Tuesday, July 19, 2011

Outlines 2

Although it is somewhat of a blunt instrument, mathematical logic is the only tool, I feel, that is capable of giving a field which hitherto has not had adequately rigorous theoretical grounding.


The thesis of this book boils down to this:

(1) "Ordered sequences of images and text consist of a series of assertions about a conceptual world."

(1.1) "In order to make sense of the assertions given, there must be a grammar around which a visual language is formed."

(1.1.1) "The grammar of this language can be adequately described by first order logic (F.O.L.)."

Descriptive language consists of assertions of the form, "It is the case such that p is true", or:
  1. ⊢p

Wednesday, July 13, 2011

Let ">" be an asymmetrical two-place predicate such that a is the "predecessor" of b, and b>a is false for ">", if {a, b, c, ...} form a well-ordered set.

Let P1 and P2 be any arbitrary sets on L.

⊦⌜ a>b⌝ & [a∈P1 & b∈P2 ] ⊃ ⌜P1>P2