According to logicians, I can prove a negative

Apologetics Book of Mormon Epistemology Philosophy Reason

I caught this post on the eSkeptic newsletter by a logician arguing that you can prove a negative based on induction (great reading for anyone interested). As that is the case, here are a few negatives I’m ready to prove:

Modern Horses in America:
1. If horses had existed in the Americas prior to the arrival of Columbus and the Spanish, then there is evidence in the fossil record.
2. There is no evidence of horses in the Americas prior to the arrival of Columbus and the Spanish.
3. Therefore, horses did not exist in the Americas prior to the arrival of Columbus.

DNA Evidence for Jewish Ancestry of Native Americans:
1. If a small group of settlers had arrived in the Americas in roughly 600 BCE and grew to a large population, possibly interbreeding with existing people, there would be DNA evidence among Native Americans tracing them back to Jews.
2. There is no DNA evidence of such a group in the Americas.
3. There never was a small group of Jewish settlers in the Americas.

The Existence of the Gold Plates:
1. If the gold plates exist, there would be evidence to support their existence in the form of actual gold plates or similar such plates – plates with reformed Egyptian writing on them made out of gold buried in stone boxes.
2. No such plates have ever been found.
3. There never were gold plates.

Joseph Smith Never Saw God:
1. If Joseph Smith had seen god or other supernatural entities, there would be independent, third party evidence that he had done so (i.e., people with no invested interest in seeing Joseph Smith succeed in his plans would vouch for him).
2. No such affidavits or testimonies exist.
3. Joseph Smith never saw a god or supernatural entity.

I could go on and on, but I think the point is clear – if logicians agree negatives can be proven, apologetic arguments are basically non-existent.

32 thoughts on “According to logicians, I can prove a negative

  1. I’d like to mention that the logicians are talking about ‘induction’, the basis upon which we live our lives. Hume’s entire life’s work can be summed up in proving that there is no logical reason for induction. The problem with that, however, is that we induct like it’s nobody’s business.

    The logical problem across your Premise A in each of those above is that a preponderance of evidence does suggest it is true. However it cannot be conclusively proved.

    Using induction is very scientific, as long as it is clear that the premise must change if different evidence exists.

    And in other news…logic has never played much of a role in apologetics work…lol

  2. There is a complete lack of fossilized evidence of horses in Bulgaria too. This despite historical records showing the horse riding Huns to have inhabited the area.

    So I suppose we can prove that nomadic Huns were never in Bulgaria too.

    Fossilized evidence is always spotty. A lot of times the bones simply decompose and nothing is left over. Any paleontologist can tell you that actually finding a fossil is a lucky find, because most of the time, no such evidence is left by a dead organism.

  3. Sorry for triple posting, but geez…

    Every last one of your #1s is pretty-much made up. None of them are logically true. You’re trying to rig the logic game in your favor. I’m not buying it. Sorry.

  4. I understand your other logical points (the book of mormon, etc.) but as far as independent third party evidence of seeing God – I’m not sure I follow that one. So I with that statement I agree with Seth.

    Is it assumed that if someone were to see God there would be third party evidence? I’m not saying that I believe JS saw God.

    Just that if one assumes that God exists, and can be seen by humans, and decides to show himself to one of those humans, I don’t think we can assume that there would be third party evidence of that. There are a lot of assumptions there.

    If you’re asking for third party evidence of the gold plates – I think the three witnesses all had some vested interest in claiming to have seen them. I would be able to follow that type of statement.

  5. I think that the important idea to glean from the article is that these claims are likely, because we have found no supporting evidence to the contrary.

  6. Intriguing responses all… I have to admit that I have, for a very long time, fallen into the “you cannot prove a negative” camp, which the logician from the link says is not accurate. I am not a logician (no big surprise there), but I thought the logic in that article makes sense. He basically says that you can prove a negative and illustrates it by proving double negatives. And, as several commenters noted, it is based on inductive thinking, which is, of course, not the same as deductive thinking (deductive meaning you have the evidence; inductive meaning you may not have the evidence, but you are open to changing your mind should evidence arise that disproves your claim). I see this as basically saying, “Until empirical evidence illustrates otherwise, I will not believe claim X.” So, it’s not as strong as definitively saying that there were no gold plates because we have scoured all of the material world and all of the non-material (a.k.a. supernatural) world and have not found them. But it is basically pushing the argument back one step further and claiming that the burden of proof for said gold plates is on those making the claim that such plates did exist.

