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Discussion in 'Off-Topic' started by Plotinus, Feb 13, 2007.

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  1. Plotinus

    Plotinus Philosopher Administrator

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    Only when people make posts while they are still writing their responses to previous posts...

    I don't know what you mean by "mathematics is empirical". That is a nonsense statement. "Empirical" is not a quality that a body of knowledge can possess. If you mean "mathematical truths can be known by empirical means", then yes, of course. If I put two things next to two other things and count them then I can learn that 2+2=4 empirically. However, I would deny that mathematical truths can be known only by empirical means. They are true by logical necessity and can be known intuitively. There's nothing particularly controversial about that. You seem to be denying the possibility of any kind of a priori knowledge at all. That seems almost impossible to believe - quite apart from being itself impossible to verify empirically.


    Well, I'll have to take your word for that as I don't know about it. But I don't see that it really makes any difference unless you explain in more detail.

    As you can no doubt tell, philosophy of mathematics is not my field so I don't want to digress too far down this road. I also note that I don't see any responses to my other points against your logical positivism and extreme pragmatism, so I'll assume that, apart from the disagreement over the truth value of mathematical statements, I've convinced you of the rest.
     
  2. Quasar1011

    Quasar1011 King of Sylvania

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    Will this convince you then?

    Daniel 7:13
    "In my vision at night I looked, and there before me was one like a son of man, coming with the clouds of heaven. He approached the Ancient of Days and was led into his presence.

    Matthew 24:30
    "At that time the sign of the Son of Man will appear in the sky, and all the nations of the earth will mourn. They will see the Son of Man coming on the clouds of the sky, with power and great glory.

    Mark 14:62
    "I am," said Jesus. "And you will see the Son of Man sitting at the right hand of the Mighty One and coming on the clouds of heaven."

    John, Daniel, Matthew and Mark all said the same thing about Jesus. Mark and Matthew even quoted Jesus explicitly. John's statement in Revelation 1:7 (which I quoted in my earlier post) is a paraphrase of what Jesus said. The Bible has many writers, yes; but God is the author of it all.*

    Are you saying that nothing ever predicted in the Bible has ever come true, so why should we believe it? On the other hand, if the Bible's record on prophecy is accurate, why wouldn't we believe its future predictions? Which view do you subscribe to?



    *although at times, God does include opposing viewpoints, as in most of the Book of Ecclesiastes- or anytime Satan speaks.
     
  3. warpus

    warpus In pork I trust

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    These things you mention are trivial truths.
     
  4. Plotinus

    Plotinus Philosopher Administrator

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    As far as I can tell, Daniel doesn't say anything about Jesus - he simply refers to a "son of man". If Matthew and Mark report Jesus' words correctly, then Jesus simply quotes Daniel. Note, in particular, that Jesus does not claim in those quotes that he is "the son of man". Even if he did, I don't see what's so remarkable about all this. If there were very good reason to suppose that Jesus had never read Daniel or heard about this passage in that book, then you might have something - but since Jesus presumably knew this passage from his childhood (it was, in fact, a central passage in apocalypticism of his day) I'm not sure what his quoting it proves.

    Also, I don't know what translation of the Bible you are using, but it is inaccurate. The Mark quotation should not be "I am... and..."; it should be "So you say... but...". He actually denies to be the Messiah in this passage (the equivalent passage in Matthew changes it completely to ensure that Jesus claims to be the Messiah). Not that this is very relevant, of course, since "Messiah" does not mean the same thing as "son of man", but I think you should be wary of that translation if it can actually reverse the meaning of a text like that...

    Similarly, I don't see the evidential force of citing all the Gospel writers as testifying to Jesus' words. Given that Luke and Matthew simply copied Mark, together they constitute only one source. Even if they were all independent, that would mean only that we have particularly good reason for supposing that Jesus really said it. But what does that prove? It doesn't mean Jesus was right, does it?

