Meta-theorem 22:

The morphology of our world implies that if there is a unicorn, life would be more beautiful, iff the union of our morphology and the statement ‘there is a unicorn’ also implies that ‘life would be more beautiful’.

Proof:

- Assume ? ? ‘there is a unicorn’ ? ‘life is more beautiful’.
- Then we know that every valuation that simultaneously satisfies ?, also satisfies ‘there is a unicorn’ ? ‘life is more beautiful’.
- For every valuation which simultaneously satisfies ?, it must be the case that V(‘there is a unicorn’)=F or V(‘life is more beautiful’)=T.
- Assume ? ? {‘there is a unicorn’} ? ‘life is more beautiful’
- Then there must be a V such that ? ? {‘there is a unicorn’} is simultaneously satisfied, but V'(‘life is more beautiful’)=F and V'(‘there is a unicorn’)=T.
- However, this is a contradiction to line 3, hence:
- ? ? {‘there is a unicorn’} ? ‘life is more beautiful’
- Now assume ? ? {‘there is a unicorn’} ? ‘life is more beautiful’.
- Then we know that every valuation which simultaneously satisfies ? ? {‘there is a unicorn’}, also satisfies ‘life is more beautiful’.
- It must be the case that V(‘life is more beautiful’)=T or ? ? {‘there is a unicorn’} is not simultaneously satisfiable, such that V(‘there is a unicorn’)=F.
- Assume that ? ? ‘there is a unicorn’ ? ‘life is more beautiful’.
- Then there is a valuation V’ that simultaneously satisfies Î“, such that V'(‘there is a unicorn’ ? ‘life is more beautiful’)=F.
- Then it must be the case that V'(‘there is a unicorn’)=T or V'(‘life is more beautiful’)=F.
- However, this is a contradiction to line 10, hence:
- ? ? ‘there is a unicorn’ ? ‘life is more beautiful’