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Try and keep it on the political/societal/cultural end of the discussion. This deals not only with gay rights but also the larger issue of looking at the interaction of religious groups within secular society, their rights and their influence, in contrast with the privileges of other groups. Which religion, if any, is right is irrelevant and arguments of that nature will be moderated. |
I tried to follow the conversation, but as a Bayesian I'm totally confused.
Beliefs should be expressed as probabilities of certainty. There aren't "beliefs that can be tested" and "beliefs that cannot be tested." There are just beliefs. And we have evidence, whether anecdotal, logical, scientific, authority-based or whatever that influences how much we believe something.
And this is for everything. Whether you think the sun will rise tomorrow, whether there's cereal in the pantry, whether that girl likes me or not, or whether I should bring an umbrella in case it rains.
There is no such thing as absolute certainty, as it is impossible to attain with Bayes' Theorem. Absolute certainty doesn't exist, and even if it did, it would be completely useless. What absolute certainty actually says is that no matter the evidence presented to me, even if I died and went to Valhalla, I would still believe in Jesus.
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On January 03 2013 13:06 Reason wrote: How is the opposite of positivism NOT claiming that all beliefs are equal or that "all beliefs have a seperate value, meaning and truthfulness which cannot be proven, tested or judged apart from by each individual".
This is actually a question I'm quite interested in and nobody has a totally secure position about this as far as I'm concerned. But this is more of a question of active research, whereas the simple refutation of positivism is by this point pretty noncontroversial. So this question is a real problem.
But you can't conclude from that, that this:
If you can't tell me what this basis for judgement is then I have to conclude it's simply what I've stated there.
It's not a legitimate move. You can't say "unless you fully explain the implications of not-X, then X, even though X is self-contradictory and subject to disproof by reductio ad absurdum."
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I don't really know what can be done about discriminatory religious beliefs. On one hand, I think it would be best to make any public organization's discrimination based upon sexual orientation illegal. On the other, I don't think it would be possible to do that without a massive protest from all religious people. It's impossible to convince someone whose beliefs are based upon faith that they are mistaken, and there are simply too many religious people to just say "they'll get over it".
Oops, I thought I was in a thread about the legalization of gay marriage in the UK. Looks like this one is a lame philosophy thread...
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On January 03 2013 13:16 JDub wrote: Oops, I thought I was in a thread about the legalization of gay marriage in the UK. Looks like this one is a lame philosophy thread...
The question is quite relevant to the discussion we've been having about this law. A lot of people's positions have been supported with claims that assume positivism, so refuting positivism is relevant.
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On January 03 2013 13:18 sam!zdat wrote:Show nested quote +On January 03 2013 13:16 JDub wrote: Oops, I thought I was in a thread about the legalization of gay marriage in the UK. Looks like this one is a lame philosophy thread... The question is quite relevant to the discussion we've been having about this law. A lot of people's positions have been supported with claims that assume positivism, so refuting positivism is relevant. Interestingly that's exactly what it comes down to... funny that.
On January 03 2013 13:13 sam!zdat wrote:Show nested quote +On January 03 2013 13:06 Reason wrote: How is the opposite of positivism NOT claiming that all beliefs are equal or that "all beliefs have a seperate value, meaning and truthfulness which cannot be proven, tested or judged apart from by each individual".
This is actually a question I'm quite interested in and nobody has a totally secure position about this as far as I'm concerned. But this is more of a question of active research, whereas the simple refutation of positivism is by this point pretty noncontroversial. So this question is a real problem. But you can't conclude from that, that this: Show nested quote + If you can't tell me what this basis for judgement is then I have to conclude it's simply what I've stated there.
It's not a legitimate move. You can't say "unless you fully explain the implications of not-X, then X, even though X is self-contradictory and subject to disproof by reductio ad absurdum." Okay... I still feel the refutation of positivism inherently implies "all beliefs are equal"...
If the process of disproving something by reductio ad absurdum results in an argument that is also disproved by the same method don't you have a paradox there or something to that effect?
So, what I'm saying is...
