Sounds good, but you still have to decide which one is more likely to be correct, so it doesn't seem to solve the fundamental question at hand.
Unfortunately, I can't help you with that, as you have your own models and feelings. You'll have to collect data on your own about which works better in what situation. You can probably start by going over past experiences to see if there are any apparent trends, and then just be mindful of any opportunity you might have to confirm or disconfirm any hypothesis you might generate. Watch out for unfalsifiables!
I don't know, but I have the impression that you have an answer in mind, care to share?
chaosmosis said it already :)
You don't have to treat your feelings and your models differently. Just use whichever one the evidence suggests is more likely to be correct in whichever situation you find you find yourself in. See?
Empiricism and logic? Just treat your emotions like a model, and judge them like you would any other. Even though you can't see the inside of your emotions, neither can you see the inside of the thought processes that produce the model. I don't see why there would be any difference between the two.
This boils down to: when do you know that your models are correct? And the answer is, you almost never know, unless it is already settled by science and even then there is room for error and further correction down the road(years away). But you need to make decisions now, every day.
Almost. It boils down to: when do you know that your models are correct and when do you know your feelings are correct. Well, how do you settle that question?
I don't intended the original quote to be an admonition against all use of models/reasoning. My point was more or less along the lines of "listen to your feelings, they might be telling you something important. Don't disregard them just because you have some neat model, your model could be wrong."
I agree, but that does not answer the question. How do you decide which to use? What do you need in order to decide?
Is this a serious question? While the modern world might have changed in a lot of aspects a big factor remains constant: people, social interactions. What use is it to choose the logically correct decision if it still makes us feel miserable?
There are situations where your feelings are more reliable than your models. Are there situations where it is the other way around? How do you decide which to use?
Feelings honed by millions of years of evolution.
To what extent can you expect evolution to have prepared you for your day-to-day experience?
Realize that your mental models might be wrong and don't put too much weight on them, instead put more weight on your feelings.
Do you have good evidence that your feelings are more often correct than your models?
Consider the equation x + 1 = x.
(Edited again: this example is wrong, and thanks to Kindly for pointing out why. CronoDAS gives a much better answer.)
Curiously enough, the Peano axioms don't seem to say that S(n)!=n. Lo, a finite model of Peano:
X = {0, 1} Where: 0+0=0; 0+1=1+0=1+1=1 And the usual equality operation.
In this model, x+1=1 has a solution, namely x=1. Not a very interesting model, but it serves to illustrate my point below.
sometimes a contradiction does point to a way in which you can revise your assumptions to gain access to "intriguing new ideas", but sometimes it just indicates that your assumptions are wrong.
Contradiction in conclusions always indicates a contradiction in assumptions. And you can always use different assumptions to get different, and perhaps non contradictory, conclusions. The usefulness and interest of this varies, of course. But proof by contradiction remains valid even if it gives you an idea about other interesting assumptions you could explore.
And that's why I feel it's confusing and counterproductive to use ironic language in one example, and serious proof by contradiction in another, completely analogous example, to indicate that in one case you just said "meh, a contradiction, I was wrong" while in the other you invented a cool new theory with new assumptions. The essence of math is formal language and it doesn't mix well with irony, the best of which is the kind that not all readers notice.
But that's the entire point of the quote! That mathematicians cannot afford the use of irony!
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-Francis Bacon