It's encouraging that his students aren't showing any visible sign of emotional disturbance at the prediction or at failing to overcome it; they have some traces of dath ilani dignity, at least.  Keltham was wondering whether a lack of training in dignity would require him to back off a little on challenges like those, but his students' dignity is unperturbed so far as he can see.

     \ h. t3(h) -> t2(h)
___________________

   \ h. ~t2(h) -> ~t3(h)

"So long as we have this reasoning tactic in our tactical repertoire - go ahead and take a moment to convince yourself that you couldn't cast an illusion violating it - we can combine it with our previous rule to get the combined rule we wanted:"

[1]    \ z. t1(z) -> ~t2(z)                (Premise)
[2]    \ h. t3(h) -> t2(h)                 (Premise)
_______________________

[3]    \ h. ~t2(h') -> ~t3(h')            (modus tollens [2])
_______________________

[4]    \ q. t1(q) -> ~t3(q)                (syllogism [1], [3])

"Anyone want to propose yet another universal rule?  Here's some other shorthand language to help you express yourself:"

blue(k) \/ red(k)             "k is blue or k is red"
blue(k) /\ ~red(k)           "k is blue and k is not k"
\k. ~(blue(k) /\ red(k))    "for every k, it is not the case that (k is blue and k is red)"
blue(k) -> small(k)         "if k is blue, then k is small"
~~~blue(k)                     "it isn't wrong that k is not blue"

It's encouraging that his students aren't showing any visible sign of emotional disturbance at the prediction or at failing to overcome it; they have some traces of dath ilani dignity, at least.  Keltham was wondering whether a lack of training in dignity would require him to back off a little on challenges like those, but his students' dignity is unperturbed so far as he can see.

     \ h. t3(h) -> t2(h)
___________________

   \ h. ~t2(h) -> ~t3(h)

"So long as we have this reasoning tactic in our tactical repertoire - go ahead and take a moment to convince yourself that you couldn't cast an illusion violating it - we can combine it with our previous rule to get the combined rule we wanted:"

[1]    \ z. t1(z) -> ~t2(z)                (Premise)
[2]    \ h. t3(h) -> t2(h)                 (Premise)
_______________________

[3]    \ h. ~t2(h') -> ~t3(h')            (modus tollens [2])
_______________________

[4]    \ q. t1(q) -> ~t3(q)                (syllogism [1], [3])

"Anyone want to propose yet another universal rule?  Here's some other shorthand language to help you express yourself:"

blue(k) \/ red(k)             "k is blue or k is red"
blue(k) /\ ~red(k)           "k is blue and k is not k"
\k. ~(blue(k) /\ red(k))    "for every k, it is not the case that (k is blue and k is red)"
blue(k) -> small(k)         "if k is blue, then k is small"
~~~blue(k)                     "it isn't wrong that k is not blue"

It's encouraging that his students aren't showing any visible sign of emotional disturbance at the prediction or at failing to overcome it; they have some traces of dath ilani dignity, at least.  Keltham was wondering whether a lack of training in dignity would require him to back off a little on challenges like those, but his students' dignity is unperturbed so far as he can see.

     \ h. t3(h) -> t2(h)
___________________

   \ h. ~t2(h) -> ~t3(h)

"So long as we have this reasoning tactic in our tactical repertoire - go ahead and take a moment to convince yourself that you couldn't cast an illusion violating it - we can combine it with our previous rule to get the combined rule we wanted:"

[1]    \ z. t1(z) -> ~t2(z)                (Premise)
[2]    \ h. t3(h) -> t2(h)                 (Premise)
_______________________

[3]    \ h. ~t2(h') -> ~t3(h')            (modus tollens [2])
_______________________

[4]    \ q. t1(q) -> ~t3(q)                (syllogism [1], [3])