"unless you fully explain to me the implications of not-X, then universe explodes, because it appears X and not-X are both self contradictory and subject to disproof by reductio ad absurdum"
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On January 03 2013 13:18 sam!zdat wrote:Show nested quote +On January 03 2013 13:16 JDub wrote: Oops, I thought I was in a thread about the legalization of gay marriage in the UK. Looks like this one is a lame philosophy thread... The question is quite relevant to the discussion we've been having about this law. A lot of people's positions have been supported with claims that assume positivism, so refuting positivism is relevant. Well it's hard to see the connection when reading the most recent 5 pages of posts I find only the philosophical debate. I guess I should go ahead and read the entire thread then...
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Hey guys, it's been 36 pages, isn't it time to bring up Hitler?
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On January 03 2013 13:20 Reason wrote: Okay... I still feel the refutation of positivism inherently implies "all beliefs are equal"...
If the process of disproving something by reductio ad absurdum results in an argument that is also disproved by the same method don't you have a paradox there or something to that effect?
Yes, you're quite right. It's a big problem. If not-positivism is equivalent to relativism, then you have a big problem. But you can't prove that this relationship is the case, because you have to assume positivism to show that relativism follows from not-positivism, and of course anything at all follows from positivism AND not-positivism.
Since both positions can be disproved by RAA, I think we are forced to conclude that it is not the case that "if not-positivism, then relativism". At this point we have to start looking for a third option which we haven't considered.
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On January 03 2013 13:25 JDub wrote:Show nested quote +On January 03 2013 13:18 sam!zdat wrote:On January 03 2013 13:16 JDub wrote: Oops, I thought I was in a thread about the legalization of gay marriage in the UK. Looks like this one is a lame philosophy thread... The question is quite relevant to the discussion we've been having about this law. A lot of people's positions have been supported with claims that assume positivism, so refuting positivism is relevant. Well it's hard to see the connection when reading the most recent 5 pages of posts I find only the philosophical debate. I guess I should go ahead and read the entire thread then...
lol yeah I know we're a bit far afield but we got here from a discussion of basic difference in our attitudes towards appropriate scope of secular power, and the disagreement hinges on this point
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On January 03 2013 13:27 sam!zdat wrote:Show nested quote +On January 03 2013 13:20 Reason wrote: Okay... I still feel the refutation of positivism inherently implies "all beliefs are equal"...
If the process of disproving something by reductio ad absurdum results in an argument that is also disproved by the same method don't you have a paradox there or something to that effect?
Yes, you're quite right. It's a big problem. If not-positivism is equivalent to relativism, then you have a big problem. But you can't prove that this relationship is the case, because you have to assume positivism to show that relativism follows from not-positivism, and of course anything at all follows from positivism AND not-positivism. Since both positions can be disproved by RAA, I think we are forced to conclude that it is not the case that "if not-positivism, then relativism". At this point we have to start looking for a third option which we haven't considered.
Well... I'm going to bed now 4:44am.
This is becoming awfully complicated. Thanks for explanations... I will now attempt to process... 
On January 03 2013 13:13 DoubleReed wrote: I tried to follow the conversation, but as a Bayesian I'm totally confused.
Beliefs should be expressed as probabilities of certainty. There aren't "beliefs that can be tested" and "beliefs that cannot be tested." There are just beliefs. And we have evidence, whether anecdotal, logical, scientific, authority-based or whatever that influences how much we believe something.
And this is for everything. Whether you think the sun will rise tomorrow, whether there's cereal in the pantry, whether that girl likes me or not, or whether I should bring an umbrella in case it rains.
There is no such thing as absolute certainty, as it is impossible to attain with Bayes' Theorem. Absolute certainty doesn't exist, and even if it did, it would be completely useless. What absolute certainty actually says is that no matter the evidence presented to me, even if I died and went to Valhalla, I would still believe in Jesus.
Okay interesting lol. Nice to hear a (possibly?) different take on this.
So you don't think any beliefs can be tested? It's all probability?
For example "testing" a dice to see if it's 1 in 6 chance to roll any number from 1 to 6, you think it's impossible to "test" this, you could just roll it a few million times and only ever be "fairly certain" that it's 1 in 6 for each number but that you haven't actualy "tested" this?
What about the belief in God, do you believe that is equally testable or untestable? Do you think either can be tested or proved to a higher degree of certainty than the other?
Does either belief then hold more "value" or "meaning"?
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On January 03 2013 13:30 Reason wrote:Show nested quote +On January 03 2013 13:27 sam!zdat wrote:On January 03 2013 13:20 Reason wrote: Okay... I still feel the refutation of positivism inherently implies "all beliefs are equal"...
