Inference to the Best Explanation (IBE)

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Inference to the Best Explanation (IBE)

• Kareem Khalifa
• Department of Philosophy
• Middlebury College

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Overview

• Description of IBE
• Theoretical virtues elaborated
• Comparison of IBE with Hypothetico-Deductivism
• Comparison of IBE with Popperian Falsificationism
• Brief discussion of IBEs weaknesses
• To be continued

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What is IBE?

• A pattern of inductive inference
• General template
• Evidence e is the case.
• h best explains e.
• Therefore, h is (probably) true.

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A slightly more precise template

• 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, ?

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IBE (Explanationist) confirmation

• Hypothesis h is confirmed by evidence e if and
  only if h is the loveliest explanation of e.
• Most natural to think of this in historical
  terms, i.e., h is confirmed by e at time t if and
  only if h is the loveliest explanation of e at t.

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Theoretical virtues elaborated consilience

• Consilience how much a theory explains
• Explanatory power
• A theory T1 is more consilient than T2 if and
  only if either
• T1 explains more classes of facts than T2 or
• T1 explains every class of facts that T2
  explains, but not vice versa.
• A class of facts a set of statements deemed by
  a scientific community in a given historical
  epoch to be a single phenomenon in need of
  explanation (Thagard 1978)

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Theoretical virtues elaborated simplicity

• TheoryT1 is simpler than T2 if and only if T1
  assumes fewer auxiliary hypotheses than T2
• An auxiliary (ad hoc) hypothesis a hypothesis
  that serves to explain no more than the narrow
  range of phenomena for which it was originally
  intended to explain.
• What counts as ad hoc depends on the assumptions
  of the scientific community

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Theoretical virtues elaboratedanalogy

• If hypothesis h1 is similar to hypothesis h2, and
  the evidence e1 explained by h1 is similar to the
  evidence e2 explained by h2, then all four
  propositions support each other.

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Example of explanatory analogyDarwin
Traits are naturally selected by eliminating
animals with traits not conducive to survival
from reproducing.
Traits are artificially selected by encouraging
animals with desirable traits to reproduce.
Wild animals have traits that are well-suited to
survival.
Domesticated animals have traits that are
well-suited to their breeders needs.
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IBE vs. HD

• Reminder HDs Problems
• Demarcation
• Induction
• Underdetermination
• Disjoined Hypotheses
• Raven Paradox

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Demarcation

• IBEs in both science and everyday practice
• So, there is no difference in kind between
  scientific and non-scientific reasoning only
  difference in degree

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Underdetermination

• Underdetermination of theory by data Many
  hypotheses can entail the same set of data (such
  hypotheses are empirically equivalent)
• However, not all of them provide equally good
  (consilient, simple, analogous) explanations of
  that data

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Disjoined Evidence

• If h entails e, then h entails e or f. Suppose
  that f is true and e is false, then e or f still
  confirms h
• However, it is not the case that if h explains e,
  h explains e or f.
• Ex. Joness perfect pitch explains how he can be
  a great musician, but not how he can be a great
  musician or a great fisherman.

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Raven Paradox

• Hypothesis All ravens are black.
• This is logically equivalent to All non-black
  things are non-ravens.
• A green shoe is a non-black non-raven.
• Thus a green shoe confirms the hypothesis that
  all ravens are black. ABSURD!
• However, on IBE, the green shoe isnt explained
  by all ravens being black, and thus doesnt
  confirm that hypothesis.

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IBE vs. PF

• Reminder PF is flawed with respect to
• Accurately describing scientific practice
• Holism (the complexity of scientific testing)
• Conjoined hypotheses
• Grue problem
• Inductions role in decision

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IBE on scientific practice

• (Thagard 1978) Lavoisier, Darwin, Huygens,
  Fresnel, etc.
• (Thagard 1992) ECHO
• Successful computer simulations of IBE with
  respect to Copernicus, Newton, Lavoisier,
  Darwin, Plate tectonics, Einstein, Quantum
  mechanics

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IBE on Holism

• Explanatory coherence theory a hypothesis is
  justified if it produces the most theoretically
  virtuous theory

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Example of Explanatory Coherence
Mr. Smith is dead.
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Explanatory coherence simplicity
The butler planted blood on Mrs. Smiths clothes
The butler stole Mrs. Smiths gun.
Mr. Smith is dead.
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IBE on Conjoined Hypotheses

• PF failed to discriminate between e.g.,
• Good hypotheses F ma and
• Good hypotheses fluff F ma and Force is
  beautiful. (Conjoined Hypotheses)
• IBE on Conjoined Hypotheses
• The latter is less simple than the former
• While the conjoined hypotheses entail the same
  data, it is less clear that they explain the same
  data

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IBE on Grue

• Let h1 All emeralds are green.
• Let h2 All emeralds are grue, i.e., green now,
  but will turn blue on May 10, 3776 (my 2000th
  birthday!)
• Why choose h1 over h2?
• h1 better optimizes conservatism, analogy,
  simplicity (why May 10, 3776?) h2 has no clear
  theoretical virtue

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IBE on Inductions role in decision

• Decisions depend on the future being like the
  past.
• In the past, subsequent events were like their
  predecessors.
• The best explanation for why subsequent events
  were like their predecessors is that nature
  behaves in a predictable, lawlike manner.
• So nature (probably) behaves in a predictable,
  lawlike manner.

