Speakpigeon said:
How often?
In fact, you just don't know what you're talking about. You are merely confusing logical intuition with something else. That's the flaw in your reasoning here. So, you're right, human reasoning is often flawed, yours is a good example, but that doesn't mean logical intuition is "often flawed".
That I do not know how often does not change the fact that I can observe it.
But it is often flawed. It is not just the reasoning done deliberately and consciously (if that is the distinction you want to make), when the person is aware she's doing it. There are cognitive shortcomings pretty common among humans (e.g., religion, other ideologies, political commitments) that damage their ability to reason in general, and their logical intuitions in particular. But moreover, logical reasoning - even done deliberately - is based on unconscious intuitions: If one is trying to prove something in mathematics, one deliberately thinks about different parts of the argument, but many things just come to one's mind as one does it. And that processing is subject to a number of flaws: even good mathematicians make mistakes and have to check and recheck and re-recheck their arguments.
Still, with training, our ability to do logic obviously improves.
Now, you might say that none of those errors are errors in the intuitions but in the reasoning. I would say that that's a terminological matter, but regardless, if you want to say that, then I would say modern logic
is good for significantly reducing errors in logical reasoning (in addition to other things, like proving things one would not be able to prove otherwise due to lack of computational resources in the brain; it gives an easier method in many cases).
Speakpigeon said:
In people in good heath, logical intuition is as good as their eyesight, something which is pretty good. 525 million years of evolution should guarantee us good logical intuition.
Of course, human eyesight is also flawed in different ways. For example, there are a number of optical illusions regarding the size of objects. Also, the colors are not clear under different light conditions, etc. And apart from the fact that most of the brain machinery of humans evolved much more recently and did not involve 525 million years, that is beside the point too, in a way: in the ancestral environment, the human flawed sense of logic turned out to be good enough.
Speakpigeon said:
That's definitely what it should be doing but also definitely not what it is doing at the moment. Instead, formal logic is worse that our logical intuition.
No, formal logic is based on our intuitions of course, but isolating some of the bad parts and doing more finely-grained logic. Of course, mathematicians and logicians (and philosophers too) are overall much better at logic than the general population, and their intuitions are also much better - mental intuitions can be trained just as muscles and other thing can, and in these cases, they have been trained.
Speakpigeon said:
Up until current mathematical logic was first conceived by Frege and Russell around 1900, formal logic was as good as our logical intuition. Arguably better since you can write very complex syllogisms which although easy to unpack for the logician would stump most people. So Aristotelian-style formal logic goes a little bit beyond our logical intuition. That was the idea of course and so it works.
Well, Aristotelian logic was an improvement over untrained, wild intutions at least for most people, at least within its scope of application. But still, it does not work well enough. Bomb#20 already provided an example that you have yet failed to address: "Daisy is one of my farm animals. All my livestock are cows or horses. All cows have hooves. All horses have hooves. Therefore, Daisy has hooves."
Now, some people can make that inference intuitively, so in that context, Aristotelian logic was not an improvement. But still, some people are not able to make that inference intuitively. And yet, if they knew formal logic, they would have no problem (though if their trained their minds enough to understand formal logic, probably they would not even need it for something as easy as that!).
Moreover, there are plenty of inferences that are much more difficult that that one, including some that are beyond human comprehension without predicate calculus, but they are doable (by sufficiently smart and trained people, at least) in predicate calculus.
Speakpigeon said:
How often is our logical intuition wrong?
I do not know, but the logical intuition of people who are not mathematicians, logicians, etc., seems to be considerably flawed, as you can see for yourself by reading these and other threads, and generally the conclusions people reach or fail to reach. Now, part of that is the result of religion or non-religious ideology, but part of that seems to be simply that people are not sufficiently well trained for some pretty complicated arguments, even if their intuitions are good enough for daily life arguments, the ancestral environment, etc. (when it comes to ideology, etc., the flaws may well have been adaptive, as failing at logic but avoiding social shunning or worse as a result was probably good for reproduction, on average).
As for mathematicias, etc., well, the intuitions are generally better, but still, even in contexts not involving religion, other ideologies, etc., errors are pretty common (you can see that in mathematics too; one need to check, and check, and check, etc.).
Speakpigeon said:
What are your examples of flawed logical intuition?
Already given.
Speakpigeon said:
What are the pitfalls of our logical intuition?
I haven't found all of them!
But there are general tendencies to error in our reason, like committment to an ideology, cause, etc., which result in motivated reasoning (for example). Motivated reasoning might even play a role outside contexts like ideology and the like: for example, if one wants to prove a result, one may end up falsely believing one did. Was that because one wanted it? Or was the tendency to error independent of one's emotional investment? I do not know. But regardless, errors like that are common even in mathematics.
Now, again, you might say that none of those errors are errors in the intuitions but in the reasoning. I would say that that's a terminological matter, but regardless, if you want to say that, then I would say modern logic
is good for avoiding errors in logical reasoning.
Speakpigeon said:
What is the justification given by mathematicians, logicians, philosophers etc. that would support your claim that the definition of logical validity you use is the correct one?
Your insistence on that is very irrational, as explained
here(for example).