Abduction and Inference to the Best Explanation Philosophy department, Shandong University WANG Huaping

Abduction and Inference to the Best

Explanation

Philosophy department, Shandong University

WANG Huaping

Content

Cases2

Abduction & IBE31

Problems33

Task4

Basic Types of Inferences: Deduction

Deduction: Derive a conclusion from given axioms (“knowledge”) and facts (“observations”).

Example:

All humans are mortal. (axiom)Socrates is a human. (fact/premise)

Therefore, Socrates is mortal. (conclusion)

The conclusion can be derived by applying the modus ponens inference rule (Aristotelian logic).

Theorem proving is based on deductive reasoning techniques.

WANG Huaping Shandong University Scientific Research Methodology 2011

Basic Types of Inferences: Induction

Induction: Derive a general rule (axiom) from background knowledge and observations.

Example:

Socrates is a human (background knowledge)

Socrates is mortal (observation/ example)

Therefore, I hypothesize that all humans are mortal (generalization)

Remarks: Induction means to infer generalized knowledge from

example observations: Induction is the inference mechanism for learning.


Basic Types of Inferences: Abduction

Abduction: From a known axiom (theory) and some observation, derive a premise.

Example:

Socrates is mortal (observation)All humans are mortal (theory)

Therefore, Socrates must have been a human (explanation)

Remarks: Abduction is typical for explanation.

If one has the flue, one has moderate fewer. Patient X has moderate fewer. Therefore, he has the flue.

Strong relation to causationWANG Huaping Shandong University Scientific Research Methodology 2011

Basic Types of Inferences



Abduction has the structure, if p then q, q therefore p. This is deductively invalid because it is possible for the conclusion to be false when the premises are both true. The fallacy is called affirming the consequent.

Nevertheless, it is hard to see how we could get by without such abductive inference. For example, we infer that it has rained from the fact that the road is wet. This inference is abduction.



The term “abduction” was coined by Charles Sanders Peirce in his work on the logic of science.

Abduction can be thought of as consisting of three steps. First, identify a phenomenon that requires explanation. Second, generate theories that would explain the phenomenon. Third, choose the theory that best explains the phenomenon. Abduction, then, involves three main elements: the phenomenon to be explained (i.e. the explanandum), the competing theories qua explanations (i.e. the potential explanans), and the principles for ranking theories.



Explanans: Explanans are theories. A theory explains a phenomenon by showing why it is as it is. A theory can explain why an event occurs, for example, by subsuming it under a law. Accordingly, a physician can explain why Lindsay catches a cold by theorizing that she was exposed to a virus, which yields a high probability of catching a cold. To see that the physician’s theory explains the phenomenon in an intuitive sense of “explain”, note that the theory should satisfy a parent who asks, “Why did my daughter catch a cold?”



The ranking. As Harman (1965) suggests, several considerations help to determine the ranking of theories, including, among many others, simplicity and comprehensiveness. Such considerations can be thought of as (non-demonstrative) inferential principles. Although the principles require specification, the idea is banal: ceteris paribus a simple explanation beats a complex explanation, a comprehensive explanation beats a narrow explanation, and so on.



When the underlying principles converge, the abduction is simple, establishing whichever claim the principles support. When the underlying principles diverge, however, they must be balanced. Abduction, then, can be thought of as a two-step process. First, one determines how each principle ranks competing theories. Second, one balances the principles in order to produce a final ranking.


What is IBE?

A pattern of inductive inferenceGeneral template:

Evidence e is the case. h best explains e. Therefore, h is (probably) true.

Inference to the Best Explanation

Facts e1, …, en are in need of explanation.

Among the hypotheses h1, …, hm that potentially explain e1, …, en, hi is the “loveliest”, i.e., optimizes the “theoretical virtues.”

So, hi is (probably) true. Theoretical virtues = consilience, simplicity,

analogy, conservatism, consistency, empirical adequacy, …?



IBE is supposed to be a rule of inference according to which, where we have a range of competing hypotheses, and all of which are empirically adequate to the phenomena in some domain, we should infer the truth of the hypothesis that gives us the best explanation of those phenomena. Gilbert Harman introduced the term ‘Inference to the best explanation’ in an article of that name in the Philosophical Review in 1965.

We usually use IBE in everyday life.



For example, you ring your friend’s doorbell and there is no answer. The following hypotheses all predict this:

(1) Your friend has become paranoid and thinks that enemy agents are ringing the bell.

(2) Your friend has suddenly gone deaf.

(3) Your friend has been pretending to live there, but in fact lives somewhere else.

(4) Your friend is out.

