LMU ☀️ CMSI 2310
LANGUAGE, THOUGHT, AND COMPUTATION
Midterm Answers
  1. A human, for whom it is impossible to act unobservantly, would quickly realize all theorems begin with M and would stop looking for UIIM very quickly. A naïve program would follow a search algorithm forever without quitting on its own.
  2. There exists no mechanical procedure for determining, in a finite duration, whether a given string is a theorem of the system.
  3. The theorems of this system are exactly the palindromes over the alphabet {a,b,c}. The derivation of abccba takes only three steps. 
    cc             (by the Axiom)
bccb           (by the Rule)
abccba         (by the Rule)
  4. Meaning comes from our recognition of isomorphisms.
  5. The ground is AEIOU. As an English speaker who has seen the alphabet written out often, I could not help but immediately see this figure as "the English alphabet with some missing letters."
  6. There are an infinite number of possible sentences, because the generation rules in the grammar allow sentences to appear within sentences. A specific example: 
    She dreamed she fell
She dreamed she dreamed she fell
She dreamed she dreamed she dreamed she fell
She dreamed she dreamed she dreamed she dreamed she fell
She dreamed she dreamed she dreamed she dreamed she dreamed she fell
...
  7. Here are the nine:

    sigma9.gif

  8. The frame message is the paper with writing on it. The outer message is English language instructions for drawing something, using a 2-D coordinate system and some familiar geometric terms. The inner message is a peace sign.
    • Sml ⊃ Bm'
      If shining_on(moon, lake) then is_buddha(this_mind)
    • ∀p.((Ip ∧ ~(p=r)) ⊃ Lpg)
      For all p, if is_italian(p) and not(p is Romeo), then likes(p, gelato)
    • FVj(℩c.Cgc)
      In the future: visit(juliet, the c such that capital_of(greece, c))
    • ∃p.(Gp ∧ ∀c.Pgc)
      There exists at least one p such that: is_guitarist(p) and for every chord c, can_play(g, c)
    • ◊(Ij ∧ Ir ∧ Ig)
      It is possible that: is_italian(juliet) and is_italian(romeo) and is_italian(guido)
  10. The Tortoise refuses to accept the rule of joining. 
  11.  1  [
 2    <p∧~p>     assumption
 3    p          separation(2)
 4    ~p         separation(2)
 5    [
 6      q        assumption
 7      p        carry-over(3)
 8    ]
 9    <q⊃p>      fantasy(6,7)
10    <~p⊃~q>    contrapositive(9)
11    ~q         detachment(10,4)
12  ]
13  <<p∧~p>⊃~q>  fantasy(2,11)