Why are Good Theorys Good- Review

WHY ARE GOOD THEORIES GOOD ?

REFLECTIONS ON EPISTEMIC VALUES , CONFIRMATION, AND FORMAL EPISTEMOLOGY

Sinu G S

Student MICS

Selected Topics in Artificial Intelligence

University of Luxembourg

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THEME OF PAPER

This paper discusses about

Comparison of Theory of Confirmation and Theory of Verisimilitude or Truthlikeness.

Connection between Logic of Confirmation with Logic of Acceptability

Connection of Confirmation Theory with Naturalism,Intertheoretic Reduction and Explanation.

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AGENDA OF PRESENTATION

Introduction Approaches of Confirmation Problems in Confirmation Huber’s Theory of Confirmation Confirmation and Truthlikeness Many Senses of Confirmation Naturalism and Bayesian Tinkering Belief Framework for modeling realistic

cognitive agents (Research Assistant Systems)

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INTRODUCTION

Epistemology Theory of Knowledge and justified belief

Theories and Evidence Theory Real World Data(Evidence) Predictions

Confirmation

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APPROACHES OF CONFIRMATION

Inductive Logic

Induction proceeds from the specific case to the general case: “probable inference”

All swans we have seen have been white; therefore all swans are white.

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INDUCTIVE LOGIC METHOD

Initial observation

New observations

Prediction

hypothesis

Do new observations match

predictions?

“Accepted truth”

suggestsgenerates experiments and data

NO, modify hypothesis

YES, confirm hypothesis

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APPROACHES OF CONFIRMATION

Deductive Logic

Deduction proceeds from the general case to the specific case: “certain inference”

For every action, there is an opposite and equal reaction. This rifle will recoil when it is fired.

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HYPOTHETIC-DEDUCTIVE LOGIC METHOD

Initial observation

New observations

Prediction A

hypothesis

Do new observations match

predictions?“Accepted

truth”

suggests

NO, falsify hypothesis

YES, repeat attempts to falsify

hypothesis hypothesis hypothesis

Prediction B Prediction CPrediction D

Multiple failed falsifications

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PROBLEMS OF CONFIRMATION

What makes an observation count as evidence ?

This piece of copper conducts electricity This confirms (increases the credibility of)

Hypothesis “All pieces of copper conduct electricity”

Law Like Hypothesis

This man performs scientific experiments This confirms(increases the plausibility) of

idea all man perform scientific experiments Accidental Hypothesis

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How do observations confirm a scientific theory ? You can know only what you observed and you

have never observed a “Law of Nature” Russell’s Chicken Story

Moral of the story: You cannot always induce the truth from past experience!

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Raven’s Paradox

P1 : All ravens are black. P2 : Everything that is not black is not a

raven

E1 : This raven, is black. E2 : This red (and thus not black) thing is an

apple (and thus not a raven).

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Moral of Raven’s Paradox Theory of Confirmation

“With in certain limits,what is the true of evidence statements is true of the whole ‘universe of discourse’ Evidences may depends on Context.

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A logical consequence of any theory T is T or S.

“Earth is center of solar system or I am 23 years old”

I am actually 23 years old. This means Earth is center of Solar System

(Logical Sequence of I am 23 years old ) is confirmed by observing ‘ I am 23 years old’

Can nature of solar system be confirmed by my age ?

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HUBER’S THEORY OF CONFIRMATION

Problem of Theory of Theory Assessment

How we compare and evaluate theories in the light of available evidence?

Given Hypothesis or Theory H Set of data,the Evidence E Some Background information B

How good is H given B ? What is the value of H in view of E and B ?

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Qualitative Theory of Hypothetico-Deductivism

(H&B) E Aims at informative theories

Quantitative Theory of probablistic inductive logic

P(H|E&B)>=r , r (.5,1) Aims at plausible or true theories

Increasing Function of Logical Strength of Theory

Decreasing Function of Logical Strength of Theory

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Conflicting Concepts of Confirmation Informativeness If E confirms H and H0 logically implies H, then

E confirms H0 . E |∼ H, H0 H ⇒ E |∼ H0.

Plausibility If E confirms H and H logically implies H0, then

E confirms H0. E |∼ H, H H0 ⇒ E |∼ H0

A good theory is true & informative

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2 virtues a good theory

Truth (or ‘plausibility’) Strength (or ‘informativeness’)

f (H, E, B) Epistemic value of Hypothesis

If E entails H → H’, then f (H, E) ≤ f (H’, E) If ￢ E entails H’ → H, then f (H, E) ≤ f (H’, E) f (H, E) = p (H, E) + p (¬H,¬E)

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CONFIRMATION AND TRUTHLIKENESS

Knowledge Justified True Belief

Belief An Idea Some one has about the world

True Corresponds with facts Justified Not just a coincidence

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Karl Popper’s view Belief

What if every one lost all their beliefs about engineering

Justified Circular Argument

Why A ? Because B Why B ? Because A

Criticise Beliefs,Don’t Justify them Knowledge is useful truth.

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Acceptable theories

Not Only High degree of confirmation But Also Capacity of explaining or predicting the

empirical evidence

Epistemic value of a theory depends on two factors

Coherence or Similarity between H and E How Informative our Empirical Evidence is ?

Vs (H, E) = [p (H&E) /p (HvE)] [1/p (E)] = p (H, E) /p (HvE)

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H is more verisimilar than H’

High Similarity High Informative

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Properties of Empirical Verisimilitude

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Properties of Empirical Verisimilitude

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MANY SENSES OF CONFIRMATION

Acceptance of Theory H can be ‘acceptable’ in the sense that the

community allows that individual scientists accept H

H can be ‘acceptable’ in the sense that the community commands its members to accept it

What makes theory so good that it is legitimate to accept it ?

What makes theory so good that it is compulsory to accept it ?

Mostly Confirmed

Best one confirmed

Alternative Theorems

Certified Knowledge

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MANY SENSES OF CONFIRMATION

X ,the set of all possible mutually exclusive sets of consequences that the choice of a demarcation level β will have for scientist i, then,the optimal choice for that scientist will correspond to:

pi(x,b) is obviously the probability with which i judges that the choice of b will lead to consequences x,

ui(x) is the utility that i would experiment under x.

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NATURALISM AND BAYESIAN TINKERING

Problem of theory evaluation’ is not a ‘philosophical’ problem, but a problem for the communities of flesh-and-bone scientists

Inter Theoretical Reduction increases epistemic values

Showing that a theory can be reducible to another increases the verisimilitude of both theories

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EXPLANATORINESS AND CONFIRMATION

A Theory H explains the facts F for the scientific community C if and only if F can be derived from H by C, and the members of C understand H, i.e., if H is ‘intelligible’ for them

Coeteris paribus, if X is easier to understand than Y, then p(Y) < p(X).

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CONCEPTUAL BELIEF FRAMEWORK (RESEARCH ASSISTANT SYSTEMS)

Background

Knowledge

Informativeness

Truthfulness

Acceptability

Hypothetico Deductive

Supportability

Inductive Supportability

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Evidence

Informativeness

Truthfulness

Acceptability

Relativism

Totality(among set of enclosure)

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Theory

Informativeness

Truthfulness

Acceptability Relativism

Supportability

Reducibility

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Queries and Suggestions

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Why are Good Theorys Good- Review

Education

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