Epimenides Trilemma

     Epimenides Trilemma

 

 

          Consider these three voters:

 

Moe says:

Some philosophers are Cretans;

All Cretans are liars;

Some philosophers are liars.

 

Larry says:

No philosophers are liars;

Some philosophers are Cretans;

Not all Cretans are liars.

 

Curly says:

All Cretans are liars;

No philosophers are liars;

No philosophers are Cretans.

 

If Moe, Larry and Curly vote, then each of these propositions pass by 2/3 majorities:

 

Some philosophers are Cretans;

All Cretans are liars;

No philosophers are liars.

 

That is the “Epimenides Trilemma”; a voter’s paradox. All three propositions pass by majority rule, but then cannot all three be true at once. If two are true, then the third must be false. So:

 

If

Some philosophers are Cretans

and

All Cretans are liars

then

Some philosophers are liars.

 

If

No philosophers are liars

and

Some philosophers are Cretans

then

Not all Cretans are liars.

 

If

All Cretans are liars

and

No philosophers are liars

then

No philosophers are Cretans.

 

 

The trilemma both defies syllogisms, and yields three of them!