I don’t know the position of squirrels on god. Or dogs on god. Or dogs on humans. I am willing to posit that dogs have a belief system.
Rocks, not having a mentality, can not be said to have a position or lack of position on anything. Except spatially.
Strong athiesm can be considered a belief. Good point about it being a belief system. Perhaps worthy of discussion.
Daniel, there are people who were raised without any structured belief system in religion. It just never came up. I know it’s hard to believe, but… let’s talk about, say, Mowlgi the Jungle Boy. Raised by scientists in a skinner box, Mowlgi never has the concept of God explained to him, and religion is just something foreign to his daily experience.
I don’t have a problem with that, but as a matter of definition, these folks have a belief system about the world that lacks a belief that says, “God exists.”
Apos, if someone were asking me to describe my hobbies, I’d be perfectly accurate to say “non-basketball-playing,” and that would be a good descriptor of one specific aspect of my hobbies.
Really, I think the point I’m making is uncontroversial if I can just phrase it correctly. Every normal sentient human has beliefs about the cosmos. Some of these beliefs include one that says, “God exists”; some don’t. Those that contain such a belief may be called theistic belief systems, just as those that don’t may be called atheistic belief systems. Not all theistic belief systems are the same. Not all atheistic belief systems are the same.
Heh, my apologies if you weren’t getting at Goedel at all and I’m the one who injected him into the debate. Just to clarify, my statement about proving an axiom from itself wasn’t meant to suggest that such a proof was unconditional and premiseless. I was just responding to your wording, in which you spoke of systems having axioms which cannot be “proven within the system”, which seemed misworded to me, on my understanding of the phrase “proven within the system” as meaning “proven from the axioms of the system”. At any rate, Goedel’s theorem doesn’t say that any of the axioms of the system are unprovable from the system; rather, it says that there are other sentences in the language of the system which cannot be proved or disproved from the system’s axioms. But, no matter.
I think, were I to find such a dialetheist as to deny the move from “P is true” to “~P is false”, I would feel the difference in use of words to be so great as that we could not possibly be substantively disagreeing, the two of us making opposite claims about the universe, with necessarily only one correct. Rather, it would appear that we were talking past one another, with him using “true”, “false”, and/or “~” to denote rather different concepts than me.
This may well be. As I understand it, though the belief that P and ~P can both simultaneously be true is central to several mystical traditions, plus Discordianism. I have known people who sincerely believe examples of this to be true; they will happily insist, for example, that all religions are true, including those that claim mutually exclusive things about the world.
In Terry Pratchett’s The Truth, talking dog Gaspode translates into human speech the account of Lord Vetinari’s terrier, Wuffles, who witnessed an assault on the Patrician: “He was in the room with God – by ‘God’ he means the Patrician, Wuffles being an old-fashioned sort of doggie . . .”
In the case of “atheist” though, we’re being asked to describe people though, not the hobbies themselves. The actual analogy would be if you said that you were a non-basketball player. That might describe you, but it isn’t describing you hobbies, only what your hobbies aren’t. For all anyone knows, you might be dead, and have no hobbies at all. It isn’t a big deal, but you have a very weird construction of language that I think isn’t quite targeting the correct referent.
As I said, for a certain definition of belief, it might be true that everyone has beliefs. But I’m not sure the same can be said for the slightly stronger “belief systems.” Not everyone has a single coherent belief system or has even thought about the matter of organizing their beliefs into a system.
Maybe. Maybe it’s okay to tell first graders that a fairy paid for their tooth. But at some point, serious students of science need to understand that science can prove nothing true; it can only prove things false (hence: falsification).
Even if we approach a scientific test without Popperian principle, the fundamental problem remains. You may do an experiment by putting down one rock and then another one rock and adding them together to get two rocks. And you may repeat this experiment numerous times until you satisfy yourself that one rock plus one rock makes two rocks. But there are two important things that you have not proved: (1) that one of anything plus one of the same thing equals two of those things (you tested only rocks), and (2) that one plus one will equal two for a future time when you try your experiment (your test is in the past). Only the proper kind of proof — an analytic one — can assure you that one plus one will always equal two.
