Producing a Robust Body of Data with a Single Technique

Thanks to all those who came to my talk tonight or emailed me about it.  I got useful suggestions for smoothing out some rough patches in my argument.

Here’s my abstract again:

Scientists use techniques that produce “raw data” that requires substantial interpretation.  In many cases, it is impossible to discover or test by direct observation methods of interpreting that raw data.  In those cases, it is natural to assume what I call the Simple Process-Theory View: the justification for a particular method of interpretation must come from a theory of the process that produces the raw data. Contrary to this view, scientists have many strategies for validating a method of raw-data interpretation.  Thus, it is possible to produce a robust body of data with a single technique.  I illustrate and support these claims with a case study of the introduction of the cathode-ray oscillograph into electrophysiology.

I will post the paper to the Philosophy of Science Preprint Archive once I got the rights to all my figures.  In the meantime, I’d be happy to share by email with anyone who’s interested.

I think it’s too late to make substantive revisions the paper, but I plan to make the following revisions to the talk:

• Put characterization of robustness in introduction rather than conclusion.
• List theoretical presuppositions of each argument to avoid hand-waving at the end when I claim that some of the arguments are more theory-dependent than others and that the arguments are collectively independent of one another.
• Rethink statement that direct causal inference is “less powerful” than process tracing
• Add the end of sections on arguments by direct causal inference and arguments by process-tracing, recap specific arguments (e.g. “AC currents”) rather than the strategies they instantiate (e.g. “Checks and calibration”)
• Address at the end two possible objections:

1. Simple Process-Theory View is obviously false, so my thesis is trivial.  Response: Culp seems to endorse Simple Process-Theory View within philosophy of experiment.  Others follow her in emphasizing importance of multiple techniques, neglecting multiple arguments for one technique.  Also, Simple Process-Tracing View often crops up as a throw-away line outside of philosophy of experiment proper.
2. Simple Process-Theory View has been denied before, so thesis is unoriginal.  Response: Simple Process-Theory View is highly dubious in light of the work of, e.g., Ian Hacking and Allan Franklin.  To my knowledge, however, it has not been specifically targeted for criticism.  I hope that targeted criticism will reduce the frequency with which it is taken on board as an unexamined assumption.

• Add a slide on what I see myself as contributing to the literature in philosophy of experiment.  Primary contribution: developing an insight latent in Hacking’s and Franklin’s work that has important methodological implications.  Secondary contributions: (1)  New case study.  (2)  Building on Allan Franklin’s “epistemology of experiment” by introducing distinction b/t direct causal inference and process tracing and by emphasizing the importance of robustness.
• Rework slide with equation for forced vibration with damping.  It’s an important slide, but I haven’t worked out a sufficiently clear way to present it.

Further suggestions are welcome!  In particular, does anyone have more elegant name for the view I’m opposing than “Simple Process-Theory View?”

Thanks,
Greg

Absent Relations: A Critical Look at Rovelli’s Relational Quantum Mechanics

by Tom Pashby

“[T]he fact that the problem of the reduction of the wave-packet has remained baffling for so long, and that we lack any clue at present to its solution, seems to me no reason at all either for despair, or for embracing … glib and inadequate pseudo-solutions. Real problems are not always ripe for solution.” Howard Stein, ‘On the Present State of the Philosophy of Quantum Mathematics’ (1982)

“Information? Whose information? Information about what?” John S. Bell, ‘Against Measurement’ (1990)

This paper concerns Carlo Rovelli’s proposed solution to the measurement problem he calls Relational Quantum Mechanics (1996, 2005, 2007, 2008). Following Brown (2009) I distinguish between the interpretative and reconstructive projects Rovelli commences in (1996), and argue that his pursuit of the interpretative project alone since then indicates that he regards it as standing independently. This project amounts to an attempt to answer the question ‘What is quantum mechanics trying to tell us?’, rather than ‘Why the quantum?’.

I begin with an analysis of Rovelli’s argument for the radically relativist position he adopts which concerns what he calls `the third person problem’ i.e. the ‘Wigner’s friend’ paradox of Wigner (1961). I argue that even if we accept the very high value he places on definiteness, the radical conclusion (that there is no observer independent description of reality) does not follow due to the availability of a similarly perspectival, but modal interpretation of Dieks (2005, 2009). The similarity of the incompatible value ascriptions allowed by these accounts is compared with the incompatibility of attributions of tense to events in Special Relativity, and a better analogy is found with Dieks’ interpretation.

The consideration that Rovelli might offer in preferring his scheme to Dieks’ – its ability to accommodate non-ideal measurements involving partial correlations – is shown to conflict with the defense offered on his behalf by Brown, where it is claimed that certain relations are invariant between observers. It is argued that this picture is inconsistent with Rovelli (1996, 1998) and that if Rovelli’s (2005, 2007) view of the quantum state as containing probabilities for certain ‘quantum events’ is taken into account, then the claimed consistency between accounts is almost entirely vacuous.