If the process of disproving something by reductio ad absurdum results in an argument that is also disproved by the same method don't you have a paradox there or something to that effect?
Yes, you're quite right. It's a big problem. If not-positivism is equivalent to relativism, then you have a big problem. But you can't prove that this relationship is the case, because you have to assume positivism to show that relativism follows from not-positivism, and of course anything at all follows from positivism AND not-positivism. Since both positions can be disproved by RAA, I think we are forced to conclude that it is not the case that "if not-positivism, then relativism". At this point we have to start looking for a third option which we haven't considered. Well... I'm going to bed now 4:39 am. This is becoming awfully complicated. Thanks for explanations... I will now attempt to process 
Sweet dreams, nice talking to you. I know it seems a little weird and vague but I actually think it's a pretty important point, processing the implications of this is sort of a watershed moment in one's philosophical education, in my experience. A lot of people I think want so badly to argue against religion, for good reasons, that they end up falling into some philosophical peril of their own. So the question for me has a lot more importance for contemporary social discourse than it might seem when you are trying to wrap your head around the idea of incompleteness and getting involved in logical stuff.
edit: basically I think there's very real danger in fetishizing "science" as the only True Path to Knowledge, which is a fairly common ideological assumption in our moment
edit: and yes you're quite right to feel that the "well then, what?" is a very troubling thing to try to think about. Trust me, they felt the same way the first time people started going around saying "there is no God"
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On December 12 2012 05:09 dAPhREAk wrote:Show nested quote +On December 12 2012 05:06 KwarK wrote:On December 12 2012 04:54 dAPhREAk wrote:On December 12 2012 04:47 KwarK wrote:On December 12 2012 04:43 dAPhREAk wrote:On December 12 2012 04:36 Klondikebar wrote:On December 12 2012 04:17 dAPhREAk wrote: debated whether to even get into this, but here is where i stand: the right to marriage (gay or not) and the right to practice religion are both fundamental rights that should not be infringed lightly. if you force a church to allow gay marriage (by forcing their priests (or whatever they call themselves) to be subject to discrimination lawsuits because they wont violate their religious principals) you are infringing their right to practice their religion as long as its an actual belief of the church. so, i am opposed to that. you may not like that result, but thats why we have fundamental rights--to prevent others from forcing their beliefs on others.
people who want to get married (gay or not) have options, they do not need to infringe believer's fundamental rights to do so.
by the way, freedom from discrimination is not a fundamental right, and never has been.
edit: by the way, i support gay marriage. But at some point, are we allowed to ask for some sort of evidence or justification for their beliefs? ESPECIALLY if we're going to be protecting those beliefs with laws. "It's in my religious text!" won't work because religions ignore TONS of stuff in their texts. The legislature needs to get them into a hearing where they say "we will protect your beliefs if you can provide some sort of evidence or coherent logic for them." Why do we just accept religious belief as something to be protected? If beliefs can't be even remotely justified, why do we treat them any differently than a belief in santa? the supreme court has a test for this. you cant question the facts of their beliefs; you can only question whether they actually have the belief. i am fine with this test. we accept religious beliefs as something to be protected because its a fundamental right. The issue secularists like myself have with this statement is the "because it is a fundamental right". In the UK it is currently against the law to discriminate against gays on the basis of their sexuality, even if you have really strongly held homophobic convictions and a load of subjective experience that validated them. This law will grant an exemption to the anti discrimination laws for churches which can't even agree amongst themselves most of the time whether or not they oppose gay marriage. Religious people do not have a monopoly on strength of conviction and yet they seem to have inherited a fundamental right to have their convictions protected. I'd like to see it justified. history and society has determined that it is a fundamental right, and in america it is written into our constitution. the justification for that is something that would take a lot of research and time to write a thoughtful piece, which i am not willing to do. =) The title says UK, if you cannot or are unwilling to justify the statement "because it is a fundamental right" then it should not be assumed to be a fundamental right in the UK. The question of why you get an exemption if a burning bush says to oppose the gays but not if a regular bush says to oppose the gays remains. i am pretty sure its considered a fundamental right through most of the modern, western world. its in the Universal Declaration of Human Rights after all. http://www.un.org/en/documents/udhr/index.shtml
This document is used way too often to promote gay rights and is just plain wrong to use. My personal opinion is of course give them the freedom of marriage, but this is not a good document to use as your argument. This document was created in the 1950's and was intended for man and woman. Gay marriage was not a prominent issue and these leaders could not have possibly predicted that it would later become an important issue. No where does it say that marriage is a fundamental right for homosexuals all it is intended for is a man and woman. There has been a precedent by the supreme court (USA) which even defined marriage as a man and woman (1970's-present), my understanding is the UK also has nothing that says marriage is equalized for everyone, but correct me if I am wrong because I am more familiar with American law. This is basically the secular argument against gay marriage. Marriage has been defined by traditional values as man and woman so it seems somewhat strange for you to use this document considering it promotes woman and man marriage and not gay rights. This document only promotes marriage between a man and woman and simply does nothing to promote gay marriage you must truly see the context of the document to understand it.
