Analogy

John D. NortonDepartment of History and Philosophy of ScienceCenter for Philosophy of ScienceUniversity of Pittsburgh

Seven Pines XVI May 2012

Background Puzzle

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What powers

analogical inference?

Things similar in some properties.

Things similar in other properties.

Is there a “Principle of Similarity” in nature?

This talktwo approaches to analogical inference

Formalthe majority view

Materiala minority view

Formal Approach to Inductive Inference

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Bare Analogy

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S1 is P.S2 resembles S1 in being M.----------------------------------[therefore] S2 is P. (Joyce, 1936)

A fixture in traditional accounts of logic back to Aristotle.

Successes

Galileo and the mountains of the moon.

Electrostatics and gravity in the 18th c.

Darwin and artificial and natural selection.…

Reynolds’ analogy.Liquid drop model of the nucleus.…

Failures

Seas on the moon have no water.

Canals of Mars aren’t.

Whales are like fish but aren’t.

Heat flows like a fluid but isn’t.

Light undulates like waves in a medium, but hasn’t got one.…

Doubts

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There is no way in which we can really assure ourselves that we are arguing safely by analogy. The only rule that can be given is this, that the more closely two things resemble each other, the more likely it is that they are the same in other respects, especially in points closely connected with those observed . … In order to be clear about our conclusions, we ought in fact never to rest satisfied with mere analogy, but ought to try to discover the general laws governing the case.William Stanley Jevons, 1879.

Merely bad luck for a good inference form? Or…

Even the most successful analogies in the history of science break down at some point. Analogies are a valuable guide as to what facts we may expect, but are never final evidence as to what we shall discover. A guide whose reliability is certain to give out at some point must obviously be accepted with caution. We can never feel certain of a conclusion which rests only on analogy, and we must always look for more direct proof. Also we must examine all our methods of thought carefully, because thinking by analogy is much more extensive than many of us are inclined to suppose.Thouless, Straight and Crooked Thinking

Two-Dimensional Account

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Source Target

Property P Property P*

Property A Property not-A*

Mary B. Hesse, Models and Analogies in Science. (1966)

Property not-B Property B*

Property Q Property Q*

Bartha’s synopsis

Positive Analogy

Negative Analogy

inferWhen the weight of the positive analogy prevails…

?? No formal

analogies??

?? The cogency of the account depends on the cogency of our account of

causation. ??

Two-Dimensional Account

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Source Target

Property P Property P*

Property A Property not-A*

Mary B. Hesse, Models and Analogies in Science. (1966)

Property not-B Property B*

Property Q Property Q*

Vertical relations:“causal relations in

some acceptable scientific sense…”

NO: Formal analogies = isomorphic interpretations of

the same formal theory

YES: Pre-theoretic material analogies between observables

Horizontal relations:

The Articulation Model

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Source Target

Property P Property P*

Property A Property not-A*

Paul Bartha, By Parallel Reasoning: The Construction and Evaluation of Analogical Arguments. (2010)

Property not-B Property B*

Property Q Property Q*is plausible.

I. Prior association:Vertical relation to be extended to target.

II. Potential for Generalization:“no compelling reason” precludes extension.

Assessment extended through multistage process:prima facie plausibility, qualitative plausibility…

determinants of plausibility

a. strength of prior association

b. extent of correspondencec. existence of multiple

favorable analogsd. only non-defeating

competing analogse. only non-defeating

counteracting causes

inductive or deductive

inductive

Vertical relations:1. Predictive2. Explanatory3. Functional4. Correlative.

MaterialApproach to Inductive Inference

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Philosophers

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Analogy is a part of thetheory of inference.It is investigated by seeking general formal rules.

…but no complete formal scheme has been found.

…so what has inference got to do with analogy?

Analogies are facts of nature. They are uncovered by empirical investigation.

Scientists

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Formal Theory of Induction

Inductive inferences are licensed by formal

schema.

versus Material Theory of Induction

Inductive inferences are licensed by facts: "material postulate".

Universal.Any substitution yields a

valid inference.

Local.The material postulate holds only in limited domains.

"All induction is local."

The warrant for any inductive inference is traced back to material facts and no farther.

The warrant for any inductive inference is traced back to

universal schema.

~B

A

A B

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Deductive inference: the model for a formal theory

Either

Therefore

The mome raths were NOT outgrabe.

All mimsy were the borogroves.

orThe mome raths were outgrabe.

All mimsy were the borogroves.

All the inductive risk is taken in accepting the material postulate.

Drop the generally and the inference becomes deductive.Demonstrative induction.

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This formal template does not work.

Inductive inference

This crystal of radium chloride is monoclinic.

All crystals of radium chloride are less than 1mm in size.

This crystal of radium chloride is less than 1mm in size.

All crystals of radium chloride are monoclinic.

A poor inference.A good inference.

Material postulate: pure crystalline substances generally agree in their crystalline forms.

No material postulate licenses it.

Material Theory of Induction applied to Analogy

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Warranting fact is the fact of analogy investigated by the scientist.

Analogical inference is powered by local facts, peculiar to each instance.

Continued quest for a formal schema will return incomplete systems of endlessly growing complexity.

There is no universal schema to which all analogical inference conforms.

Fact of analogy uses similarity as an expressive convenience for describing properties of target system.

Analogical inference is not powered by similarity.No principle of similarity.

Strength of an analogical inference is not gauged by checking against rules.

Strength is set by content of warranting fact and gauged by empirically checking the fact.

Case Studies

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All three turn out to be demonstrative inductions! Inductive risk taken in accepting fact of analogy.

Galileo and the mountains of the moon

Fact of analogy Inference

Reynolds analogy

The mechanism of momentum and heat transfer the same.Rates are proportional.Stanton = friction factor/8

From rates of momentum transport (pressure drop) to rates of heat transport.

Liquid drop model of the nucleus

Energy term in(nucleon number)2/3.Excitation modes match classical liquid drop.

Which nuclei are stable. (OK)

Energy of nuclear excitations. (poor)

Darknesses on moon due to prominences obstructing linearly propagating sunlight, similar to shadows on earth.

There are mountains and valleys on the moon.The mountains are up to 4 miles high.

The End

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