A key concept Rovelli employs is that of ‘information’. He takes care to distinguish two uses, one of which he claims corresponds to the technical concept of Shannon information. Following Timpson (2008), I point out that the technical concept is inalienably tied to the practical problem of communication and so argue that his use of the term ‘information’ cannot avoid being associated with the everyday, epistemic, concept closely linked to knowledge. As such, he faces Timpson’s potentially fatal dilemma for information-based accounts of measurement, implicit in Bell’s third rhetorical question: ‘Information about what?’ Timpson claims that the information in any such interpretation must either be about the values that a quantity takes prior to measurement (hidden variables), or the measurement outcomes themselves (i.e. instrumentalist).

Rovelli’s ontology of quantum events, and his assertion that his account is non-anthropocentric, indicates an attempt to avoid the second horn of this dilemma and the associated charge of instrumentalism. However, I argue that this attempt fails on three counts: a failure to take into account the epistemic character of ‘everyday’ information and the nature of communication, an inability to meaningfully distinguish the quantum events of Rovelli’s ontology from measurement results, and the failure of RQM to meet a key requirement for the naturalization of an observer within a theory: that it allow a representation of observers within the description of reality provided by the theory.  These complaints entail that in Rovelli’s interpretation the probabilities contained within the quantum state refer only to the relative frequencies of measurement outcomes, hence the charge of instrumentalism is unavoidable.  Furthermore, I argue on this basis that his position is unavoidably solipsistic.

Finally, it is suggested that the information-based approaches of Fuchs’ Quantum Bayesianism, where the probabilities are associated with subjective degrees of belief, and Bub’s reconstructive project (with Clifton and Halvorson), whose interpretation by Bub (2005) is essentially communication driven, are to be preferred. Markopoulou’s causal quantum histories approach is discussed as an alternative, or perhaps complimentary, event-based account that would provide some objective relations between events.

Thanks to all who managed to attend the talk on Friday.  Apologies for the ridiculous quantity of slides I had managed to churn out (62 in case you’re wondering) which meant I ended the talk with a whimper half way through the argument.  This actually helped concentrate my attention somewhat on what I was really trying to say.  The above is the product of that reflection. I would be happy to add more detail if anyone is interested, hopefully at a level in between quick-and-dirty abstract and tedious-and-endless presentation.

On Actual Causation, Part III

By Jonathan Livengood

Intuitions

In the case of two-candidate, simple-majority elections without abstentions, it seems plausible that those who support the winning candidate are responsible for that victory.  Since there is no way to distinguish among the supporting voters (i.e. all of the votes have equal weight in determining the outcome), symmetry requires that all of the voters be considered equally responsible.  Hence, all of those who voted for the winning candidate are actual causes of that candidate’s victory.  So far, so good.

In the case of two-candidate, simple-majority elections with abstentions, whether or not our intuitions support the claim that abstentions are actual causes depends on the cover story one tells.  If seven voters support candidate A, three voters support candidate B, and one voter abstains, then it seems unreasonable to say that the abstention causes candidate A to win.  However, suppose that five voters support candidate A, four voters support candidate B, and six voters abstain.  And suppose further that we have reason to believe that among those who abstained, two-thirds of the voters would have supported candidate B had they been forced to vote.  Then, had everyone been forced to vote, the tally would have been seven votes for candidate A and eight votes for candidate B.  So, the abstentions matter to candidate A’s victory.  To put the point differently, if we simply take “abstentions” as “non-votes,” it happens routinely in actual elections that one side or the other tries to prevent their opponent’s supporters from voting.  In the most recent U.S. Presidential election, many out-of-state university students were told that they could not vote in their school’s state.  This was false.  But knowing that students overwhelmingly support the Democratic Party, the Republican Party sought to keep as many students away from the polls as possible.  Had John McCain won the election, it might fairly have been said that the students not voting was an actual cause of that victory.

Thus, it seems that whether or not (according to ordinary judgment) an abstention is an actual cause depends on two contingencies about the election and the electorate.  First, the vote totals in the election have to come out close enough for the abstentions to have potentially made some difference, holding everything else fixed.  Second, there must be some expectation that the abstaining voters would have voted in the right way had they voted.  In the non-voting student case, we know that students vote for Democratic candidates with a much greater frequency than they do for Republican candidates.  This makes their non-vote a cause in case the Republican wins.  But if the Democrat wins, then the Democrat wins despite the non-voting students.  The students are simply irrelevant.  So even non-votes do not always count as actual causes, but both accounts we have seen endorse the judgment that abstentions are always actual causes of the winning candidate’s victory.

In the case of three-candidate, simple-plurality elections, one might think that two relatively recent U.S. Presidential elections provide examples supporting the conclusion that every vote is an actual cause of the outcome of the election.  For instance, when Clinton defeated Bush in 1992, some pundits suggested that Perot had siphoned off enough votes from Bush to give the election to Clinton.  Similarly, when Bush defeated Gore in 2000, some suggested that Nader cost Gore the victory.  (Going back a little further, it is clear that Wilson won his first term because Taft and Roosevelt split the votes of their supporters.)  But this is only superficial.  The intuition is not symmetric with respect to the losing candidates.  One might concede that Nader cost Gore the election, but no one seriously believes that Gore cost Nader the election.

