[danbruc]

I have to disagree, science is not inconsistent. Science, more precisely natural science, is in the business of building models of our world and if the model is any good it is consistent with our world. Some models are precise to 10 digits, some models only describe the behavior of a school of fish on average. If a theory is found to disagree with reality it will get modified or maybe get abandoned and this is no problem because natural science never claims to provide any truth but only a good model of our world that may have to change in the future.

Religion is similar in the regard that it provides a model of our world but a very poor model under scientific standards like verifiability, predictability and falsifiability. While science constantly challenges its own results and even methods religion is far, far more in the eternal truth corner.

Finally mathematics is a very different thing and comparing it with physics or religion may be misleading. Like religion but unlike natural science mathematics is in the eternal truth business but unlike religion and natural science it is not in the describing the world business. Mathematics is used to describe the world but does not so on its own. And things like Gödel's incompleteness theorems are not a weakness of mathematics but a strength - knowing in principal limits is something that seems completely out of reach for everything but mathematics.

[waps]

There is a mathematical definition of consistency that I was referring to. It basically means that you can prove that a model can't be used to create a contradiction. In maths, any model where you can't prove that is disqualified for most work.

Problem is, the numbers we use don't actually satisfy that standard. There is at least a chance that it isn't possible to create a correct model at all using what we generally call "numbers". If someone were to stand up and "complete" Godel's work, so to speak, that would invalidate all of science (Godel proved it isn't possible to prove science correct, so completing his project would be to find an actual deep, unsolveable problem with numbers. A number of good candidates have crept up over the years, famously the axiom of choice debacle, and a lot of interesting paradoxes, like "does the collection that contains every collection that doesn't contain itself contain itself ?" (last 4 words - not a typo))

There's actually 3 different consistency standards for models (and number 4 is that it's not consistent at all):

1) consistent <- we can prove it !

2) inconsistent <- we don't know, but we may find out at some point in the future

3) inconsistent <- we don't know, and we can prove we don't know, that we will never know

4) inconsistent <- we have an actual counterexample, and thus a proof that it's inconsistent

Science falls in the third category. So does (Christian) religion [1]. There is no real difference in consistency between science and faith by this standard. Problem is that other standards have similar problems. Again a distinction should be made between different religions, as there's only one where I've ever seen any serious discussion on the side of the religion.

a) verifiability : faith is not verifiable. A Christian would say that's part of the point. Of course, neither are most sciences. Certain aspects of mathematics are not verifiable (the other godel theorem), either not at all, not by any finite procedure, or not by any reasonable amount of effort. For physics there is actually only a relatively small portion that is directly verifiable, and once you go down the ladder ... verifiability becomes a distant memory by the time you get to things like history.

Btw: a misconception you seem to have is that theories get modified because of inconsistencies. Well, I'm not saying it never happens, but in practice theories get modified because there's a need for it. Architecture, for example, works with pre-Newtonian physics (buildings architects calculate on stand on a disc suspended in space, with a constant gravity vector straight down, in a barely viscous liquid. Has been that way since before Newton was born, and there's no good reason to change it, so nobody did (in fact there's good reasons not to change it, complexity for one)). Yes this is the utilitarian argument, but it's true. It may not control all academic activity but it controls 99.99% or more. If anything, it's been getting worse.

An illustration of that fact can be found in physics for example. Relativity was discovered because of the black body problem. You see, Newtonian physics predict that if you heat up any object, the universe should explode. Obviously it doesn't, and this was an eyesore. Now keep in mind that Einstein was a patent office clerk with a weird hobby, and this is no coincidence : there wasn't all that much attention going to that problem. Every theory has eyesores. Currently there are 2 huge established theories, and one that everybody believes in but no convincing predictions have been made using it. Here's the current eyesores : relativity theory only has gravity, doesn't have particles or any force (gravity's not actually a force in that theory), has a continuous infinite universe that is either flat or just ever so slightly bent (like a millimeter per lightyear or so). The standard model doesn't have gravity, yet things fall, it has a discontiuous universe that is bent twisted and shifting beyond recognition at small scales, it fails to predict large scale objects in any reasonable manner (e.g. large scale universe is obviously mostly flat ... why ? How does the shifting particle soup that is the standard model's playground become the flat expanse we call space where a photon can fly undisturbed for millions of lightyears ? This, to me, is not a small detail you can just gloss over), yet we can design things like cell phone radios and cpus using it. Then there's string theory ... string theory however is a theory with so many open ends that you can do pretty much anything what you want with it. It answers the question "hows does the universe work", by giving you a brainfuck compiler and get cracking on a simulation, stating that the answer is in there (and of course, it is, in the sense that you can probably write a correct simulation in it). Those are current eyesores. I sure hope some people at the patent office are about to fix them, because I doubt significant heyway will be made any time soon.

