Finance, Mathematics, Software

That is mathematics in a nutshell. People seem to overestimate the expressiveness of mathematics.
Math is limited to propositions: statements that are either true or false.
Philosophers have the luxury of making statements that cannot be proved either true or false.
“As synthetic a priori judgments, the truths of mathematics are both informative and necessary.”
What the heck does that mean?

Math is just following your nose. The real truth tellers in this world have no choice. They are
born artists that suffer from a need to communicate what they see.

Propositional Calculus

When you limit yourself to statements that are either true or false, you also limit the vocabulary you can use.
The only words used in the Propositional Calculus are ‘not’, ‘and’, ‘or’, and ‘implies’.

Syntax

What you can say in mathematics is easy. What it means, not so much.
There is no limit on the number of atomic propositions you
have. P₁, P₂, P₃,…
The rules for making propositions are

1. Atomic propositions are propositions.
2. If P is a proposition, then (~P) is a proposition.
3. If P and Q are propositions, then
   (P∧Q), (P∨Q), and (P⇒Q)
   are propositions.

That’s it.

Symantics

When the atomic propositions in a proposition are assigned true or false values,
that determines the value of the proposition. This is described by truth tables.

P	~P
T	F
F	T