The Inference of Common Cause Naturalized

Aviezer TuckerQueen’s University Belfast

Fig 5.1 Fifteen possible rooted trees (A) and three possible unrooted trees (B) for four species. 5.2 Tree-Building Methods

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Phylogenetic Trees (gpd) - Ascomycetes, Basidiomycetes & Zygomycetes

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Linguistic common cause trees

The Galapagos Finches

4 possible philosophical treatments of the inference of common cause: • Philosophers may try to deduce rules of inference, principles of common

cause from a more general principle or law of nature, as Reichenbach (1956) attempted to deduce his principle of the common cause from the second law of thermodynamics.

• Philosophers may try to explicate principles of inference of common causes in the logical positivist prescriptive and unempirical sense of the term.

• It is possible to attempt to discover a principle of inference of common cause as a probabilistic natural law by inductive inference.

• Naturalize the discussion of the inference of common cause by examining how do scientists actually infer common causes, especially in cases that are broadly appreciated as successful such as Darwin’s inference that all the finches in the Galapagos islands and all men and apes had common causes; Rasmus Rask and Franz Bopp’s inference that all the Indo-European languages had a common cause; or the kind of inferences editors of scientific editions of classics like the Bible, Homer or Plato make in attempting to infer the most authentic version of the texts they collate.

Reichenbach’s Common Cause Inference

When A & B are probabilistic frequencies and C is their common cause, if:

• P(A & B) > P(A) x P(B)• Pr(A & B|C) = Pr(A|C) x Pr(B|C).

================================• Then C is the common cause of A &B

“If an improbable coincidence has occurred, there must

exist a common cause.” (Reichenbach 1956, 157)

Problems with explication• Reichenbach’s principle is too narrow: in many successful cases of

inference of a common cause it is possible at most to make only a rough estimate of frequencies. In some cases, it is easier to infer common causes of species or languages on the basis of evidence for causal chains that led to them, irrespective of whether the relevant frequencies are known or not.

• Reichenbach’s principle is too broad: The universe is patently replete with such positive correlations between frequencies of events that do not result from any common cause. In popular culture correlations between frequencies connect winnings in sport, movements of the stock market and election victories with frequencies of features of the weather, animal behavior patterns, somebody’s uncle intensity of rheumatism pain, the voting patterns in certain remote tiny out of the way places and the Zodiac.

• There are plenty of improbable correlations that require no explanation at all.

Some Common Cause Vs. A Particular common Cause

• in many of the paradigmatic cases of inferences of a common cause, the properties of common cause unknown. For example, Darwin was certain that his Finches in the Galapagos Islands had a common cause-ancestor.

• . Reichenbach suggested that if for frequencies A and B, P(A&B) > P(A) x P(B), it is likely that A and B share a common cause given that A and B do not affect each other. The common cause C “screens” A and B from each other, iff P(A & B|C) = P(A|C) x P(B|C). But, if C means that some common cause of A and B existed without specifying its properties, C could be identical with A, B, the conjunction of A and B, or several common causes that may include A and B. In such a case, Reichenbach’s condition for screening may be satisfied, A and B would be independent of each other and dependent on C, yet since C could be A or B or a conjunction of the two, they would still not be screened from each other. If C=A then, Pr(A&B|A) = Pr(A|A) x Pr(B|A).

Type Vs. Token Common Cause

• Salmon and Hitchcock’s confusions

• Historical sciences of tokens vs. Theoretical sciences of types.

Naturalizing the Inference of Common Cause

• The hypothetical effects of a common are best considered as properties of events rather than events (Sober 1999). Groups of events that share a certain variable or property are variational groups, distinguished from a contrast class that does not share the variable.

• The properties that scientists look for in variational groups in order to infer their common causes are those that tend to preserve information.

• Some processes tend to preserve in their end states information from their initial state more than others do. Processes have varying levels of information preservation, varying levels of fidelity. Fidelity measures the degree to which a unit of evidence tends to preserve information about a given cause. Fides, fidelity, is a term used by textual critics to evaluate the reliability of texts (Maas 1958). Fidelity is used in this context as reliability is used in probability theory or credibility in jurisprudence (Friedman 1987). The evaluation of the fidelity of properties of events may also involve the examination of evidence for the causal chains that purportedly transmitted information from some common cause to members of the variational group, for example, the fossil record.

The Meanings the existence of Some Common Cause 1. A single ancestral common cause. For example, a variational

group of exams may be explained by plagiarism from a common single common cause like a book.

2. Several common causes. For example, the exams in the variational group may have plagiarized identical common sources, websites, books, “spark notes,” etc.

3. The common cause may be a member or several members of the variational group itself. For example, one or more exams of better students were copied by less diligent students.

4. All the members of the variational group may mutually cause each other. For example, similar exams may be the result of the collective work of all who submitted them.

5. Combinations of 1 or 2, with 3 or 4. For example, the students consulted several encyclopedias (2) before composing together (4) the exam.

Likelihoods of the Variational Group given Common and Separate Causes

P(variational group|some common cause) Pr(common cause)

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P(variational group|no common cause)Pr(no common cause)

{[Pr(E1|C) x Pr(C|B)] x [Pr(E2|C) x Pr(C|B)] x …x [Pr(En|C) x Pr(C|B)] }

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{[Pr(E1|S1) x Pr(S1|B)] x[ Pr(E2|S2) x Pr(S2|B)] x…x [ Pr(En|Sn) x Pr(Sn|B)] }

Sober’s 3 Interpretations

• 1. Comparison of likelihoods of a variational group given some common and given separate causes as between the best particular common cause hypothesis that specified the properties of the hypothetical common cause and the best separate causes hypothesis that likewise specifies the hypothetical properties of the separate causes.

• 2. Compare the likelihoods of the variational group given all the particular common cause hypotheses, multiplied by their priors, and given all the separate causes hypotheses multiplied by their priors.

• 3. If it is assumed that rates of preservation of information, of fidelity, are uniform at the same time across separate causal chains: “If two branches are contemporaneous, then any conditional probability that describes the one also describes the other.” (1999, 260) Sober argued that given uniform rates, a variational group is more likely given some common cause than given separate origins, and a more recent ancestor is more probable than a more distant one.

Homoplasies: Higher likelihood of separate causes

Homoplasies

Homoplasies: Invention of printing

Chinese and European

Homologies

Number of members in the variational group

• When the likelihood of each member of the variational group given separate causes is low, the effect of multiple members, such as several similar testimonies, is to decrease exponentially the likelihood of the similarity given separate causes. Therefore, evolutionary biologists, comparative linguists, as well as policemen and journalists, exert themselves to discover multiple testimonies, witnesses and units of evidence, to increase the size of the variational group. When useful for the inference of some common cause, multiple members of a variational group such as witnesses do not increase the posterior probability of some common cause; rather they decrease exponentially the probability of its only alternative, separate causes.

Alternative Common Cause Hypotheses

• Sometimes there is enough evidence to prefer one of the five possible types of common causes, though the evidence is still insufficient for determining the causal-informational net. For example (Greg 1927), suppose that a set of similar documents can be divided into three variational groups:

• Group one has: "To you I tell."• Group two has: "To you I say."• Group three has: "I say to you."

The search for the common cause