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Learn about: Apologetics
Apologetics: Formal argumentation in defense of something, such as a system of beliefs.  -Dictionary.com

CARM.org -Christian Apologetics
Infidels.org -Secular Apologetics
American Atheist -Atheistic Apologetics
Tekton Apologetics -Christian Apologetics
TrueOrigins.org -I.D. Apologetics
TalkOrigins.org -Macro-evolutionary apologetics
 
Christian Truth & Defense -Christian Apologetics (summary)
BeThinking.org -Christian Apologetics
DaVinci Uncoded -A look at the book The DaVinci Code
Christian Think Tank -Christian Apologetics
Ravi Zaccharius -Christian author/apologist
C.S. Lewis -Christian author/apologist

Learn about Logical Fallacies:
A fallacy is, very generally, an error in reasoning. This differs from a factual error, which is simply being wrong about the facts. To be more specific, a fallacy is an "argument" in which the premises given for the conclusion do not provide the needed degree of support. -source

Philosophy
 
Encyclopedia of Philosophy from a priori to Zizek

Propositional Calculus
A simple but powerful system of logic for representing implications between logically compound sentences, such as `either A or not B', `if B then A', etc. The system will prove, for example, that each of these two sentences implies the other. See also Predicate Calculus/Predicate Logic, Rules of Inference.
 
 
"You take the blue pill and the story ends. You wake in your bed and you believe whatever you want to believe. You take the red pill and you stay in Wonderland and I show you how deep the rabbit-hole goes. " - Morpheus from The Matrix
Propositional Calculus is the red-pill of Philosophy.

The Laws of Thermodynamics
Thermodynamics is the study of the effects of work, heat, and energy on a system.
 

Economics
Learn about the Austrian School of economics.
The Classic works of Frederic Bastiat: Vol1 & Vol2 (Includes his seminal piece What Is Seen & What Is Not Seen)

The Politics you thought you knew: