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