    Neither. You present a false dichotomy. I don't say that nothing predicted in the Bible has ever come true or that everything in the Bible has come true. But I do say that many of the predictions in there have not come true. I have already mentioned Jonah's preaching to the people of Nineveh (he said the city would be destroyed, but it wasn't; note that he did not say it would be destroyed unless they repented). And 1 Kings 22, where God instructs his prophets to lie to the king. We could also mention Ezekiel 29:8-14, according to which Egypt will be completely desolated and uninhabited for forty years. This comes immediately after a terribly long and dramatic prophecy (16-28) that Tyre would be permanently destroyed by Nebuchadnezzar - in fact he never defeated the place at all, let alone destroyed it (which is confirmed in other sources and also in Ez 28:18-19 itself!).

    There are other well-known discrepancies between prophecies and what really happened. Compare Jeremiah 34:4-5 (Zedekiah will die peacefully) with Jeremiah 52:10-11 (Zedekiah dies in anything but a peaceful way).

    I've already mentioned Jesus' prediction of the Temple's destruction in Mark 13:2 - look again and you'll see that he predicts that not one stone will be left on another. Well, there are still stones of that Temple resting on each other - that's what the Wailing Wall is.

    The fact that a prophecy and its non-fulfilment can be recorded in the same biblical book suggests strongly that the biblical writers didn't see this sort of thing as a problem. They didn't think that the sign of a divine prophecy is fulfilment. I'm sure you know that Deuteronomy 13:1-3 speaks of the possibility of false prophets who nevertheless predict future events with perfect accuracy. If it's possible to make accurate predictions but be a false prophet, and possible to make inaccurate predictions but be a true prophet, then what is the criterion? That Deuteronomy passage suggests that the only criterion of whether a prophet comes from God is whether or not he tells people to love only God. And whilst that may be very edifying, I'm not personally inclined to believe everything someone says simply because they tell me to love only God, especially if God is not particularly bothered about ensuring that everything his prophets say is true anyway.

    I'm really not clear what you're trying to argue for. Are you saying that everything in the Bible is true because some things are true? But that would clearly not be a good argument (there are probably true things in The Da Vinci Code too, but it doesn't follow that it's all true) and besides, you haven't given any examples of things in the Bible that are true, only things in the Bible that are supposedly supported by other bits of the Bible. If you're trying to argue that the Bible is wholly consistent, then simply citing texts that support each other won't prove that either - you need to look at the passages that seem to contradict each other and explain why they don't. But of course, even if you could show the Bible to be completely consistent, it still wouldn't make it true. The Da Vinci Code is internally consistent but it's not true.

    I don't know what you mean by a "trivial truth". Even so, they are still true, and they are still known without having to use "the scientific method" that Perfection insists is the sole method of knowing any truth whatsoever. Yet I would say that not only are these truths that are known by other means, but the scientific method itself wouldn't be applicable without assuming them. Their supposed "triviality" is really neither here nor there.
     
  5. The Last Conformist

    The Last Conformist Irresistibly Attractive

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    If an idle thought be allowed in this august thread, I wonder what had happened if they'd had set theory back then - it tends to make you very blasé about infinities.
     
  6. Plotinus

    Plotinus Philosopher Administrator

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    TLC, your idle thoughts are more august than most people's non-idle ones!

    Interesting point. It seems to me, though, that set theory is likely to make you blasé about infinite numbers of things, rather than about the idea of a single thing which is infinite or has qualities to an infinite degree. I may be wrong there though.
     
  7. The Last Conformist

    The Last Conformist Irresistibly Attractive

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    This, I am afraid, says more about your lack of mathematical schooling than anything else.

    Let's look at an example you happent to be aware of, if unconsciously, namely the modulo 24 math of the (24h) clock. 21 eleven hours plus 5 three ours isn't 26 hours but 2 hours. This may seem a mere "trick" to you, but it's actually an instantiation of an different algebra that's just as consistent and valid as our usual sort.

    What isn't conventional, though, is what sort of mathematical laws a given model of a given physical system obeys. 90=450 when discussing angular orientation (in deg), but not when discussing the number of doublons in your treasure chest!

    *****​

    Re: evolution and God, I think you've got it basically right, and Perf and Dawkins basically wrong. Evolutionary theory does remove a slew of god-of-the-gaps arguments, but it does not in itself constitute an argument against the existence of the omnific God.

