- f(x) is essentially a hypothetical proposition, i.e. If x then f(x).
- A mathematical model is a series of hypothetical propositions awaiting some premises (i.e. xi) from which to derive conclusions.
- These conclusion have mathematical certainty. They are also meaningless. F = ma is in itself meaningless. It is the movement of attributing qualitative character to the quantitative abstraction that makes models useful and models.
- This is itself a proposition that affirms a sufficiency to the analogy. It is the rise and fall of models.
- The Black Scholes Equation is pretty which has no qualitative meaning anywhere in it. It is an act of interpretation to start talking about hedging stocks with particular qualitative and quantitative characteristics.
- The movement from equation to reality demand certain assumption, i.e. Additional premises. Stocks follow geometric Brownian motion. There is such a thing as risk free rate. Volatility is constant. Most importantly, the relevant features can be adequately quantified.