I use the mnemonic z=(y=x) to help me negotiate the confusing aspects of propositional calculus.The statement has two logical (Boolean) levels, a lower, predicate level where 0=Nonexistant and 1=exists, and an upper propositional level where 0=false and 1=true. Here is the 'kicker'- propositions only result when two predicate variables (eg a subject and predicate) are compared for sameness.

Consider 'John has a blue shirt'. This is a legal combination of predicates. 'John' and 'has a blue shirt' (or equivalently, the affordance 'John has' and 'a blue shirt') can both exist in a possible world. therefore 1. You can put y = x together legally so the Boolean computation (y=x) resolves to either true or false.

In the possible micro-world 'John has a blue shirt' , the statement is either true (yep, I can see him on the surveillance video, running out the door to work in the morning, suitcase in hand, pecking the wife on the cheek) or false (no, he's late again, his favourite shirt is dirty, he has a brown shirt on today).

But the micro-world 'John has a blue horizon' DOES NOT COMPUTE, not in a reality processor like our mind, which consist of a conceptual part and an embodied part. We CAN form the statement above, and if we were a magic realist author, or creative poet, we might even get a literature prize, but as soon as the statement (which exists in the conceptual mind) is compared on the basis for similarity with the knowledge of predicate constructs in the 'realistic, possible' embodied mind, we obtain a '0' which doesn't mean 'false' (it isn't a proposition) it means 'cannot exist' because it is a predicate.

The problem arises because our minds ( and all computers) are ultimately binary machines, but the world is not. It has a predicate layer which uses unary 'base 1' in which there is arity=1. If something isn't possible in the real world, it simply doesn't exist, because it was never created. It was evolution which created brains and computers, in which binary images of unary reality are possible. The main reason for this was to model propositional falsity (past and future) , not modelling predicate falsity.