William M. Briggs

Statistician to the Stars!

The One-True-Religion Fallacy. (It’s Not What You Think)

He is Spartacus

At the end of the eponymous movie, the slave army led by gladiator-cum-general Spartacus (Kirk Dougla) lies defeated before the creator of the First Triumvirate, General Marcus Licinius Crassus (Laurence Olivier). But Crassus does not know which of the multitude is his enemy. He offers to commute the sentence of crucifixion on the condition the survivors identify the body or person of Spartacus.

One after the other the men rise, defiantly shouting, “I am Spartacus!

Crassus, who knows his logic, realizes that because each man claimed to be the one true Spartacus, there could be no one true Spartacus, and so he released them all in the names of Diversity, Tolerance, and Rationality.

Kidding! I’m kidding.

Because Crassus knew (from the evidence of the war) there had to be one true Spartacus, he crucified everyone. Ouch. Based on subtle behavioral clues, he most suspected two of the men. He saved this pair for last and had them fight to the death. The one true Spartacus mercifully killed his lieutenant and was then himself crucified. Crassus never knew for certain he had his man—and to add to the subtlety, the one true Spartacus never shouted “I am Spartacus!”—but reasoned that, given the evidence he had, he made the best choice.

Which he did. Make the best choice, I mean.

If Crassus reasoned as we first supposed, by saying that because every man claimed to be the one true Spartacus there could not therefore be a one true Spartacus, he would have committed the One-True-Religion fallacy. This fallacy says because there is a choice or there is disagreement, there can be no right answer.

Stated so simply, it’s obviously silly and you might figure nobody would ever wield such a limp noodle. Wrong, naturally.

The One-True-Religion fallacy is particularly beloved of new atheists who use it to deny that all other religions except theirs is false, which is a sort of two-for-one solecism. First comes the OTRF then the denial that their religion is one, the latter error likely arising from the false belief that religions must have nameable gods.

Regardless whether I’m right about that, it is certain the OTRF for the new atheist plays the same role as “Peer review!” (the Peer Review fallacy; coming soon) does for foamy-mouthed global warming apocalypse fanatics. The new atheist’s favorite joke is to list minor deities in whom they disbelieve and then to quip that they “reject” one more deity than the traditional theist, which is God. As a plain statement of observation, this is not problematic, but if it is used, as it almost always is used, to imply that the one more deity (God) does not therefore exist, it is the OTR fallacy.

Here (use your imagination) are two theists of different religions and an atheist. Theist One says, “My religion is the one true religion.” Theist Two says, “No, my religion is the one true religion.” The atheist says, “What loons. All religions claim to the one true religion. Therefore there is no one true religion.” Given just the information available, the atheist has committed the OTR fallacy and at least one of the theists has made an error—but we cannot say that both have.

Theists fall into error as often as atheists. Usually this is because of humility coupled with justified uncertainty, which are no bad things, or perhaps a too liberal interpretation of ecumenicism, which is. The polite theist resists claiming his religion is the one true religion, even though he believes it is, in an effort to spare the feelings of his audience, perhaps hoping to win his listeners over with coyness. The danger is that this practice becomes habitual and the theist forgets what he believed.

The OTRF isn’t limited to religion. For example, I believe it is true that the only sensible and correct interpretation of probability is logical (as a branch of logic). Bluntly, I claim probability-as-logic is the one true interpretation. From this follows the conclusion that all other interpretations are wrong. I may (and do) allow, as theists allow of rival religions, that other interpretations have their good points; but taken strictly, they are false.

I might be wrong about this, of course. But it is no criticism and a clear instance of the OTR fallacy to argue that “One shouldn’t be dogmatic in philosophy or science,” (as Ian Hacking on this subject argues), or “We should be pragmatic in our understanding of probability theory,” or “What conceit to suppose one knows the one true theory!” Conceit it may be, but neither my mood nor my critics’ has probative value on the truth of the theory.

The OTR fallacy is always invoked when a critic can’t be bothered to do the hard work of refuting a claim. Refutation is hard labor. Scorn is easy and free. And to the believer I say, the time for humility is in the face of uncertainty. Where there is certainty, plain speaking is best.

I would thou wert cold or hot. So then because thou art lukewarm, and neither cold nor hot, I will spue thee out of my mouth.

62 Comments

  1. The “One True Religion” fallacy is never meant to logically disprove God. The fact that you think it is merely speaks about your ignorance of the argument rather than the weakness of it.

    Its purpose is manyfold. First, to disencourage hardcore believers to think that their model of God is the True One. Obviously, if they had never heard of any other model of God, they would assume this is the only model of God that exists, and the question “Is there a God or Not” is reduced to “Is your particular model of God true or not”. This opens a breach of thought, and we all know how thought is enemical to religion so it’s a Good Thing in itself.

    Second, to show that while believers are all really adamant to tell us what does happen after we die, what God thinks we should do, what positions we should have sex and with whom, if he’s really going to heaven or hell, etc.,etc., the sight of other believers that are equally adamant with equal amounts of evidence that believe quite really different things is always something that ought to make any believer ponder whether if he’s sufficiently justified in saying the things he says. And as said before, thinking is a Good Thing.

    Never has it been said that if there are many God models, then every single one of them is wrong. What has been proclaimed though is, if there’s a million of models of God, then at best, only one of them is correct. So that puts your version of God’s chances of existing, a priori, really near zero. And let’s not even discuss the whole possible sets of models of Gods that haven’t been discovered or believed yet.

    But I guess you just had to write a post today, and why not make it a click bait type of fallacy yourself? It worked for me.

  2. Briggs

    March 19, 2014 at 8:34 am

    Luis,

    That’s a lot of words to say, “I agree.” But I appreciate it.

    Of course, just like in the Spartacus example, no matter how many men claimed to be Spartacus—let it be every man ever—there still was just one true Spartacus.

  3. Luis,
    I sort of understood your position in the first three paragraphs but then you go and totally contradict yourself in the fourth. That is you said:

    “So that puts your version of God’s chances of existing, a priori, really near zero.”

    The fallacy is not committed because a claim of near zero and not zero is made? Although I am not a biblical scholar, I still find it odd that you claim that sexual positions are specified in the Bible. Where is that?

  4. What is a “God model”? If “God models” are wrong, then aren’t they products of the human mind? They aren’t something that could be discovered.

    Also, there aren’t “millions” of competing conceptions of God, there are actually very few (more than 50% of the population believes in the same God after all, and, while Isis and Athena may differ in specifics, they are of the same kind. They are therefore not different “god(ess) models” in any meaningful sense I can discern. On top of this we have the fact that, for example, Neoplatonic pagan understandings of God or Hindu philosophical accounts are quite similar to the Christian understanding (as David Bentley Hart points out in his new book).

