People are having inconsistent thoughts all the time, so it is clearly possible to think while not being consistent.

How do you get the idea, that I'm rejecting the ability to compare?

I'm not rejecting the ability to compare, but the ability to know if you are inconsistent. If you are inconsistent, it isn't guaranteed that you will be able to find out. And if you were consistent and add "I'm consistent" you will get inconsistent as a result. "If an axiomatic system can be proven to be consistent from within itself, then it is inconsistent." So it is impossible to know if you are consistent.

Exactly.

The important thing is: If you can't be sure that your experiments are not manipulated, then you can't throw out any conjecture. Any failed test of a conjecture could possibly be the result of an manipulated experiment, while the conjecture could still be true. Even if you are able to repeat that experiment with the same results it would be possible that all of your experiments have been manipulated. Falsification of any conjecture is impossible, if you can't rule out systematic manipulation. You would be back to induction with all its problems.

I wouldn't. But I would need to assume that is not happening if I want to do science, cause otherways I just can't do science. I and everyone else must assume that there is nosystematic and undetectable manipulation my or their experiments. You can't falsify the conjecture that there is no systematic manipulation, but you still need to accept it to be able to do science and if you are wrong and there really is systematic manipulation of your experiments, you won't be able to know.

You can't guarantee ether that they people will accept your value of not accepting anything that is not falsifiable. I'm not claiming to provide a magic bullet, I'm just saying that there is no magic bullet.

Then you basically agree that the set of values "I need to be consistent" and "I need to be able to know if I'm wrong" is inherently inconsistent. Now that you noticed that, shouldn't you try to find a different and possibly consistent set of values?

Sure, but that would be inconsistent with your value "I need to be able to know if I'm wrong". With that rule your set of values will always be inconsistent if includes basic logic and math, without that rule it is at least possible that your set of values is consistent.
Inconsistency doesn't need to be easy to notice, often inconsistent systems will work pretty well, e.g. naive set theory worked really well until Russel found his paradox.
Naive set theory contained a small number of extremely easy rules, still it took many years to spot its inconsistencies. Because of that even "I need to be consistent" seems to be highly problematic. Most likely there is no existing set of values that is truly consistent.

Sure, your set of values would clearly include these rules. If you say: logic and some extremely basic math isn't part of my values, maybe they are wrong. Then and only then "I need to be consistent" and "I need to be able to know if I'm wrong" could be part of a consistent set of values.

Insane people rarely consider themselves insane. Also people often have been called insane just because they believed or not believed something, that was not shared by their community.

You seem to have a weird idea of inconsistent. A set of rules is inconsistent if there is at least one formula X that can be shown to be both true and false by its rules. So "2 is a prime" and "all primes are odd" is inconsistent cause you can use the first rule to show that "2 is prime" is true and the second rule to show that "2 a prime" is false. However "2 is a prime" and "All primes but 2 are odd" isn't inconsistent, cause with this restriction you now can't use the second rule anymore to show that "2 is a prime" is false.

I believe that is pretty useful, yes. But it is just another unfalsifiable rule about what is considered "reason".

You need to make some basic assumptions about the reality otherwise science would be pointless. If god, the universe, aliens, whatever would be constantly manipulating your experiments, then science couldn't work. You could never really falsify anything, because you couldn't trust any of your experimental results.

The only reason? Fortunately most scientists don't share that idea. There are always a lot of different conjecture, which can't be all right at the same time, but all of them are falsifiable. So scientists need other reasons why they prefer one conjecture over another. Values like preferring conjectures which are aesthetically pleasing have proven to be pretty helpful.

In all likelihood? I would say there is a huge set of shared values where many people will agree with you, because they share the same feelings or agree that something is true a priori.

I think these are actually not as common values as you believe they are.

What is taken seriously during debate depends on the values of the audience. In this case the someone will not be taken seriously for multiple reasons:
Language: There are some keywords ("simply" and not just "feels good" but "feels good man") in that sentence that will cause people in an "intellectual debate" to believe that the speaker is not a intellectual himself and many people will tend to reject stuff they hear from outside of their group

Values: To be taken seriously during an debate you need to appeal to values shared by the audience. If the audience doesn't share this feeling you are unlikely to hear this argument.

Actually even the smaller set of values "I need to be consistent" and "I need to be able to know if I'm wrong" is inconsistent as soon as you included the basic rules of logic and math to it:
Gödel's second incompleteness theorem: "For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, if T includes a statement of its own consistency then T is inconsistent."
If your set of values/theorems is consistent and contains basic arithmetical truths then you can't prove that it is consistent. But if a set of theorems is inconsistent it is not guaranteed that you will be able to show its inconsistency. If there would be an guarantee that you are always able to find a counterexample within the theory itself for every inconsistent theory, that would be a contradiction to Gödel's theorem cause then you could just prove consistency by showing that couldn't find a counterexample. So you can't be consistent and able to know if you are wrong at the same time. You can either know that you are consistent, but then you won't be able to know if you are wrong or you won't be consistent, but then you will know nothing.
Or you could just remove that problem if you replace "I need to be able to know if I'm wrong" by "I like to know if I'm wrong, but this is just one of many criteria I'll use, when I decide which conjectures to prefer. I may decide to prefer an conjecture even if I'm not able to know if it is wrong."

Uh, why that? If someone says: "2 is prime number", "3 is prime number", "5 is a prime number" , ... and "All prime numbers are odd." Then this set of statements is clearly inconsistent, but you wouldn't fix it by saying: "okay, then 2 can't be a prime number" but by adding an exception: "All prime numbers but 2 are odd."