    As for the third-party, independent witnesses with Joseph Smith, I absolutely think they are necessary. Let me give an example. I’m sitting in my office right now typing this. If I were to claim that I just dug a hole in my wall (at the behest of a resurrected Native American named Moroni-ha) and found a bunch of gold plates with writing on them in reformed Egyptian but as soon as I began to read them Moroni-ha took them away, ascended through my roof, and headed to heaven, how many people on here would believe me? I’m guessing none. But now I insist that it really happened. What would it take for me to convince you that it did happen?

    1) Independent verification from witnesses who have no vested interest in my story being true?
    2) The gold plates?
    3) Undoctored video footage filmed by independent witnesses who have no vested interest?
    4) all three?

    In short, until there is reason to believe it actually happened (other than me saying it happened), no one on here is going to believe it. Just like no one on here really believes that the whack job in Brazil who claims he is is Jesus is actually Jesus. So, why do we believe Joseph Smith’s extraordinary claims when there is no extraordinary evidence to support them? Based on this logic, it never happened!

  7. Seth,

    If you could dig up information on those Panamanian horses, I’d be interested. As I understand it, there were horses in the Americas up until about 10,000 years ago (about the time humans were reaching South America). They died out and the Americas were horseless until modern horses were brought across the Atlantic. Anyway, I couldn’t find a reference to this discovery which I would imagine would be higher profile if it changed our dating of the extinction of horses in the Americas.

  8. Hey Jonathan. Remember, I said “prehistoric.” Which would mean – well before the Nephites. I don’t pretend such a find proves anything about the Book of Mormon really. But I’d hate for people to be running around claiming there never were horses in the American continents when there definitively were. Camels too, by the way.

    I heard the story on PRI’s “The World” this is the closest story I found:

    http://www.theworld.org/?q=node/10291

  9. You know, we can go on a laundry list of proofs about this, but I’m not sure how useful it is with regards to matters of faith.

    For instance, the Book of Mormon mentions barley being grown. For a long, long time, critics held this up as evidence that the BoM was false since there was no evidence of barley ever being in the New World.

    Well, you can probably guess the next part. They found out that barley actually was grown in the Americas.

    Did this cause some big change in opinion about the Book of Mormon? Of course not. Critics simply moved on to the next item in the laundry list of complaints.

    So, what if we discovered horse remains from around the time of the BoM? What if we then discovered some iron weapons (if you think that kind of stuff is simple to find, guess again)? What if we discovered a bunch of bronze breastplates, helmets, etc?

    What then? Are you convinced? Does it matter?

    I would hope not. I’d be rather disappointed in you if you gave up your convictions that easily.

    When does this end?

    Even if discovered Egyptian writings in some Mayan ruin somewhere… Let’s make it even better – on gold discs of metal bound together. What if we discovered that and it was some sort of ceremonial document? Would that clinch it for you?

    Does that really change your opinion that a lying polygamist, charlatan who believed in magic couldn’t have possibly pulled God’s word out of a hat?

    What if we find traces of Middle Eastern DNA in the Native Americans?

    Does that prove Lehi and company sailed the ocean blue and started a civilization in Central America? Or does it simply indicate that some of those Siberian Eskimos picked up some genes from migrating Asiatic peoples?

    You see where I’m going with this. We Mormons will never be done defending this. It’s an endless thing. The moment one problem is dealt with, another arises (illusory or real). If you’re hoping to prove the BoM, you’ve got a long row to hoe.

    Wouldn’t it be better to simply take the Book of Mormon at face value for its spiritual teachings and leave it at that? It certainly would be a lot less work and might even benefit your life in the meanwhile.

