However, it can be proved in some logical systems.

And that was for arithmetic, the simplest logical system known!

The notion of "logical system" here is formalized as an institution.

The approach was later published in 1976 as a logical system in its own right.

All of these logical systems can also be defined axiomatically, as is shown in the next section.

And perhaps, in a logical system different from ours, our moronism is wisdom.

Some logical systems do not have all four properties.

The inevitable result is a more complicated, less logical system.

The theory of institutions does not assume anything about the nature of the logical system.

Any given set of axioms leads to a different logical system.