Sunday, February 20, 2011

Social Justice Banana Bread

The UN General Assembly regards February 20 as the World Day of Social Justice. One way to further the cause of social justice is to fuck up Escalades.

I used Isa's banana bread recipe and mixed in 1/4 c. chocolate chips. I only baked it for an hour but might try 50 min. next time. Or just buy a proper bread pan.

Here's a sketch of a derivation of an inductive principle for S5, that if A→□B is a theorem, then ◊AB is a theorem:

1.  A→□B [hypothesis]
2. BB [T axiom]
3. AB [propositional logic] 
4. A→◊A [T◊ theorem]
5. ◊AB [propositional logic] 

We can then use this inductive principle — call it IP — to prove that ◊□A→□◊A is a theorem:

1. A→□◊A [B theorem]
2. □(A→□◊A) [rule of necessitation]
3. □(A→□◊A)→(□A→□□◊A) [K axiom] 
4. A→□□◊A [modus ponens]
5. ◊□A→□◊A [IP]

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