Is mathematics an eternal truth?

Discussion in 'Defending the Faith' started by Gesetveemet, Aug 29, 2011.

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  1. Gesetveemet

    Gesetveemet Puritan Board Freshman

    Please excuse my ignorance on this subject.

    My question is is 3+3=6 an eternal truth?

    Thank you,

    Last edited: Aug 29, 2011
  2. TimV

    TimV Puritanboard Botanist

    I've read it is because there are places in the Bible that say things like so and so reigned in such and such a place for 33 years and another place for 7 years, therefore so and so reigned for 40 years.
  3. Phil D.

    Phil D. Puritan Board Junior

    Hmmm... Good question. However, Three equals One definitely is! ;)
  4. BobVigneault

    BobVigneault Bawberator

    I guess I need to ask you what you mean by eternal. Is 3 + 3 = 6 a True truth? Is is true outside of space and time? Is it true within the mind of God? Is there a sense or world in which it is not true?

    My answer would be that 3 + 3 = 6 is true, according to the laws of logic and that logic is an essential property of God. In that God is transcendent and eternal, this truth is also eternal.
  5. BobVigneault

    BobVigneault Bawberator

    William, if these things fascinate you then you might enjoy listening to Ronald Nash teach on Christian Apologetics. He's a lot of fun to listen to with a winsome sense of humor. I sure miss him. You can link to his lectures here.
    Last edited: Aug 29, 2011
  6. Pergamum

    Pergamum Ordinary Guy (TM)

    Was there ever a time when 1+1 did not equal 2?
  7. TimV

    TimV Puritanboard Botanist

    It would seem it would always be the same, from a debate I followed (without completely understanding) some years ago.
  8. BobVigneault

    BobVigneault Bawberator

    Trevor, in the last 55 years I don't remember a time when it didn't but then again, I was sleeping for about a fourth of the time (55/4 = 13.75)
  9. TimV

    TimV Puritanboard Botanist

    6 hours of unconscious per day is impressive!

    ---------- Post added at 07:41 AM ---------- Previous post was at 07:40 AM ----------

    edit: 24 divided by 4 is 6. We should do like McArthur and always give proof texts and calculations.
  10. BobVigneault

    BobVigneault Bawberator

    I don't need a lot of sleep Tim. If I get more than that, it deprives me of my normal stupor. (Hey, I'm gonna go use that for my update today. Don't tell anyone.)
  11. Marrow Man

    Marrow Man Drunk with Powder

    The numbers in the equation are only symbolic representations of the abstract entities and there are assumptions in the operation (i.e., the properties of addition are axiomatic; equality is also an assumption and can have different meanings in different contexts).

    There are also limits to mathematics -- not necessarily because numerical principles are flawed, but because our understanding of them is limited and incomplete. We have a difficult time comprehending infinity, for instance. The existence of irrational numbers is difficult for some.

    Or try to wrap your brain around this one: 0.9 as a repeating decimal (that would be 0.9 with a line over the nine, but I don't know how to represent that on here) approaches 1 in value, but it does not equal one. Yet consider the following equations:

    First, an easy one: N = .3 (non-repeating)

    Then, by multiplication, 10N = 3.0

    By subtraction:

    10N = 3.0
    N = 0.3

    Making 9N = 2.7
    Thus (by division), N = 2.7/9 or 27/90, which equals 3/10.

    We have just shown that 0.3 = 3/10.

    Now try N = 0.3 (this time, a repeating decimal).

    10N = 3.3 (still repeating)
    N = 0.3 (repeating)

    Making 9N = 3

    So N = 3/9 or 1/3

    We have just shown that 0.3 (repeating) = 1/3. So far, so good.

    Now consider N = 0.9 (repeating)

    10N = 9.9
    N = 0.9

    If we subtract, we get:

    9N = 9

    Thus, N = 1.

    So we started with N = 0.9 (repeating) and ended with N = 1. Thus, 0.9 (repeating) = 1. :scratch:
  12. Pergamum

    Pergamum Ordinary Guy (TM)

    My question is that if half the number in the world are odd and half even, and you add two odds you get an even and you add two evens and you get an appears that evens outnumber odds by at least 2 to 1.
  13. TimV

    TimV Puritanboard Botanist

    Or, as Bilbo said

    "I don't know half of you half as well as I should like; and I like less than half of you half as well as you deserve.”
  14. Phil D.

    Phil D. Puritan Board Junior

    Three men went to get a hotel room, and were told it would be a total of $30.00 for all of them - or, $10 apiece. Later the clerk decided that he would would give the guys a break, and refund a total of $5. The bellhop was on his way to their room to deliver the refund, but realized he didn't have the proper change to give an equal amount to each man. So he decided to give each one $1 and to keep $2 for himself (Yes, that would be a violation of the 8th Commandment, but this is only a mental exercise, people...) So, the men spent $9 each for the room ($10 initially <-> $1 refund = $9), and the bellhop kept $2. But then where is the "other" dollar ($9 X 3 = $27 + $2 = $29)?
  15. GulfCoast Presbyterian

    GulfCoast Presbyterian Puritan Board Junior

    I don't think that there is an "other dollar." This wording just sets up a logical fallacy. Break down the math:

    $30.00 was originally given to the hotel owner
    Correct price of the room = $25
    Each man receives $1 dollar refund = $3
    The bellhop receives a $2 "theft bonus"
    $25 for room + $2 for the bellhop= $27

    $30 - $27 = $3 which is how much the men collectively receive back as a refund.