    The reason for all the fireworks is that evolution relegates Genesis (and certain bits of the Koran) to the status of, at best, myth. It's an obvious point, but somehow tends to get forgotten in these discussions; the belief in the omnific is not even remotely the entirety of the Christian faith. Something can be an argument for Christianity (or certain versions thereof) being false without being an argument against the venerable Sr Omnifico.


    (I myself, of course, do not believe in the old guy - it's just that evolution isn't a reason for my lack of faith.)
     
  8. Plotinus

    Plotinus Philosopher Administrator

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    Thank you for explaining. Yes, this makes sense. And I agree that while it does seem that you can have different mathematical systems that arbitrarily follow different laws, you can't arbitrarily decide what system you're using in every context.

    Besides, I suppose you could say that you can still generate true statements using any of these systems. "In a 24-hour clock system (defined thusly...), 21+5=2" is a true statement. Of course the statement would be analytically true rather than synthetically true, but that's no big deal - it's still true.

    Now of course we need to distinguish between the theory of evolution per se (that is, the theory that evolution has occurred) and the theory of natural selection (that is, a theory about the mechanism that drives evolution). As you know, the one preceded the other. The early nineteenth century saw considerable debate between scientists over whether gradual evolution was true, according to which new organisms developed out of older ones, or "catastrophism", according to which each set of organisms was destroyed and then replaced by a brand new set. The interesting thing is that none of these seemed to both the church very much. In 1837, Charles Babbage wrote:

    In other words, the apparent non-literal truth of the Genesis creation stories didn't seem to be such a big deal - any more than the apparent non-literal truth of geocentric texts was much of a big deal once science had pretty much proved heliocentrism. In both cases, the church was surprisingly happy to re-interpret the texts in question once it was clear what the truth really was. Babbage's position (that evolution was probably true and the Genesis account should not be taken literally) was probably the majority opinion, at least in Anglican circles, in the 1840s and 50s. Things only really changed with Darwin in the 1860s, and I think this was because he showed how evolution could occur following natural laws without any need for divine supervision. That really re-ignited the whole problem, and it was in reaction to that that significant numbers of Christians woke up to the whole thing and decided they not only didn't believe in Darwinism but didn't believe in evolution at all. And that was the beginning of modern fundamentalism, the essence of which is that everything in the Bible must be true and the Bible is the sole authority, and any scientific claims which disagree with it are just false.
     
  9. The Last Conformist

    The Last Conformist Irresistibly Attractive

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    Yup. In fact, Penrose (and presumably others) have built a case for mathematical platonism (ie. that there is mathematical truth independent of human convention) on precisely such considerations. Now, I shall refrain to comment further on this, partly cause the relation to theology is tenuous at best, partly because the philosophy of math isn't my field - I'm one of those heretical applied types. :)
     
  10. The Last Conformist

    The Last Conformist Irresistibly Attractive

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    Re: the Christian reception of Darwin, it is of course plenty of Christians who have no problem with Genesis as myth. In fact, perhaps because I grew up in a liberal Christian family, I think that the mythic reading is the one that best fits the text itself, irrespective of any biological or geological concerns. But the Christians who think this way are not the ones making the fireworks.
     
  11. warpus

    warpus In pork I trust

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    Trivial - simple, transparent, or immediately evident. So obvious that you don't even need the scientific method to determine whether it's true or not.

    So, for example, "The number 42 is a number" would be a trivial truth.

    Would you be able to come up with a truth that you don't need the scientific method to determine, that isn't trivial?
     
  12. The Last Conformist

    The Last Conformist Irresistibly Attractive

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    The continuum hypothesis is undecidable under Peano arithmetic.
     
  13. El_Machinae

    El_Machinae Colour vision since 2018 Retired Moderator

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    I've said it elsewhere, but you really cannot empirically prove mathematics. The statement "1 + 1 = 2" assumes that the two ones are the same thing and completely equal to each other. From this, we can build a clever foundation that leads to all types of mathematical fun.

    However, in the real world, there are not two of anything that are exactly the same. I don't have ten fingers, I have 1 right index finger, 1 left index finger, etc.

    If we were trying to use a real-world approximation, we're at best saying "1 + ~1 = 2 (or ~2)" (~ meaning "kinda").

    Math is just a complex analogy, which we find useful. (Terribly so). OTOH, the Superman comics are another analogy and not actually true, but I find them useful as well.

