5.3 Deriving scope ambiguities

1. Start simple
   1. [ ${}_{\mathrm{S}}$ Every man$_{x}$ walks.]
   2. [ ${}_{\mathrm{S}}$ [Every man]$_{x}$ [ ${}_{\mathrm{S}}$ x walks.]]
   3. [ ${}_{\mathrm{S}}$ Every${}_{x}$ [x man]${}_{x}$ [ ${}_{\mathrm{S}}$ x walks.]]
   4. $\mathrm{\:Every\:}\:x\:\lbrack\mathrm{\:man\:}(x) \rightarrow \mathrm{\:walk\:}(x)\rbrack$
2. Two NPs
   1. [ ${}_{\mathrm{S}}$ [Every man]$_{x}$ loves [some woman]${}_{y}$]
   2. [ ${}_{\mathrm{S}}$ [Every man]$_{x}$ [ ${}_{\mathrm{S}}$ x loves [some woman]${}_{y}$.]]
   3. [ ${}_{\mathrm{S}}$ Every${}_{x}$ [x man]${}_{x}$ [ ${}_{\mathrm{S}}$ x loves some woman${}_{y}$.]]
   4. [ ${}_{\mathrm{S}}$ [some woman${}_{y}$] [ ${}_{\mathrm{S}}$ Every${}_{x}$ [x man]${}_{x}$ [ ${}_{\mathrm{S}}$ x loves y.]]]
   5. [ ${}_{\mathrm{S}}$ some${}_{y}$ [y woman]${}_{y}$ [ ${}_{\mathrm{S}}$ Every${}_{x}$ [x man]${}_{x}$ [ ${}_{\mathrm{S}}$ x loves y.]]]
   6. $\mathrm{\:Some\:} y \lbrack \mathrm{\:woman\:}(y) \wedge \mathrm{\:Every\:}\:x\:\lbrack \mathrm{\:man\:}(x) \rightarrow \mathrm{\:love\:}(x,y)\rbrack \rbrack$
3. Two NPs another way
   1. [ ${}_{\mathrm{S}}$ [Every man]$_{x}$ loves [some woman]${}_{y}$]
   2. [ ${}_{\mathrm{S}}$ [Some woman]$_{y}$ [ ${}_{\mathrm{S}}$ [every man]${}_{x}$ loves y.]]
   3. [ ${}_{\mathrm{S}}$ Some${}_{y}$ [y woman]$_{y}$ [ ${}_{\mathrm{S}}$ [every man]${}_{x}$ loves y.]]
   4. [ ${}_{\mathrm{S}}$ [every man${}_{x}$] [ ${}_{\mathrm{S}}$ some${}_{x}$ [y woman]${}_{x}$ [ ${}_{\mathrm{S}}$ x loves y.]]]
   5. [ ${}_{\mathrm{S}}$ every${}_{x}$ [x man]${}_{x}$ [ ${}_{\mathrm{S}}$ some${}_{y}$ [y woman]${}_{x}$ [ ${}_{\mathrm{S}}$ x loves y.]]]
   6. $\mathrm{\:Every\:} x \lbrack \mathrm{\:man\:}(x) \rightarrow \mathrm{\:some\:}... ...\lbrack \mathrm{\:woman\:}(y) \rightarrow \mathrm{\:love\:}(x,y)\rbrack \rbrack$
4. So now this IS a syntactic ambiguity

5. A new architecture for grammar
   1. Classical aspects model (c. 1965)

      

   2. T-model (c. 1976)
      
6. Some evidence against the classical model:

   (i) Everyone in this room speaks two languages.
   (ii) Two languages are spoken by everyone in this room.
   

   $$\begin{array}[t]{l} 2\: x \: \mathrm{\:language\:}(x) \wedge... ...language\:}(x) \wedge \mathrm{\:speak\:}(y,\:x) \\ \end{array}$$

   (iii) It is certain that no one will leave
   (iv) No one is certain to leave.

   $$\begin{array}[t]{l} \neg \exists x \mathrm{\:person\:}(x) \w... ...mathrm{\:person\:}(x) \wedge \mathrm{\:leave\:}(x) \end{array}$$