    Interestingly, there is one thing that all the adherents to various “God models” have in common, a fact which is little recognized by the atheist, they all firmly believe that the atheist is wrong, wrong, wrong. Somehow though, this never entails that the chances of atheism being correct are “a priori, really near zero” (probably because most theist philosophers know what “a priori” means).

  5. The comments on that AGW-fanatic website are unnerving. Science by intimidation seems to have a lot of traction.

    ===
    Luis,

    “So that puts your version of God’s chances of existing, a priori, really near zero”

    Well, if each version is equally likely given some evidence for each AND if there really are millions and millions of different Gods that people believe in (instead of many different beliefs about a handful of Gods), I suppose you might be able to make this argument. I think you’d have a hard time substantiating those things, though.

  6. Briggs, be careful then in choosing the exactly right one, lest you find yourself in hell in some decades from now (centuries, I’d wish?).

    Scotian, I said “your version”, not “any God”. Pay attention. The Bible is also almost pretty irrelevant to what I said, I spoke of “versions of God” and what we are supposed to do according to his law, etc.

    Josh, that was the point and the interest of my comment which is relevant regarding this post, thanks for those words of agreement.

  7. Luis,
    Maybe I misunderstood you. You are saying that the atheist position is on an equal footing with any one of the theist positions and not on an equal footing with them all together. This would put the atheist position at a near zero probability as well, which seems to me to be Briggs’ position, and thus confirms his statement that the two of you agree on some level. I can not agree with this reasoning, however, since the ability to spin an unlimited number of additional theories (on any subject) can not in itself reduce the probable validity of the original. I don’t think that Briggs is claiming this but it is implied by your statements.

    “I spoke of “versions of God” and what we are supposed to do according to his law.” Could you give an example to support your “sexual positions” claim?

    Personally I think that the problem is that when people use the “they all claim to have one true religion” argument is that an out is left by omitting the concluding sentence from the syllogism. Everyone knows what this conclusion is supposed to be, as given explicitly by Briggs, and so the argument has served its intended purpose. But because of the out they can respond as you have. This does not seem entirely honest to me.

  8. @Luis

    Fallacy on top of fallacy!!

    Let’s look at what you wrote:

    “What has been proclaimed though is, if there’s a million of models of God, then at best, only one of them is correct.”

    False. There can be multiple correct models of God. In most cases, one has a finite number of observations or finite propositions about God and there is a lot of room in constructing distinct models of God that fit the observations and propositions. How do you infer uniqueness of the solutions for your God model?

    “So that puts your version of God’s chances of existing, a priori, really near zero. And let’s not even discuss the whole possible sets of models of Gods that haven’t been discovered or believed yet.”

    I believe that the One True Religion on this website is that of logical probability. I’m surprised Briggs did not complain about your transgression here.

  9. I look at the Bible like an owner’s manual for life. The purpose of an owner’s manual(written by the designer and manufacturer) isn’t about telling you what not to do. It’s about telling you how you will maximize value and health of the product. My lawnmower owner’s manual doesn’t tell me I can’t use it to knock down corn stalks in my garden. However, that’s not the intended use so I can’t expect complete enjoyment of this product if I use it in a way it was not intended to be used. The Bible is beautiful in its elegant way that it instructs us how get the most fulfilling life according to the designer. Therefore, when someone says it tells us what positions and what not, it tells me they don’t have a real understanding of the Bible. They are railing against a caricature of the Bible.

  10. The whole One True Religion (OTR) analysis overlooks the “elephant in the room” — all those self-proclaimed OTRs arise from:

    – The Same Documents (more or less; there are some minor version distinctions),

    AND

    – They cite the VERY SAME PERSON!

    From one (one guy/one book) comes many (OTRs)…

    Why is that?

    One doesn’t need philosophy or much in the way of logic to:

    – Read the source documents;
    – Compare the inconsistencies presented in those documents;
    – Compare the stories & themes & symbols with myths that preceded The Guy & Those Documents

    And then…

    ….objectively assess if a self-inconsistent story* containing themes & symbols & even phrasing from prior unrelated myths, bolstered by a Church (that was founded & supported by Roman Emperor’s intervention) that, over hundreds of years, had to hold Councils (of Nicaea, for example) to dictate which debated key elements of the story’s plot elements were true & which were false…and which vigorously tried to destroy as many of those competing & preceding myths by destroying as much documentation as possible (doing an impressive job of it but not quite pulling it off) is most likely reflective of the work of people plagiarizing basic elements & making up a new, but not innovative, story as they went along, or, the logical outcome of a divine, all-powerful deity that, in setting the human race on proper course, somehow garbled the single most important message of the single most important intervention He would apply such that it necessitated such political (human) interventions & clarifications.

    It just seems to so many of us that an Almighty God, Creator of the Heavens and Earth, All that is seen & unseen (what a resume!) could, with hardly any effort at all, convey a short story to just one of His (“It’s”?) many created species such that He got the story straight & conveyed the same message once & for all to all…as opposed to a mishmash needing a Roman Emperor (at least once) to mandate the Earthly Church leadership to sort some of it out.

    That kind of documentary & doctrinal foundational pedigree seems more in line with what one would expect from a gaggle of first-year law students fumbling thru their first contract-writing class in parallel with their English(or Greek, in the case of the NT)-as-a-second-language coursework. Not the handiwork of a Creator of all seen & unseen….

    Just examine the documents & history–ALL of them & it, not some selective samplings–and follow where it leads…and…not via some mental filter that has the outcome fore-ordained (THAT is a “logical” approach typical of adherents of any of the many OTRs who, if they applied it to the evidence for or against Santa Clause or the Easter Bunny could, likewise, never accept and thus could never conclude those figures do not exist & never did).

    It’s not that there’s so many OTRs & only one can be true…the mere existence of so many from the SAME source material — and flawed inconsistent material at that — attributed to such a PERFECT AUTHOR itself makes no sense. The outcome (many self-asserted OTRs) is just one–of many–indicators of fallible human origination.

    Put another way, the straightforward analytical approach is simplicity itself and is captured by the cliché:

    “If it walks like a duck and quacks like a duck it’s probably a duck.”

    * So many OTRs will recite, like a nervous tic, that there are no contradictions, that the entire Bible is perfect & self-consistent, but that just ain’t so, which is readily found if one reads & pays attention (e.g. reading side-by-side & documenting key points of the Gospels — and if one really wants to understand them & really see the differences, learn to read the original Greek….undistorted by multiple translations the differences are very often radically dramatic).

  11. Briggs, you’ve mapped out a nice way of using the OTRF for passing a course with a logic-deficient instructor. Get him/her to use the fallacy and then argue that since there are multiple answers to exam questions, none of them can be correct so everybody passes the test. Of course, the prof. may be a Crassus-type so knowing the expected answers would be a judicious fallback, especially if you are a Spartacus-type.