b) predictability. I would argue that religion makes predictions, and I would argue that, averaged, they're pretty good. E.g. islam says camel piss is good for you [2]. This sounds ridiculous of course, but taking 2 facts into account it makes sense, somewhat. First urine is the one bodily liquid that is sterile. If you care about disease spreading, you can't eat or touch the same food as someone else, you can't drink the same water, you of course can't have sex or other things that exchange bodily fluids, certainly not with animals, but urine is an exception, it's fine, it's sterile, it's safe. If you don't have a water source you trust, camel piss may be preferable. Knowing that poisoning water supplies was standard Roman army practice, it may make sense if you're waging a war on them. Eventually of course, it'll kill you, but only after months of drinking it. But it's not a stupid, random piece of gibberish either. And religion certainly makes predictions about what will happen, most of which you'll find yourself in agreement with.

A lot of sciences don't care about predictability. Maths would be one example. We study models, because of their implications, and because we like the idea of, shall we say, "classifying" logic. This is a fool's errand, but it's fun. "This does not predict a thing" is a perfectly valid criticism of all but one project I'm involved in, and that's because it's beside the point.

Obviously predictive ability is one aspect of the utilitarian view of science, so it can't be ignored completely. But most physics theories that are being actually worked on (in other words : string theory and nothing else), do not have any demonstrated predictive ability that I am aware of.

And how does e.g. history fit in with predictability at all ? I would argue that religion definitely scores higher on predictive ability than the humanities, somewhat lower than most exact sciences.

c) falsifiability. Again most sciences aren't falsifiable. Mathematical models work with axioms, and falsifying correctly constructed models is impossible (with of course, the glaring exception of the natural numbers (and thus rational numbers, and real numbers, complex numbers and anything based on them), which we know may be falsifiable. This is considered very, very bad)

But string theory for example isn't falsifiable. And again, how does that work for the humanities ? Any statistical work effectively isn't falsifiable. Take climate theory for example. It hangs together from approximated differential equations. The predictions made using them by the IPCC in 1990's ... well, they were wrong. I mean I'm not saying the earth isn't warming, but the IPCC's numbers from the 1990s are bullshit, but they correctly point out that that doesn't actually falsifies their models' claims (although, frankly, it does prove their error margins calculation is ridiculous). They only claim that to a best approximation, their model is what should happen to the variables they're monitoring over time. Medicine is the same. For most medicines we have a double blind study. Now you should think, really hard, about what the exact claim is that is made by those studies and how it's verified. You'll see the truck-sized hole in the thinking.

d) ...

The greater point here is that these are all standards of correctness, trustworthiness, "truth". They're all different, they all have their uses, and they are followed in various ways by various sciences. Within individual sciences, there tends to be a whole spectrum of theories that rank differently on all of these standards. Religion is no different. It simply has a place on the spectrum, just like any science does. Various components of religion very on where they fall on all these standards.

But it is certainly not the case that sciences score higher than religion on all of these standards, it is simply the case that there is utilitarian need for both, and for criticism of both. Science has it's uses, and so does religion. Where things fall on standards of consistency, falsifiability, predictive ability, ... is simply a property of whatever fills that particular niche best.

[1] https://www.uwgb.edu/dutchs/PSEUDOSC/RammReconcile.HTM [2] https://au.answers.yahoo.com/question/index?qid=201204210704...

[acct_0053]

I'm definitely out of my league here, but it seems like you're overcomplicating the question.

I won't pretend to be qualified to say whether you are right or wrong, but I'd like to make a few points.

I get the impression that you are trying to address whether science is as [in]consistent with itself as religion is [in]consistent with itself in their attempts to land upon some truth or as another commenter put it, "model of our world".

But the question posed by the article is whether science is consistent with faith. For the author, it is. At least a few commenters are simply stating that the reasons given by the author for this consistency don't resonate with them.