The above test, by the way, is similar to the Gambler’s Fallacy. Just because you got “two rocks” many times in a row does not imply that you will always get two rocks, just as flipping a coin and getting heads a thousand times does not prove that you will always get heads when you flip a coin. (Analytic analysis will give you the correct answer, that you are as likely to get either heads or tails for every flip.)
Scientists define proof as “the resolution of doubt.” That’s why I said that you could achieve a scientific, not a mathematical, proof. You can (if you note the next paragraph) prove 1+1=2 in the same way that you can prove that baking soda plus vinegar creates carbon dioxide. It’s a whole different standard of proof.
You left out another point, which is that you haven’t removed observer bias. So you design careful experiments.
To remove issue #1, you test a wide variety of objects. WHen you inevitably find something that doesn’t work (1 cup of a substance plus one cup of a substance doesn’t necessarily equal two cups of a substance, for example), you modify your theory or your terms to narrow down what you mean by “1”. Eventually you get something along the lines of, “When you place one discrete, visible object next to another discrete, visible object, not allowing the two to interact, you may then count two discrete, visible objects.” The theory of 1+1=2 will constantly be modified, since that’s how science works, although as time goes on the modifications will get progressively smaller.
To remove issue #2, you rely on the assumption underlying all scientific experiments, the assumption of causality. You freely admit that this is an assumption, but you do it anyway, since that’s the price of playing the game.
To remove issue #3, you test the theory in a wide variety of ways. You give the same test to infants and to chimpanzees (perhaps creating a device where they can see you adding 1 object to another similar object and where you can choose whether they see 2 objects as a result or 1 or 3 objects, and paying attention to which result causes them the most alarm). You give the test to people in other cultures. You try to confound the test–that is, you try to falsify it.
This is true in mathematics. It is not true in science.
This is an excellent point. Your analytic analysis will tell you that you’re as likely to get either heads or tails for every flip, but my scientific analysis tells me that we’re not dealing with a fair coin here–and given those results, I’ll bet you 100:1 that the next flip will come up heads, and I’ll think you’re a total sucker if you take me up on my bet :).
To be fair, the analytic analysis will only tell you heads and tails are equally likely on each flip if you give it an assumption like “The coin is fair”. Without any assumptions about the probability distribution of the coin’s flips, the analytic analysis will just keep its mouth shut and avoid saying anything potentially incriminating later on. With the right sort of assumptions about the probability distribution of the coin’s flips (assumptions which build in the right sort of inductive principles, like assigning higher probability to “Heads for 1001 flips” than “Heads for 1000 flips, then tails”), the analytic analysis can give the same conclusion as your scientific analysis, that the coin will probably come up heads on the next flip, or even that it will probably come up heads forevermore.
That’s true. I was continuing the analogy because I think it illustrates an important point: an analytic analysis makes the assumption and then sticks with it, to the gambler’s doom. The empirical analysis may make the assumption, but is willing to modify the assumption given the evidence at hand.
If a coin comes up heads on each of 1,000 flips, the probability that the coin is fair is one in 8.299031137761986e+180. Someone more adroit with statistics than me can tell me how many monkeys flipping 1 coin per second you’d have to fill a room with in order to get one result like this by the time the universe suffers heat death. The probability that the coin is not fair? Much greater.
At any rate, having searched for the definition of proof I used above (“the resolution of doubt”), I’m unable to find it. I believe I read it in a Skeptical Inquirer magazine in the mid-nineties, and it’s stuck with me as a great description of what folks mean when they talk about science proving something. Now, however, all I’m able to find is scientists discouraging the use of proof in science.
I guess I can see the reason for that. I will back away, out of respect for their reasoning, from saying that science can prove that 1+1=2, and simply say that all the evidence is consistent with the theory that 1+1=2.
Two more notes about this. First, comparing the use of concrete items in the use of mathematical pedagogy to telling stories about the tooth fairy is a lousy analogy, inasmuch as the first helps students arrive at the truth and the second does not. Second, as I understand it now, scientists object to the word “prove” in connection with science; I therefore think you’re probably wrong when you say that science can prove things false. If it’s sloppy to use the word in one sense, it’s sloppy to use it in the other sense, as well. What we may say is that science can show that the evidence is inconsistent with a theory.
So by some twisted logic are you claiming the scientific method is equal to a religious belief system with zero evidence. No lacking repeatability but incident at all. The threshold for science may be imperfect but it greatly exceeds the level for religious proof.