  12. The original Mr. X

    March 19, 2014 at 1:14 pm

    Luis:

    “Second, to show that while believers are all really adamant to tell us what does happen after we die, what God thinks we should do, what positions we should have sex and with whom, if he’s really going to heaven or hell, etc.,etc.”

    I really think there ought to be a religion version of Godwin’s Law, that “As the topic of religion is discussed on the internet, the probability of an atheist bringing up irrelevant and unprompted complaints about religious sexual ethics approaches 1.” Anybody who does this would, of course, be considered to have lost the argument.

    “the sight of other believers that are equally adamant with equal amounts of evidence”

    Yeah, but that relies on the assumption that all religions have equal amounts of evidence to back them up, which is clearly false. For example, the evidence that Jesus Christ rose from the dead is much stronger than the evidence that Zeus defeated an army of Titans in battle on Mt. Olympus.

    “if there’s a million of models of God, then at best, only one of them is correct. So that puts your version of God’s chances of existing, a priori, really near zero.”

    First of all, why, as others have asked, does atheism get a free pass on all this “a priori probabilities” business? Secondly, it’s quite easy to eliminate a lot of religions very quickly. For example, the Cosmological Argument shows that there can only be one Creator God, which puts polytheistic religions out of the running.

    Ken:

    “The whole One True Religion (OTR) analysis overlooks the “elephant in the room” — all those self-proclaimed OTRs arise from:

    – The Same Documents (more or less; there are some minor version distinctions),

    AND

    – They cite the VERY SAME PERSON!”

    Clearly false, unless you think that (a) the Torah, Bible and Koran are all the same (not to mention all the various non-Abrahamic religions’ scriptures), or (b) that the Jewish prophets, Jesus Christ, and Muhammad were all the same person.

  13. Scotian, that is a good question whether if the atheist position is in “equal footing” with any of those. I don’t think so. If we are to take this in the simplest terms possible, I would say there’s a split in the question “Does some God exist?” Yes / No would follow and then if Yes, “Which God is the case?”. While this is too simplistic it works in relation to the post above.

    @anona OMG so many fallacies!!! And exclamation points!!!

    Wrong, there should only be one correct model of God. If there are multiple “correct” models of God, then by definition they are exactly the same. What you are saying is rather “There are many *almost* correct models of God” and that could well be true. A pity that it is impossible to have any sensible feedback on how these models deviate from its supposed “truth”.

    I believe that the One True Religion on this website is that of logical probability. I’m surprised Briggs did not complain about your transgression here.

    I’m not surprised however that you didn’t even read my comment properly.

    @The Original Mr X,

    I agree with your Godwin like proposal. When the pope and all the christian and muslim preachers stop telling us when and how and why we should and could have sex then I will sign that proposal with confidence and joy! Glad to have you in this struggle as well.

    Look, the cue here is not to whine about how they talk about these things. I couldn’t personally care less. The problem is, obviously, how you can obtain a correct model of God that is so tuned precisely to his wishes and commands that it even gets to details like those of sexual positions, etc., when it’s flagrantly obvious that no one ever has any grasp of what is really going on on such a godlike mind. Of course, what is really going on is an attempt to control and manipulate the masses by moralizing and legalizing on their most fundamental desires and lusts.

    (I wouldn’t even have a problem if it was just said something in the order of “These practices won’t get us in better places”. But this is not said. What is said is that it goes “against the Law of God” or any other asinine bull crap).

  14. Nullius in Verba

    March 19, 2014 at 2:37 pm

    The aim of the argument isn’t to say “There are many incompatible religions, therefore none of them is correct”, it’s to say there are many incompatible religions, each of them rejected by all the others, therefore firstly, there are reasons and arguments for rejecting the existence of each of those gods that are acceptable to ‘religious people’, and secondly there is no obvious way to distinguish between them – when looked at collectively, all the religious mythologies look much the same, and so a valid reason to reject any of them tends to be applicable to all of them. Similarly, the reasons offered in favour of each religion are indistinguishable, and if any of them were valid then the same argument would be applicable to all the others making them *all* true, which is impossible. This doesn’t prove they’re all untrue, but it does prove that arguments for the existence and non-existence of particular Gods that can be applied equally well to permutations of them cannot be valid.

    So to apply this to the Spartacus example – whether or not any particular person is Spartacus, them *saying* that they are Spartacus is not a valid demonstration of it, nor is the fact that their companions say they are not Spartacus a valid demonstration that they are not. The fact that anyone can (and does) say “I am Spartacus!” means that it cannot count as evidence that any one particular person is indeed the man himself.

    If we suppose further that Spartacus himself got knocked on the head during the final battle and has amnesia, we can consider the situation where the only only argument each person has themselves is the one they speak aloud. Now since all their arguments are the same, and cannot all be right, they all must be mistaken. If any of them is right, it is only by chance, not on the basis of any valid evidence.

    And for that matter, we could consider the possibility that there might not be exactly one ‘Spartacus’. Consider for example the mathematician Nicolas Bourbaki – if somebody stands up and says “I am Bourbaki”, and then somebody else stands up and says the same thing, must one of them be wrong? Or could the leader of a group be entirely fictional, a cipher designed to throw off the enemy, or to inspire unity in an organisation of cells none of who know any of the others? It’s not a safe assumption to reject 0 or n as the number of Spartacuses (Spartaci?) that exist.

    In short, we don’t know. We have no reason to accept or reject *any* number of Deities – zero, ten, twenty one million, some number so big we don’t have room in the universe to write it down. Because without any empirical evidence (i.e. something none of the other religions could have), it’s *all* pure speculation.

    Given the number of possibilities, the odds of us hitting the right story purely by chance without any independent evidential input are pretty slim. I’ll leave it to others to discuss whether 1/infinity is *actually* zero or not, though…

  15. “The fact that anyone can (and does) say “I am Spartacus!” means that it cannot count as evidence that any one particular person is indeed the man himself.”

    I would think the fact that someone -is- Spartacus would actually make all the difference in the world.

    ===
    “And for that matter, we could consider the possibility that there might not be exactly one ‘Spartacus’.”

    If each Spartacus claims to be the sole Spartacus, only one or zero can be correct. Since religions have incompatible claims, this is the same scenario that plays out with religions being compared with each other. Contradiction is impossible.

    ===
    “Similarly, the reasons offered in favour of each religion are indistinguishable”

    This is demonstrably false. In fact, its another common fallacy: The “All-Religions-Are-True” fallacy of postmodernism.

    ===
    “We have no reason to accept or reject *any* number of Deities – zero, ten, twenty one million, some number so big we don’t have room in the universe to write it down.”

    There aren’t anywhere near this many proposed deities, nor is your claim that we have “no reason to accept or reject” true.

    ===
    “Because without any empirical evidence (i.e. something none of the other religions could have), it’s *all* pure speculation.”

    You make two fallacious statements in one sentence. First, “empirical evidence” is not the only evidence that exists. You accept the validity of reason, no? Second, there -is- empirical evidence for some religious beliefs.

