Saturday, May 9, 2015

There is Logic In...Unity!

Hello all -

Is anyone still reading?  Comments would be so appreciated - I'd love to know who readers are (if any) and wonder if this is indeed still worth doing...

Anyway, On Intercept comments, I started using an end tag-line of "Divided = Conquered But United = Empowered!"  Another commenter, Cindy, wasn't sure exactly what I was saying and Benito M.  went on to explain what I probably meant (along the lines of 'united we stand but divided we fall." Well, they also developed an 'alternate reading' - which I'll get into a bit later.

Well, I let them know I did indeed appreciate another interpretation and wondered if I should use parentheses to make my meaning clearer.  It is said that the brain is continually working on making connections, but sometimes my neurons take their sweet time in doing so.  After this being put in the back of my mind and getting some sleep (although I didn't know I was sleeping on this!) it occurred to me that - whoa -I used to teach a unit on logic and in translating to English - from logic symbols, what we would use in place of parentheses was the comma!  Well, that really got me started and I thought: 'Hmmmm... wonder if I could really translate my phrase into logic symbols and do a truth table?' 

(Now if you're unfamiliar with logic, have forgotten, or want more info, here's a nice reference, as I can't put a whole unit on logic in one post.)

Getting to a truth table is what I did. First, there was the matter of the equals bit.  In logic there is 'is logically equivalent to' but that would be quite unwieldy to do in this case.  Then I thought, well, how about the biconditional - the "if and only if" construction in logic.  Then there was the matter of divided/united and conquered/empowered.  For simplicity, I considered them to be pairs of opposites. In other words, united is the logical negation of divided and empowered is the logical negation of conquered.  The word but didn't seem to be a problem as in logic it traditionally gets translated as the logical operator 'and.'

So I thought of it in English as:  "Divided if and only if conquered, and united if and only if empowered."  I translated that into logic symbols and did the truth table, but the results weren't exactly as I'd hoped.

So I tried this:  "If divided if and only if conquered, then united if and only if empowered."

Here is the resulting truth table:

If you look at the final result column, it tells us that what this compound logic statement is is called a tautology.  That is, the statement as a whole is true regardless of the truth values of its substatements.

Now Cindy and Benito M. were thinking of an interpretation which I think I can best express as a statement  to translate into logic symbols as:  "If divided if and only if conquered and united, then empowered."  (deeper meaning, uniting after being divided and conquered leads to empowerment).

If I used that construct, the result was also a tautology:

So one might say I finagled a bit (maybe?). And of course our English language isn't the most precise means of communication sometimes.  Still, I think this exercise shows that there IS a certain logic to being united, to coming together to work for common goals and the common good.  Conclusion:

  "Divided = Conquered, But United = Empowered!"

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