  10. Actually, Seth, as a full blown skeptic, I have set the standards by which I would support the BofM and accept it as historical. Here they are:
    1) the golden plates have to be found, given to actual scientists for translation, and they have to be somewhat similar to Joseph Smith’s translation (not word for word, but pretty damn close)
    2) archeology has to support the claims of the BofM

    Yes, my proofs are inductive and they put the burden of proof on those making the claims, but if I saw the evidence, I’d change my opinion in a heartbeat. That’s it. That’s all I need to believe the book is historical.

    Now, you raise another issue, and that is changing criteria. Even if the book was found to be historical, that doesn’t mean I would recognize it as “divinely inspired” or even worthwhile. There is still the issue of its messages. Don’t get me wrong; I think there are some good messages in the BofM (e.g., King Benjamin working with his people is a good one), but there are also a lot of really crappy messages as well:
    1) dark skin is a curse (not that I want to debate this one)
    2) you can arrive at the truth of something through prayer (Moroni’s Promise)
    3) god smites those who don’t believe in him
    etc.

    So, I can accept the BofM as a historical work pending evidence. But whether I can accept it as a book of worthwhile messages that is not historical or not is up to the messages themselves. And, just like the violent, misogynistic Bible, I am not a general fan (though there are some okay messages there too). If I was going to take just the good messages, I could cut both the BofM and the Bible down to about a dozen pages.

    In short, I can be convinced it’s historical – any true skeptic/scientists is always open to the evidence. But that doesn’t necessarily mean I’d return to Mormonism.

    I have to wonder, and if this isn’t true just tell me, if the reason you ask is because there is nothing that can be said about the BofM that will convince you it isn’t some how “true”. If that is the case, then you aren’t a true skeptic (not that you care to be), but more importantly, you aren’t honestly seeking truth. At some level you are behaving irrationally if there is nothing that can be said or illustrated that would change your mind.

    Daniel Dennett makes this argument quite well in his latest book. He uses a hypothetical that I thought was compelling. Imagine you are debating abortion’s legality and the person you are debating simply says, “It is wrong because my friend says it is wrong and my friend is always right, so it must be wrong and I cannot change my opinion.” Do you continue to debate with someone like that? I wouldn’t. If they cannot be convinced to change their mind in light of the evidence or compelling logic, they are irrational – end of story.

  11. Exmoron said

    “So, why do we believe Joseph Smith’s extraordinary claims when there is no extraordinary evidence to support them? Based on this logic, it never happened!”

    Because you’re limiting what you will accept as evidence of his claims. What counts as ‘extraordinary’ evidence? I get the feeling that the only acceptable evidence to an atheist regarding the existence of God is a personal sensory experience.

  12. Seth,

    You see where I’m going with this. We Mormons will never be done defending this. It’s an endless thing.

    Piling up evidences against the BoM could also be an endless task, depending on whom you’re trying to convince.

    I’m with exmoron regarding taking spiritual values from the BoM. There’s a lot of stuff in there that I consider worthless. It’s full of questionable teachings that I reject. I can think of only two teachings that I currently agree with: “there is an opposition in all things” and the bit about love that Moroni borrowed from 1 Corinthians 13. I’m sure there are others, but I can’t think of any. I scanned the scripture mastery list for a sample.

    dpc,

    I get the feeling that the only acceptable evidence to an atheist regarding the existence of God is a personal sensory experience.

    Is there any other kind of evidence?

  13. “Is there any other kind of evidence?”

    This is why I just never can warm up to atheism. It just doesn’t seem open to a universe of wonder and possibilities.

    And yes, I believe there are other kinds of evidence.

  14. For instance, the Book of Mormon mentions barley being grown. For a long, long time, critics held this up as evidence that the BoM was false since there was no evidence of barley ever being in the New World.

    Well, you can probably guess the next part. They found out that barley actually was grown in the Americas.

    Did this cause some big change in opinion about the Book of Mormon? Of course not. Critics simply moved on to the next item in the laundry list of complaints.

    I don’t think “moving on to the next item” is a fair characterization of the situation. It’s more like there is such a long list of things which are wrong that it takes more than crossing one or two items off the list of the most blatant errors to make the book plausible.

