Why Do You Believe?

[muon2]

I don't think that it can be proven either way and for me that is a reason not to believe.
There are many hypotheses that can't be proven. Why should I believe in any of them?

Our system of rational mathematical and scientific thought is based on hypotheses that can't be proven.

For example in classical geometry the statement "Given a line and a point not on the line, at most one line can be drawn through the point that is parallel to the given line." cannot be proved or disproved without introducing some other hypothesis that itself cannot be proved. The statement is called the parallel postulate (Playfair's version) and must be accepted as true to derive other aspects of geometry and mathematics.

In physics centuries were spent trying to measure the medium that carried light waves with no success. Einstein hypothesized that the speed of light was the same to all observers in straight line motion. This unproved postulate led to the development of Einstein's relativity and did away with the notion of a medium for light waves. Subsequent measurements of the effects of relativity didn't prove the postulate, but justified scientific belief in the unproven hypothesis.

In fact in the early 20th century Gödel proved that given any system of axioms there must be true statements about the natural numbers that are unprovable in the system. Essentially he delivered a logical proof that there there will always be unprovable hypotheses that are nonetheless true. Thus one must be prepared to believe in some unprovable hypotheses or choose to disbelieve statements that are true.

[muon2]

Our system of rational mathematical and scientific thought is based on hypotheses that can't be proven.

For example in classical geometry the statement "Given a line and a point not on the line, at most one line can be drawn through the point that is parallel to the given line." cannot be proved or disproved without introducing some other hypothesis that itself cannot be proved. The statement is called the parallel postulate (Playfair's version) and must be accepted as true to derive other aspects of geometry and mathematics.

In physics centuries were spent trying to measure the medium that carried light waves with no success. Einstein hypothesized that the speed of light was the same to all observers in straight line motion. This unproved postulate led to the development of Einstein's relativity and did away with the notion of a medium for light waves. Subsequent measurements of the effects of relativity didn't prove the postulate, but justified scientific belief in the unproven hypothesis.

In fact in the early 20th century Gödel proved that given any system of axioms there must be true statements about the natural numbers that are unprovable in the system. Essentially he delivered a logical proof that there there will always be unprovable hypotheses that are nonetheless true. Thus one must be prepared to believe in some unprovable hypotheses or choose to disbelieve statements that are true.

Yes, but in every one of those cases, there's some extrinsic reason those hypotheses are accepted above other consistent hypotheses.  The fact we accept some unfalsifiable hypotheses does not mean that all unfalsifiable hypotheses are equally valid or reasonable.  Certainly you're not trying to argue that all hypotheses are equally reasonable, so if not that, what?  (I feel like this is bordering on the same exchange we had in the vegan thread, and you never resolved my questions about how far, and to what purpose, you were drawing the bounds of your apparent shrugging subjectivism.)

My response was specifically to the quote I linked, but was dropped in your reply. It suggested that unproven hypotheses should not be believed. I disagree.

I don't think that it can be proven either way and for me that is a reason not to believe.
There are many hypotheses that can't be proven. Why should I believe in any of them?

I believe that the human mind intrinsically lends itself to contradiction. Furthermore that contradiction is not necessarily a concern, since internal contradictions are unavoidable in a complete logical system. 

[muon2]

My response was specifically to the quote I linked, but was dropped in your reply. It suggested that unproven hypotheses should not be believed. I disagree.

(...)

I believe that the human mind intrinsically lends itself to contradiction. Furthermore that contradiction is not necessarily a concern, since internal contradictions are unavoidable in a complete logical system.  

OK, then again: why hold any given belief over any other given belief, ever?  Is it entirely arbitrary and removed from empirical observation, or are there some unfalsifiable hypotheses that are more reasonable to operate on than others?  If so, why?

This isn't a pedantic question.  I recognize what you're saying about the necessity of unfalsifiable hypotheses, but how do we incorporate that without reaching a conclusion that all beliefs and ideas are equally reasonable?  Oftentimes I see this as a defense of believing unfalsifiable religious hypotheses, by why those, but not others?  The answers that apply to the mathematical examples you cited do not, as far as I know, really apply to religious hypotheses, which this thread is about.  I see this invoked to defend religious beliefs frequently, but I've never seen someone seriously explain how this extension doesn't defend all possible beliefs.

