Identity Templates

Question 1

Only:

Only Edison invented the photograph

Answer 1

Pe∙(x)(Px→x=e)

Question 2

The Only:

The only person who is guilty is David

Answer 2

(Pd∙Gd)∙(x)[(Px∙Gx)→x=d]

Question 3

No… except:

No one except Bell invented the telephone.

Answer 3

(Pb∙Tb)∙(x)[(Px∙Tx)→x=b]

Question 4

All… except:

All European countries except Switzerland declared war.

Answer 4

(Es∙~Ds)∙(x)[(Ex∙~x=s)→Dx]

Question 5

Superlatives:

The tallest mountain is Mount Everest

Answer 5

Me∙(x)[(Mx∙~x=e)→Tex]

Question 6

At most:

There is at most one god

Answer 6

(x)(y)[(Gx∙Gy)→x=y]

Question 7

At most:

There is at most two gods

Answer 7

(x)(y)(z)([(Gx∙Gy)∙Gz]→[(x=y∨x=z)∨y=z])

Question 8

At least:

There is at least one utilitarian

Answer 8

(∃x)Ux

Question 9

At least:

There are at least two utilitarians

Answer 9

(∃x)(∃y)[(Ux∙Uy)∙~x=y]

Question 10

Exactly one:

There is exactly one solipsist

Answer 10

(∃x)Sx∙(x)(y)[(Sx∙Sy)→x=y]

Question 11

Exactly two:

There are exactly two solipsists

Answer 11

(∃x)(∃y)([(Sx∙Sy)∙~x=y]∙(z)[Sz→(z=x∨z=y)])

Question 12

Definite Descriptions:

The present King of France is bald.

Answer 12

(∃x)[Kx∙(y)(Ky→y=x)∙Bx]