Thus, Woodward’s account fails for three-candidate, simple-plurality elections (and by a simple extension to all simple-plurality elections with three or more candidates with or without abstentions).  Moreover, it fails rather spectacularly, as one can see in the following example.  Suppose a corporate board consisting of ten members takes a vote to decide whether to build their new facility in New York or Los Angeles.  The vote is seven for New York and three for Los Angeles.  In this case, Woodward’s account tells us that the seven who voted to build in New York are actual causes of that vote passing, while the other three are not.  But now suppose that one of the board members thinks the board should consider building in Chicago, though he himself does not think Chicago is really the best place to build.  So, the board votes on whether to build in New York, Los Angeles, or Chicago.  The vote is seven for New York, three for Los Angeles, and none for Chicago.  Although nothing has changed in the vote totals, Woodward now tells us that the three board members who voted to locate in Los Angeles are actual causes of the company locating in New York!

We can now see three contingencies that must be satisfied for votes against the winning candidate to count as actual causes of the outcome.  The first two are similar to the conditions we noticed for abstentions.  First, the election must be close enough between the first- and second-place finishers that re-distributing the third-place votes could have changed the outcome.  Second, we have to have some reason to think that the third-place voters would have voted in a way that would have changed the outcome.  This might obtain by comparing the remaining candidates to the excluded candidate.  In our real-world example, Gore is more similar to Nader than Bush is to Nader.  Third, only the third-place voters can be actual causes.  This is to say that third-place finishers can be spoilers, whereas second-place finishers cannot.

There is more to come on diagnosing what exactly is going wrong and providing an alternative to intuitions for constraining theories of actual causation.

On Actual Causation, Part II

By Jonathan Livengood

Elections

Now, consider three voting scenarios: two-candidate, simple-majority elections without abstentions; two-candidate, simple-majority elections with abstentions; and three-candidate, simple-plurality elections with or without abstentions.  Given the vote cast by a specific voter in some election and the result of that election, I ask whether the vote is an actual cause of the result according to Woodward’s proposal.

All three election scenarios share the structure pictured in Figure 2 below.  In this figure, each vote (or voter) is labeled with a “V_i,” and the outcome is labeled “Win.”  This greatly simplifies our work, since for any vote, there is only one path to the outcome and that path contains a single directed edge.

Figure 2

This is not meant to be a particularly realistic description of actual voting scenarios.  It assumes, unreasonably, that the votes are independent, whereas they might be causes of one another (say, due to voters influencing one another by political argument) or they might be effects of a common cause (say, due to the influence of a demagogue, like Rush Limbaugh).  This more complicated scenario is pictured in Figure 3.

Figure 3

It also assumes, sometimes reasonably and sometimes not, that there are direct connections between the voters (or their votes cast) and the outcome of an election, whereas some elections process votes through voting machines that (either by accident or by design) might distort the influence of a vote on the outcome of an election from what we want that influence to be.  This scenario is pictured in Figure 4.

Figure 4

On the other hand, there are interesting cases that correspond to the simple picture in Figure 2.  For example, weighing collections of one-gram masses in a simple, two-pan balance corresponds to Figure 2 for two-candidate, simple-majority elections.  Moreover, if the accounts of actual causation under consideration cannot get these simple cases right, it seems unreasonable to hold out hope that they will get more complicated variations right.

Before getting into the details, let me summarize the results.  For two-candidate, simple-majority elections without abstentions, every vote for the winning candidate (or proposition) is an actual cause of the result, and no vote for the losing candidate (or proposition) is an actual cause of the result.  For two-candidate, simple-majority elections with abstentions, every vote for the winning candidate (or proposition) is an actual cause of the result, every abstention is an actual cause of the result, and no vote for the losing candidate (or proposition) is an actual cause of the result.  For three-candidate, simple-plurality elections with or without abstentions, every vote is an actual cause of the result.

Two-candidate, simple-majority

The scenario envisioned here is very simple.  Everyone must cast a vote.  Each vote cast is for exactly one of the two candidates.[1] If both candidates receive the same number of votes, then the election results in a tie.  Otherwise, whichever candidate receives the most votes wins the election.  Thus, the election may end in a victory for one or the other of the two candidates, or it may end in a tie.

Consider an election in which there are 2k voters.  (I leave it to the reader to show that elections with an odd number of voters produce identical results.)  Suppose that j votes are cast for candidate A, and suppose without loss of generality that 2k – j < j.  Thus, candidate A is the actual winner of the election.

Is a vote for candidate A an actual cause of candidate A’s victory?  To decide, choose a vote V_A for candidate A.  There is only one path from V_A to the result of the election, and no other vote is on this path.  Hence, we are free to change any of the other votes, so long as candidate A wins the election after the changes.  Distribute the votes such that there are k + 1 votes for A and k – 1 votes for B.  Now, change the value of V_A from A to B.  Since such a change results in a tie (k votes for A against k votes for B), V_A is an actual cause of A’s victory.  Because V_A was chosen arbitrarily, the same reasoning applies to every vote for candidate A.  Hence, every vote for candidate A is an actual cause of candidate A’s victory.

