Science
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Economics and other sciences.
A recent discussion :
Start of #economics buffer: Sun Feb 20 2005
<pavlicek> Are you reading the paper on labor contracts and profit-sharing? [[at http://www.stanford.edu/~stadelis/partnerhips081604.pdf , Ed.]]
<teralaser> huh?
<teralaser> well, that first one comparing partnerships with other organizations
<teralaser> I like there is an integral in there.
<teralaser> For once , not those stupid P = a b c equations
<pavlicek> Yeah, I gotta admit that integrals are flashier than linear equations.
<clausen> economics has been taken over by mathematicians :)
<clausen> (in academia, anyway)
<teralaser> as it should be.
<clausen> indeed
<pavlicek> I sorta waver between viewing economics as a mathematical field and viewing it as not.
<clausen> it clearly has an empirical aspect as ell
<pavlicek> When you're a student learning say, microeconomics, the mathematics is just another language for
illustrating economic concepts. It's not driven by any need to compute quantitative relationships.
<clausen> maths != computation
<clausen> the fundamental theorems of welfare economics, for example...
<pavlicek> Applied maths (ie., modelling physical systems) generally ==> computation.
<clausen> economics is mostly pure maths, not applied
<clausen> (i.e. analysis)
<pavlicek> It's ostensibly the application of mathematical optimization theory to problems of resource allocation.
<clausen> the fundamental welfare theorems definitely fit in on the "pure maths" end of the spectrum
<teralaser> well, I am just repulsed by people just making largely unsubstantiated claims like PI = a b c d
involving a set of macro parameter, such as Cabbage likes to do.
<clausen> pavlicek: optimization theory has pure and applied aspects
<clausen> pavlicek: economics mostly uses the pure stuff
<teralaser> not really Newtonian to me.
<teralaser> (but surely maths is just a language to show some point)
<clausen> teralaser: economics usually need not make such assumptions
<clausen> assumptions usually look more like: assume the consumer has a concave utility function
<clausen> assume production technologies are convex
<clausen> etc.
<teralaser> ok
<teralaser> so, basically, the classic mathematical newtonian way > Assume some axioms, deduct something.
<pavlicek> I can see why there are philosophers of economics who object to the mathematization of the field. If
the 'pure math' is purely illustrative then it probably is little more than attempt to create a scientific veneer for
economics.
<teralaser> That's fair enough.
<clausen> pavlicek: "illustrative" ?
<teralaser> I guess economics like a few other non-classical sciences (say, psychology, sociology) has the basic
problem, that there is no such thing as repeatable experiments.
<clausen> reality is irrelevant to much of economics
<clausen> it's just reasoning about incentives and the like
<teralaser> aaaah... a bit strong statement there, I hope.
<teralaser> (being the nerdy engineer among us)
<clausen> I did qualify it
<clausen> ("MUCH of economics")
<clausen> experiments can inform which incentives should be modelled
<clausen> and can tell you which assumptions are not met in models
<clausen> so, experiments can tell you which theories are relevant to the real world
<clausen> but economic theory is "true" regardless
<clausen> experiments just tell you what is relevant and irrelevant
<clausen> I'm prepared to make that claim universally... there are no exceptions
<teralaser> huh... so you are basically claiming that economics are entirely in the realm same as math ,
completely abstract and thus always true (provided the axioms are)
<clausen> teralaser: economic theory is entirely maths, yes
<teralaser> as opposed to the realm of physics, which depends on empirical verification.
<clausen> right
<pavlicek> Heh, economics goes out of its way to point out that the axioms are manifestly false.
<clausen> pavlicek: agreed
<clausen> pavlicek: but it depends on the situation...
<clausen> pavlicek: pick the most relevant model at hand...
<teralaser> So, say, if Einstein's theory of E=mc2 can be disputed with an experiment, his theory to you would
still be "true" ?
<clausen> teralaser: yes
<clausen> teralaser: it would describe a possible world different to our own
<pavlicek> I think clausen is conflating truth and validity.
<clausen> pavlicek: yes, I am, and proud of it :)
<teralaser> But wouldn't be of quite interest , that Einsteins theory is not true, especially since someone might
base some policy on it ?
<clausen> pavlicek: validity => truth
<clausen> (trivial!)
<clausen> teralaser: right, einstein's theory would become irrelevant
<clausen> teralaser: and not worth studying
<teralaser> So experiment (or some equivalent empirical verification) out in the scary "real world" are of
interest to economics or what ?
<teralaser> experiments
<pavlicek> valdity != truth. validity truth = soundness.
<clausen> teralaser: yes, they are interesting
<clausen> pavlicek: ?
<pavlicek> General equilibrium theory is valid but unsound.
<clausen> I thought "soundness" was a property of a logical system
<clausen> not a predicate/proposition/whatever
<clausen> and validity is a property of a predicate/propostion
<pavlicek> Soundness is a property of inferences.
<clausen> pavlicek: really?
<pavlicek> Validity is a property of inferences.
<clausen> pavlicek: can you find me a reference for that?
<pavlicek> Truth is a property of propositions.
<pavlicek> I'm using the terms somewhat loosely to describe a theory.
<clausen> pavlicek: I don't think "truth" is used in logic at all
<clausen> ("consistent" is the politically correct term)
<clausen> hmmm, you are right about the distinction between truth and sound, btw
<clausen> sound => truth, but not vice versa
<pavlicek> Soundness is valid inference from true premises.
<pavlicek> An inference is valid or invalid regardless of the truth value of the premises.
<cabbage> hmmm
<pavlicek> An example: [[ (p -> q)
