Logic:
http://www.uky.edu/~rosdatte/phi120/lesson1a.htm
https://people.umass.edu/klement/100/logic.html
http://utminers.utep.edu/omwilliamson/ENGL1311/fallacies.htm
https://sites.google.com/site/mccormickphilosophy/home/critical-thinking-syllabus/critical-thinking-schedule/reconstructing-arguments
https://gmat.economist.com/gmat-advice/gmat-verbal-section/critical-reasoning/how-find-premise-critical-reasoning-questions
So in logic, premises are true statements that lead to a sound conclusion. If the premises are faulty, the conclusion will be too.
To practice logic, take a newspaper or newsfeed and examine its articles to identify the premises and conclusions. As few people study logic closely, these are usually buried. But it's great practice for identifying bottom rungs.
Philosophy:
http://www.joshdmay.com/teaching/philosophy-basics/
http://www.jimpryor.net/teaching/vocab/argument.html
https://www.philosophybasics.com/movements.html
http://bigthink.com/scotty-hendricks/10-schools-of-philosophy-and-why-you-should-know-them
https://en.wikipedia.org/wiki/List_of_schools_of_philosophy
In philosophy, premises are ideals that inform decisions. They're basic concepts about how the world does or should work, which indicate a moral or effective course of action through a dilemma. That means they're not necessarily falsifiable, because people can value different virtues. But some philosophies really do work better or worse in the real world.
Now go back to your news and look for dilemmas where people have to take a stance on an issue. Pick several schools of philosophy whose premises you understand. Describe how each of them would frame that issue and what their premises would say to do about it. The answers will usually vary, which is why people get into fights over this stuff.
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