    The thing is that quite a lot is known about the pre-Colombian societies and their languages, and the Book of Mormon — as a historical document — doesn’t correspond to any of it at all. And even if the events of the Book of Mormon took place in an area as small as (I forget which state you mentioned), it’s still a non-trivial area that has to be somewhere. Where???

    The Book of Mormon spells out the configuration of a number of cities (explaining distances and which are on which coasts, etc.), and there aren’t that many places in the Americas that fit the bill. So logically, it should be possible to find this place if it exists.

    If the Book of Mormon‘s history corresponded to actual archaeological sites — if we found at least a few of these ancient cities, with writing that corresponded to the writing Joseph Smith copied and sent to Professor Anton, and if the writings were found to correspond to things written in the Book of Mormon — then, yes, the Book of Mormon would deserve a more serious analysis as a possible historical document. As it is, there is no corroborating evidence for it, and since it claims to be a history of a whole civilization, that’s a pretty big strike against it.

    It has another strike against it in that Joseph Smith apparently believed he could translate actual (not reformed) Egyptian, and was wrong. And — unlike the Book of Abraham — for the Book of Mormon, we don’t have the writing itself for scholars to examine nor any other example of writing in this same language, thus no reason to believe Joseph Smith would have been capable of translating such a document as he claimed.

    Again, if we had evidence that Joseph Smith was capable of translating such a document or if we had evidence corroborating the Book of Mormon‘s historical claims, then the Book of Mormon would deserve to be analyzed as a historical document. Both of these are reasonable to expect of an actual historical document. We have neither. Until that changes, I don’t think it’s rational to believe that the Book of Mormon is nonfiction. Of course I’m not a logician… 😉

  15. This is why I just never can warm up to atheism. It just doesn’t seem open to a universe of wonder and possibilities.

    And yes, I believe there are other kinds of evidence.

    This perhaps points to a bit of a stylistic difference. Reading the above made me smile because it reminded me of one of the Christmas specials I wrote about last year:

    There’s more to the world than meets the eye,
    when doubt’s in your mind give your heart a try,
    let up a little on the wonder why
    and give your heart a try.

    Please see my Christmas article I Believe in Santa Claus where I talked about how skeptics and believers don’t understand each other.

    And Merry Christmas!!! (Even if we have some divergence of opinion 😉 )

  16. Seth,

    Without asking for a clarification on what you mean by “wonder and possibilities”, I feel no real lack of wonder in my life. The lack of a supernatural dimension in my understanding of the universe hasn’t decreased my propensity for awe.

    I just finished a final exam for a class in electrical and magnetic materials. It was a fascinating class. It is a pleasure to learn how the world that I live in works. It made me smile to learn why most solid materials expand when heated (it has to do with the shape of the potential energy curve as a function of distance between two atoms in the solid). I meditate on the beauty of my natural surroundings as I walk from my car to my office every morning, a trip that takes 15 minutes or so. I’m doing a simple evaporation experiment with my oldest daughter and I’m still thrilled to see the water slowly disappear from the glass, especially knowing why it does. The beauty of the world isn’t lost on me because I don’t posit a magical cause for these things.

    Anyway, the reason I ask for another kind of evidence is rooted in my beliefs about experience. I don’t see any reason to believe in the existence of an experience that isn’t physically mediated by our sensory organs or brains. I also don’t believe that it is possible to transcend the limits of our personal brain to see what someone else’s subjective experience is like. If these are true, then there is no evidence other than personal sensory evidence.

  17. This is a follow-up regarding personal sensory experience.

    The only reason that I know what things look like, smell like, taste like, sound like, and feel like is because I have experienced them before. If one was to perceive God, how would you know that you were perceiving him?

    What does God sound like? What does God look like? And so forth. If I experience something that I haven’t experienced before, I always ask, “What was that?” If a person was to experience God in a physical sensory way, how would they know what they were experiencing?

    Jonathan:

    “I don’t see any reason to believe in the existence of an experience that isn’t physically mediated by our sensory organs or brains.”

    On what metaphysical basis is your belief (or more properly, lack thereof) supported? I can play the same logic game above:

    1. If sense perception was the only way to gain knowledge about the world, science would have verified that it is the only way.