Many people think gay marriage hasn't passed just because of non secular, but truly there is a large community of secular that disagree with gay marriage just because it goes against traditional values.
I disagree with the traditional value and think it's important to look at our society as of today and think gay marriage should finally be accepted throughout the world. Saying gay marriage is a fundamental right is technically false as there has been no historic value for this and there is no historic document that promotes gay marriage as of my understanding.
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The language in the UDHR seems ambiguous to me.
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On January 03 2013 14:24 sam!zdat wrote: The language in the UDHR seems ambiguous to me. I agree but you have to look at the context of when it was written it was no intended for gay marriage. 10 December 1948 this was when the document was created. To say gay marriage was an issue in 1948 and they addressed it in the UDHR is pretty silly considering countries created a precedent in 1973 saying marriage was between a man and a woman.
http://en.wikipedia.org/wiki/Defense_of_Marriage_Act "is a United States federal law that defines marriage as the legal union of one man and one woman for federal and inter-state recognition purposes in the United States" enacted on 1996. Although it is a US law and this topic is on the UK it just goes to show that the UDHR is in no way agreeing with gay marriage.
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Quoting the UDHR is fine if you want to refer to the message is conveys : everyone is equal and must be treated fair etc even if the thing is outdated or doesn't specifically speak out for gay people it was still written in the best interests of humanity and is a useful if slightly blunt tool to use on occasion.
On January 03 2013 13:25 JDub wrote:Show nested quote +On January 03 2013 13:18 sam!zdat wrote:On January 03 2013 13:16 JDub wrote: Oops, I thought I was in a thread about the legalization of gay marriage in the UK. Looks like this one is a lame philosophy thread... The question is quite relevant to the discussion we've been having about this law. A lot of people's positions have been supported with claims that assume positivism, so refuting positivism is relevant. Well it's hard to see the connection when reading the most recent 5 pages of posts I find only the philosophical debate. I guess I should go ahead and read the entire thread then... For all of a similar mind, don't read pages 32 - 36 if you want to avoid the "philosophy" part of the debate... though if you follow the first 30+ pages you will probably begin to understand why this came up in the first place 
On January 03 2013 13:25 Zrana wrote: Hey guys, it's been 36 pages, isn't it time to bring up Hitler? Somebody already tried, failed and then was banned. Good luck with that though.
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On January 03 2013 13:30 Reason wrote:Show nested quote +On January 03 2013 13:27 sam!zdat wrote:On January 03 2013 13:20 Reason wrote: Okay... I still feel the refutation of positivism inherently implies "all beliefs are equal"...
If the process of disproving something by reductio ad absurdum results in an argument that is also disproved by the same method don't you have a paradox there or something to that effect?
Yes, you're quite right. It's a big problem. If not-positivism is equivalent to relativism, then you have a big problem. But you can't prove that this relationship is the case, because you have to assume positivism to show that relativism follows from not-positivism, and of course anything at all follows from positivism AND not-positivism. Since both positions can be disproved by RAA, I think we are forced to conclude that it is not the case that "if not-positivism, then relativism". At this point we have to start looking for a third option which we haven't considered. Well... I'm going to bed now 4:44am. This is becoming awfully complicated. Thanks for explanations... I will now attempt to process...  Show nested quote +On January 03 2013 13:13 DoubleReed wrote: I tried to follow the conversation, but as a Bayesian I'm totally confused.
Beliefs should be expressed as probabilities of certainty. There aren't "beliefs that can be tested" and "beliefs that cannot be tested." There are just beliefs. And we have evidence, whether anecdotal, logical, scientific, authority-based or whatever that influences how much we believe something.