Where did you get that number? Without making any a priori assumptions about the probability distribution of probability distributions of the coin’s flips [yeah, second-order probability distributions; if P(the coin is fair) is to be meaningful, it seems we are forced to something like this], it does not seem to be possible to determine P(the coin is fair | some flip pattern), only P(some flip pattern | the coin is fair).
Well, your use of the word “prove” in the scientific context for a scientific standard of uncertainty reduction isn’t all that odd to me; I’m perfectly cool with it. My only problem with the claim that science can prove 1+1 = 2 is that what science is proving, to a scientific standard, does not seem to be 1+1 = 2, as such, but some related, not-quite-purely-mathematical statement about combining rocks and/or other physical objects. And yet, I can’t really hold to this distinction absolutely, as the rock experiment is not that far off from things which aren’t normally viewed as so problematic, such as adding large numbers by computer (or abacus), which gives us a proof of sorts of mathematical claims, but one which is grounded in experimental evidence and scientific assumptions. At any rate, as long as you understand the distinction between scientific proof and mathematical proof, which you clearly do, I’m perfectly happy with the particular way you were employing the term of scientific proof.
Well, it looks like your number is 1 out of 2^601, which is probably some sort of typo* on your part, but, at any rate, that would only be P(the first 601 flips are heads | the coin is fair), not P(the coin is fair | the first 601 flips are heads). [Where P(A|B) is the conditional probability of A given B].
*: Well, maybe a typo. Maybe it’s not, and it’s based on some reasoning beyond what I can figure out.
I got my number by finding an applet that allows you to put in two numbers, X and Y, and get the result of X^Y. If my number is screwy, I blame the applet :).
And I think we agree on what’s tested, although I may have said it poorly. It’s tremendously unlikely that the coin is fair, if 1,000 flips come up universally heads; given a fair coin, that’s an astronomically unlikely result. The two statements are almost certainly not going to be paired together.
I’m sorry, but I have no idea what you mean by that. It’s possible you mean that the scientific method has much more scientific evidence to support its efficacy than does, say, fundamentalist Christianity; if that’s what you’re saying, then of course I agree. I hope you’ll similarly agree that fundamentalist Christianity has much more fundamentalist Christian evidence to support its efficacy than does, say, the scientific method.
Personally, I find the scientific method far more useful, valuable, and likely to be an accurate representation of the world. But that’s because I take on faith, or at least on a contingent basis, the accuracy of certain assumptions that underlie the scientific method. I recognize that these assumptions exist.
Fundamental Christianity offers no evidence. That’s why they rely on faith. Faith is not evidence. You ask way too much if you want your indoctrination to be accepted as proof of anything.
(I seem to get in an awful lot of arguments about probabilities and coin flips. If this post doesn’t make you sick of me, I spoke about this at further length in this thread, which may be informative.)
I agree with the statement “given a fair coin, [1000 all heads is] an astronomically unlikely result.” I feel that is pretty much tautologous; the definition of a coin being fair is such that we know P(1000 all heads | the coin is fair) = 1/2^1000.
However, without further assumption, I would not agree with the statement “It’s tremendously unlikely that the coin is fair, if 1,000 flips come up universally heads”. On what grounds? Supposing I flipped a coin 1000 times and got the precise result HTHHHTHHTHTHT…TTTHTH. This result also has probability 1/2^1000 of occurring, given a fair coin; does that mean this result is also evidence that the coin I flipped was not fair? We would be led to absurdity; every possible sequence of 1000 flips of a coin would cause us to determine that it wasn’t fair. We never think to ourselves “Oh, yes, this coin, when flipped 3 times, came up HTH. I guess that means it has probability 1/8 of being fair”, because, indeed, such reasoning is not probabilistically sound.
That is to say, without some special assumptions, it’s entirely unclear to me what P(the coin is fair | 1000 all heads) is. I can expand it out a bit, to P(the coin is fair)/[P(the coin is fair) + 2^1000 * P(the coin is unfair and 1000 heads come up)], where P(the coin is fair) is the unconditional a priori probability of a fair coin and similarly for the other such term, but without any assumptions about the a priori probabilities of the coin being fair, of the coin giving 1000 heads if it’s not fair, etc., it’s impossible to evaluate this term and conclude that it’s small, large, whatever.