It's an interesting way to phrase the question. I think the answer lies in the paradigm a person operates under, and I'll start with science since I know it best. To me a scientific paradigm includes hypotheses, observations, key pieces of derived knowledge, standard points of discussion and inquiry, and methodology to derive additional knowledge. Taken as a whole the paradigm is logically consistent, including the unfalsifiable hypotheses. Some unproven hypotheses are inconsistent with the paradigm, and these would fall into the category of those which are not believed. So not all beliefs in the field are equally reasonable.

I'm not a sociologist, but I believe there has been work on the application of paradigms to social science as well. I would think that a social paradigm should include relevant religious beliefs as hypotheses within that paradigm. As in the scientific paradigm the rationale for those beliefs would be their consistency with the overall social paradigm. As with science the social paradigm would provide a standard by which not all beliefs are equally reasonable.

As an aside for TJ, the statement that each effect has a cause is highly debatable in the world of quantum mechanics. The dominant view now is that some quantum effects (including some of those that underpin semiconductor electronics) do not have a cause per se, but are based on the probabilities of particular occurrences. The notion of strict causality at the atomic level does not fit into the current paradigm.

[muon2]

As an aside for TJ, the statement that each effect has a cause is highly debatable in the world of quantum mechanics. The dominant view now is that some quantum effects (including some of those that underpin semiconductor electronics) do not have a cause per se, but are based on the probabilities of particular occurrences. The notion of strict causality at the atomic level does not fit into the current paradigm.

That's a fair point and one I completely glossed over with my simple language about cause and effect. I would say for the relevant purposes here that "causation" is not necessarily limited to strict causality but rather that there is matter, field, or law constraining what is happening, ie. the probability is coming from somewhere and is not entirely arbitrary. For example, if we used the analogy of a coin flip where I got 'tails' (assuming it were truly random), the 'tails' result would not be strictly caused by something that could not also have caused 'heads' but is still caused by the fact that I have a coin with a 'heads' side and a 'tails' side.

Your reply highlights an example of conflicting paradigms. I expect that most people would agree with your assertion that "the probability is coming from somewhere and is not entirely arbitrary." Most physicists would not agree with that in the context of the modern paradigm of measurement and quantum mechanics. Einstein and others tried to assert that there were "hidden variables" that created cause and effect for quantum processes, but their models were unsatisfying to physicists as a community, and we are left with the belief that there are truly random processes that are entirely arbitrary.

Even beyond the quantum level there are events that hinge on measurements that intrinsically can not be made with sufficient precision, and would require a computer with more atoms than in the universe to project an effect from the cause. upon seeing an effect one might philosophically claim these "chaotic" events have a cause, but if that cause cannot be discerned by any physical means does that sense of cause have meaning?

This is really interesting.  Can you elaborate a bit on how the social paradigm could provide such a standard?  I understand how the scientific paradigm might -- consistency with other observed phenomena -- but how would such a standard work in the social paradigm?

I'm doing a little bit of thinking on this while I'm grading qualifying exams. I want to make sure we are on the same page about paradigms. A paradigm is more than just a consistent set of hypotheses, observations, and knowledge derived from them. It also importantly includes a framework for thought that specifies the types of questions one might reasonably ask and proper methods for discerning the answers to those questions. For example it is grammatically correct to ask "How many centimeters are in a pound?", but that is a nonsense question to a scientist, because there is no framework in our scientific paradigm to compare a measurement of length to one of weight.

From what I've read the famous question about the number of angels that can dance on the head of a pin is a similar example that seems nonsensical to modern western thought. Yet it meant something entirely different in the paradigm of the medieval scholar. We would view it as something that should be answered with a physical counting. The ancient scholar would not have thought about it that way, but instead would look at the question as a way to understand the nature of the immaterial world of the divine.

[muon2]

As an aside for TJ, the statement that each effect has a cause is highly debatable in the world of quantum mechanics. The dominant view now is that some quantum effects (including some of those that underpin semiconductor electronics) do not have a cause per se, but are based on the probabilities of particular occurrences. The notion of strict causality at the atomic level does not fit into the current paradigm.

That's a fair point and one I completely glossed over with my simple language about cause and effect. I would say for the relevant purposes here that "causation" is not necessarily limited to strict causality but rather that there is matter, field, or law constraining what is happening, ie. the probability is coming from somewhere and is not entirely arbitrary. For example, if we used the analogy of a coin flip where I got 'tails' (assuming it were truly random), the 'tails' result would not be strictly caused by something that could not also have caused 'heads' but is still caused by the fact that I have a coin with a 'heads' side and a 'tails' side.

