I'm also confronting the possibility that what I, lacking formal training in this area, have believed to be logical thought my whole life might actually be a different, related philosophy called 'Rationality'. This was suggested to me by one person, while another has told me that rationality and logic are synonymous and a third has suggested that both of these are somehow true.
First...
Logic as applied to mathematics and computers is different from logic as applied to philosophy and thinking.
For one, a computer doesn't 'think' it runs a program. It's logic is related to 'do I understand this program or not'. If it does not understand the program, then it returns an error (which can be viewed as illogic). Mathematics is based on the presumption that something is always true or not true. That the equation is based on the truth of the formulations.
So - the logic of mathematics is dependent on a very simple 'if' statement that has but two possible outcomes - a value if true and a value if false.
If 2+2 = 4 then 2+2 must always equal four (until you move out of base 10 but then again, the same applies). This is logic of mathematics.
Going back into the conversation:
Logic is predicated on that which is true and proven.
Rational is based on that which can be proven.
They are similar and can lead to the same place (and I firmly believe in order to get actual logic you must employ rationality).
For example: It would be illogical for me to say "I jumped into the lake and didn't get wet." However, I could rationally say "I jumped into the lake and didn't get wet."
The first is illogical because it is not true and cannot be proven to be true.
The second can be rational because all available factors are not in so therefore it is possible to make that statement, rationally, because arguments can prove it to be true.
However, an irrational statement would be "I jumped into a lake, naked, and didn't get wet." Arguments to this statement would be irrational because it would take a stretch to prove them to be true.
So...in order to get to get to logic one must understand that a rational conclusion must follow from another rational conclusion until there is but one conclusion left possible. But the rationality cannot be or ambiguous.
When dealing with thinking, however, the waters become muddy.
One has to ask: Is grief logical?
Is anger logical?
Is happiness logical?
The answer to these questions come from rational conclusions but can never be truly answered. Because a true, logical answer cannot be distilled to just a value if true/false.
Think of this - is suicide logical?
An argument can be made for it - especially when one takes the emotion out of the discussion.
And don't feel bad...this is a question that has plagued philosophical thinkers since way before Aristotle.
But those you are having the conversations with have to be able to demonstrate rational thinking themselves.
Rabe...
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