    ===
    “Given the number of possibilities, the odds of us hitting the right story purely by chance without any independent evidential input are pretty slim.”

    Granted, by chance (which means ignorance) alone, you’d have a hard time landing on the right belief system. Atheism, included.

  16. Correction: I meant “All-Religions-Are-The-Same”, not“All-Religions-Are-True”.

  17. “The atheist says, “What loons. All religions claim to the one true religion. Therefore there is no one true religion.” ”

    Really, Briggs? That’s what atheist say? lol.

    An atheists says, properly, “There is no evidence that god exist.”

  18. Briggs

    March 19, 2014 at 3:28 pm

    All,

    Wow. Last thing I expected were attempts to resurrect the OTR fallacy based on (weak) probabilistic grounds!

    Something about all fallacies that draws people in, even after they (the fallacies) have been quashed. Too enticing? Too fun? Too rebellious?

    Jim S,

    Come. Let’s not pretend many new atheists say exactly what I claim they say (and many are much worse). And some even say, and say falsely, there is “no evidence.” A minority say, “There is no evidence which convinces me.” Those guys are still wrong, but they have the best of it.

  19. @Luis

    Please look up the meaning of the word model in logic. You seem to lack a sense of humor.

  20. The original Mr. X

    March 19, 2014 at 5:55 pm

    Luis Dias:

    “Look, the cue here is not to whine about how they talk about these things. I couldn’t personally care less. The problem is, obviously, how you can obtain a correct model of God that is so tuned precisely to his wishes and commands that it even gets to details like those of sexual positions, etc.,”

    Oh, I know that’s the point you’re trying to make, I just find it… interesting that sexual morality always seems to be the go-to example for such matters. I mean, if nobody can know the mind of God, nobody can know whether or not He approves or disapproves of murder, or theft, or cruelty to animals, but for some reason those examples never come up. Instead we keep getting lectured on how religion is unjustifiably trying to restrict people’s sexual activities. Why, it’s *almost* as if there’s some kind of hidden motive behind these objections…

    “when it’s flagrantly obvious that no one ever has any grasp of what is really going on on such a godlike mind.”

    Why is it flagrantly obvious, exactly? And, for that matter, I presume you have a refutation ready for the arguments which major religious traditions give on sexual morality? Otherwise your point here is just an appeal to personal incredulity, and why should anybody else care about what you personally happen to find incredible or not?

    “Of course, what is really going on is an attempt to control and manipulate the masses by moralizing and legalizing on their most fundamental desires and lusts.”

    You do the same, Luis, unless you refuse to condemn rape, adultery, paedophilia and so forth.

    Nullius:

    “The aim of the argument isn’t to say “There are many incompatible religions, therefore none of them is correct”, it’s to say there are many incompatible religions, each of them rejected by all the others, therefore firstly, there are reasons and arguments for rejecting the existence of each of those gods that are acceptable to ‘religious people’, and secondly there is no obvious way to distinguish between them – when looked at collectively, all the religious mythologies look much the same, and so a valid reason to reject any of them tends to be applicable to all of them. Similarly, the reasons offered in favour of each religion are indistinguishable, and if any of them were valid then the same argument would be applicable to all the others making them *all* true, which is impossible. This doesn’t prove they’re all untrue, but it does prove that arguments for the existence and non-existence of particular Gods that can be applied equally well to permutations of them cannot be valid.”

    Obviously false. The God of, say, Islam is completely different to the gods of the Ancient Greek pantheon, and disproving the latter by climbing up Mt. Olympus and showing that there are no gods there is going to do absolutely nothing to disprove the former.

  21. Nullius in Verba

    March 19, 2014 at 6:41 pm

    “I would think the fact that someone -is- Spartacus would actually make all the difference in the world.”

    How do you know? Do you have independent evidence, not mentioned here? If so, what is the analogous evidence for the one particular deity?

    “If each Spartacus claims to be the sole Spartacus, only one or zero can be correct.”

    No, any number could be correct, because they might *all* be wrong (or lying).

    “This is demonstrably false. In fact, its another common fallacy: The “All-Religions-Are-True” fallacy of postmodernism.”

    Then it would speed things up enormously if somebody just demonstrated it.

    “There aren’t anywhere near this many proposed deities, nor is your claim that we have “no reason to accept or reject” true.”

    In what sense are there not this many proposed deities? I just proposed them!

    The Hindu religion is noted for having proposed 330 million gods (devas). If deities can breed like people (as many polytheist religions seem to propose), and there are 7 billion people, then it doesn’t seem an unreasonable number. Given superhuman abilities, immortality, and several cycles of the world to multiply (a Brahma year as I’m sure you remember is 72,000 kalpas, or roughly 311 trillion years, and we are about 51 Brahma years into the lifespan of the current Brahma) then I imagine the numbers of descendents could get quite large.

    However, if you’re going to pick a non-negative integer at random, it’s probably going to be a lot bigger even than that. What if the universe was eternal? What’s the limit?

    “First, “empirical evidence” is not the only evidence that exists. You accept the validity of reason, no?”

    Reason is empirically determined, too.

    “Second, there -is- empirical evidence for some religious beliefs.”

    Of course. Religions contain plenty of mundane knowledge of the sort that everybody knows.

    More seriously, I know of at least one (claimed) divinely inspired scripture that contains mathematical truths of such deep profundity and beauty that one could seriously entertain the possibility that the author of the universe might have had something to do with it. It’s not the Judeo-Christian one, though.

    But what evidence is there for the one with the talking donkeys and the stuff about the beast with seven heads and ten horns? What empirical evidence is there that the sun was actually created on the fourth day? How does that work? There are religious beliefs and then there are religious beliefs.

    I personally don’t have any objection to people believing that sort of stuff. So long as they’re not interfering with how anyone else lives their lives, it does no harm and keeps people happy, which is fine. But I have somewhat more respect for those who do so honestly, acknowledging the contradictions and difficulties – rather than either claiming their beliefs are different to what they obviously are, or that the scientific facts are different to what they are. Stop over-thinking it, and just sit down and enjoy the story. It’s what humans do.

  22. Nullius in Verba

    March 19, 2014 at 6:49 pm

    “The God of, say, Islam is completely different to the gods of the Ancient Greek pantheon, and disproving the latter by climbing up Mt. Olympus and showing that there are no gods there is going to do absolutely nothing to disprove the former.”

    Obviously one would have to go to the location of God proposed by Islam, which is up in the sky somewhere. (The Night Journey speaks of “ascending” to heaven.)

  23. @Nullius,

    “Reason is empirically determined, too.”

    This is a very curious claim that you make. I don’t understand this. Can you elaborate in what sense reason is *determined* by empirical tests?

    I’m guessing that your answer is going to have as a corollary the claim that all mathematical reasoning is empirically determined. That would be news to many mathematicians I know, especially the ones who are not physicists.