On the other hand, a vote for candidate B is not an actual cause of candidate A’s victory.  To see this, choose a vote V_B for candidate B.  Again, there is only one path from V_B to the result of the election, and no other vote is on this path.  Hence, we are free to change any of the other votes, so long as candidate A wins the election after the changes.  However, there is no redistribution of the votes such that A is the winner of the election but would not have been the winner had V_B not voted for candidate B.  Let r be the redistributed votes for candidate A.  Since candidate A must be the winner after any redistribution, 2k – r < r.  For v_B to be an actual cause of candidate A’s election, there must be k, r ≥ 0 such that 2k – r – 1 ≥ r + 1.  That is, a change in vote V_B must result in a change in the election, either to a tie or to a victory for B.  But 2k – r < r2k – r < r + 22k – r – 1 < r + 1.  So, V_B is not an actual cause of candidate A’s election.  Because V_B was chosen arbitrarily, the same reasoning applies to every vote for candidate B.  Hence, no vote for candidate B is an actual cause of candidate A’s victory.

Two-candidate, simple-majority with abstentions

In this scenario, every vote cast is for exactly one of the two candidates (just like in the previous scenario described in Section 2.1).  However, in this scenario, voters are not obligated to cast a vote.  As before, if both candidates receive the same number of votes, then the election results in a tie.  Otherwise, whichever candidate receives the most votes wins the election.  So again, the election may end in a victory for one or the other of the two candidates, or it may end in a tie.

Consider an election in which there are 2k voters.  (I leave it to the reader to show that elections with an odd number of voters produce identical results.)  Suppose that i votes are cast for candidate A, j votes are cast for candidate B, and l voters abstain.  Further, suppose without loss of generality that i > j.  Hence, candidate A is the actual winner of the election.

Is a vote for candidate A an actual cause of candidate A’s victory?  To decide, choose a vote V_A for candidate A.  There is only one path from V_A to the result of the election, and no other vote is on this path.  Hence, we are free to change what any of the other voters do, so long as candidate A wins the election after the changes.  Distribute the votes such that there is one vote for candidate A, zero votes for candidate B, and 2k – 1 abstentions.  Now, change the value of V_A from A to B.  Since such a change results in a victory for candidate B (zero votes for A against one vote for B), V_A is an actual cause of A’s victory.  Because V_A was chosen arbitrarily, the same reasoning applies to every vote for candidate A.  Hence, every vote for candidate A is an actual cause of candidate A’s victory.

Is a vote for candidate B an actual cause of candidate A’s victory?  No.  To see this, choose a vote V_B for candidate B.  Again, there is only one path from V_B to the result of the election, and no other vote is on this path.  Hence, we are free to change what any of the other voters do, so long as candidate A wins the election after the changes.  However, there is no redistribution of the votes such that A is the winner of the election but would not have been the winner had V_B not voted for candidate B.  Let r be the redistributed votes for candidate A and a be the redistributed abstentions.  Since candidate A must be the winner after any redistribution, 2k – r – a < r.  For V_B to be an actual cause of candidate A’s election, there must be a, k, r ≥ 0 such that 2k – r – a – 1 ≥ r.  That is, a change in vote V_B must result in a change in the election, either to a tie or to a victory for B.  (Since the change need not be in favor of candidate A, we do not add one to the right hand side of the inequality as we did in the previous case.)  But 2k – r – a < r2k – r – a < r + 12k – r – a – 1 < r.  So, V_B is not an actual cause of candidate A’s election.  Because V_B was chosen arbitrarily, the same reasoning applies to every vote for candidate B.  Hence, no vote for candidate B is an actual cause of candidate A’s victory.  (Notice that if we had changed the vote to favor A instead of making it an abstention, V_B still would not have been counted as an actual cause of A’s victory.)

And, now, what about abstentions?  Are abstentions actual causes of candidate A’s victory?  Yes, they are.  Choose an abstention, call it V_none.  There is only one path from V_none to the result of the election, and no other vote is on this path.  Hence, we are free to change what any of the other voters do, so long as candidate A wins the election after the changes.  Distribute the votes such that there is one vote for candidate A, zero votes for candidate B, and 2k – 1 abstentions.  Now, change the value of V_none from an abstention to a vote for B.  Since such a change results in a tie (one vote for A against one vote for B), V_none is an actual cause of A’s victory.  Because V_none was chosen arbitrarily, the same reasoning applies to every abstention.  Hence, every abstention is an actual cause of candidate A’s victory.

Three-candidate, Simple-plurality

In this scenario, every vote cast is for exactly one of the three candidates.  (It should be noted that allowing abstentions changes nothing.  Furthermore, adding additional candidates leaves the result here unchanged as well.)  If all three candidates receive the same number of votes or if two candidates have the same number of votes as each other and more votes than the third candidate, then the election results in a tie.  Otherwise, whichever candidate receives the most votes wins the election.  (In other words, a candidate need not receive the majority of the votes, and there are no run-offs.)  So again, the election may end in a victory for exactly one of the three candidates, or it may end in a tie.

Consider an election in which there are 2k voters.  (I leave it to the reader to show that elections with an odd number of voters produce identical results.)  Suppose that i votes are cast for candidate A, j votes are cast for candidate B, and l votes are cast for candidate C.  Further, suppose without loss of generality that i > j ≥ l.  Hence, candidate A is the actual winner of the election.

To see that every vote for candidate A is an actual cause of candidate A’s victory, we proceed as before.  Choose a vote V_A for candidate A.  There is only one path from V_A to the result of the election, and no other vote is on this path.  Hence, we are free to change any of the other votes, so long as candidate A wins the election after the changes.  Distribute the votes such that there are k + 1 votes for candidate A, k – 1 votes for candidate B, and no votes for candidate C.  Now, change the value of V_A from A to B.  Since such a change results in a tie (k votes for A against k votes for B), V_A is an actual cause of A’s victory.  Because V_A was chosen arbitrarily, the same reasoning applies to every vote for candidate A.  Hence, every vote for candidate A is an actual cause of candidate A’s victory.