    2. Science has not verified that sense perception is the only way to gain knowledge about the world.

    3. Therefore sense perception is not the only way to gain knowledge.

  18. Notice, the fact that you cannot prove a negative applies only to universal statements such as “There is no black swan.”

    If the statement is limited in space and time then negatives may be demonstrable. For example, I can prove that there is no black swan in my room today.

  19. dpc,

    Interesting questions. I don’t have a metaphysical basis for my belief that there are only sensory/physical experiences. To attempt to bring this back on topic, my belief is based on induction from the body of evidence that all experiences that we’ve investigated so far have entailed activation in portions of the brain. Aside from that, I have seen no reason to believe otherwise. All my experiences appear to have a physical basis. It seems more likely to me that all experiences are purely physical events.

    If a person was to experience God in a physical sensory way, how would they know what they were experiencing?

    It depends on how you define “God”. I’m not going down that road until we agree to a definition first. 🙂

    1. If sense perception was the only way to gain knowledge about the world, science would have verified that it is the only way.

    This premise is flawed. Let me substitute another example: if there was a cure for cancer, then science would have found it by now.

    Also, how would we falsify the assertion that physical senses are the only source of experience? If it isn’t falsifiable, then it’s probably beyond the reach of science to provide a satisfactory answer, though it can be very suggestive.

  20. Jonathan — I agree with you on your point in comment #17: knowing more about how something works doesn’t decrease my joy or sense of awe. Quite the inverse: when I see something that amazes me, it sparks my curiousity and makes me want to learn more about it. Similarly, understanding that a fanciful story is fiction increases my enjoyment of it because it opens up the possibility of building on it in whatever imaginative way I like. If you think a fanciful story is real, then you’re locked into thinking that the new questions sparked by the story have fixed right answers.

    Still, I feel like there’s some sort of fundamental personality or stylistic difference between skeptics and people who want to believe in magic. I can’t put my finger on quite how to describe it, but I saw another post just today here describing the joy of believing in magic…

  21. There also seems to be an assumption that if you believe in “magic” (to use the term brought up here), you cannot believe in science.

    Bogus.

    I happen to believe in both. You’ve chosen to only believe in one of them.

    Who is being more open to the possibilities?

  22. Seth, I think I understand what you mean by possibilities. In that way, it is true that I have closed myself off inasmuch as I don’t believe in the supernatural, but I am still open to it inasmuch as I’m willing to believe in it if given a reason.

    I agree with you, chanson, that it seems to be a matter of personal taste. In my blog post Red Pill, Blue Pill, I pondered this personal choice that I believe comes down to picking the pursuit of truth or the pursuit of happiness. I can’t say that one strategy is absolutely better than the other. I know which side I favor, but some days the other side looks really tempting. It seems that I’m just not constitutionally suited to make the other choice.

  23. There also seems to be an assumption that if you believe in “magic” (to use the term brought up here), you cannot believe in science.

    I don’t mean to attribute the term “magic” to you — I was quoting the author of the post I linked to in the above comment. It seemed like she was talking about the same sort of thing we’re talking about here.

    I happen to believe in both. You’ve chosen to only believe in one of them.

    Who is being more open to the possibilities?

    Interesting argument. It seems like this back and forth exchange of attempting to describe our respective perspectives is starting to repeat. It may be time for the old “agree to disagree.” 😉

  24. Actually, if I can point one thing out, I think it might change the tone. Seth has turned the argument to his favor. Seth is using “belief” as his measure. In the sense that science and revelation/magic are methods of arriving at something, then yes, we can say we “believe” in the methods, which inherently leads to which is better or worse.

    But I don’t think this is a matter of belief. Science doesn’t lead to beliefs, it leads to facts. Revelation/magic does lead to beliefs, not facts. (This is, of course, the definition of science – it is a methodology that leads to empirically verifiable facts.) So, while Seth is welcome to “believe” one methodology is better than the other and even accept the beliefs that result from his revelation/magic, in no sense does he result with facts. Which, to me at least, changes the argument.

