User blog comment:Vel!/1+w/@comment-5982810-20141011205302/@comment-1605058-20141011211624

Without theory we cannot have any proofs. We cannot show that your notation is well-defined. You cannot show that there always is a rule which can be applied. If we were to work without background logic, we could struck things like 2+2 and we would have no idea what to do with this.