To see that every vote for candidates B is an actual cause of candidate A’s victory, choose a vote V_B for candidate B.  There is only one path from V_B to the result of the election, and no other vote is on this path.  Hence, we are free to change any of the other votes, so long as candidate A wins the election after the changes.  Distribute the votes such that there are k votes for candidate A, one vote for candidate B, and k – 1 votes for candidate C.  Now, change the value of V_B from B to C.  Since such a change results in a tie (k votes for A against k votes for C), V_B is an actual cause of A’s victory.  Because V_B was chosen arbitrarily, the same reasoning applies to every vote for candidate B.  Hence, every vote for candidate B is an actual cause of candidate A’s victory.

Similarly, every vote for candidates C is an actual cause of candidate A’s victory.  Choose a vote V_C for candidate C.  There is only one path from V_C to the result of the election, and no other vote is on this path.  Hence, we are free to change any of the other votes, so long as candidate A wins the election after the changes.  Distribute the votes such that there are k votes for candidate A, k – 1 votes for candidate B, and one vote for candidate C.  Now, change the value of V_C from C to B.  Since such a change results in a tie (k votes for A against k votes for B), V_C is an actual cause of A’s victory.  Because V_C was chosen arbitrarily, the same reasoning applies to every vote for candidate C.  Hence, every vote for candidate C is an actual cause of candidate A’s victory.

Thus, on Woodward’s account, every vote cast in an election having three (or more) candidates is an actual cause of the result of the election!  Notice that this result does not in any way depend on the actual number of votes cast for each candidate.  Even if no one votes for candidate C, every vote for candidate B is an actual cause of candidate A’s victory (assuming we have fixed candidate A as the winning candidate as we did above).

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[1] One may also think of two-candidate elections in terms of “yes” or “no” votes respecting a proposition.  In the three-candidate case, the analogy only holds when there are three propositions (or, more wildly, three truth-values respecting a single proposition).

On Actual Causation, Part I

By Jonathan Livengood

I’ve been working recently on an objection to the theories of actual causation proposed by Woodward and by Halpern and Pearl.  In what follows, I restrict my attention to Woodward, since his account is easier to follow and space is limited.  Moreover, I am breaking up my discussion into three parts.  The first part sets up some things that one needs to know about the theories of causation that I am playing with and about Woodward’s account specifically.  The second part describes three simple elections.  I describe some judgments that Woodward’s account endorses (I find these judgments very odd!).  In the last part, I discuss the election scenarios and my intuitions about them somewhat less abstractly.  I argue that Woodward’s proposal often makes the wrong judgments about actual causes in elections.  I then diagnose what is going wrong in Woodward’s account and ask, non-rhetorically, how it might be fixed.  I also consider how one might replace the intuition game being played here with something else.

Whew!  Okay, the pre-introduction is out of the way.  So now, on with the show!

————————————————————————————

Part I

Causal claims come in two varieties.  On the one hand, there are causal claims about populations.  When one says that smoking causes lung cancer, this entails that if one were to implement a policy forcing the entire population to smoke, then one would see an increase in the amount of cancer in that population.  On the other hand, there are causal claims about individuals.  When one says that Joe got lung cancer because he smoked two packs a day for forty years, this entails that if Joe had not smoked, then he would not have gotten lung cancer.  Both kinds of claim are causal in part because of their relation to hypothetical interventions.  However, they are not equivalent.  Smoking might cause lung cancer in the population and yet not have caused Joe’s lung cancer.  Similarly, Joe’s smoking might have caused his lung cancer despite the fact that smoking does not cause lung cancer in the population.

Pearl (2000) and Spirtes et al. (2000) provide an account of causation for populations, which is closely related to the path models of Wright (1921) on the one hand and to the simultaneous equation models of Haavelmo (1943) on the other.  Call this account the structural model account of causation.  The structural model account is a theory of causation for populations, but recently, it has been adapted by Woodward (2003), Halpern and Pearl (2005), Glymour and Wimberly (2007), and Glymour et al. (ms) to produce accounts of causation for individuals, or accounts of actual causation.  I will talk about causation between random variables and causation between values of random variables.  Actual causation is a sub-type of the latter kind of causation.

Actual causation is central both to law and to history.  Determining the actual cause of damages is central in the practice of tort law (see Hart and Honore 2002, where “cause in fact,” “material cause,” and “conditio sine qua non” are synonyms for “actual cause”), and questions of moral responsibility more generally depend on facts—if there are any—about actual causation.  Moreover, in historical research, explaining why specific historical events occurred (e.g., the Boshin War, the Boston Tea Party, or the coronation of Napoleon), determining the relative contributions of various actors to history (e.g., Caesar, Galileo, or Tesla), or deciding the truth-value of historical counterfactuals (e.g., would Japan have surrendered had the United States not dropped atomic bombs on Hiroshima and Nagasaki) are all problems that turn on actual causation (see Reiss 2008 for a philosophical discussion; thumb through any recent historical journal for verification of the claim about research in history).

