It's been a looong few days..... I'll try to add some things, but I hate doing the Reader's Digest version of important concepts.

If I tell you that 'water runs downhill' and that 'gardens need water'... and then say, 'therefore, you can't grow a garden at the top of a hill', almost everyone would jump in and say, "but you're missing something, because there are other ways to get water on a garden".

   I could invent a dozen of that sort of silly (read-invalid) arguments that are obviously wrong. I could say, 'Turnips smell like roses' and 'magnesium is heavier than lead', therefore Trump should be elected president.... and (almost) everyone would say," but those assertions are not only wrong. but they have nothing to do with the political situation!".........Yet, people make less obvious, but still just as fallacious, arguments everyday.... (and some who want Trump elected 'might' even say "right on!") Now if I ask "WHY are those things bad logic?", most people would could give generally similar reasons, but phrased very differently and not...ummm.. 'tight'..... but logicians & philosophers have worked out the specific things that define valid arguments. They do this partly by **induction**.... meaning that they look at obviously good arguments and obviously bad arguments and 'extract' the common elements of each. Then they work to state those rules as clearly & unambiguously as possible.
It might help to read about New Eleusis, a card game based on one player choosing a set of rules, and the others trying to figure them out from trying various plays and being told whether the plays are legal or not, based on the secret rule. (simple example...'a red face card must always be followed by a black non-face card.')
   I have played the game, and it ain't easy to invent a rule that is fair, not too easy, and not too hard. Some people take to the game, and some hate it!

   As Rap showed above, there are fairly formal ways, similar to mathematics, to show whether simple ABC syllogisms are valid or not, even when the 'truth' of the conclusion in debated..("well, I may not have used the right proof, but I KNOW the answer is correct")

There are also a lot of rules (the exact number varies) that deal with mistakes in just everyday human attempts to explain, defend or attack some idea or conclusion. These are harder to pin down than the rules of formal logic, and are called informal fallacies. and that page has about the longest list of them I have seen. Now, even when you study and analyze them for years, it can still be hard to take someone's 'bothersome' assertion and extract the specific error...or combination of errors... involved. It is not that the rules are flawed, but that the assertions are not usually 'formal'... they are expressions in ordinary language, expressed in arbitrary ways, often using 'loaded' words that people don't always agree about the exact definition.... (and this is one of the most common fallacies..equivocation... using a word differently than its usually accepted way.)

Read some of the example on the page noted above.... some are obvious.. some are not... and the very expression OF the specific fallacy can be hard to get agreement about...However... they do describe classic ways people commonly twist 'common sense' in trying to make some point. The rules are correct, even if it is hard to figure out when and in what ways any specific rule is being broken.
...Now I don't dare re-read this, as I will find problems with my own explanations.... and it needs pages of examples for clarification. A good exercise is to take political speeches... or children's excuses when they get in trouble... and try to figure out which FORMAL and/or INFORMAL rules are being broken. None of this automatically leads you to **truth**, but it can sure point out when two or more **versions** of truth cannot possibly be correct, and when any ONE version is improperly stated and/or defended.

*gasp*... that's my stream of consciousness for tonight...