Now, as it happens, I do, as a human being, make further assumptions. To the extent that it’s meaningful to speak of some coins as fair and some coins as unfair*, I happen to assume an unfair coin is more likely to give 1000 heads than to give, say, heads on every prime numbered flip below 1000 and tails on the others. And I also happen to assume that a coin is reasonably likely to be unfair, so that the second term in the denominator above is not too small. Quantifying and putting these assumptions together, I could indeed determine that P(the coin is fair | the first 1000 flips are all heads) is tiny. But those assumptions definitely need to be made and noted.
*: Presumably, the fairness or unfairness of a coin is not to be found in its flip sequence alone, a fair coin being capable of giving whatever sequence you name, and similarly for an unfair coin. So, then, what is it about a coin that constitutes its fairness? [It’s a similar situation with predicates like “X has a probability exactly 0.7 of having brown eyes.” Does this predicate hold of anyone? How could we know? All we know of a person is that they either really do have brown eyes or really don’t]. The fairness of a coin could just be a hidden unobservable variable in the universe, that some coins have set to FAIR and others to UNFAIR, but that would be an odd entity to introduce. What we really mean when we speak of some coins as unfair is something causal; we are saying that the coin has a weight upon it, or is controlled by magnets, or this or that; that it has some concrete properties which, according to the laws of physics, make it more likely to assume some flip patterns than others. But as the laws of physics are themselves inductively derived, this begins to complicate the reasoning above, in terms of avoiding circularity.
At any rate, it would simplify things if, rather than discussing P(the coin is fair | the first 1000 flips were heads), we discussed P(the next flip will be heads | the first 1000 flips were heads), which avoids the whole problem of the legitimacy of second-order probability. Nothing from above is essentially changed; in order to conclude that P(the next flip will be heads | the first 1000 flips were heads) is high, we must have had an a priori assumed probability distribution on flip sequences where P(1001 heads) was much higher than P(1000 heads followed by a tail). Making such an assumption is essentially the same thing as assuming the legitimacy of inductive argument, and thus not unreasonable, but we should be aware of what exactly we are doing, so that we don’t conflate it with things it’s not [we’re not using purely mathematical probabilistic argument alone, and we certainly need to avoid the mistake of simply equating the values of P(A|B) and P(B|A)], and, furthermore, so that we are aware of what exactly are the potential pitfalls of what we are doing and how best to grapple with them [e.g., why should we assume P(1001 heads) >> P(1000 heads followed by a tail)? Isn’t the latter just as much some kind of pattern as the former? What makes some patterns better for inductive extrapolation than others, such that we would readily rate the pattern “Heads on every even-numbered flip” as much more likely than the pattern “Heads on every even-numbered flip below 708 and every odd-numbered flip above it”?]
Of course fundamental Christianity offers evidence: it offers the Bible as evidence.
That’s not scientific evidence, to be sure, but it is evidence within the fundamental Christian belief system. Within that belief system, the scientific method does not constitute strong evidence.
And I sincerely hope your last sentence is using the impersonal “you,” because if it’s not, you’re really off-base.
E-Sabbath, what I said is, IMO, relevant because folks were denying that atheism is a belief system. I was clarifying that it is a trait of some belief systems: it is an adjective, not a noun. In the same way, theism is an adjective.
Indistinguishable, I think I agree with everything you said, inasmuch as I could follow it :). The one addition I’d make is that a coin that could predictably make a specific series of flips–e.g., HTHHTTHHHTHTTHTHTHTTHT…–would be equally unlikely to be fair. The universe does not consider HHHHHH… to be a particularly interesting series, but we humans do; we’d notice this pattern whereas we wouldn’t notice others. It’s unlikely in the extreme that a coin would create this particular noticeable pattern, far more likely that it’d create something like the random jumble listed above.
But you’re absolutely right that portraying the odds of the coin being a fair coin as I did above was nonsense. I still maintain that in the real world, the odds of such a coin being unfair (or more likely being a “fair” coin that happened to look identical on both sides) are far, far likelier than the odds of the coin being a normal fair coin, and that a gambler who stuck with a mathematical model in the face of empirical evidence would lose his shirt.