Most contemporary philosophical theories of causation are theories of actual causation, since they typically treat causation as a relation between two actual events.  (One sometimes sees the labels “token” or “singular” instead of “actual,” though it should be noted that actual causation is a proper subset of singular causation.)  As Glymour (2005) points out, the methodology for constructing such theories is “proposals, examples, counterexamples, more proposals” (728).  A proposed theory is correct if and only if it endorses the intuitive judgment about every imaginable scenario.  What makes a scenario an example of (or counter-example to) a proposed theory is that the theory entails that an event or variable-value x is a cause of another event or variable-value y just in case intuition says that x is (or is not) a cause of y.

Though I agree with Glymour in opposing this method, I’m not sure how to replace it, yet, with respect to theorizing about actual causation.  So the objection has the Socratic form.

A directed graph is an ordered pair G = <V, E>, where V is a finite set of vertices and E   (V V) is a finite set of directed edges.  An edge <V1, V2> is directed from V1 into V2.  Denote the directed edge <V1, V2> by V1  V2.  A path of length n > 0 from Vi to Vj, denoted Vi Vj, is a sequence V(1), V(2), …, V(n+1) of vertices such that Vi = V(1), Vj = V(n+1), and V(k)  V(k+1), for k = 1, …, n.  A path Vk Vk is called a cycle.  A directed graph without any cycles is called a directed acyclic graph (DAG).  If V1  V2, then V1 is said to be a parent of V2.  The vertices Vk such that Vj Vk are called the descendants of Vj, denoted de(Vj).  Similarly, the nondescendants of Vk are nd(Vk) = V \(de(Vk)  {Vk}).

Graphs are iconic mathematical objects, in which vertices are represented by labeled circles, and directed edges are represented by arrows, as seen in Figure 1:

Figure 1

The graph in Figure 1 is an example of a directed acyclic graph.  Paths in Figure 1 include A B E, C H, and D G H (and there are many others as well).  The descendants of B are E, F, and H.  The non-descendants of B are A, C, D, and G.

The structural model account of causation makes use of graphs to represent both statistical and causal facts.  A random variable X is a function mapping a sample space that contains possible outcomes of an experiment to real numbers.  The real numbers in the image of X are the possible values of X, denoted by x.  Associated with each random variable is a probability distribution (if discrete) or density (if continuous).  Each vertex in a graph is associated with a random variable.  To simplify the language in what follows, we will freely interchange “vertex” and “variable”: henceforth, the vertices in a graph simply are random variables.  Each vertex is associated with a unique error term, which gives the variable its stochastic properties.  Each vertex is also associated with a structural equation, in which that vertex is represented as a function of its graphical parents and its associated error term.  For example, in Figure 1, H = f(C, D, E, F, G, εH), where εH is the error term associated with H.

Woodward’s Proposal

Woodward (2003) develops an interventionist account of actual causation.  He begins with the theory that X = x is an actual cause of Y = y if the following two conditions are satisfied:

(AC1)    The actual value of X = x and the actual value of Y = y.

(AC2)    There is at least one route R from X to Y for which an intervention on X will change the value of Y, given that other direct causes Zi of Y that are not on this route have been fixed at their actual values.  (It is assumed that all direct causes of Y that are not on any route from X to Y remain at their actual values under the intervention on X.) (Woodward 2003, 77)

However, the second clause fails to be satisfied if the putative effect’s value is over-determined.  Thus, in cases of over-determination, Woodward’s first attempt says that there are no actual causes.  Perhaps this fits some intuitions.  Lewis (1986, see appendix E) seems to have thought that in cases of over-determination there simply were no causes.  However, Woodward sees this as a deficiency in his account, so he supplements (AC2) with (AC*2):

(AC*2)    For each directed path P from X to Y, fix by interventions all direct causes Zi of Y that do not lie along P at some combination of values within their redundancy range.  Then determine whether, for each path from X to Y and for each possible combination of values for the direct causes Zi of Y that are not on this route and that are in the redundancy range of Zi, whether there is an intervention on X that will change the value of Y.  (AC*2) is satisfied if the answer to this question is “yes” for at least one route and possible combination of values within the redundancy range of the Zi. (84)

Woodward defines the redundancy range of the Zi as follows:

Consider a particular directed path P from X to Y and those variables V1 … Vn that are     not on P.  Consider next a set of values v1 … vn, one for each of the variables Vi.  The     values v1 … vn are in what Hitchcock calls the redundancy range for the variables Vi     with respect to the path P if, given the actual value of X, there is no intervention that in     setting the values of Vi to v1 … vn, will change the (actual) value of Y. (83)

As he states it, the redundancy range will almost always be empty, since there will almost always be some fat-hand intervention that sets Vi to vi and also changes the value of Y directly.  But I do not think this is what Woodward has in mind.  Rather, I think he means to say that a value vi of Vi is in the redundancy range if an ideal intervention setting the value of Vi to vi does not change the value of Y.