And this is for everything. Whether you think the sun will rise tomorrow, whether there's cereal in the pantry, whether that girl likes me or not, or whether I should bring an umbrella in case it rains.
There is no such thing as absolute certainty, as it is impossible to attain with Bayes' Theorem. Absolute certainty doesn't exist, and even if it did, it would be completely useless. What absolute certainty actually says is that no matter the evidence presented to me, even if I died and went to Valhalla, I would still believe in Jesus. Okay interesting lol. Nice to hear a (possibly?) different take on this. So you don't think any beliefs can be tested? It's all probability? For example "testing" a dice to see if it's 1 in 6 chance to roll any number from 1 to 6, you think it's impossible to "test" this, you could just roll it a few million times and only ever be "fairly certain" that it's 1 in 6 for each number but that you haven't actualy "tested" this? What about the belief in God, do you believe that is equally testable or untestable? Do you think either can be tested or proved to a higher degree of certainty than the other? Does either belief then hold more "value" or "meaning"?
Well, how do you know it's not a weighted die? You must have evidence, even if that evidence is simply that nearly all dice are unweighted.
"Fairly certain" isn't really accurate. Bayesian inferences can be pretty dramatic. Having a 99.99% certainty is the same thing as "knowing" something, by the colloquial term "know."
Yes, belief in God is the same thing. Often, the main evidence is based on Authority by parents and priests.
Beliefs obviously are meaningful because they affect our decisionmaking. And believing is false statements can obviously make bad and harmful decisions.
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The question then becomes, what sort of false statements can we believe in that do not lead to bad and harmful decisions ?
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Can someone please tell me why we can't just let everyone get married and then if you don't want to call it "marriage" and instead want to call it "an abomination against god" you can go and do that to your heart's content? It seems to me that if a group of people wanted to specify that a "sandwich" was exactly [2 parts bread 1 part mayo 1 part ham 1 part cheese] and that every other bread/meat/condiment/bread combination was a "festering sacrilege" they would be allowed to be crazy by themselves off in a corner while the rest of the population who give no shits what is on their sandwich could still call it a sandwich and eat it in peace.
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On January 04 2013 01:20 DoubleReed wrote:Show nested quote +On January 03 2013 13:30 Reason wrote:On January 03 2013 13:27 sam!zdat wrote:On January 03 2013 13:20 Reason wrote: Okay... I still feel the refutation of positivism inherently implies "all beliefs are equal"...
If the process of disproving something by reductio ad absurdum results in an argument that is also disproved by the same method don't you have a paradox there or something to that effect?
Yes, you're quite right. It's a big problem. If not-positivism is equivalent to relativism, then you have a big problem. But you can't prove that this relationship is the case, because you have to assume positivism to show that relativism follows from not-positivism, and of course anything at all follows from positivism AND not-positivism. Since both positions can be disproved by RAA, I think we are forced to conclude that it is not the case that "if not-positivism, then relativism". At this point we have to start looking for a third option which we haven't considered. Well... I'm going to bed now 4:44am. This is becoming awfully complicated. Thanks for explanations... I will now attempt to process...  On January 03 2013 13:13 DoubleReed wrote: I tried to follow the conversation, but as a Bayesian I'm totally confused.
Beliefs should be expressed as probabilities of certainty. There aren't "beliefs that can be tested" and "beliefs that cannot be tested." There are just beliefs. And we have evidence, whether anecdotal, logical, scientific, authority-based or whatever that influences how much we believe something.
And this is for everything. Whether you think the sun will rise tomorrow, whether there's cereal in the pantry, whether that girl likes me or not, or whether I should bring an umbrella in case it rains.