"Anyone want to propose yet another universal rule?  Here's some shorthand language to help you express yourself:"

blue(k) \/ red(k)             "k is blue or k is red"
blue(k) /\ ~red(k)           "k is blue and k is not k"
\k. ~(blue(k) /\ red(k))    "for every k, it is not the case that (k is blue and k is red)"
blue(k) -> small(k)         "if k is blue, then k is small"
~~~blue(k)                     "it isn't wrong that k is not blue"

It's encouraging that his students aren't showing any visible sign of emotional disturbance at the prediction or at failing to overcome it; they have some traces of dath ilani dignity, at least.  Keltham was wondering whether a lack of training in dignity would require him to back off a little on challenges like those, but his students' dignity is unperturbed so far as he can see.

     \ h. t3(h) -> t2(h)
___________________

   \ h. ~t2(h) -> ~t3(h)

"So long as we have this reasoning tactic in our tactical repertoire - go ahead and take a moment to convince yourself that you couldn't cast an illusion violating it - we can combine it with our previous rule to get the combined rule we wanted:"

[1]    \ z. t1(z) -> ~t2(z)                (Premise)
[2]    \ h. t3(h) -> t2(h)                 (Premise)
_______________________

[3]    \ h. ~t2(h') -> ~t3(h')            (one person's modus ponens is another person's modus tollens [2])
_______________________

[4]    \ q. t1(q) -> ~t3(q)                (syllogism [1], [3])

"Anyone want to propose yet another universal rule?  Here's some shorthand language to help you express yourself:"

blue(k) \/ red(k)             "k is blue or k is red"
blue(k) /\ ~red(k)           "k is blue and k is not k"
\k. ~(blue(k) /\ red(k))    "for every k, it is not the case that (k is blue and k is red)"
blue(k) -> small(k)         "if k is blue, then k is small"
~~~blue(k)                     "it isn't wrong that k is not blue"

It's encouraging that his students aren't showing any visible sign of emotional disturbance at the prediction or at failing to overcome it; they have some traces of dath ilani dignity, at least.  Keltham was wondering whether a lack of training in dignity would require him to back off a little on challenges like those, but his students' dignity is unperturbed so far as he can see.

     \ h. t3(h) -> t2(h)
___________________

   \ h. ~t2(h) -> ~t3(h)

"So long as we have this reasoning tactic in our tactical repertoire - go ahead and take a moment to convince yourself that you couldn't cast an illusion violating it - we can combine it with our previous rule to get the combined rule we wanted:"

[1]    \ z. t1(z) -> ~t2(z)                (Premise)
[2]    \ h. t3(h) -> t2(h)                 (Premise)
_______________________

[3]    \ h. ~t2(h') -> ~t3(h')            (one person's modus ponens is another person's modus tollens [2])
_______________________

[4]    \ q. t1(q) -> ~t3(q)                (syllogism [1], [3])

"Anyone want to propose yet another universal rule?  Here's some shorthand language to help you express yourself:"

blue(k) \/ red(k)             "k is blue or k is red"
blue(k) /\ ~red(k)           "k is blue and k is not red"
\k. ~(blue(k) /\ red(k))    "for every k, it is not the case that (k is blue and k is red)"
blue(k) -> small(k)         "if k is blue, then k is small"
~~~blue(k)                     "it isn't wrong that k is not blue"

It's encouraging that his students aren't showing any visible sign of emotional disturbance at the prediction or at failing to overcome it; they have some traces of dath ilani dignity, at least.  Keltham was wondering whether a lack of training in dignity would require him to back off a little on challenges like those, but his students' dignity is unperturbed so far as he can see.

     \ h. t3(h) -> t2(h)
___________________

   \ h. ~t2(h) -> ~t3(h)

"So long as we have this reasoning tactic in our tactical repertoire - go ahead and take a moment to convince yourself that you couldn't cast an illusion violating it - we can combine it with our previous rule to get the combined rule we wanted:"

[1]    \ z. t1(z) -> ~t2(z)                (Premise)
[2]    \ h. t3(h) -> t2(h)                 (Premise)
_______________________

[3]    \ h. ~t2(h) -> ~t3(h)            (one person's modus ponens is another person's modus tollens [2])
_______________________

[4]    \ q. t1(q) -> ~t3(q)                (syllogism [1], [3])

"Anyone want to propose yet another universal rule?  Here's some shorthand language to help you express yourself:"

blue(k) \/ red(k)             "k is blue or k is red"
blue(k) /\ ~red(k)           "k is blue and k is not red"
\k. ~(blue(k) /\ red(k))    "for every k, it is not the case that (k is blue and k is red)"
blue(k) -> small(k)         "if k is blue, then k is small"
~~~blue(k)                     "it isn't wrong that k is not blue"