    Really curious to see your response.

  24. Briggs,
    The God issues is very simple. There is no evidence that god exists. Period. It’s not that complicated. Most theologians would have no problem with that statement. The need for evidence shows a lack of faith on the part of the believer.

    One does not say “There is no evidence that convinces me” because that would be redundant. I don’t go around saying “there is no evidence that convinces me that {elves, unicorns, wizards, etc.} don’t exist.

    When the clouds part, and a beam of light comes down from the sky, and a person who looks like Charlton Heston and speaks like James Earl Jones says to me “Repent, ye sinner!” – then I’ll believe. Until then, I’m not buying it.

    Let me ask you… What evidence would you require to say that God does not exist?

  25. I mean, certainly, the christian god doesn’t look like James Earl Jones and speak like Charlton Heston, right?

  26. ““If each Spartacus claims to be the sole Spartacus, only one or zero can be correct.”

    No, any number could be correct, because they might *all* be wrong (or lying).”

    You know, I really don’t know how to respond to this. I can’t tell if you’re joking or serious, and at this point I’m not sure which would be better.

  27. The original Mr. X

    March 19, 2014 at 9:56 pm

    Nullius:

    “Obviously one would have to go to the location of God proposed by Islam, which is up in the sky somewhere.”

    I’m pretty sure that Islam doesn’t think God exists anywhere in the physical universe, so good luck finding Him.

    Jim S:

    “When the clouds part, and a beam of light comes down from the sky, and a person who looks like Charlton Heston and speaks like James Earl Jones says to me “Repent, ye sinner!” – then I’ll believe. Until then, I’m not buying it.”

    Uh-huh, riiight. Because, you know, that sort of thing doesn’t really make you look that open-minded or serious, in which case why exactly should we take your assessment of the evidence for God’s existence (or lack thereof) at all seriously?

  28. “why exactly should we take your assessment of the evidence for God’s existence (or lack thereof) at all seriously?”

    By all means, Mr. X, give me some evidence.

  29. Why do I suspect that I won’t actually get any?

  30. @Jim S

    “Why do I suspect that I won’t actually get any?”

    Probably because you are still in your mom’s basement? The pretty girls are having fun outside and they are not coming to your mom’s basement. Sorry for breaking the news to you, dude.

  31. For the record, I believe in God and Allah and Brahman and the First Cause and that Existence exists … and I also believe they are the same entity.

  32. @anona

    When I hire a structural engineer for one of my buildings, I expect him to provide “evidence” that he has accounted for the live, dead and lateral forces that may impact the structure. Funny that he has no problem doing so. But Zeus forbid that you should provided me evidence that the prime mover exists!

    Real smart reply there, anona. Typical.

    Yawn. To bed now. I’ll await your witty riposte for the morrow.

  33. Briggs I never would have guessed that you are a modernist.

  34. The original Mr. X

    March 20, 2014 at 7:21 am

    Jim S:

    “By all means, Mr. X, give me some evidence.”

    I would do so gladly, if you’d given any sign of actually being open to it.

  35. David L. Hagen

    March 20, 2014 at 9:01 am

    RE: “So, because you are lukewarm, and neither hot nor cold, I will spit you out of my mouth.” Source Revelation 3:16 ESV

    Jim S.
    Re: “There is no evidence that god exists”
    To the blind, all appear blind.
    You and everything you use are evidence that God exists.
    It takes far greater faith to believe that the enormous genomic complexity by which you were born, and the incredible fine tuning of the universe just burst from nothing.

  36. Nullius in Verba

    March 20, 2014 at 2:53 pm

    “This is a very curious claim that you make. I don’t understand this. Can you elaborate in what sense reason is *determined* by empirical tests?”

    Logic can be constructed according to many different axiom systems – we pick one to use that works for our physical universe. Reasoning is a form of computation. And computation is a physical process dependent on the laws of physics – which determines what sorts of computers you can build – see for example the debate over whether quantum computers can compute anything classical computers cannot.

    Even things like numbers are empirically based; a consequence of the behaviour of particles under conservation laws. (And an approximation, at that. In quantum mechanics, the number of particles is a quantum operator that can exist in superposition, so there can be both none, one and many particles in the box all at the same time.)

    “You know, I really don’t know how to respond to this. I can’t tell if you’re joking or serious, and at this point I’m not sure which would be better.”

    I’m perfectly serious – why would I not be? Each Spartacus claiming to be the sole Spartacus does *not* imply that only one or zero can be correct.

    There might be other evidence available that does, but what people say about it does not. What if there are two guys called Spartacus and neither of them are there? If everybody says “I am Spartacus and Spartacus is one”, does that make it so? Why is this impossible?

  37. “Even things like numbers are empirically based”

    Methinks you don’t know what “empirical” means. Let me help you:

    ‘Empirical: Pertaining to, derived from, or testable by observations made using the physical senses or using instruments which extend the senses.’

    How do you personally test 2 + 2 = 4? Which of your senses do you use to understand that A is equivalent to A?

    ===
    “I’m perfectly serious – why would I not be? Each Spartacus claiming to be the sole Spartacus does *not* imply that only one or zero can be correct.”

    Here are the possibilities, laid out as simply as possible if “all claim to be the sole Sparticus”, which is the situation in question:

    1. There is a sole Sparticus
    1.a. One Sparticus is telling the truth (else (1) is contradicted)
    1.b. Every other Sparticus is lying (else (1) is contradicted)

    2. There is no sole Sparticus (logical inverse of (1))
    2.a. All Sparticus’ are lying (else (2) is contradicted)

    I can’t believe we’re having this disagreement.

    ===
    “What if there are two guys called Spartacus and neither of them are there?”

    Then there is no sole Sparticus. Next.

    ===
    “If everybody says “I am Spartacus and Spartacus is one”, does that make it so? Why is this impossible?”

    No. It doesn’t make it so. Nor does it have anything to do with anything.

  38. The original Mr. X

    March 20, 2014 at 6:42 pm

    Of course, Nullius, empirical experiments themselves presuppose certain laws of logic, e.g., the law of non-contradiction or the law of causality. That’s why when Isaac Newton saw an apple falling to the ground, he didn’t think to himself “Hmmm, maybe it’s both falling and not falling at the same time” or “Oh well, maybe my seeing the apple falling is just a brute fact with no cause or correspondence to external reality”.

  39. Nullius in Verba

    March 20, 2014 at 8:33 pm

    “How do you personally test 2 + 2 = 4? Which of your senses do you use to understand that A is equivalent to A?”

    2+2=4 is an abstraction of a range of physical facts: two pebbles plus two pebbles gives four pebbles, two sheep plus two sheep gives four sheep, two oranges plus two oranges gives four oranges, and so on. There are so many physical systems that exhibit this behaviour that it is worth systematising them all as examples of a single pattern. But it is a pattern we see repeatedly in the world around us, a consequence of a general conservation law.

    But it doesn’t have to be that way. Mathematicians routinely develop versions of addition where 2+2 is not necessarily 4, and indeed it doesn’t have to be the case in physics either. One example of the rule is that velocities add – if the train is moving at 2 mph relative to the ground, and I am moving at 2 mph in the same direction relative to the train, then the addition rule says I must be doing 4 mph relative to the ground. It seems like common sense.

    Except that it isn’t so. In special relativity, the ‘sum’ is (a+b)/(1+ab/c^2), and I would be moving at very slightly less than 4 mph. There are even complications with regard to adding the pebbles.

    We pick the conventional addition operation we do only and precisely because it is so useful for describing the physical world we live in. Likewise, we use equivalence operations (in which A is equivalent to A by definition) because they are so widely applicable to and useful for studying the universe. And also because it’s one way that our brains, following those same rules of physics, can behave.

    There are forms of reasoning that we cannot do, because they cannot be implemented with physical arrangements of matter – although they’re still mathematically valid. Mathematicians sometimes study them by proposing ‘Oracle machines’ that contain modules able to perform physically impossible tasks, just to see what new sorts of things you would be able to calculate. Reasoning is computation and computation is a physical process. Different physics would result in different ways of reasoning.

    “Then there is no sole Sparticus. Next.”

    Then “next” you need to explain why that means there can be only zero or one.

    “That’s why when Isaac Newton saw an apple falling to the ground, he didn’t think to himself “Hmmm, maybe it’s both falling and not falling at the same time””

    Schrodinger might have had a different opinion.

    In quantum mechanics, the apple *can* be falling and not falling at the same time. Things don’t *have* to follow one particular set of ‘laws of logic’. Things could have been different. We only use this particular set because it describes our universe fairly (but not perfectly) accurately.

  40. “Mathematicians routinely develop versions of addition where 2+2 is not necessarily 4”

    “In quantum mechanics, the apple *can* be falling and not falling at the same time.”

    “Likewise, we use equivalence operations (in which A is equivalent to A by definition) because they are so widely applicable to and useful for studying the universe. And also because it’s one way that our brains, following those same rules of physics, can behave.”

    So many claims, yet you seem to be such a radical skeptic I don’t know how you can actually believe you are making them. I genuinely don’t know how you believe you are having a conversation or how you believe meaning is being transferred. You’ve just trampled upon any possible foundation for meaning.

  41. Maybe I’m both responding and not responding to you. Maybe you can both choose and not choose to respond and not respond back.

  42. @ The Mr. X
    “I would do so gladly, if you’d given any sign of actually being open to it.”

    Nonsense. You won’t provide evidence because you have no evidence.

    @David L, Hagen.
    “It takes far greater faith to believe that the enormous genomic complexity by which you were born, and the incredible fine tuning of the universe just burst from nothing.”

    I make no such claim that the “universe just burst from nothing”. I don’t have the slightest idea of how things “came to be”, and just I’m honest enough to say so. And I don’t have to invent a myth to help me sleep at night.

    I learned at a young age that a real sign of maturity is to be able to say “I don’t know”.

  43. The whole Spartacus nonsense can be solve by understanding that Spartacus CAN exist. Were as the convoluted, contradictory, self-serving definitions of “god” cannot.

  44. @Nullius in Verba:

    “But it is a pattern we see repeatedly in the world around us, a consequence of a general conservation law.”

    2 + 2 = 4 is not a consequence of any conservation law, in any meaningful sense whatsoever.

    “But it doesn’t have to be that way.”

    Yes, it does (hint: you are equivocating).

    “In special relativity, the ‘sum’ is (a+b)/(1+ab/c^2), and I would be moving at very slightly less than 4 mph.”

    Which presupposes the correctness of elementary arithmetic. And you are equivocating again, because in mechanics (relativistic or not), speed is not an integer, not even a real scalar, but a vector.

    “We pick the conventional addition operation we do only and precisely because it is so useful for describing the physical world we live in.”

    Who is we? Since quite obviously you are no mathematician, why the pronoun? Either way, this is simply wrong.

    “There are forms of reasoning that we cannot do, because they cannot be implemented with physical arrangements of matter – although they’re still mathematically valid.”

    Forms of mathematical reasoning that are “mathematically valid”, which presumably means they can be *recognized* as valid, even more so because “Mathematicians sometimes study them”, but that we “cannot do, because they cannot be implemented with physical arrangements of matter”. Right.

    “In quantum mechanics, the apple *can* be falling and not falling at the same time.”

    No it cannot.

    Do not let me stop you, but maybe you should not talk about things you quite obviously do not understand? Just a suggestion.

  45. The original Mr. X

    March 21, 2014 at 7:22 am

    Jim:

    “Nonsense. You won’t provide evidence because you have no evidence.”

    No, I won’t provide evidence because I strongly suspect that any attempt to do so will rapidly devolve into an exercise in jumping through a set of whatever arbitrary hoops you choose to set up. I’ve seen this sort of challenge often enough to know where it ends up, and I have no interest into getting sucked in to this sort of thing.

  46. Nullius in Verba

    March 21, 2014 at 7:32 am

    “2 + 2 = 4 is not a consequence of any conservation law, in any meaningful sense whatsoever.”

    Yes it is.

    “Yes, it does (hint: you are equivocating).”

    No it doesn’t and no I’m not.

    “Which presupposes the correctness of elementary arithmetic.”

    Which uses one model of addition to implement another.

    We could, equally well, have taken the addition of velocities as our basic operation and then expressed the addition of reals in terms of it.

    I’m not claiming that elementary arithmetic is “incorrect”, I’m saying that many arithmetics are possible, and that we only use *this* particular one because it corresponds to observed physics.

    “And you are equivocating again, because in mechanics (relativistic or not), speed is not an integer, not even a real scalar, but a vector.”

    Wrong! I said “in the same direction”. The component of a vector in a particular direction is a scalar. And who said anything about integers? When I was talking about pebbles, that would be Natural numbers, as any real mathematician would know, and of course integers and reals are used to represent the behaviour of different physics-implemented groups.

    “Forms of mathematical reasoning that are “mathematically valid”, which presumably means they can be *recognized* as valid, even more so because “Mathematicians sometimes study them”, but that we “cannot do, because they cannot be implemented with physical arrangements of matter”. Right.”

    Glad you agree. Or was that supposed to be sarcasm? You could have easily looked up ‘oracle machines’ and quickly found links to the various sorts of hypercomputer that are studied, so I’ve no idea why you’d be sceptical, unless you’re incapable of using Google. No, you must have been agreeing, right?

    “No it cannot.”

    Yes it can. It’s the same principle as Schrodinger’s cat. (I’d have thought mentioning the name would have given a Big Clue.)

    “Do not let me stop you, but maybe you should not talk about things you quite obviously do not understand? Just a suggestion.”

