Epimenides Trilemma

Epimenides Trilemma

Consider these three voters:

Moe:

Some philosophers are Cretans;

All Cretans are liars;

Some philosophers are liars.

Larry:

Some philosophers are Cretans;

No philosophers are liars;

Not all Cretans are liars.

Curly:

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.

This 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.