INDUCTIVE AND DEDUCTIVE

Transcription

1 INDUCTIVE AND DEDUCTIVE Péter Érdi Henry R. Luce Professor Center for Complex Systems Studies Kalamazoo College, Michigan and Dept. Biophysics KFKI Research Institute for Particle and Nuclear Physics of the Hungarian Academy of Sciences, Budapest

2 Deductive arguments If the premises are true The conclusions must be true Though they are not always phrased in syllogistic form, deductive arguments can usually be phrased as syllogisms, or as brief, mathematical statements in which the premises lead to the conclusion. Deduction is truth preserving.... While studying to become a doctor, Doyle became greatly impressed by the ability of one of his professors, a surgeon, to use deductive reasoning to uncover information about patients. Doyle modeled Sherlock Holmes on this doctor, as well as on another professor who taught forensic medicine...

3 Inductive arguments Francis Bacon ( ) Sir Francis Bacon (later Lord Verulam and the Viscount St. Albans) was an English lawyer, statesman, essayist, historian, intellectual reformer, philosopher, and champion of modern science. Early in his career he claimed all knowledge as his province and afterwards dedicated himself to a wholesale revaluation and re-structuring of traditional learning. To take the place of the established tradition (a miscellany of Scholasticism, humanism, and natural magic), he proposed an entirely new system based on empirical and inductive principles and the active development of new arts and inventions,

4 a system whose ultimate goal would be the production of practical knowledge for the use and benefit of men and the relief of the human condition.

5 Inductive arguments If the premsies are true it is more likely to be true. But it is not guaranteed to be true. P1. There are heavy black clouds in the sky. P2. The humidity is very high. It will soon rain. - are never valid in the logician s sense of the term, because their premises do not entail their conclusion.

6 Newton Principia broke with (Francis Bacon s) purely inductive method used minimal experimental data everything was deduced from a few observation-based conclusions ( mathematical principles of philosophy ) Blake William: Isaac Newton

7 Principia Mathematica (Whitehead and Russell) was a big enterprise to deduce mathematics from logic. Even the whole program was finally not successful, in any case, it showed the power of deduction... I think Whitehead and Russell probably win the prize for the most notation-intensive nonmachine-generated piece of work that s ever been done... (S. Wolfram)

8 Vienna Circle IVC The Vienna Circle was a group of philosophers and scientists organized in Vienna under Moritz Schlick. They met weekly, for the most part, beginning in 1922 and ending in 1932, when Schlick was shot to death by an irate graduate student. Rudolf Carnap, Otto Neurath, Herbert Feigl etc.. Many members left Austria during the rise of the Nazi party, and the circle had dissolved by Their approach to philosophy came to be known as Logical Positivism.

9 logical positivism Logical positivism, (later referred to as logical empiricism): philosophy should aspire to the same sort of rigor as science -> it should be able to provide strict criteria for judging sentences true, false and meaningless. The most characteristic claim of logical positivism: statements are meaningful only insofar as they are verifiable statements can be verified only in two (exclusive) ways: (1) empirical statements, including scientific theories, which are verified by experiment and evidence (2) Analytic truth, statements which are true or false by definition, and so are also meaningful. Everything else, including ethics and aesthetics,is not literally meaningful, and so belonged to metaphysics. One conclusion is that Serious philosophy should no longer concern itself with metaphysics.

10 Karl Popper falsification inductive inference is unjustified growth of human knowledge: evolutionary epistemology Werner Horvath (Linz)

11 Cybernetics Bridge between the Natural and Artificial Organisms vs. Machines Control, Communication, Information The Macy Conferences ( ) Warren McCulloch; Experimental Epistemology Norbert Wiener; Cybernetics (Control and Communication in the Animal and Machine) John von Neumann: The Computer and the Brain (Principia Cybernetica:

12 Herbert Simon from mechanism to function (from Cybernetics to AI, from zeros and ones to general symbols) How do people make decisions? first AI program: Logic Theorist theorems from Principia Mathematica The Architecture of Complexity Bounded Rationality

13 Russell and Simon (... he wrote back that if we d told him this earlier, he and Whitehead could have saved ten years of their lives. He seemed amused, and I think, pleased.)

14 Inductive Reasoning and Bounded Rationality: from Herbert Simon to Brian Arthur Simon (1957): Boundend rationality better describes the behavior of economic agents than optimal rationality B. Arthur:rediscoveries? Studied the positive feedbacks or increasing returns in the economy in particular their role in magnifying small, random events. Inductive Reasoning and Bounded Rationality (Amer. Econ Review 1994) Popper s critic and Simon are not mentioned!! dominating paradigm in the discipline Economy as a Complex System

15 Minority Game The so-called Minority Game is simply a game with agents with partial information and bounded rationality. El Farol Bar Problem iterative game Those who happen to be in the minority win. (Hierarchical extension)

16 From Russell to B. Arthur A famous Bertrand Russell story cited by B. Arthur: A schoolboy, a parson and a mathematician are crossing from England into Scotland in a train. The schoolboy looks out and sees a black sheep and says, Oh! Look! Sheep in Scotland are black! The parson, who is learned, says, No. Strictly speaking, all we can say is there is one sheep in Scotland that is black. The mathematician says, No, still not correct. All we can really say is that we know that in Scotland there exists at least one sheep, at least one side of which is black.

17 Deductive arguments If the premises are true The conclusions must be true Inductive arguments If the premises are true it is more likely to be true. But it s not guaranteed to be true. P1. There are heavy black clouds in the sky. P2. The humidity is very high. Concl>: It will soon rain. logic Principia Mathematica Whitehead and Russel deduction mathematics paradox Vienna Circle : confirmation, verification Karl Popper: falsification, Inductive inference is unjustified Herbert Simon Human problem solving, symbol manipulation, AI, cognitive science, complexity Bounded rationality Newton s Prinicipa dynamics: position, velocity, motion Cybernetics Warren McCulloch, Norbert Wiener John von Neumann: The Computer and the Brain Brian Arthur Complexity and Economy Inductive reasoning and bounded rationality clockwork worldview