The statement of (AC*2) is also not perfectly clear (even apart from the notion of the redundancy range), but I understand it as prescribing that X = x is an actual cause of Y = y if one can find some path P from X to Y such that there is a choice of (possibly non-actual) values for all the variables not on P such that Y retains its actual value y but also such that some change in the value of X changes the value of Y.  Assuming this is correct, in order to check whether X = x is an actual cause of Y = y, one applies the following algorithm.  First, one picks some path from X to Y.  Second, one picks values for all the variables not on the path such that Y keeps its actual value y.  (That is what it means for the off-path values to be in the redundancy range.)   Third, one sets X to each of its alternative values in turn, checking whether any such change requires a downstream change in the value of Y.  If any such change in X results in a change in Y, then stop, X is an actual cause.  Otherwise, repeat the above steps with a new path from X to Y.  If no untried paths from X to Y exist, then declare that X is not an actual cause of Y.

New WIP URL

The Pitt HPS WIP Website has moved to: http://www.hpsgrad.pitt.edu

Experimental Philosophy of Consciousness at Consciousness Online

By Justin Sytsma

I currently have a multimedia presentation up as part of the Consciousness Online conference. The title of the talk is “Folk Psychology and Phenomenal Consciousness” and it can be viewed, along with a commentary by Adam Arico, here. In the talk I present the results of four new studies exploring whether non-philosophers are generally naïve realists. I focus on two cases, one where many have thought that they are (colors) and one where most have thought that they are not (pains). The setup and results for the studies are given below (for framing and discussion, see the talk).

Study 1:

To test whether non-philosophers hold a naïve realist view of colors I gave 52 subjects a brief paragraph introducing them to the philosophical disputes concerning colors. They were then asked four questions (counterbalanced for order):

1. Do you think that a ripe tomato would still be red even if there was nobody around to see it?

2. Do you think that the red you see when you look at a ripe tomato is in your mind?

3. Do you think that the red you see when you look at a ripe tomato is in the tomato?

4. Do you think it is possible that somebody else might actually see the color that you call “blue” when they look at an ordinary ripe tomato, despite having normal visual acuity (i.e., without being color-blind)?

Each question was answered on a 7-point scale anchored at 1 with “clearly no,” at 4 with “not sure,” and at 7 with “clearly yes.” High answers to questions 1 and 3, and low answers to questions 2 and 4, follow the naïve view of colors. The mean response for the first and third questions were significantly above the neutral point of 4 (M=5.92, SD=1.98, p<0.001; M=4.88, SD=1.67, p<0.001), while the mean response for the second and fourth questions were significantly below 4 (M=3.27, SD=1.98, p=0.010; M=3.19, SD=2.16, p=0.009):

Study 2:

In Study 2, 56 subjects were given a description of a situation in which, on the naïve view, it would be natural to hold that a pain existed unfelt. Subjects were asked:

It is common for people who have been badly injured and are in ongoing pain to report being distracted from the pain by an interesting conversation, an intense movie, or a good book. Afterwards, the person will often reflect that for a period of time they hadn’t noticed any pain at all! In such a situation, do you think that the injured person still had the pain and was just not feeling it at the moment? Or, that there was no pain during that period?

They answered on a 7-point scale anchored at 1 with “clearly in pain, but not feeling it,” at 4 with “not sure,” and at 7 with “clearly not in pain.”

The average response was 2.54, indicating that contrary to the philosophical consensus, the subjects surveyed hold that pains can exist unfelt. Planned analysis showed that the mean response was significantly different from 4 (SD=1.66; p<0.001).

Study 3:

If non-philosophers hold a naïve view of pains we would also expect them to say that pains can be shared, at least in those atypical cases in which a body part is shared. My third and fourth studies presented subjects with descriptions of two such cases and asked them whether the numerically identical pain was felt by two different people. In Study 3, 41 subjects were given the following two scenarios in sequence, counterbalanced for order:

Henry and Johnny are normal undergraduates at a state university. They are distinct people with their own beliefs and desires. One day they were participating in a three-legged race in a park with Henry’s right leg tied to Johnny’s left leg. While running toward the finish line their “third-leg” forcefully kicked a large rock that, unbeknownst to them, was hidden in the grass. Henry and Johnny both grimaced and shouted out “Ouch!”

Bobby and Robby are conjoined twins that are joined at the torso. While they are distinct people, each with their own beliefs and desires, they share the lower half of their body. One day while running through a park they forcefully kicked a large rock that, unbeknownst to them, was hidden in the grass. Bobby and Robby both grimaced and shouted out “Ouch!”

After each vignette, subjects were asked whether the runners felt one and the same pain or two different pains. They answered on a 7-point scale anchored at 1 with “clearly same pain,” at 4 with “not sure,” and at 7 with “clearly different pains.”

The mean responses were significantly different (p<0.001), with the mean for the three-legged race scenario significantly above the neutral response of 4 (M=5.20, SD=1.45, p<0.001) and the mean response for the conjoined twins scenario significantly below 4 (M=3.27, SD=2.09, P=0.030).

Study 4:

In Study 4, 60 subjects were given the following vignette:

As part of an experiment, a mad scientist attached two men who had lost their arms to the same donor hand! To do this, the scientist carefully connected each of the patients’ nerve fibers to the new appendage. The two of them now share the one hand. After the operation, the doctor tested their ability to use the new hand. He found that while the two patients have some difficulty picking things up with the shared hand, they show normal pain responses. In particular, when the doctor cut the palm of the shared hand, both patients grimaced and shouted out “Ouch!” Upon questioning, they told the doctor that it had hurt when he cut them.

