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Revision as of 22:41, 4 January 2007
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) & p ]] -> q (modus ponens) is valid; if p is true, it's also sound.
<pavlicek> Make that, if [[ (p -> q) & p ]] is true, it's also sound.
<clausen> economics has no premises
<clausen> (nor does maths)
<cabbage> to me an inference is a deduction ie. conclusion drawn from firt principle or law apprehended in the
mind (apriori) OR an inference is induced from the particular to a conclusion
<clausen> it's all of the form (A => B)
<teralaser> sure it does, there was the famous set theory premise breakdown
<cabbage> a posterori ... ie. after experience
<pavlicek> I would call economics' first principles postulates.
<teralaser> (is axioms also a premise ? )
<clausen> teralaser: that research was all valid/true though
<clausen> yeah, axioms is what we mean
<teralaser> no it wasn't
<clausen> you can always substitute axioms for requirements in a theorem
<clausen> teralaser: it was just vacuous
<teralaser> it did break down, because an axiom didn't hold.
<clausen> it's still possible to have sound systems in which axioms don't hold
<teralaser> No
<clausen> well, you can just remove the axiom
<pavlicek> You mean valid systems.
<clausen> and add it into your propositions
<pavlicek> If the axioms fail to hold, the system is unsound.
<clausen> pavlicek: agreed
<clausen> pavlicek: but you can still transform it all trivially
<clausen> like, you can get by without any axioms
<clausen> axioms are merely a convenience
<clausen> so you don't have to write "a, b, c, d => e" all the time
<clausen> just make a,b,c axioms
<teralaser> if your axioms doesn't hold, a paradox might arise in your theory rendering it invalid.
<clausen> teralaser: I'm just saying, all of maths can be interpreted as having no axioms
<pavlicek> I'd describe a theory logically as: (axiom1 & axiom2 & ... axiomN) -> (theorem1 & theorem2 & ...
theoremK). If the axioms are false, the theorems are nonetheless proven.
<clausen> but, you end up with counterfactuals, like you say
<clausen> pavlicek: you can always rewrite the theorem so there is no axiom required
<teralaser> hm.
<clausen> (I could be wrong about all of this, of course, because I haven't studied logic properly)
<pavlicek> My own study of logic is fairly limited.
<cabbage> an axiom is only an axiom in so far as one is prepared to look
<clausen> but, to my knowledge, there is nothing special about axioms
<teralaser> Well, one axiom for natural number are, for two number a and b, there exists a third such that a+b=c
<teralaser> how will you go around not having that ?
<clausen> they are just like "subroutines" in programming languages
<pavlicek> Axioms are simply true statements unprovable in terms of other axioms, iirc.
<clausen> teralaser: well, whenever you want to prove a theorem
<clausen> teralaser: you include that requirement as one of the conditions for the theorem being true
<clausen> pavlicek: which isn't very special
<teralaser> pavlicek : Right.
<clausen> pavlicek: they aren't really very important
<pavlicek> Well, such a notion of axioms doesn't require them to be assumptions or metaphysical truths or first
principles or whatever. They need only be true and unprovable. You need a metatheory of some sort to justify their
presence in the first place.
<teralaser> if there was such two numbers a and b , but no number c such that c = a + b, I'd say it would be
pretty important.
<teralaser> for the rest of your theorem
<clausen> I'm just saying that a logical system with aximos a1,...an in which a theorem t1 is true
<clausen> you can create another system with no axioms
<clausen> and then the theorem "(a1, ..., an) -> t1" is true in that system
<clausen> it's a totally trivial concept
* clausen has lunch
<teralaser> ok
Should economics stand the test of time or could it ?
<pavlicek> Suffice it to say that counterfactual economic theories do considerable damage to economics' claim to being a science. * teralaser is confused. <teralaser> Indeed. <teralaser> And thus, it is bad for economic theory not to be interested in reality. <clausen> it is interested in reality <clausen> well, the people are <clausen> that's why we have empirical people telling us what is relevant and irrelevant <clausen> the theory is motivated by reality <clausen> but is independent from it <pavlicek> It purports to be interested in reality the way a mechanical model that discounts friction is interested in reality. <teralaser> I agree there. <clausen> pavlicek: to be honest, I think science is exactly the same <teralaser> But perhaps somehow the crux of weeding out those conflicting economical theories are to make some kind of empirical verification, that can stand the test of time (in physics that would be repeatability) <clausen> the mathematical theory is 100% independent (logically) <clausen> but is entirely motivated, and compared with reality <clausen> it's the same with economics <pavlicek> When I call economics applied mathematics I still expect it to make use of measurement at some point. <clausen> teralaser: as technology changes, the reality on which economics rests changes <clausen> teralaser: it will never stand the test of time <clausen> pavlicek: it does... it's called econometrics ;) <teralaser> Well, in science you can find papers that are 200 years old and still true 100% <clausen> (unless there is a general economics theory) <clausen> teralaser: that's because the nature of atoms doesn't change over time <teralaser> (well , physics not science) <pavlicek> Scarcity is probably a timeless, universal economic law. <teralaser> but isn't that a bogus argument ? <teralaser> yeah, what pav said. <clausen> well, economics has no "general" models <teralaser> Hell , even astrophysics seems to be governed by some economical set of laws. <clausen> the best you can get is "general equilibrium" I guess <pavlicek> Scarcity is pretty close to a universal first principle, though. <clausen> (rational expectations equilibrium?) <clausen> anyway, asymmetric information is something that could change markedly <teralaser> or evolution of species. <clausen> which would have massive implications for institutions <clausen> anyway, I really should be spending this energy writing my report <clausen> it's just too tempting having this window open! <teralaser> hehehe <clausen> bye! <teralaser> Yeah, and I should have finished my program. End of #economics buffer Sun Feb 20 03:47:05 2005
