Well dumb me I always thought logic meant that when something is done over and over again like say an experiment and has identical outcomes then it becomes logical in the sense that you mix A with B and you get C always. The opposite would be speculation or illogical because you would not be able to account for the many possible outcomes. Science says that smoking causes cancer but someone comes along and smokes like a chimney and has no ill effects from it so I would say that saying smoking causes cancer is illogical a better statement would be smoking MAY cause cancer- logical pertaining to the statements. yes/no?
Just because one can find a flaw in an argument does not always mean the facts are wrong, sometimes facts are misrepresented, unreliable or unavailable which the latter is usually the case especially pertaining to human behavior and sometimes science, in short we don't always know everything because most people operate out of fear and that causes them to do illogical things.
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Your post shows you don't understand what "logic" is -- it's not scientific experimentation or research, but simply a mathematical approach to "if...then.." types of statements. When something isn't logical, it's often because the argument falls into one of the many logical fallacies -- basically, something must be true because of something else, when that explanation is not always so.
For example, the logical fallacy "argument from incredulity" goes like this -- "I can't imagine how it could work that way, therefore it didn't." Well, if you can find examples of something unimaginable by one person still working, then that argument no longer carries logical validity. Another way to look at it is when you make rules that fit in one situation but contradict yourself by going against the rules for another, and still claiming both sides of the contradiction to be always true.
For example, the colloquialisms "birds of a feather flock together" and "opposites attract" cannot both be absolutely always true, and that being the case, neither is a valid proof of something else being true based on the presumption that either is always true.
Another common logic example utilizes nonsense categories, with a series of statements that describe the relationships of these categories, and trying to determine whether another relationship is true within that context. "If all quarkles are bindiggles, and all bindiggles are horties, and all vimps are horties, then is it true that...."
Learning about logic allows a person to apply mathematics to an argument, and efficiently disprove something as "always being so" if it doesn't fit. And it works.