Constructive mathematics and agent-based modeling.
Though I suspect that its not only me who saw similarities between the philosophy of the two, I still find it valuable to write some sentences about this issue here.
For one example Leigh Tesfatsion does explicitly refer to constructivism in the philosophy of Mathematics in his Handbook chapter (CHAPTER 16. AGENT-BASED COMPUTATIONAL ECONOMICS:A CONSTRUCTIVE APPROACH TO ECONOMIC THEORY). He highlights that in constructivist circles one have to have an actual construction of a mathematical object if it is to be said to exist. Furthermore he mentions that proofs can be understood as computer programs in constructivist terms. And this is the line of symmetry between philosophies of mathematics and economics.
The symmetry may seem accidental but it may be not. Computational interpretation of constructive mathematics is most famously developed by Kurt Gödel, that became known as the Dialectica interpretation of constructive mathematics. Before that the notion of mathematical construction was somewhat obscure (that is a philosophical notion). Gödel managed to give a precise mathematical description of constructions with the help of recursive functionals. And recursive functions are computer programs, as defenders of functional programming paradigm like to say.
So I'm about to argue that as in the history of constructive mathematics a human cognitive notion (mathematical construction) was made more and more precise mathematically, the same process can be observed in economics, where human rational behavior is being explained with computer programs (that are precise formal entities with definite properties).
Constructive mathematics is usually disdained by mathematicians working in the classical paradigm (as something unusable) and in the same manner ACE is being overlooked by classical economists. On the other hand development of computer science showed how important and insightful discipline is the constructivist theory of mathematics, and I expect that development of multi-agent systems will display similar success for ACE.
Though I suspect that its not only me who saw similarities between the philosophy of the two, I still find it valuable to write some sentences about this issue here.
For one example Leigh Tesfatsion does explicitly refer to constructivism in the philosophy of Mathematics in his Handbook chapter (CHAPTER 16. AGENT-BASED COMPUTATIONAL ECONOMICS:A CONSTRUCTIVE APPROACH TO ECONOMIC THEORY). He highlights that in constructivist circles one have to have an actual construction of a mathematical object if it is to be said to exist. Furthermore he mentions that proofs can be understood as computer programs in constructivist terms. And this is the line of symmetry between philosophies of mathematics and economics.
The symmetry may seem accidental but it may be not. Computational interpretation of constructive mathematics is most famously developed by Kurt Gödel, that became known as the Dialectica interpretation of constructive mathematics. Before that the notion of mathematical construction was somewhat obscure (that is a philosophical notion). Gödel managed to give a precise mathematical description of constructions with the help of recursive functionals. And recursive functions are computer programs, as defenders of functional programming paradigm like to say.
So I'm about to argue that as in the history of constructive mathematics a human cognitive notion (mathematical construction) was made more and more precise mathematically, the same process can be observed in economics, where human rational behavior is being explained with computer programs (that are precise formal entities with definite properties).
Constructive mathematics is usually disdained by mathematicians working in the classical paradigm (as something unusable) and in the same manner ACE is being overlooked by classical economists. On the other hand development of computer science showed how important and insightful discipline is the constructivist theory of mathematics, and I expect that development of multi-agent systems will display similar success for ACE.
posted by fagyuri at 2:45 PM
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