs to be made between subjective evidence and objective evidence. By “subjective” I include evidence that is internal or personal to the individual and not being experienced by others. Objective evidence is evidence that can be tested, that is, supported or disconfirmed.” [John]

    Again, yes, well said! My concern between the nature of subjective and objective evidence has informed my life, and I discuss it in that talk I gave with my wife titled, “Excuse Me, Is Anyone Out There.” I gave the link in a previous post.

    Now for some clarifications on my part to some of your comments:

    “‘Faith’ is one of those words that has multiple meanings each of which can carry different connotations. Your understanding of the word is very different from mine, and I’m not sure I even understand it….

    “You state that faith ‘is personal belief based on evidence, not demonstration.’ First, I don’t know what you mean by ‘not demonstration.’ Second, my sense is that you are using ‘faith‘ specifically in a religious context, perhaps as a synonym for belief in God, but I am not sure of that. I would ask you to clarify your meaning.
    [John]

    I believe faith is required in mathematics, just as it is in theology, because of two things: the nature of the axiomatic method, and because of the existence or non-existence of the infinite.

    Euclid’s Elements begins with Definitions, Postulates, and Axioms. I have before me the English translation of “Euclid’s Elements,” “all thirteen books complete in one volume,” published by Green Lion Press in 2013.

    Page 1, Definition 1: “A point is that which has no part.”

    It takes faith to accept that statement. Physics does not currently know whether such an infinitely small entity actually can exist. Some physics postulates, but cannot currently demonstrate the following: “According to the generalized uncertainty principle…the Planck length is, in principle, within a factor of 10, the shortest measurable length – and no theoretically known improvement in measurement instruments could change that.” (http://en.wikipedia.org/wiki/Planck_length)

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  8. Continuing…

    Are there an infinite number of points between zero and one on the number line? If I say yes, I must also recognize I am finite and so I cannot count them. But I can use deductive methods, based on my faith in the definitions and axioms of my axiom system, to demonstrate the need for the infinite. However, there are mathematicians, currently alive, who do not accept the infinite. However, they cannot specify a maximum number, so they too are in need of faith to believe such a number exists. Please see the video I mentioned earlier of the debate on the infinite.

    Regarding the infinite, the ancient Greeks had a huge dilemma about this, based on the discovery that the square root of 2 cannot be represented by the ratio of any two whole numbers, no matter how big they are. In other words, there is an absolutely zero probability that we will ever find two positive integers such that their ratio is the square root of 2. I will be happy to send a proof of this by way of email. However, my proof, as well as all other proofs in mathematics, depends on my faith in the axioms of the geometry I select to use.

    I personally believe in the infinite, but I respect the mathematicians who reject that belief. In either case, faith is involved. My faith in the infinite, partly based on Biblical claims, informs my faith in the infinite in mathematics, and vice versa.

    Psalms 147:5 NASB says, “Great is our Lord and abundant in strength; His understanding is infinite.”

    When I look at the square tiles on the kitchen or bathroom floor, I am reminded that the length of the diagonal of that square, if the side is one unit, is an irrational number with an infinite number of non-repeating digits. Computers have calculated the sq. root of 2 to over 2 trillion digits, without finding any pattern, but that does not prove such a pattern might not begin after the septillionth digit. However, I believe that is convincing evidence for my faith in the axioms of the geometry I use to “prove” the irrationality of the sq. root of 2. It is not, however, a demonstration. A demonstration is a complete enumeration of the population of the sample space under discussion. If that sample space is infinite, I cannot enumerate it.

    My faith in the irrationality of the sq. root of 2 rests on my faith in certain definitions, postulates, and axioms of geometry and the convincing, to me, evidence of recent computer calculations. However, there are mathematicians who reject this because they put their faith in other definitions and axioms.

    The proof that the Greeks worked out to “prove” the irrationality of the sq. root of 2 is even more convincing evidence than the computer calculations—but it still requires faith.

    Cantor’s faith in the existence of infinite sets has had a huge influence on modern mathematics. However, not all mathematicians share that faith.

    What do you believe in regard to the axiomatic method and the infinite?

    Thanks,
    Jim

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