Human reasoning is of limited power. This claim may seem extraordinary in the light of what it has achieved—from a deep understanding of the physical world to the potential solution of many of humanity’s problems. Yet, it is limited in comparison with the superhuman intelligence that I have invoked from time to time. Indeed, we confront inferential problems that would defeat even this powerful being in their computational demands. Reasoning with multiple premises containing if’s, and’s and or’s, as I have remarked before, is intractable. Another source of intractability is our need to juggle multiple goals and beliefs, which are not always compatible with each other. And still another source is our need to coordinate our actions with one another.
[1.] I email you to invite you to lunch next Tuesday;
[2.] you email me accepting.
[3.] I email you back so that you know that I’ve received your acceptance; otherwise, you might think that it got lost in cyberspace, and that I won’t expect you for lunch.
[4.] You email me back so that I
know that you know that I’ve received your acceptance.[I colored this in grey.]
[5.] Perhaps, I should email you so that you know that I know that you know that I’ve received your acceptance. In fact, only those of us punctilious to the point of paranoia proceed to this interminable round of emails. But the task of co-ordination gets even worse if several of us are trying to schedule an appointment in this way. These problems can all grow to a size that defeats any computational system. Our reasoning is limited in power.
How can I understand 4 and 5? The multiple 'know's stump me.
Would one way to help me understand be to explain incidents where 4 and 5 are necesssary?