There is no such thing as absolute certainty, as it is impossible to attain with Bayes' Theorem. Absolute certainty doesn't exist, and even if it did, it would be completely useless. What absolute certainty actually says is that no matter the evidence presented to me, even if I died and went to Valhalla, I would still believe in Jesus. Okay interesting lol. Nice to hear a (possibly?) different take on this. So you don't think any beliefs can be tested? It's all probability? For example "testing" a dice to see if it's 1 in 6 chance to roll any number from 1 to 6, you think it's impossible to "test" this, you could just roll it a few million times and only ever be "fairly certain" that it's 1 in 6 for each number but that you haven't actualy "tested" this? What about the belief in God, do you believe that is equally testable or untestable? Do you think either can be tested or proved to a higher degree of certainty than the other? Does either belief then hold more "value" or "meaning"? Well, how do you know it's not a weighted die? You must have evidence, even if that evidence is simply that nearly all dice are unweighted. "Fairly certain" isn't really accurate. Bayesian inferences can be pretty dramatic. Having a 99.99% certainty is the same thing as "knowing" something, by the colloquial term "know." Yes, belief in God is the same thing. Often, the main evidence is based on Authority by parents and priests. Beliefs obviously are meaningful because they affect our decisionmaking. And believing is false statements can obviously make bad and harmful decisions.
Not really sure what you're saying here...
On January 03 2013 13:13 DoubleReed wrote: Beliefs should be expressed as probabilities of certainty. There aren't "beliefs that can be tested" and "beliefs that cannot be tested." There are just beliefs. And we have evidence, whether anecdotal, logical, scientific, authority-based or whatever that influences how much we believe something.
So with the example of rolling the die, are you saying that the belief the die in not weighted can't be tested?
The evidence is rolling it a few million times and being 99.99% certain it's not weighted.
What about belief in God? Can you ever remove that from square on 50% certain vs 50% uncertain?
I think the former is a belief that can be "tested" and the second cannot. This would seem to contradict what you're saying..
What if I have anecdotal evidence that the die isn't weighted, because I'm never used a weighted die before, and I have authority-based evidence because my parents who never learned to count to three promised me that the die isn't weighted, but I've rolled the die a few billion times and that "evidence" shows there's a 99.9999% chance that it is weighted... You are saying all types of evidence hold the same level of importance? Is this two against one and I should ignore the mathematical data and instead trust my gut instinct and my parents?
On January 04 2013 03:11 Arghmyliver wrote: Can someone please tell me why we can't just let everyone get married and then if you don't want to call it "marriage" and instead want to call it "an abomination against god" you can go and do that to your heart's content? It seems to me that if a group of people wanted to specify that a "sandwich" was exactly [2 parts bread 1 part mayo 1 part ham 1 part cheese] and that every other bread/meat/condiment/bread combination was a "festering sacrilege" they would be allowed to be crazy by themselves off in a corner while the rest of the population who give no shits what is on their sandwich could still call it a sandwich and eat it in peace. Lol, nice analogy, I think the problem is that we want to buy our "festering sacrileges" from their "sandwich shop" and we also want them to be branded as "sandwiches" and not "festering sacrileges". 
Now, we've already forced every other sandwich shop to sell all types of sandwiches and brand them as sandwiches despite their own personal tastes, but unfortunately this is a religious sandwich shop.
This means, apparently, that they don't have to confirm to the same laws as every other sandwich shop, which is essentially the crux of the debate here.
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When did I say all evidence is the same importance? Where did you even come up with that? I suggested no such thing.
What do you mean by "tested"? If I pray to God and nothing happens, do you consider that evidence against God? Certainly it is evidence against a God that answers prayers.
Why would we be unable to get away from 50/50 for God? Are you really saying that we have absolutely zero information about the world that we live in? This is not at all accurate. You might want to actually look up Bayes Theorem.
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On January 04 2013 04:46 DoubleReed wrote: What do you mean by "tested"? If I pray to God and nothing happens, do you consider that evidence against God? Certainly it is evidence against a God that answers prayers.
Well, strictly speaking, that would be evidence against a God that would answer that prayer from you at that time 
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I wrote this in a PM but I thought it might be useful so I'll post it. Then I'll leave you guys alone and we can let this thread die maybe.
When I say that you have to assume positivism to show that relativism follows from not-positivism, this is what I mean:
1) it is not the case that positivism, i.e. "it is not the case that a belief is legitimate if and only if it is scientific"
if you want to get
2) not-positivism -> relativism, i.e. "if it is not the case that a belief is legitimate if and only if it is scientific, then all beliefs are equally legitimate"
you have to assume
3) positivism, i.e. "a belief is legitimate if and only if it is scientific."
which leads to the corollary
4) "there is no way for a belief to be legitimate unless it is scientific."
if you reject (4), then (2) does not follow from (1). Since assuming (1) already implies that (4) is not the case, then there's no way to derive (2) without a contradiction.
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