    At least I think that is right.
  16. Phil D.

    Phil D. Puritan Board Junior

    Exactly, Mark!

    The proper question to address in a situation like this is "where are each of the $30 now?"

    The clerk has $25
    The bellhop has $2
    Each of the 3 guys has $1
    $25 + $2 + $1 + $1 + $1 = $30

    Still, you'd be surprised how many people get freaked out trying to solve the "dilemma"!

    A similar fallacy with the same situation would be to say that the room cost $27, the bellhop has $2, and yet each of the 3 men has $1 - so, where did the "extra" $2 come from ($27 + $2 + $1 + $1 + $1 = $32)?

    It's all a matter of asking the right question - or, rather, asking the question right!
    Last edited: Aug 29, 2011
  17. Backwoods Presbyterian

    Backwoods Presbyterian Puritan Board Doctor

    Someone get the exorcism kit ready...Marrow Man is speaking in tongues!!!
  18. BobVigneault

    BobVigneault Bawberator

    Pastor Ben, speaking in tongues does not necessarily mean he has a "familiar" spirit. It could just mean he's reading a bit too much Grudem. Either way, throw some holy water on him if you see Pastor Tim coming near.
  19. GulfCoast Presbyterian

    GulfCoast Presbyterian Puritan Board Junior

    Who gonna interpret all that, anyhow!!! :)
  20. Philip

    Philip Puritan Board Graduate

    To the original question, I would ask whether God could create the world such that 2+2 does not equal 4.
  21. Marrow Man

    Marrow Man Drunk with Powder

    Mr. Vice President, now that you have seen my math skills at work, you know balance the federal gov't will not be a problem.

    Does this then become another way of stating the "can God create a rock so big He can't move it" fallacy?
  22. Philip

    Philip Puritan Board Graduate

    More or less, since a world where 2+2 does not equal 4 is just as logically absurd as a world that contains a rock too big for an omnipotent being to lift.
  23. VictorBravo

    VictorBravo Administrator Staff Member

    As Tim pointed out, the rules of math are axiomatic. So 3 + 3 = 6 is a defined truth.

    Given that these math rules are based upon axioms, I think it is indeed possible for a reality in which 2 + 2 does not equal 4.

    All that is required is a different definition. If "+" means combine the terms and replicate one of them too, rather than merely "combine" the terms, then 2 + 2 = 6.

    Of course, that is equivocation, but that is the point I'm trying to make. We recognize relationships and then come up with equations as short hand to represent them. That is where empiricism has a use--it reminds us of the law of identity: one apple, another apple, we call it two apples. They are never the same apple and they are never more than the two apples. We intuitively understand that this relationship applies to anything we can think of, be it oranges, stars, or multivariate functions.

    So the real question is whether the law of identity is fundamental. If you have one thing and another separate thing, and consider them together, do you always have a group of separate things that you can designate as amounting to "2"? If not, then there is no such thing as identity.

    If no identity, then all we have is absurdity and might as well just play backgammon.
  24. Marrow Man

    Marrow Man Drunk with Powder

    Agreed. God can do whatever is consistent with His nature. There are things He cannot do (e.g., He cannot lie -- Titus 1:2; Hebrews 6:18). Hence, it is a logical absurdity to claim that God should be able to do all things, which is part of the problem with those kinds of arguments. I would say that it is also impossible for God to commit a logical fallacy and, in keeping with the discussion in the OP, it would be impossible for God to commit a mathematical error.
  25. Marrow Man

    Marrow Man Drunk with Powder

    A different symbolic notation of the numerals could also generate this. "2" is merely a symbol for "two-ness." If "4" were a symbol for "three-ness," then you could have a situation where 2 + 2 does not equal 4. But all you done is redefined things. The concept of "two-ness" added to "two-ness" is still equivalent to "four-ness" (if we are going with the accepted axiom of addition ).
  26. VictorBravo

    VictorBravo Administrator Staff Member

    Well, yes, I agree. I thought I admitted that by calling it an equivocation. ;)
  27. Marrow Man

    Marrow Man Drunk with Powder

    I thought that was just lawyer-speak. :D
  28. Philip

    Philip Puritan Board Graduate

    Careful there---there are all kinds of persuasive arguments that involve formal falllacies. Appeal to authority, for instance, is a formal fallacy, even though it can be a very useful type of argument.
  29. TimV

    TimV Puritanboard Botanist

    I knew kids in High School who would have said "heavy, dude" after that. Me, I'll just tattoo it in three colors on the lower part of my back :D
  30. jwright82

    jwright82 Puritan Board Senior

    I think we need to follow Van Til here and point out that dealing with God's nature in an ordered and abritrary fashion leads to bounding God in ways that he has not revealed to us. God can do whatever he wants to do, no matter what. All we need to know is that for us 2+2=4, that is all that needs to be known. There is the creator, who is beyond all human comprehension outside of his revealation, and the creature, who can only understand things as creatures.
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