Your reply highlights an example of conflicting paradigms. I expect that most people would agree with your assertion that "the probability is coming from somewhere and is not entirely arbitrary." Most physicists would not agree with that in the context of the modern paradigm of measurement and quantum mechanics. Einstein and others tried to assert that there were "hidden variables" that created cause and effect for quantum processes, but their models were unsatisfying to physicists as a community, and we are left with the belief that there are truly random processes that are entirely arbitrary.

Even beyond the quantum level there are events that hinge on measurements that intrinsically can not be made with sufficient precision, and would require a computer with more atoms than in the universe to project an effect from the cause. upon seeing an effect one might philosophically claim these "chaotic" events have a cause, but if that cause cannot be discerned by any physical means does that sense of cause have meaning?

I am aware of the notion of hidden variables and that most of modern physics has rejected the notion but I am a little confused by your response. Are you saying that the probability itself of an event is arbitrary (not the outcome but the probability)? Aren't the probabilities of events contingent upon variables such as the existence of particles, positions, and fields? Sorry for being obtuse, I recognize here that my knowledge of quantum mechanics is only at the undergrad physical chemistry level.

It is true that if I knew the exact state of a system and the type of measurement that was performed, I could precisely calculate the probability of a particular value for the measurement. Ironically the same quantum mechanics tells us we cannot know with absolute precision all the variables of the state of the system, so my calculation would be something other than ideal. However, when we have very large numbers of very small quantum particles, my lack of knowledge can be a help. In the limit of large statistics the probabilities become more certain, much as a casino counts on a large number of players to guarantee their long term winnings.

However, I do think most people would ascribe a cause not to the calculation of the probability, but to the realization of an event that depends on the probability. In the famous thought experiment about Schrodinger's cat, the random decay of an unstable atom triggers the poison that would kill the cat. There is a natural tendency for people to say we don't know when the atom will decay, but some unknown factors are causing it to decay at the moment that it does. That tendency is essentially the hidden variable view of quantum mechanics.

I think this takes care of Torie's question, too.

[muon2]

I'm doing a little bit of thinking on this while I'm grading qualifying exams. I want to make sure we are on the same page about paradigms. A paradigm is more than just a consistent set of hypotheses, observations, and knowledge derived from them. It also importantly includes a framework for thought that specifies the types of questions one might reasonably ask and proper methods for discerning the answers to those questions. For example it is grammatically correct to ask "How many centimeters are in a pound?", but that is a nonsense question to a scientist, because there is no framework in our scientific paradigm to compare a measurement of length to one of weight.

From what I've read the famous question about the number of angels that can dance on the head of a pin is a similar example that seems nonsensical to modern western thought. Yet it meant something entirely different in the paradigm of the medieval scholar. We would view it as something that should be answered with a physical counting. The ancient scholar would not have thought about it that way, but instead would look at the question as a way to understand the nature of the immaterial world of the divine.

OK, but how do we determine what are reasonable unfalsifiable hypotheses to believe in the social paradigm?  I understand the reason (more or less) why we accept and proceed with unfalsifiable hypotheses in mathematics -- they're necessary for consistency with observable phenomena.  I assume you agree that there are some beliefs, in the social paradigm and elsewhere, that aren't reasonable...or do you think that all beliefs, if unfalsifiable, are equally reasonable to hold?

Let's consider the universe of all unfalsifiable hypotheses. Within this universe some of these hypotheses are contradictory at some level. A paradigm requires some of these hypotheses as the basis of its internal logic, so a subset of the hypotheses will exist in any paradigm. The paradigm uses the hypotheses and applies them along with accepted methods of interaction within the paradigm to make decisions. If the selection of hypotheses is too narrow there will be true but unprovable assertions that are left out, yet if all such unprovably true hypotheses are included there will be internal contradictions. The result is a set of hypotheses that can entertain some, but not too many, internal contradictions. This is true for any rational system of thought, not just science.

Because the paradigm is more than just its set of hypotheses it provides the means to judge the reasonableness of other hypotheses. It has the accepted history of events in the paradigm and accepted procedures for evaluating information in context. If a new unfalsifiable hypothesis is introduced it is interpreted in the paradigm to see if it pushes inconsistencies too far. The farther it pushes inconsistencies, the less reasonable it will seem.