It's also worth noting that while you're using a "mathematical definition of consistency", the commenters you are refuting are probably just meaning that whatever conclusions one reaches via the scientific method are often in disagreement with those arrived at via faith. Now, I don't know what the Christian faith tells us about String Theory - heck, I don't even know enough about what science says about string theory to speak of it with any clarity. But I do know that with the help of science we can figure that the earth we live on is spheroid and revolves around the sun, and I know that the Bible hints slightly at a vastly different conclusion, or at least it was interpreted to do so at one time. On one side of the coin, we can look at evidence, or at the very least hold a theory as probable - and if it's falsified - well it's sad, but the theory changes to better suit the findings. On the other side of the coin, we must take somebody's unchanging word for it, and maybe revisit our interpretations of the same idea only if we're forced to - and otherwise, any objections must be false. I just don't see how anyone can say there's no difference there.

[waps]

It's not just about consistency. The post mentioned 5 different standards of "truth". In reality the method we use to judge something to be true or false is not uniform : there are lots of variations, even within single sciences.

My point is that for all the methods the parent poster pointed out, science does not actually fare better than (Christian) faith, barring a few exceptions.

He cherry-picks little pieces of specific theories that satisfy a high standard of truth, I merely point out that, first that does not mean science as a whole satisfies that standard, second you can do the same for the bible. And, when it comes to historical opinions that were held up using less-than-gentle means, science also has loads of black spots. E.g. http://en.wikipedia.org/wiki/Lysenkoism, so again that is not a valid criticism of faith, or at least isn't black and white.

As an alternative I defend utilitarianism : scientific theories are not true or false, or better or worse than the bible, but they are more useful in some cases. Nobody will design a cell phone using the bible. Nobody should base their moral decisions on biology.

The big problem here seems to be that Christianity uses internally the same standards of truth to some extent, and so it can be attacked on those points. It's actually pretty consistent so I think the attacks against it are less than convincing, because there is no better alternative, there is just a completely unjustified faith in science that makes no sense whatsoever : logic, the branch that actually analyses whether science could be wrong and how and why trust in science should exist, has a simple conclusion since the 1950s or so : science fails it's own standards. Somehow this part is always missing from these arguments : there is nothing to back them.

[danbruc]

You are confusing and mixing up a lot of things. Let me start with mathematics. Mathematics is a very special case and very different from other sciences. It is completely made up by humans and has nothing to do with our world. We use mathematics in other sciences to describe our world but on its own mathematics has nothing to say about our world. You are also kind of misinterpreting Gödel's incompleteness theorems. The first incompleteness theorem states that a system of axioms is either inconsistent or there are true statements that can not be proved from the axioms. Intuitively - but probably wrong in a strict sense - one could say that the number of true statements is just larger than the number of proofs, see Cantor's diagonal argument. The second incompleteness theorem states the consistency of a system of axioms is one of the statements you can not prove by the system of axioms itself. But while you can not prove the consistency of a system within itself you can use a different system and so for example Gentzen's consistency proof proves the consistency of first order arithmetics within primitive recursive arithmetics. I also don't understand why you think of the axiom of choice as a debacle. The axiom of choice is independent of Zermelo-Fraenkel set theory and it is up to you whether you want to accept and use it as an axiom or not. And also Russell's paradox has been resolved long ago when mathematicians realized that not all collections of objects are sets.

Verifiability in the context of science means you can reproduce and verify results, i.e. when your quantum physics book says that electrons hitting a barrier with two slits will cause an interference pattern on a screen you can just do the experiment yourself and verify that it is true what your book says, no need to blindly believe anything, at least in principle. As far as I can tell religions lack this property.

You are also confusing natural sciences like physics and engineering disciplines like architecture. In physics a theory gets replaced by a new theory when discrepancies between theory and reality are found - Newtonian gravity does not exactly explain all gravitational phenomena and therefore got replaced by the general theory of relativity. Engineering disciplines on the other hand are not concerned with understanding the world and just use whatever fits their needs - why use the complex theory of general relativity to construct a building when Newtonian gravity is a simple and good enough approximation? By the way, black body radiation lead to the quantization of light, not to the special or general theory of relativity and there are a few more misconceptions in there but I will not go into them.

Predictibility means that a new theory predicts something nobody has observed before and you can look for it. If you actually find, it is a strong hint that the theory might be up to something. In 1928 Paul Dirac formulated a relativistic quantum theory for the electron and realized that this theory predicted an antiparticle, the positron, and four years later it was actually discovered. In 1916 Einstein completed the general theory of relativity and predicted the deflection of light by heavy masses, in 1919 this deflection was observed during a solar eclipse. Sitter precession and Lense–Thirring precession were predicted in 1918 but it took until 2004 that we were able to build Gravity Probe B and launch it into space to test the prediction. The Higgs particle was also predicted 50 years before it was discovered in 2013. Again as far as I can tell religions lack this property and your examples don't really fit into this category.

