This document discusses two approaches to analogical inference: the formal approach and the material approach. The formal approach views analogical inference through formal rules, while the material approach sees it as licensed by facts in specific domains. The document examines several case studies of analogical reasoning in science and argues they are best understood through the material approach. It concludes that analogical inference is powered by local warranting facts rather than a universal principle of similarity.
1. Analogy
John D. Norton
Department of History and Philosophy of Science
Center for Philosophy of Science
University of Pittsburgh
Seven Pines XVI May 2012
4. Bare Analogy
4
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.
…
5. Doubts
5
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
6. Two-Dimensional Account
6
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
infer
When the weight of the
positive analogy prevails…
7. ?? No formal
analogies??
?? The cogency of
the account depends
on the cogency of
our account of
causation. ??
Two-Dimensional Account
7
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:
8. The Articulation Model
8
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 correspondence
c. existence of multiple
favorable analogs
d. only non-defeating
competing analogs
e. only non-defeating
counteracting causes
inductive or
deductive
inductive
Vertical relations:
1. Predictive
2. Explanatory
3. Functional
4. Correlative.
10. Philosophers
10
Analogy is a part of the
theory 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
11. 11
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.
12. ~B
A
A B
12
Deductive inference: the model for a
formal theory
Either
Therefore
The mome
raths were
NOT
outgrabe.
All mimsy
were the
borogroves.
or
The mome
raths were
outgrabe.
All mimsy
were the
borogroves.
13. All the inductive risk is
taken in accepting the
material postulate.
Drop the generally and the
inference becomes deductive.
Demonstrative induction.
13
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.
14. Material Theory of Induction applied to Analogy
14
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.
15. Case Studies
15
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.
