Tutorial Contents Tutorial Six: Predicate Calculus with Identity - TRussell's Theory of Descriptions -
Scope - Tableau Rules for Identity
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Exercise 6.2

 

1

Using the following interpretation:

 

Domain: everything in 12 Main Street, Anytown
 

a: John
 

b: Mary
 

Mx: x is a man
 

Wx: x is a woman
 

Lxy: x likes y
 

Hx: x is human

to formalise the following:
  (i)

The man likes Mary
  (ii)

The person who likes Mary everyone likes.
  (iii)

The man who likes Mary likes the woman who likes John.
  (iv)

John is the man who likes everyone.
  (v)

There is no such person as the man who likes everyone.
  (vi)

If John is the man who likes everyone, he likes Mary.
  (vii)

Something exists.
  (viii)

12 Main Street, Anytown is not empty.
  (ix)

There are at least two things.
  (x)

There are exactly two things.

2.

Using the following interpretation:

 

Domain: People and colleges
 

Ux: x is an undergraduate
 

Cx: x is a college
 

Px: x is reading Philosophy
 

Ex: x is reading Economics
 

Mxy: x is a member of y
 

Txy: x is one of y's tutors

formalise the following:
  (i)

Every undergraduate has a tutor
  (ii)

No tutor has a tutor
  (iii)

Some undergraduates have more than one tutor
  (iv)

No undergraduate is a member of more than one college
  (v)

Some members of different colleges share a tutor
  (vi)

No two members of different colleges have exactly the same tutors
  (vii)

Every college has both Philosophy and Economics undergraduates

3.

Using the same interpretation as in question 2, translate the following into English. (Try to make the English as natural as possible.)
  (i)

$x$y[[UxÙUy]Ù[[PxÙPy]Ù[ExÙ¬Ey]]]
  (ii)

$x[[CxÙ¬$y[[MyxÙUy]Ù¬Py]]Ù"z[[CzÙ¬$u[[MuzÙUu]Ù¬Pu]]®z=x]]
  (iii)

"x[$y[PyÙTxy]®"y[Txy®¬Ey]]
  (iv)

$x$y$z$u[TxyÙ[CzÙ[CuÙ[¬z=uÙ[MxzÙMxu]]]]]
  (v)

$x$y$z$u[TxyÙ[CzÙ[CuÙ[¬z=uÙ[MxzÙMyu]]]]]
  (vi)

"x[$y[PyÙTxy]®$y[EyÙTxy]]
  (vii)

$x[["z[Pz®Txz]Ù"y["z[Pz®Tyz]®y=x]]Ù "z[Ez®¬Txz]]

 

 

 
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