Subjects where then asked whether the patients felt one and the same pain or two different pains, answering on the same scale used in Study 3.

Again, the mean response was significantly below four (M=3.42, SD=1.82; p=0.016), with the majority of subjects indicating that the two patients felt the same pain.

[Cross-posted at Experimental Philosophy]

How to solve the regress of justification problem: justification as a three-valued variable

By Peter Gildenhuys

The regress of justification problem results from a deep principle about justification, what I call the principle of infection. That principle states that unjustified claims cannot justify. It is best put as a moral constraint on good justificatory practice: individuals should not purport to justify claims using claims they regard as unjustified. I call this principle the principle of infection because should it turn out that any claim in a putative justificatory chain is unjustified, its status as unjustified “infects” the rest of the claims in the chain, ultimately undermining the justification of lead claim in the chain.

It is straightforward to see how the principle of infection sparks the regress problem. For if claims that one regards as unjustified are not available as justifiers, one is forced to justify using only justified claims. But these have either one of two statuses, justified or unjustified. If the latter, then they cannot successfully justify other claims; if the former, then they would seem to be in need of their own justifications. The claims supplied as justifications for them will in turn themselves need justification, and so on.

The standard response to the regress problem is to invoke metajustification, to assign claims the status of justified without inferring them from other claims. Metajustification is problematic for all sorts of reasons, but the natural question to ask here is whether claims asserting metajustification, e.g., “X is justified,” must themselves be justified. If yes, then metajustification presents no solution to the regress problem since a metajustification will spark a new regress while terminating another. If no, then metajustifications cannot be effectively policed.

That last point is by no means obvious, so let me explain. My point about metajustification is perfectly general, but to be clear let’s consider an arbitrary form of metajustification, the familiar foundationalist version. The foundationalist asserts that claims about observable states of affairs get the status justified without being inferred from other claims. But consider the foundationalist who assigns metajustification to a claim that is patently not about observable states at all, say that electrons have negative charge. She is clearly violating her rule about what sorts of claims may be assigned the status justified by metajustification, but what of it? She is merely unjustified in making the metajustification. But, ex hypothesi, her metajustifications need not be justified, meaning that they may be unjustified, thereby obviating any token restriction she might undertake concerning what sorts of claims she can metajustify. This is what I mean when I say that metajustification cannot be effectively policed.

I suggest that the regress problem can be solved, while holding on to the principle of infection, by formalizing justification as a three-valued variable. The above arguments assume that justification is bivalent. We should deny this. A claim may have one of three exclusive justificatory statuses: justified, unjustified, or gap. (An initial plea: Do not think that claims with the status gap are partially justified, or have some limited evidence in their favor. Everyone thinks this when they initially hear my idea but my stance has nothing to do with partial justification.)

An adequate theory of justification, no matter how many justificatory statuses it involves, must make explicit under what conditions each justificatory status is assigned and must equally make explicit the implications of each status for justificatory practice. (Indeed, anyone who has bothered to read up until this point should be told that that last claim about what it takes to offer a philosophical account of justificatory statuses is perfectly general and applies to any philosophical account of any fragment of language whatsoever.) I offer such an account now for each of the justificatory statuses I invoke for my paradigm case, I-thou interlocution (two people talking to each other).

justified
A claim gets the status justified if it is inferred from claims that are either justified or gap. A justified claim can serve as a premise in a successful justification; that’s what having the status “justified” implies for justificatory practice.

gap
A claim gets the status gap if it is endorsed by both parties to the conversation prior to its commencement. Just like justified claims, gap claims can serve as premises in a successful justification; that’s what having the status “gap” implies for justificatory practice.

unjustified
A claim gets the status unjustified if it is neither justified nor gap. Unlike justified claims and gap claims, an unjustified claim cannot serve as a premise in a successful justification; that’s just the principle of infection.

The three-status model of justification allows the principle of infection to be endorsed without requiring that all successfully justifying claims must themselves have the status justified, since gap claims can function as premises in successful justifications. The claims that are gap are the ones that participants in the conversation agree upon anyway, so it is no wonder that their justification is not pursued despite the fact that they are invoked as legitimate justifiers.

The account of justification I offer is an attempt to formalize, the express in rigorous terms, the norms that govern justificatory practice in I-thou conversations. To extend it to cover cases of intrapersonal reasoning, simply assign claims the status gap if they are endorsed prior to the bout of reasoning. To extend it to cover cases of interlocution involving more than two individuals, simply assign claims the status “gap” when everyone agrees to them prior to beginning the conversation.

It is worthwhile to note that this account of justification makes the notion entirely context-relative. It is incompatible with a JTB account of knowledge; knowledge is not justified true belief but simply true belief. The illusion that knowledge requires justification is fostered by the consideration of cases in which we are invited to undertake new knowledge by inference, a circumstance in which the candidate knowledge claim must indeed be justified to be undertaken. But we should not regard all knowledge commitments as undertaken on the basis of inference.

Welcome to WIPLASH

WIPLASH is a group blog authored by History and Philosophy of Science graduate students at the University of Pittsburgh.  The purpose of the blog is to provide a forum in which to post and discuss our Work-In-Progress (WIP) projects.

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