I assume a social paradigm is not the same as one in natural science, but like a scientific field a society has a collection of accepted historical events and accepted norms for evaluating information to make decisions. A field of science has a belief system (ie unfalsifiable hypotheses) that is generally consistent within its paradigm, and it seems to me that a society likewise has a belief system that is generally consistent within its paradigm. Here I use generally to mean that some inconsistencies are permitted to increase the pool of unprovably true statements accepted in the paradigm. If it makes sense to speak of social paradigms, then it seems that a society will adjust to new beliefs in a way that is consistent with its own paradigm. Those beliefs will seem most reasonable that are least contradictory to the existing set of beliefs and to the other features of the paradigm.

[muon2]

Let's consider the universe of all unfalsifiable hypotheses. Within this universe some of these hypotheses are contradictory at some level. A paradigm requires some of these hypotheses as the basis of its internal logic, so a subset of the hypotheses will exist in any paradigm. The paradigm uses the hypotheses and applies them along with accepted methods of interaction within the paradigm to make decisions. If the selection of hypotheses is too narrow there will be true but unprovable assertions that are left out, yet if all such unprovably true hypotheses are included there will be internal contradictions. The result is a set of hypotheses that can entertain some, but not too many, internal contradictions. This is true for any rational system of thought, not just science.

Because the paradigm is more than just its set of hypotheses it provides the means to judge the reasonableness of other hypotheses. It has the accepted history of events in the paradigm and accepted procedures for evaluating information in context. If a new unfalsifiable hypothesis is introduced it is interpreted in the paradigm to see if it pushes inconsistencies too far. The farther it pushes inconsistencies, the less reasonable it will seem.

I assume a social paradigm is not the same as one in natural science, but like a scientific field a society has a collection of accepted historical events and accepted norms for evaluating information to make decisions. A field of science has a belief system (ie unfalsifiable hypotheses) that is generally consistent within its paradigm, and it seems to me that a society likewise has a belief system that is generally consistent within its paradigm. Here I use generally to mean that some inconsistencies are permitted to increase the pool of unprovably true statements accepted in the paradigm. If it makes sense to speak of social paradigms, then it seems that a society will adjust to new beliefs in a way that is consistent with its own paradigm. Those beliefs will seem most reasonable that are least contradictory to the existing set of beliefs and to the other features of the paradigm.

I'm not sure whether you're simply describing a phenomenon that happens, or advocating for accepting traditional beliefs or social norms as a paradigm and then accepting unfalsified hypotheses that are consistent with those beliefs/norms.  It doesn't necessarily follow, though, that any given paradigm necessarily justifies affirming unfalsifiable hypotheses.  I understand (loosely) why mathematical paradigms would justify that -- because we have clearly, manifestly identifiable ways in which mathematics function that require certain preconditions/hypotheses to be true.  So I "get" why we accept unfalsifiable hypotheses for mathematics.  But why would we give that treatment to a social paradigm, and how do we decide which one?

The paradigms I use as a basis are from science, not mathematics. It was for science that the modern notion of a paradigm was constructed. Science does deal with untestable hypotheses and does make value judgments about which should be pursued. When a paradigm shifts. the value set shifts as well. It's not purely from the observational data, but also by the belief system of the scientists that influences how they interpret the observations.

My invocation of mathematics is in looking at the set of untestable hypotheses as a set of logical propositions that can be true or false. Mathematics and the philosophy of logic say that I cannot have a subset of such hypotheses that is simultaneously complete and consistent. There will either be true statements that are outside my subset or there will be statements within the system that are logical contradictions.

My connection is that in science, and I suspect in other areas of life we naturally deal with this dissonance for good reason - it's unavoidable. Paradigms in science must contain unfalsifiable hypotheses to function, including some that can lead to inconsistencies, because without them the logical framework is too narrow to deal with world. It is with that in mind I look to extend the analogy from science to other areas of society where belief sets include unfalsifiable hypotheses and internal inconsistencies.

[muon2]

The paradigms I use as a basis are from science, not mathematics. It was for science that the modern notion of a paradigm was constructed. Science does deal with untestable hypotheses and does make value judgments about which should be pursued. When a paradigm shifts. the value set shifts as well. It's not purely from the observational data, but also by the belief system of the scientists that influences how they interpret the observations.

My invocation of mathematics is in looking at the set of untestable hypotheses as a set of logical propositions that can be true or false. Mathematics and the philosophy of logic say that I cannot have a subset of such hypotheses that is simultaneously complete and consistent. There will either be true statements that are outside my subset or there will be statements within the system that are logical contradictions.

