"When I was a bit younger and learning this stuff for the first time, I went straight to the Watcher - the adult who was there to make sure the older kids weren't teaching us anything too wrong - and demanded that I immediately be taught the most powerful kind of logic there was.  The Watcher told me that the logic I was learning was, in fact, the most powerful kind of logic on offer - that it was, in fact, the most powerful kind of logic there was.  I didn't see how anyone could possibly know that even if it was true, so I figured this was another of the lies-they-tell-children, or maybe that the best kind of logic was probably being kept secret by the Keepers.  Those being the people who would learn a more powerful kind of logic, if it existed, and was too dangerous for everybody to have.  I wanted that for myself, so I tried inventing other kinds of logic with more powerful symbols in it, symbols that could connect three or even four propositions together, instead of just the one-or-two symbol connectors the older kids were telling me about."

"But before I tell you about the results of that particular journey of thinking, and whether or not it did turn out to be a lie-they-tell-children in the end, let me pause and ask another question first.  In algebra we have rules for producing new equations from old equations, or combining old equations.  Here we have rules for producing new statements from old statements, if those statements are written in a particular language.  Both algebra and the statement-rules obey the higher principle of Validity - we have ways of comparing equations and statements to worlds, to see if they're true or false; and if an equation or statement is true in a world, the rules for manipulating it should produce only more true equations or true statements.  In the world of statements, we managed to reduce 'or' to 'and' and 'not'.  In the world of algebra, we reduced the rule 'divide both sides by a nonzero quantity' to 'multiply both sides by an inverse'.  Can we in some way combine the rules of algebra, and the rules of statements, since they are both born of the same truth-preserving principle?  Can we reduce algebra-rules to statement-rules, or reduce statement-rules to algebra-rules, and so simplify our mastery of truth-perservation?"

"This one's actually quite hard to solve from scratch at our intelligence level - I didn't get it as a kid and wouldn't expect myself to get it now, if I didn't already know it.  But it is important to know your own emptiness before trying to fill yourself, so go and speak aloud any really bad wrong answers you come up with here."

"When I was a bit younger and learning this stuff for the first time, I went straight to the Watcher - the adult who was there to make sure the older kids weren't teaching us anything too wrong - and demanded that I immediately be taught the most powerful kind of logic there was.  The Watcher told me that the logic I was learning was the most powerful kind of logic on offer - that it was, in fact, the most powerful kind of logic there was.  I didn't see how anyone could possibly know that even if it was true, so I figured this was another of the lies-they-tell-children, or maybe that the best kind of logic was probably being kept secret by the Keepers.  Those being the people who would learn a more powerful kind of logic, if it existed, and was too dangerous for everybody to have.  I wanted that for myself, so I tried inventing other kinds of logic with more powerful symbols in it, symbols that could connect three or even four propositions together, instead of just the one-or-two symbol connectors the older kids were telling me about."

"But before I tell you about the results of that particular journey of thinking, and whether or not it did turn out to be a lie-they-tell-children in the end, let me pause and ask another question first.  In algebra we have rules for producing new equations from old equations, or combining old equations.  Here we have rules for producing new statements from old statements, if those statements are written in a particular language.  Both algebra and the statement-rules obey the higher principle of Validity - we have ways of comparing equations and statements to worlds, to see if they're true or false; and if an equation or statement is true in a world, the rules for manipulating it should produce only more true equations or true statements.  In the world of statements, we managed to reduce 'or' to 'and' and 'not'.  In the world of algebra, we reduced the rule 'divide both sides by a nonzero quantity' to 'multiply both sides by an inverse'.  Can we in some way combine the rules of algebra, and the rules of statements, since they are both born of the same truth-preserving principle?  Can we reduce algebra-rules to statement-rules, or reduce statement-rules to algebra-rules, and so simplify our mastery of truth-perservation?"

"This one's actually quite hard to solve from scratch at our intelligence level - I didn't get it as a kid and wouldn't expect myself to get it now, if I didn't already know it.  But it is important to know your own emptiness before trying to fill yourself, so go and speak aloud any really bad wrong answers you come up with here."

"When I was a bit younger and learning this stuff for the first time, I went straight to the Watcher - the adult who was there to make sure the older kids weren't teaching us anything too wrong - and demanded that I immediately be taught the most powerful kind of logic there was.  The Watcher told me that the logic I was learning was the most powerful kind of logic on offer - that it was, in fact, the most powerful kind of logic that could exist.  I didn't see how anyone could possibly know that even if it was true, so I figured this was another of the lies-they-tell-children, or maybe that the best kind of logic was probably being kept secret by the Keepers.  Those being the people who would learn a more powerful kind of logic, if it existed, and was too dangerous for everybody to have.  I wanted that for myself, so I tried inventing other kinds of logic with more powerful symbols in it, symbols that could connect three or even four propositions together, instead of just the one-or-two symbol connectors the older kids were telling me about."

"But before I tell you about the results of that particular journey of thinking, and whether or not it did turn out to be a lie-they-tell-children in the end, let me pause and ask another question first.  In algebra we have rules for producing new equations from old equations, or combining old equations.  Here we have rules for producing new statements from old statements, if those statements are written in a particular language.  Both algebra and the statement-rules obey the higher principle of Validity - we have ways of comparing equations and statements to worlds, to see if they're true or false; and if an equation or statement is true in a world, the rules for manipulating it should produce only more true equations or true statements.  In the world of statements, we managed to reduce 'or' to 'and' and 'not'.  In the world of algebra, we reduced the rule 'divide both sides by a nonzero quantity' to 'multiply both sides by an inverse'.  Can we in some way combine the rules of algebra, and the rules of statements, since they are both born of the same truth-preserving principle?  Can we reduce algebra-rules to statement-rules, or reduce statement-rules to algebra-rules, and so simplify our mastery of truth-perservation?"

"This one's actually quite hard to solve from scratch at our intelligence level - I didn't get it as a kid and wouldn't expect myself to get it now, if I didn't already know it.  But it is important to know your own emptiness before trying to fill yourself, so go and speak aloud any really bad wrong answers you come up with here."