Hi. Great videos- but what determines that these logical rules though? Where are they derived from / what evidence gives us these answers? I’m struggling because they do not align with the English language, so the rules seem kind of arbitrary and something to simply memorise rather than something to genuinely ‘know’.
The truth tables for these five basic logical connectives can be taken as the definitions. However, each of them is motivated by one possible English interpretation. “And” and “not” come from the only English interpretation. “Or” is the English “inclusive or” and “if and only if” is used to say that two statements have the same truth value. “If…then” is based on one possible English interpretation, but most importantly, it is defined in the most useful way for proving theorems.
@@ms16648 Again, it’s just the definition of the conjunction. However, it models what we do in English. Your example disagrees with the meaning of “and” in English, so it would be confusing to make that the mathematical definition.
Hi. Great videos- but what determines that these logical rules though? Where are they derived from / what evidence gives us these answers?
I’m struggling because they do not align with the English language, so the rules seem kind of arbitrary and something to simply memorise rather than something to genuinely ‘know’.
The truth tables for these five basic logical connectives can be taken as the definitions. However, each of them is motivated by one possible English interpretation. “And” and “not” come from the only English interpretation. “Or” is the English “inclusive or” and “if and only if” is used to say that two statements have the same truth value. “If…then” is based on one possible English interpretation, but most importantly, it is defined in the most useful way for proving theorems.
@@ms16648 Again, it’s just the definition of the conjunction. However, it models what we do in English. Your example disagrees with the meaning of “and” in English, so it would be confusing to make that the mathematical definition.
unfortunately cats can bark