My connection is that in science, and I suspect in other areas of life we naturally deal with this dissonance for good reason - it's unavoidable. Paradigms in science must contain unfalsifiable hypotheses to function, including some that can lead to inconsistencies, because without them the logical framework is too narrow to deal with world. It is with that in mind I look to extend the analogy from science to other areas of society where belief sets include unfalsifiable hypotheses and internal inconsistencies.

I understand that and the basic rationale for that, and I wish I knew more about the original of the unfalsifiable hypotheses that are accepted, but I have a vague sense of why such hypotheses are accepted for consistency with the paradigm.  I also understand that your point was just meant to rebut the idea that it's inherently unreasonable to accept unfalsifiable hypotheses.  However, I'm a lot less clear on how you see applying the affirmation of these unfalsifiable hypotheses to unfalsifiable hypotheses in the social realm.  You specifically invoked consistency with "accepted historical events and accepted norms for evaluating information to make decisions."  The parallels between "accepted historical events and accepted norms" in scientific/mathematical paradigms and social paradigms are unclear to me.  Mathematical/scientific paradigms are not merely traditional beliefs.  They're rooted in observations and inductive thinking in a way a lot of social norms and beliefs like religion are not.  I assume you understand what I'm getting at -- obviously, not all unfalsifiable hypotheses are reasonable to believe; the arbitrary belief in unfalsifiable hypotheses is the characteristic trait of delusion.  So, what trait of unfalsifiable hypotheses related to the social paradigm make some reasonable to affirm?  You can be really concrete here (relate it to religious views, even your own specific ones), if you want.

I' not sure I agree with the strength of your assertion that I emphasized. The whole notion of the scientific paradigm exists to explain how science can ignore facts and reasoning if they fall too far outside the existing paradigm. Consider part of the history of the speed of light.

In the 17th century Newton and Huygens investigated the speed of light but differed on its nature. Newton believed it to be a particle and Huygens thought it a wave, but both agreed that it must be one or the other. In order to explain optical and gravitational phenomena which reached across a vacuum both believed in an aether of small particles that acted to transmit those phenomena. This was not based on observational evidence, but simply a belief by analogy with water which acted as a medium for its waves. Newton rejected the wave model of light in the aether because it would disturb the motions of planets, yet couldn't remove himself from belief in the aether.

In the 18th century there were discoveries such as observation of stellar aberration, which was inconsistent with a waving aether unless only the Earth moved but not the observed stars. This gave more weight to Newton's particle view, until at the beginning of the 1800's Young showed that only the waves nature of light could explain his double slit interference patterns. This left theoreticians to construct elaborate and unverifiable frameworks to explain stellar aberrations and planetary motion with respect to light. Fizeau's experiments in the 1840's and 50's on the Doppler shift of light through water didn'treally fit any model, but it best fit Fresnel's aether dragging theory. However, the physicists had measured effects with light of different colors that plainly meant it didn't fit Fresnel's theory either.

In the 1860's Maxwell derived his famous equation that held that light in a vacuum could only have one speed. But to the science of the day, believing in the aether and the exclusive wave nature of light, that meant the aether must be static and we move through it. This was despite all the contradictory results over the prior two centuries, which came to a head in the 1880's when Michelson and Morley were unable to measure any motion of the Earth in the aether at very high precision. After those observations Lorentz, Fitzgerald and Poincare had worked out detailed equations to describe the effects but they were still embedded in theory of magical aether. Neither observations nor mathematics were enough to change the fundamental beliefs about light.

In 1905 Einstein publish two papers that ended the old beliefs. He showed that the equations of Lorentz could be derived without any recourse to the aether, which he did by postulating that the speed of light was itself a universal constant. Since the time of Newton (and even back to Galileo) it was understood that physical constants would be the same to all observers regardless of their relative motion. That his postulate was based on other parts of the old paradigm allowed science to discard the aether postulate. At the same time Einstein also published his explanation of the photoelectric effect (for which he won his Nobel prize) and described light as a particle that could act like a wave. This resolved the Newton-Huygens debate by showing that both were right, depending on which type of experiment one did.

My point of the long history is to provide an instance (there are others) where science locks into  hypotheses and are willing to accept contradictory evidence in order to hold on to the fundamental beliefs. Note that many of the continuously held hypotheses in the above history had been falsified for decades! New beliefs came about in the context of the paradigm - accounting for the benchmark theories and experiments that have gone before.

[muon2]

Now it's my turn to be faced with multiple claims on my time. I appreciate the discussion, and hope you can be patient as well.