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
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..”.
Inductive arguments
Francis Bacon (1561-1626)
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,
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.
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.
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
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)
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 1936. Their approach
to philosophy came to be known as ”Logical Positivism.”
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.
Karl Popper
• falsification
• inductive inference is unjustified
• growth of human knowledge: evolutionary epistemology
Werner Horvath (Linz)
Cybernetics
Bridge between the Natural and Artificial
Organisms vs. Machines
• Control, Communication, Information
• The Macy Conferences (1946-1953)
• 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: http://pcp.lanl.gov/
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
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.)
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”
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)
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.”
Deductive arguments
Inductive arguments
If the premises are true
The conclusions must be true
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.
Principia Mathematica
Vienna Circle : confirmation, verification
Whitehead and Russel
Karl Popper: falsification,
logic
deduction
mathematics
Inductive inference is unjustified
paradox
Herbert Simon
Human problem solving , symbol manipulation, AI, cognitive science,
complexity
Cybernetics
Newton’s Prinicipa
Warren McCulloch, Norbert Wiener
dynamics:
position, velocity, motion
John von Neumann: The Computer and the Brain
clockwork worldview
Bounded rationality
Brian Arthur
Complexity and Economy
Inductive reasoning and bounded rationality