    Suggest away! It’s incredibly amusing and entertaining to watch somebody pompously ‘correcting’ material they themselves have failed to understand or think through properly. I *do* understand what I’m talking about. It’s entirely possible I’m not explaining it very well, but it’s all perfectly conventional stuff.

    But it might be helpful if I was to point out that all the Argument ad Verecundiam stuff doesn’t work on me. Not even slightly. If you want to present an argument to explain *why* you think I’m wrong, I’d be happy to debate it (if I have time). But if you think that saying “This is simply wrong” with no supporting argument is going to settle the matter, I’m just going to laugh at it. *Anyone* can say “That’s wrong”, about anything. It doesn’t get us anywhere.

    It’s far more pleasant and just as effective in the long run to skip all the ‘you’re an ignorant idiot’ side-comments and just present the arguments to demonstrate it. Such side-comments can only entrench positions, make you look bad in the more civilised forms of debate, and make you look ridiculous if you do it when you’re mistaken. As everyone is from time to time – nobody is infallible. There are no upsides I can see to it, and I’d encourage anyone who wants to be taken seriously to avoid it.

    But it’s just a suggestion.
    🙂

  47. @Nullius in Verba:

    “It’s far more pleasant and just as effective in the long run to skip all the ‘you’re an ignorant idiot’ side-comments and just present the arguments to demonstrate it.”

    If it is “far more pleasant” I am not sure, for as with so many other things in life, tastes differ. As far as presenting arguments, the only thing you have graced us with was a baseless, unargued ream of ignorant claims. And while I submit to the charge of pedantery and pompousness, I confess I am but little trouble by it when on the other side is someone who revels in a pompous display of his own ignorance.

    For one example, your response to:

    “2 + 2 = 4 is not a consequence of any conservation law, in any meaningful sense whatsoever.”

    Was

    “Yes it is.”

    Arguments? None. Now, I realize that you are just serving me the same poison and thus I can hardly fault you. But if you are going to do it, then do not whine about others doing it.

    The fact is, there is little to say in response except “you are wrong; RTFM”. There *would* be, if I were addressing any real arguments, or even if there were any real arguments to address. So no, I am not going to explain to you that yes, elementary arithmetic is logically prior to vector addition or the law of addition of velocities (do you want me to serve up a first course on real analysis in a combox? Yes, there is a logical asymmetry, for even to be able to talk about vector addition you already have to have in place elementary arithmetic, in the form of a model of second order PA inside ZFC, say); how you are equivocating all over the place with “models of addition” and “many arithmetics”; that while there is a sense in which there are “many arithmetics”, it lends exactly zero support to what you claim; that no, mathematicians are interested in them for reasons having nothing to do with “observed physics” (although those factor in, or may factor in, as well); that yes, oracle machines have little to nothing to do with the self-contradicting mumbo-jumbo about forms of mathematical reasoning that are both “mathematically valid” and that we “cannot do”; that by the same i-logic, physics itself is positively littered with reasonings we “cannot do” (e.g. appeals to non-constructive principles like Dependent Choice to set up even elementary calculus; let alone the much stronger choice principles needed for the functional analysis used in QM); that no, the “principle as Schrodinger’s cat” implies nothing in the neighborhood of “the apple *can* be falling and not falling at the same time” (do you want me to serve a first course on QM in a combox?), etc. and etc.

  48. “It’s far more pleasant and just as effective in the long run to skip all the ‘you’re an ignorant idiot’ side-comments and just present the arguments to demonstrate it. Such side-comments can only entrench positions, make you look bad in the more civilised forms of debate, and make you look ridiculous if you do it when you’re mistaken. As everyone is from time to time – nobody is infallible. There are no upsides I can see to it, and I’d encourage anyone who wants to be taken seriously to avoid it.”

    Previously, you said:

    “Reasoning is a form of computation. And computation is a physical process dependent on the laws of physics”

    Why are you trying to reason with the laws of physics? I suppose that’s not quite accurate. The laws of physics that make up yourself are merely interacting with other laws of physics. There is no “you” and no “me” and no one else exists either. Just particles and forces.

    Of course, if you hold this view you are espousing, I don’t understand why you expect other people to take you seriously and reason with you, since you have undermined the common ground upon which reasoning can occur. Just seems like a silly waste of time to me.

  49. @nullius, rodrigues, josh

    you are all helpful…

    reminds me of Feynman and his take on “Babylonian” vs “Greek” mathematics. that was from a popular lecture and it is somewhat vague. in that lecture, Feynman insists that he’s talking about “something” as a physicist and prefers Babylonian math to look at it

    i don’t understand any of these things well enough. it’s like there is a Heisenberg principle for looking at the truth – it always seems to evade me whenever I try to look closely 🙂

  50. Nullius in Verba

    March 21, 2014 at 11:41 am

    “So no, I am not going to explain to you that yes, elementary arithmetic is logically prior to vector addition or the law of addition of velocities”

    Only for a particular conventional sequence of proof/presentation based on a particular set of axioms. There are generally many different choices of axioms, all generating the same system of theorems.

    It’s perfectly possible to *start* with a vector space and then *construct* its base field as the set of mappings (scale transformations) from vectors to vectors that preserve the additive structure on all subspaces. Multiplication of scalars is the result of composing the mappings. Addition of scalars is derived from the addition operation on the set of vectors resulting from applying the mappings to any single vector.

    Then the vectors would be logically prior to the scalars. We don’t normally do it that way because we’re intuitively more familiar with base fields like the reals, and we’re normally trying to introduce vector spaces as the new idea, but neither is in any fundamental sense logically prior to the other.

    “do you want me to serve up a first course on real analysis in a combox?”

    No thanks. Ive already seen it.

    ” the self-contradicting mumbo-jumbo about forms of mathematical reasoning that are both “mathematically valid” and that we “cannot do””

    You can solve the Turing Halting problem in all cases? Please, do tell!

    ” the “principle as Schrodinger’s cat” implies nothing in the neighborhood of “the apple *can* be falling and not falling at the same time” (do you want me to serve a first course on QM in a combox?)”

    If you set up an apple in a box wired to a Geiger counter so it drops the apple onto the cat depending on the outcome, the apple is both falling and not falling at the same time in exactly the same way that the cat can be both dead and not dead at the same time. The extension from one to the other is obvious. And I’ve already been on the introductory QM course, too!

    Josh,

    “There is no “you” and no “me” and no one else exists either. Just particles and forces.”

    There *is* a you and me, and we both *consist* of nothing but particles and forces. Why do you think particles and forces are unable to be people, and do all the things people do? Do you think particles and forces are unable to reason?

  51. @Nullius in Verba:

    “It’s perfectly possible to *start* with a vector space and then *construct* its base field as the set of mappings (scale transformations) from vectors to vectors that preserve the additive structure on all subspaces.”

    A vector space is an abelian group with an action of the scalar field… oops.

