Sunday, September 11, 2016

Brian Romanchuk — If The Mathematics Of New Keynesian Economics Were Solid...

Brian comments on Alex Douglas, linked to this AM, if you are following.

Bond Economics
If The Mathematics Of New Keynesian Economics Were Solid...
Brian Romanchuk


Matthew Franko said...

The Douglas guy is a Philosopher so he doesnt make the mathematical argument like Brian does ....looks for logical consistency, etc.. ... Brian being STEM trained is looking for the mathematical illustration...

Tom Hickey said...

Logic and math are subsets of syntactics, which is a branch of semiotics.

The branches of semiotics are 1) syntactics, that is, the study of sign use, 2) semantics, that is, the study of the use of signs as symbols, and 3) pragmatics, that is, the application of signs and symbols in context.

Math and logic are about consistency of sign use, which is basic to proof. Logic is used to develop mathematics as well as to apply it. Logic underlies all meaningful communication.

Because it is broadly conceptual, logic is more inclusive than math, math being chiefly quantitative, and number-based. Math developed from counting while logic developed out of argumentation. Often the same people contribute to both, but the subjects are somewhat different although they overlap at the margin.

There are various degrees of formal expression in logic from symbolic or mathematical logic to formal logic to informal logic to the logic of ordinary language. Similarly, math can be chiefly numeric as in arithmetic or symbolic as in algebra.

Set theory is a subset of logic. Modern math is largely based on set theory. Modern number theory is mostly derived from set theory.

Mathematicians are a particular type of philosopher, while philosophers are not necessarily types of mathematicians. Most people using math, like scientists and engineers, are not mathematicians. They use applied math.

Obviously, philosophers not highly trained in pure or applied math will be at disadvantage in debates that are deeply mathematical, But that doesn't mean that they cannot add anything of significance. Brian criticizes DEGE abased on a circular argument. That's a logical attack.

In argumentation, the basic strategy is to drive back to foundations. Foundationally, all argument involving semantic truth has to come to a stop foundationally in true premises. Thera are criteria for assessing the truth of premises. In science, this is an empirical warrant. Sophistical arguments are based on either circular reasoning, infinite regress or stipulation without adequate justification.

All argumentation that is syntactical must be grounded in tautology that traces to axioms and it is disproved by contradiction.

Math and logic are based on consistency and justification is by proof based on definitions, axioms and postulates using operators (definition and formation and transformation rules). Semantic argument is grounded in empirical warrant and ultimately depends on justification that is empirical.

Scientific theory is syntactical in expression and subject to proof, while hypothesis generated from the theory are subject to empirical testing. Necessity in science is logical necessity generated by the logical consistency of the theory, and semantical truth derives from empirical evidence through testing. Science also justifies itself pragmatically through successful application in technology.