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Some preliminary problems for IBE

• What is an explanation?
• Are consilience, simplicity, and analogy the only
  theoretical virtues?
• Are a theorys explanatory abilities the most
  important criteria? What about prediction and
  control?
• Are Thagards definitions correct?
• More to come!

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What is an explanation?

• Basics if h explains e, then
• h is called the explanans
• e is called the explanandum
• Main challenge
• The problem of explanatory relevance
  articulating the relationship between h and e.

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What is an explanation?

• Different slogans/proposals
• Showing that the explanandum was to be expected
• Fitting an explanandum into a larger conceptual
  framework Systematizing/unifying our knowledge
• Reducing the unfamiliar to the familiar
• Furthering understanding of the explanandum
• Answering a why-question about the explanandum
• Citing the cause of the explanandum
• These need not be incompatible

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Causal Model and The Difference Condition

• To explain why P rather than Q, we must cite a
  causal difference between P and not-Q, consisting
  of a cause of P and the absence of a
  corresponding event in the case of not-Q. (Lipton
  1991)
• Here P fact and Q foil

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Objections to causal model

• Not a clear concept of causation
• Liptons reply Even if we cant articulate a
  clear concept, we use causal concepts clearly
  enough.
• There are non-causal explanations
• Reply But causal explanations are the most
  important
• Over-permissive not all causes explain
• Liptons reply Difference condition rules out
  most of the non-explanatory causes

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Spelling out the slogan

• IBE Inference to the Loveliest Potential
  Explanation
• Actual explanation of P any true causal account
  of why P happened
• Potential explanation of P any causal account
  of why P happened true or otherwise
• Loveliest explanation of P provides optimal
  blend of theoretical virtues
• Likeliest explanation of P provides most
  probable explanation of P

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Why IBE is Inference to the Best Potential
Explanation

• If IBE is Inference to the Best Actual
  Explanation, then
• All of our inferences would lead to true
  conclusions.
• There would be a limited role for competing
  explanations in inference.
• No false-but-potential explanations should be
  considered in our inferential practices.
• We would need to judge the truth (actuality) of
  an explanation prior to using IBE.
• None of these are true. So IBEs deal with
  potential explanations

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Likeliness versus loveliness

• If IBE is inference to the likeliest of all
  potential explanations, then IBE would be
  trivial.
• Explanatory considerations are supposed to be a
  guide or symptoms of truth, but likelihood is
  not a symptom, but more or less synonymous with
  truth.
• Theoretical virtues (loveliness) are nontrivial
  symptoms of the truth.

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An even more precise template

• Evidential contrasts e1 rather than f1, , en
  rather than fn are in need of explanation.
• Among the hypotheses h1, , hm that are potential
  causal differences between e1 and f1, , en and
  fn, only hi is part of the optimally consilient,
  simple, and analogically robust theory T.
• So, hi is (probably) true.

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Objections to IBE

• Non-causal explanations
• Problems with Potential Explanations
• Psychologically impossible
• Bad lots
• Unborn hypotheses
• Problems with Loveliness
• Likeliness ? trivial symptom
• Brain Candy

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Problem 1 Noncausal explanations

• History of science, nonscientific practice have
  many noncausal explanations.
• Reply Many of these are guided by theoretical
  virtues, in which case IBE is even broader than
  Liptons model

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Problem 2 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 8.
• This would it psychologically intractable to
  infer the best explanation.
• Reply potential explanation of e any causal
  account of e that is a live option, any serious
  candidate for an actual explanation

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Basic Dilemma with Live Options

• What makes a live option a serious candidate?
  Two approaches
• Option 1 Serious what we take as a serious
  explanatory candidate
• Leads to Bad Lots, Privilege
• Option 2 Serious likely
• Leads to loveliness not being a guide to
  likeliness

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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 isnt the best of a bad lot?

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Unborn hypotheses

• There are many more explanations that we never
  think ofunborn hypothesesthan 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.

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In defense of likeliness

• Suppose we infer from the pool of potential
  explanations that are likely.
• Then likeliness is a necessary for loveliness to
  work as a guide to likeliness.
• But then why do we need loveliness?
• Furthermore, Being probable ? true
• So probability may be a nontrivial guide to truth
  (wait for Bayesianism)

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Is loveliness just brain candy?

• If IBE is correct, then either the world is
  theoretically virtuous (e.g., simple) or these
  virtues help us to understand the world
• There is no non-circular way to argue that the
  world is virtuous.
• But if these virtues only apply to us, then how
  is loveliness a guide to likeliness?

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Recap

• IBE seems a substantial improvement over HD and
  PF.
• However, it suffers from problematic notions of
• Explanatory relevance
• Potential explanations
• The relationship of loveliness and likeliness