    Again Re: Evolution. It doesn't disprove God, but it disproves that whoever prayed to God about Genesis 1 (and got an answer confirming its literalness) was actually communicating with God.
     
  14. warpus

    warpus In pork I trust

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    Never heard of it, but I'm guessing that's because it's NP complete?
     
  15. The Last Conformist

    The Last Conformist Irresistibly Attractive

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    Nope. NP-complete problems are merely tedious to solve, requiring potentially impractical amounts of computing time. The continuum hypothesis under Peano arithmetic is a Gödel statement - both it and its denial are compatible with the Peano axioms, and thus neither can be proved or disproved.
     
  16. Plotinus

    Plotinus Philosopher Administrator

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    I'll do that, if (a) you define "the scientific method", and (b) you explain why trivial truths don't count. The claim was that we cannot know anything except by the scientific method, and I haven't been given a reason why logical truths are not good counter-examples to this. I don't see why their triviality is really relevant.

    No, it doesn't. If you have a banana and an apple you've got two things, even though a banana is not an apple...

    However, I agree with TLC that this is taking us too far OT, so these matters can be discussed further in other threads if need be - let's try not to get too distracted here!

    Of course, in the west, Christians who don't believe in evolution are a tiny minority: the vast majority don't have the slightest problem with it, either because they interpret Genesis metaphorically or allegorically, or because they just don't think that Genesis is true. People often confuse those two positions but of course they are quite different: to think that something is true but not literally true is not the same thing as to think it false.

    In other parts of the world, though, especially eastern Europe and Africa, Christians who do believe in evolution are the tiny minority. Since the church is becoming very strong in Africa and has withered to next to nothing in the west, I suspect that this means that Christians who think Genesis is literally true now outnumber those who do not. Which cannot be a good thing for Christianity.
     
  17. Veritass

    Veritass Chieftain

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    I think that this has been one of the best threads to date on theology and philosophy, and Plotinus, you have brought quite a lot of interesting information to light. It is clear that you are a true philosopher, i.e. lover of truth.

    I consider myself a philosopher at heart, but I have been struggling lately with the question of: What is the point of philosophy?

    What is the point of trying to study such a huge field whose body of already-existing knowledge is much larger than I will be able to absorb in a lifetime? Many of the discussions we have been having go something like this:
    • What about the question of X?
    • That was explored most thoroughly by philosophers A, F, and H, in their works...
    • What about the question of Y?
    • Exploring that fully requires distinguishing and defining M versus N, and P versus Q. Of course that brings up the question of R-S-T.

    This is quite a bit of learning, and quite a bit of work. Given the limited number of hours in a day, I allocate other parts of it to work, eating, learning music and dance, racquetball, acting, etc. Don't get me wrong: I still enjoy it. I just started reading a collection of essays on myth by Joseph Campbell for my bedtime reading.

    But I can certainly understand how people just stop progressing. One day you just get tired of exploring even further, and decide, "OK, this is what I believe." People with a very low tolerance for such exploration we call "fundamentalists," and people with a very high tolerance we call "Ph.D. in Theology." As with most things, there is a big bell curve of those of us in the middle who seek to have some growing understanding of the world, tempered with the other realities of daily life.

    I believe that belief is a choice we make, and that we (hopefully) evolve that choice over our lifetime of learning and experiencing the world. My question for the theologian is:

    What do you believe?

    In 100 words or less, what beliefs do you hold, and hold most dear?
     
  18. Eran of Arcadia

    Eran of Arcadia Stormin' Mormon Retired Moderator

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    Or, possibly, that they misunderstood the answer.
     
  19. The Last Conformist

    The Last Conformist Irresistibly Attractive

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    Which, of course, would paint God as an imperfect communicator. I realize this might not disturb you, but it should disturb the omnificists.
     
  20. Eran of Arcadia

    Eran of Arcadia Stormin' Mormon Retired Moderator

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    It could be argued that God communicates perfectly, but we, being imperfect, don't understand.

    . . . which raises the question of why a perfect being would have imperfect creations. Yes, it doesn't bother me, but it is a problem for the "omnificists" (great word by the way).
     
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