(I will answer to the remaining points tomorrow but right now I am running out of time.)

[waps]

The problems I find with your argument are that you are taking a partially true statement and extending it as if it fits the whole of science. Yes there are parts of physics theories that support direct verifiability. The double slit experiment with electrons is not one of them. After all, nobody has ever seen an electron, only indirect observation is possible. You can see the result on phosphor, you can measure the induced voltage, ... none of these are direct observations.

But with the double slit experiment we are not that far from direct observation. Let's take the theory that there is a black hole in the center of the milky way ... would you care to explain to me how I can observe that directly ?

So your statements are misleading. Some tiny parts of some physics theories are directly verifiable. Some are indirectly verifiable. Most current ones are not really verifiable at all. Astronomic theories are both especially important for physics, they are used as support arguments, and let's just say they are very good examples of indirect observations, and there are plenty of historical arguments for physics theories coming out of astronomy that turned out to be wrong. One of the initial proofs of relativity theory, the measurement of the movement of Saturn's moons was a wrong measurement. It lead to the right conclusion, but the measurement itself was incorrect, which makes it especially interesting to me.

But that's just peanuts. The real kicker is : some physics theories are known to be wrong (which was the real point of referring to black body radiation : it was a known hole in a theory for almost a century), but we don't know how they're wrong, and nobody's ready to dump the theories. E.g. does the standard model match the "real" structure of the universe ? Well, we know it doesn't, yet everybody's using the standard model. Everybody believes in electrons and positrons and protons and large antiprotons ... yet we know something doesn't match up because we can run experiments that don't match predicted outcomes of the standard model theories. Have you seen anybody claim that the standard model is wrong ? See anyone dumping it ? I haven't. Did I miss something ?

Some theories in physics are direct contradictions. Take relativity versus big bang theory for example. Care to explain how the speed of light limit fits in with inflation theory (which as far as I know is still part of the current state of the art) ?

TLDR: In physics we have different theories that don't really interact, not in the maths part anyway. In order to progress within physics we just assume that you can just pick and choose whatever matches the observed data best. Gravity resistance in neutron stars ? Oh that involves the Pauli exclusion principle ... that sounds cool but the Pauli exclusion principle comes from a theory that ... doesn't have gravity. How is this consistent ? Whatever you want to call it, I call foul on this reasoning.

But such arguments, while wrong to any logical mind, have one big redeeming quality : they work. That's how science really works : part of it is giving us the ability to make cell phones, cpus, ... what have you. Part of it is an interesting story to tell "the public", and to put on grant requests of course. Part of it is interest and what appears to make sense to human minds, however broken the logic is.

But all of it flies in the face of the idea that science, without pick-and-choose tactics, satisfies any reasonable standard scientists sometimes claim it does. Physics, taken as a whole, doesn't satisfy either falsifiability, verifiability, or predictive ability, and you'd be hard pressed to find even small portions of it that have no known, shall we say "bugs" : observations that don't match, math that doesn't quite work. Hell, the theories don't even satisfy mutual consistency.

I remember the first physics lesson I had. I remember it because of the math the professor used. You start with constructing an equation for the path of an electron flying through a magnetic field. Then there was five minues of "this is nearly zero" (professor scratches that part of the equation out). This matches that, not exactly, but under normal circumstances they're more or less equal (scratches two non-matching things from above and below the fraction line) ... I was shocked. But let's be fair here : while yes, there are better methods for this particular problem, but this is how physics works. Mathematical rigour destroys most physics methods.

The argument you're making about maths is similarly flawed. You're taking a single example, and extending it around the entire theory, which is not a valid reasoning.

The axiom of choice was one of the initial tries to fix incompleteness, it's a debacle because the attempt was flawed. Also maybe pertinent here : English is not my first language, so if debacle is not the right word, just pretend I used another. It was triumphantly held up as a solution to incompleteness, and was flat-out wrong.

As for Gentzen's proof, proving that one theory is consistent using another theory that may not be consistent itself, while a remarkable achievement, does not resolve the problem Godel raised. It does not pull us out of the mud.

And let's not be too strict here. E.g. I realize what you mean by referring to Cantor's diagonal argument, but technically it is not applicable to logical statements. You're right that I confused relativity and quantization when referring to black body radiation.