Normally we would infer (4) was correct because it offers a simple explanation of the data that coheres with our other beliefs.


Case 1

It was discovered that the orbit of Uranus, one of the seven planets known at the time, departed from the orbit as predicted on the basis of Isaac Newton's theory of universal gravitation and the auxiliary assumption that there were no further planets in the solar system.

One possible explanation was, of course, that Newton’s theory is false. Given its great empirical successes for (then) more than two centuries, that did not appear to be a very good explanation.


Case 1

Two astronomers, John Couch Adams and Urbain Leverrier, instead suggested (independently of each other but almost simultaneously) that there was an eighth, as yet undiscovered planet in the solar system; that, they thought, provided the best explanation of Uranus' deviating orbit.

Not much later, this planet, which is now known as “Neptune”, was discovered.


Ernest Rutherford (1871-1937)

Learned physics in J. J. Thomson’ lab.

Case 2


In 1909 Rutherford undertook a series of experiments He fired particles at a very thin sample of gold foil According to the Thomson model the particles would only be

slightly deflected Rutherford discovered that they were deflected through large

angles and could even be reflected straight back to the source

particlesource

Lead collimator Gold foil

Case 2

beam of alpha particles

radioactive substance

gold foil

circular ZnS - coated

fluorescent screen

Case 2


Rutherford’s Apparatus

Dorin, Demmin, Gabel, Chemistry The Study of Matter , 3rd Edition, 1990, page 120

beam of alpha particles

radioactive substance

fluorescent screencircular - ZnS coated

gold foil


Speaker gives“click” for

each particle

Window

Particlepath

Argon atoms

Case 2


Lead block

Polonium

Gold Foil

Florescent Screen

Case 2


What Expected The alpha particles to pass through

without changing direction (very much) Because The positive charges were spread out

evenly. Alone they were not enough to stop the alpha particles

Case 2


What expected…


Because the mass was evenly distributed in the atom.

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What got…


The Predicted Result:

expected path

expected marks on screen

mark onscreen

likely alphaparticle path

Observed Result:

Case 2


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gold foil

deflected particle

undeflected particles

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.beam ofalpha particles

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Case 2

Rutherford interpreted this result by suggesting that the particles interacted with very small and heavy particles

Particle bounces off of atom?

Particle attracts to atom?

Particle goes through atom?

Particle path is alteredas it passes through atom?

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Case A

Case B

Case C

Case D


Case 2

alpha rays don’t diffract

alpha rays deflect towards a negatively charged plate and away from a positively charged plate

alpha rays are deflected only slightly by an electric field; a cathode ray passing through the same field is deflected strongly

... alpha radiation is a stream of particles

... alpha particles have a positive charge

... alpha particles either have much lower charge or much greater mass than electrons

observation hypothesis


Case 2

Plum-pudding atom

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Alpha particles

Nuclear atom

Nucleus

Thomson’s model Rutherford’s model


Case 2

Results of foil experiment if plum-pudding had been correct.

Electrons scatteredthroughout positive

charges

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Conclusions:

Atom is mostly empty space

Nucleus has (+) charge

Electrons float around nucleus


Case 2

The Rutherford Atom

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This is the modern atom model.

Electrons are in constant motion around the nucleus, protons and neutrons jiggle within the nucleus, and quarks jiggle within the protons and neutrons. This picture is quite distorted. If we drew the atom to scale and made protons and neutrons a centimeter in diameter, then the electrons and quarks would be less than the diameter of a hair and the entire atom's diameter would be greater than the length of thirty football fields! 99.999999999999% of an atom's volume is just empty space!


Case 2

Problems

What is an explanation? Are consilience, simplicity, and analogy

the only theoretical virtues? Are a theory’s explanatory abilities the

most important criteria? What about prediction and control? More to come!


Problems

Noncausal explanations: History of science,

nonscientific practice have many noncausal

explanations.

Bad Lots: Suppose we infer only from the

pool of potential explanations that we take

seriously. How will we ever know that the

best explanation in this pool isn’t the best of

a bad lot?


Problems

Psychologically impossible:

Potential explanation of e = any causal account of why e happened; true or otherwise

Thus pool of potential explanations of e = h1,…, hm, then m = ∞.

This would it psychologically intractable to infer the best explanation.


Problems

Unborn hypotheses

There are many more explanations that we never think of—”unborn hypotheses”—than that we take seriously. The best explanation is a random member of this much larger class of explanations.Therefore, the best explanation is very unlikely.


Task

Please give an example of

abductive inference in every

life or scientific research.


Documents

Abduction and Inference to the Best Explanation Philosophy department, Shandong University WANG Huaping