    We can argue whether facts are important, but that, to me at least, is a stupid argument. I think we had this discussion last time – it is a fact that if you jump off a fairly high cliff without a means of slowing your fall you will injure yourself and maybe even die, regardless of your belief.

    So, at best we can argue which non-facts are better than other non-facts. This is really the only realm where Seth’s argument holds any weight. He wants to believe his beliefs are better than beliefs not based on his particular revelation/magic. The question, then, is how do you quantify what makes one belief better than another? Until Seth and Jonathan can answer that, they will continue arguing past each other.

    As far as I’m concerned, fact always trumps belief. And as far as beliefs go, belief closer to fact or belief based on fact generally trumps belief based on revelation/magic. But that is a gray area and is open to debate.

  25. “As far as I’m concerned, fact always trumps belief.”

    If facts were normative, that might be true. But they never are. If you want normatives, you ALWAYS have to add in something external to the facts. This is where belief comes into play.

    Neither am I trying to say which is superior – science or “magic” (sorry Chanson, the term seems apt for the discussion at hand). Neither am I talking about whose beliefs are superior.

  26. Seth has turned the argument to his favor.

    Sneaky, sneaky Seth… 😉

    But seriously, I think that scientific (rational) reasoning leads to conclusions, which can also be called “beliefs.” Personally, my main problem with believing in both science and magic/revelation is that they lead to contradictory conclusions, and to me the former is the more trustworthy of the two.

  27. Unfortunately, that avoids the issue Chanson.

    Let’s take an example. As a child in the 1980s, I was diagnosed with ADD (which illuminates my obsessive blogging habit). Science has shown that ADD brains are structured a certain way such that they have a hard time dealing with certain inputs from our surroundings. Science has established that certain medications seem to work. It’s a fact that some ADD kids have a very hard time in your typical school classroom.

    OK… Now what? What do we do with that information?

    Do I take medication for this condition or not? Is my condition somehow deficient and must be corrected? Or is society deficient and unaccommodating to my particular needs and personality such that IT must change and not me?

    Does science have an answer for those questions? I’d say it really doesn’t. You have to add external values to answer those questions and those external values have little to do, at their most basic core, with fact.

    I’d posit that fact will never yield useful information absent these external normatives. Absent any operative normative, you’re just playing a meaningless trivia game.

    In essence, all human experience consists of a series of informed gut-checks.

  28. Haven’t we covered this before? I don’t think scientific-type reasoning always provides a unique answer to “What should I do?”-type (strategy) questions. In this respect, I lean towards what exmoron was saying about facts: scientific reasoning helps you make conclusions about which facts most accurately describe the universe around you, but it doesn’t tell you how to live your life.

  29. exmoron,

    This may be a matter of how we’re defining “fact”, but the end products of science are theories and models, not facts. Facts are the input of science. Experiments generate facts which we observe and then draw conclusions from.

    Like chanson, I find the conclusions of science to be more reliable. They have a proven track record of making material improvements in our lives. Faith-based religion with its desire to make conclusions that are not well supported by publicly observed facts leads to a multitude of contradictory conclusions. Its promised benefits are less observable.

    For example, science promises and delivers a cure for smallpox. Religion promises happiness in this life and in the life to come. It seems to do well enough with its promises in this life, though the jury is still out on how well it delivers after death. Science has just begun to investigate human happiness and may have a lot to tell us about how to live happily. Science’s answer may never beat a belief that an omnipotent creator will make everything OK for you in the end.

    All that said, it still comes down to personal taste, hence the need to agree to disagree.

  30. This may be a matter of how we’re defining “fact”, but the end products of science are theories and models, not facts. Facts are the input of science. Experiments generate facts which we observe and then draw conclusions from.

    That’s a good way of putting it. It is to some degree a question of semantics, but essentially science provides some (approximate) concrete information about the universe around us and how it works.

    I still think strategy and ethical questions are a bit outside the realm of science, though, because they depend on your values (what outcomes you value) and science can’t choose those for you. Even if science were to provide a formula for perfect happiness, that doesn’t necessarily mean you should follow it. Elliptica wrote a very interesting post on this question recently, here.

Leave a Reply

Your email address will not be published. Required fields are marked *