Judge not, that you be not judged. For with the judgment you pronounce you will be judged, and the measure you give will be the measure you get. Why do you see the speck that is in your brother's eye, but do not notice the log that is in your own eye? "Let me take the speck out of your eye," when there is the log in your own eye? You hypocrite, first take the log out of your own eye, and then you will see clearly to take the speck out of your brother's eye. [Mt 7:1-5]
Therefore we mustn't judge others, because there are many "logs" in ourselves. Only LORD is the judge.
But that doesn't mean we should not form "judgement". In fact we should exercise care and judgement and prayer at all times.
I studied Maths at University. I learned Logic in my first year. Mathematics demands proof. We start from a set of "axioms", and then, using purely logic and nothing else, derive some results (theorems etc.). Then we say, if the "axioms" are true, then the "theorems" derived from them are true. If one of the axioms is false, then ALL theorems derived from them cannot be relied upon.
Because of this training, at an very early age, I wouldn't believe hearsay, until I have investigated it myself and convinced myself of its truth.
To form correct judgement is NOT easy. Recently, I wish to ascertain something I have read on the Internet - (partial extracts). I cannot form judgement just by these extracts. I have no way but to find out the whole. I located the book, which is a 400 pages book, and I read it. (I read the first 65% complete, for the rest 35%, I skipped a lot). THAT WAS NOT AN EASY TASK. After reading that, I think I can form better judgement on that.
To exercise care and judgement and prayer is NOT easy. Not to exercise our judgement but blindly listen to what other says is easy, but that way will surely lead us to hell, and we cannot stand before the Judgement Seat in the Final Day.
Logic has come a long way. There is a book "From Frege to Godel" (author I cannot remember), which detailed the development of logic, and is quite worth reading. "Introduction to Logic, by Patrick Suppes" is also a valuable book.
Lastly, I recommend my webpage,
which is very short, and one may work over it all in a few hours (though conversant with Logic may take time to develop.)
(One final note : after praying to LORD, usually some ideas will come out of our mind, or we will be able to locate some material on the Internet, etc. But still, we have to exercise care and judgement in choosing the material. It is we ourself that will have to answer for all our actions before the Judgement Seat of LORD one day, therefore we must be careful at all times.)