People usually don't completely rule out the possibility of being wrong. They just assume that something is true or false. Being undecided doesn't really help here, because when people make decision they usually need to make assumptions for stuff where they don't know the answer, even when they might never know the answer.

Okay, what you claiming here is: If X is unfalsifiable, then there is no reason to assume X is true, right?
This seems false to me, e.g.: If people believe X, because assuming X makes them feel better, they clearly have a reason why they prefer believe X over not X.
So I guess: "X makes me feel better" is not a valid reason? What is a valid reason then?

Having conflicting rules is inconsistent, sure. But most of the time an value system with conflicting rules can be transformed quite easily into an system without conflicting rules or at least into a system with fewer conflicts by adding small restrictions to its rules, that will fix conflicts people noticed. People do this all the time, works pretty well.

This will only work if their value system is inconsistent. This doesn't need to be the case. There are many different consistent value systems and even if a value system isn't consistent it is often easy to fix the inconsistency by just adding a few additional restrictions.

Not really. People will never know the truth about unfalsifiable beliefs, no matter what strategy they choose to deal with something that is unfalsifiable. It doesn't matter if they hold unfalsifiable beliefs, actively reject them or try to stay undecided. Because of this, all of these strategies are consistent with a value of knowing what is true and what's not.

Okay, so in your point of view there can't be any position based on reason that includes moral realism? So if you believe in a universal human rights, you are not acting reasonable? This doesn't just reject the viewpoint of most theists, but also the viewpoint of most atheists.

Okay, but following arbitrary goals can't be based on reason, otherwise they won't be arbitrary. So if we are following your definition of reason, there is no single action that is purely based on reason, every intentional action people do is always partly determined by unreasonable and arbitrary goals and values. So reason is at best a tool to reach arbitrary goals more easily.

Sure, but if I follow your argument, this seems to be a just as unreasonable value as some other persons value of telling everyone about Jesus.

So which consequences follow directly from the assertion "There is a god."? You can be theist without following any particular religion.

Again: You can be a theist without following any religion or holy book. And a religion or a holy book is also a "source other than theism", because theism is just the believe in god or gods, nothing else is implied just by being a theist.

Often this will work, but not always. You might get an answer like "Oh, I believe there is only one god and all the holy texts out there contain wisdom collected during eons about the complex relationship of god and humans." If you get an answer like this it is pretty clear that you talking to a theist, but you will need to ask a lot of additional questions until you will be able to build a basic map of the moral and ethical tree of this person. But even if you get an answer like "I believe in the Christian god and follow the bible" you still won't know if this person is going to eat meat, if the person is going to be pro-life or pro-choice, if the person believes homosexuals or non-christians should be burned, etc.

How is "do you follow any named kind of life stance that includes atheism" not an atheism-related question? And if you get an answer like "I'm a secular humanist" or "I'm a marxist" you will know quite of a lot of stuff about this persons morals and ethics. Sure, many atheists won't attach any name to their life stance and most theists will attach some kind of name to their life stance, but you can be theist without attaching any name to your life stance. But even if people do attach a name like "Christian" or "Humanist" to their life stance, the life stances of two people that used the same name can still be wildly different.

Or we can talk about probabilities: Just ask a random person a single question: "Do you believe in god? Yes or No" Then depending on that answer guess whether the person is pro-life or pro-choice. Your guessing will be much more accurate for atheist than for theists. Even if the theist also tells you that he believes in the Bible your guessing accuracy will still be lower for random Christians than for a random atheists.

We both can easily agree that logic needs to be part of reason, but we still won't be able to prove this to someone who claims otherwise. But let us consider this problem solved:
So you got a binary relationship to compare things. Now prove that the golden rule "One should treat others as one would like others to treat oneself." or any other moral value is valid. Or if you say: I can't prove things, but I can falsify things then try falsify "killing non-believers is good".
You can also use the other rules of logic and you can also use observations to falsify things. But even with all of these tools you still won't be able to prove or falsify any moral value valid.
Falsifiability is a very useful concept to decide if something is science or not, but it is not a criterion to decide whether something is meaningful or not. Values are important to people, but can't be falsified.

Inductive reasoning isn't the problem. The problem is that people always need some unfalsifiable claims to begin with. You can't falsify the rules of logic, but you still need them to do any kind of reasoning. But logic is not such a problem because people usually be able to agree on one set of rules there. But other stuff is much complicated, e.g.: Is there good and evil? You can't falsify this stuff, but still people will care a lot about this. Not just religious people but also nearly every atheists got some kind of moral code and many will claim that their moral code is somehow based on reason. Still any claim of "X is good" is always an unfalsifiable claim.

Reason is always based on some set of a priori premises, but different people will consider wildly different sets of a priori premises to be true and thus arrive at wildly different conclusions.

You can say the same in regard to theism. Claiming "There is a god or gods." doesn't say "stone the unbelievers" or "go to church" or anything. But people will rarely stop there. People will always try to build a set of values and rules. Because of that people will always develop religions or ideologies. These ideologies may include atheism and a such a ideology can be called "atheistic ideology" just like a theistic ideologies, which will usually be called religions. And just like it often has been a short way from theism to "burn the disbelievers", it also often has been a short way from atheism to "burn the believers".

The same thing is true for theism.

Not really. Atheists still ascribe to values, morals, tenets, etc. They aren't directly from atheism, just like the values, morals, etc. of theists aren't from Theism but from their religion, but all people ascribe to some kind of values.