    But even if you were correct, it would still lend zero support for your claim, because for example, while there are “many arithmetics” in the sense that first order PA has non-standard models, second order PA is categorical and natural number objects in topoi are all isomorphic. And as far as I know, no one besides logicians cares about non-standard models of arithmetic; they are only interesting insofar as showing things about arithmetic, but can have all sorts of pathological properties (e.g. addition is non-computable). The rest about “models of addition” is just equivocation, etc.

    “You can solve the Turing Halting problem in all cases?”

    Huh?

    “And I’ve already been on the introductory QM course, too!”

    In the conceptual Schroedinger’s cat experiment, the cat is in a mixed state

    c_1 |alive> + c_2 |dead>

    where c_1 and c_2 are complex numbers. The cat is *not* both alive and dead, rather the *state* is a (complex) linear combination of the |alive> and |dead> states. You are just equivocating the + with the logical and connective. I mean, there is an easy way to prove me wrong: observe a cat that is both alive and dead. Oh wait, by the collapse of the state vector we will never see that.

    But enough of this.

  52. @Nullius in Verba:

    And by the way:

    “It’s perfectly possible to *start* with a vector space and then *construct* its base field as the set of mappings (scale transformations) from vectors to vectors that preserve the additive structure on all subspaces.”

    This is also wrong. Suppose it is true. Apply it to the scalar field itself as a one-dimensional space. The modular lattice of linear subspaces is isomorphic to {0, 1} and thus the set of mappings that preserve that the additive structure are simply the abelian groups endomorphisms of R, that is, those maps T that satisfy the Cauchy equation:

    (1) T(r + s) = Tr + Ts

    But it is well known that the Axiom of Choice provides many solutions to (1).

  53. The original Mr. X

    March 21, 2014 at 7:25 pm

    G. Rodrigues:

    “I mean, there is an easy way to prove me wrong: observe a cat that is both alive and dead. Oh wait, by the collapse of the state vector we will never see that.”

    Wait, you mean Nullius is appealing to a concept that cannot even in principle be empirically observed? Well colour me shocked.

  54. Nullius in Verba

    March 22, 2014 at 3:33 am

    “And as far as I know, no one besides logicians cares about non-standard models of arithmetic”

    And why is nobody else interested in non-standard models of arithmetic?

    “but can have all sorts of pathological properties (e.g. addition is non-computable)”

    In what way is that pathological?

    In different models of computation, different functions will be non-computable. We have a bunch of functions that are non-computable in our universe that the people in some other universe with different physical laws might regard it as ‘pathological’ that we couldn’t compute.

    Although I’m fascinated to see you tell me about these marvelous functions that mathematicians study but which we cannot compute by any physical arrangement of matter in *our* universe. Right…!

    “The cat is *not* both alive and dead, rather the *state* is a (complex) linear combination of the |alive> and |dead> states.”

    “Both alive and dead” and “in a superposition of the alive state and dead state” appear to have the same meaning. Is it alive or is it dead?

    “I mean, there is an easy way to prove me wrong: observe a cat that is both alive and dead.”

    Depends what you mean by “observe”. Can you observe the cat in a superposition, as you’ve just described it? You can certainly observe phenomena that *imply* the superposition of dead and alive cats.

    “Oh wait, by the collapse of the state vector we will never see that.”

    If the wavefunction collapses, that is. Since there are no observable consequences of it doing so, (and given that the mechanism and conditions for it doing so are left rather vague,) we can’t know if it actually does.

    And don’t you think the cat itself would collapse the wavefunction, if it does indeed collapse? I thought that was the point of putting a cat in the box, rather than some other device.

    “But it is well known that the Axiom of Choice provides many solutions to (1).”

    Cool! Thanks. I didn’t know about that.

    The good old Axiom of Choice, eh? Tell me, how, in a physical sense, do you actually *pick* a representative element from each of these uncountably many sets? Sounds to me like an operation that mathematicians study but cannot actually *do*, but I hear some people are sceptical about those things…

  55. @Nullius in Verba:

    “In different models of computation, different functions will be non-computable.”

    False; Computation theory 101.

    ““Both alive and dead” and “in a superposition of the alive state and dead state” appear to have the same meaning.”

    They do not. Go learn QM.

    “Tell me, how, in a physical sense, do you actually *pick* a representative element from each of these uncountably many sets?”

    You do not. For the particular case of the Cauchy equation, in Solovay’s model of ZF + DC all subsets of the real line are measurable — call this LM; a standard exercise in measure theory shows that a measurable map that preserves the additive structure is automatically linear. And then again, Shelah proved that ZF + DC + LM is equiconsistent with an inaccessible cardinal hypothesis, so pick your poison.

    Either way, Mathematics is not physics, notwithstanding all your crackpot stuff about computation.

  56. Nullius in Verba

    March 22, 2014 at 4:15 pm

    “False; Computation theory 101.”

    This sounds interesting. OK. Tell me how that works.

    Model A is the usual Turing-complete model from a Turing machine. Model B is a hypercomputer consisting of a Turing machine attached to an oracle that in one step returns 1 or 0 depending on whether the ordinary Turing machine with index n halts or not.

    The sequence for which the nth bit is 1 if and only if the nth Turing machine halts is not computable in model A. There is no algorithm that returns it. But in model B we can have the Turing machine simply count, and pass each number to the oracle. The output is the number desired.

    So the computable functions would appear to differ between A and B. Where does this go wrong?

    “They do not. Go learn QM.”

    Already did, and they do. I think we already agreed this sort of non-argument is stupid, yes?

    “You do not.”

    I’ll rephrase that. How *can* you pick one element from each of the sets? Is this something a mathematician or a computer or any other physical device can *actually do*?

  57. @Nullius

    “In different models of computation, different functions will be non-computable.”

    “computation is a physical process dependent on the laws of physics”

    “Model B is a hypercomputer consisting of a Turing machine attached to an oracle”

    The oracle probably does not obey the laws of physics – can it? And hence you have not convinced me that you are still talking about computation (as per your constraint) when you talk about what a hypercomputer can do.

  58. Nullius in Verba

    March 22, 2014 at 7:39 pm

    “The oracle probably does not obey the laws of physics – can it?”

    Which laws? The ones in this universe or the ones in the hypothetical alternative one where the laws of physics are different and allow hypercomputers of this sort?

  59. There was this fellow who claimed to agree with me about all the people of whom I do not believe are President then said he only disbelieves in one more person being President than I do.

  60. 60 comments and not one mention of this: I’ve almost exclusively seen the OTRF cop-out used in refuting Pascal’s Wager (going something along the lines of “Well, even if it were true, it… it… it can’t be because every religion claims to be ‘true'”).

    Please help find one convincing refutation of the Wager that does not involve the fallacy… Even the post on here last August was plump with it.

    This thought made me smile pretty wide, Briggs.

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