Logic... well, I'm an expert in it (for some degree of expert.) This is why dealing with nearly anyone else else turns me into an even greater misanthrope.
Logic is analogous to math. Logical proofs are much like mathematical ones. Proving something like the proof for "Or" in logic is much like the mathematical proof showing how multiplication or division is possible. Logic as a system is technically separate from anything that is plugged into it, much like math. Multiplication as a mathematical rule is completely separate from any number plugged into said rule.
For example, 3x2=6 is true. However, the numbers are moot. The key to multiplication is not the number, but rather what multiplication does to whichever numbers you plug in. Logic works the same way. Here's an example of a logical truth.
If A then B
Obviously, if you plug ANYTHING into each variable, you won't get an output that's true. Obviously. But that's the same with math. You can't randomly plug in 64 into "((7)xX = 4)) for 7x62=4. You don't get to throw in random numbers and come out with a proper value. So lets plug in something true.
If I am drinking a pepsi then I am drinking a soda
I am drinking a pepsi
Therefore I am drinking a soda
(You can do an additional proof to prove that Pepsi is soda, but sorta moot here)
You see, logic is analogous to math. Just think of the overly abundant moron who may utter the phrase, "Using your logic..." well, let us just say if you said "Using your mathematics..." you'd see how absurd implying (laymen wise) that there's a personal mathematics or logic. You wouldn't say, "According to your Math, blah blah blah." You'd simply point out that their damn arithmetic was wrong.
So here's the infuriating problem I have, every time I have to deal with the average person.
Math is the system in which you use to manipulate numbers to reach their conclusion. Logic is the system in which you manipulate empirical evidence, and just about everything else including absurd hypotheticals, to reach their conclusions.
The problem, however, is that everyone thinks their opinions and beliefs are both valid and sound, logically. Imagine that the person on the corner can do basic addition and subtraction. Now imagine that they do not understand multiplication or division, much less anything more complex, but believe every algebra or calculus problem they "solve" is correct.
Now... imagine that the person's religion, political, moral and social beliefs are all based on being able to solve calculus problems. The person who has no idea what multiplication or division is (or has heard the word, but has no idea what actually using them entails) will make a giant argument saying how his answer is correct. When you ask him to actually detail what the multiplication sign does to the numbers, he says something incoherent and incorrect, but this time louder.
Something terribly simple, like (2x(7+3))^3, would be unsolvable by this person, at least if you wanted a correct answer. The person does not understand order of operation. He does not understand multiplication or what taking something to the third power means. The end result of this formula he's trying to solve is the person's opinion on, say, global warming. Now, imagine someone took this problem, got the answer of 15, and believed that was correct regardless of what degree holders in mathematics said or attempted to teach them.
This is my every day, with nearly every personal opinion I see. This, sadly, is not hyperbole. The average person's ability to use logic is just as bad as the average child's ability to do algebra or calculus (depending on the complexity of the discussion at hand) However, math and logic are analogous, for athe's sake. The inability to do algebra while trying to solve algebraic equations would be an obvious farce to anyone. The inability to actually use the most rudimentary logic to reach conclusions, however, is done constantly, by nearly every person.
And the sad part is they are too ignorant to understand just how inept their attempts are. When you try to explain to them that the use of 5 logical fallacies in their argument is like using addition where there was a multiplication sign five times in a math problem, then using the answer they got as infallible truth, they become more adamant that addition = multiplication . When you point out the mistakes, they simply don't understand what multiplication is and refuse to become educated because -- hey, their answer can't be wrong, it's THEIR answer. Who's this asshole with expertise coming in trying to act like he knows more than I do just because he does?
So, yes, the average person on the street on anything more complicated the logical equivalent addition is like a six year old yelling at someone with a degree in mathematics that X is a letter not a number; you can't have X in a math problem. When you try to explain about variables they either don't understand or continue yelling as loud as they can, then start crying. This is how I feel dealing with the average person. Mind you, this is the average person, not the extremely sub-average tea-party moron carrying signs that say Taxes = Slavery. This is the sad reality I have to deal with nearly every time someone shares their opinion. This is also why, odds are, your opinion should be disregarded, even if you have the right one. As far as logic with the average person goes, if you have the right answer about a problem, it's more likely you copied it from someone than solved it, or were lucky enough to stumble upon it by accident. Opinions never deserve respect, only facts.
If you honestly don't believe that, please, tell me how much you respect (Godwin alert) Hitler's opinions.