Abstract
In this paper, I show how one might resist two influential arguments for the Likelihood Principle by appealing to the ontological significance of creative intentions. The first argument for the Likelihood Principle that I consider is the argument from intentions. After clarifying the argument, I show how the key premiss in the argument may be resisted by maintaining that creative intentions sometimes independently matter to what experiments exist. The second argument that I consider is Gandenberger’s (Br J Philos Sci 66(3):475–503, 2015) rehabilitation of Birnbaum’s (J Am Stat Assoc 57(298):269–306, 1962) proof of the Likelihood Principle from the (supposedly) more intuitively obvious principles of conditionality and sufficiency. As with the argument from intentions, I show how Gandenberger’s argument for his Experimental Conditionality Principle may be resisted by maintaining that creative intentions sometimes independently matter to what experiments exist.
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Notes
A frequentist who uses a binomial model for the sampling problem here and who assumes the standard 0.05 significance level for a test of the hypothesis that the true proportion is fifty percent will reject the hypothesis when using the rule “stop at 19 successes” (p = 0.0427). But such a frequentist will fail to reject the hypothesis when using the rule “stop at 50 total observations” (p = 0.0595). The canonical example is due to Savage (1962, 18).
The Likelihood Principle may be formulated in several different ways. Berger and Wolpert (1988, 1) begin their monograph on the Likelihood Principle as follows: “Among all prescriptions for statistical behavior, the Likelihood Principle (LP) stands out as the simplest and yet most farreaching. It essentially states that all evidence, which is obtained from an experiment, about an unknown quantity θ, is contained in the likelihood function of θ for the given data. The implications of this are profound, since most non-Bayesian approaches to statistics and indeed most standard statistical measures of evidence (such as coverage probability, error probabilities, significance level, frequentist risk, etc.) are then contraindicated.” Edwards (1972, 30) states the Likelihood Principle this way: “Within the framework of a statistical model, all the information which the data provide concerning the relative merits of two hypotheses is contained in the likelihood ratio of those hypotheses on the data.” Gandenberger (2015, 476–477) says that according to the Likelihood Principle, “two experimental outcomes are evidentially equivalent if they have proportional likelihood functions—that is, if the probabilities that the set of hypotheses under consideration assign to those outcomes are proportional as functions of those hypotheses.”
The term “experiment” as I use it in this paper and as it is widely used in probability theory, such as in the Berger and Wolpert quotation in this footnote, does not implicate the presence of experimental control but means something closer to “empirical observation” or perhaps “empirical test of a conjecture.” As Gandenberger (2015, 478) remarks, “This broad use of the term ‘experiment’ is not ideal, but there is no alternative that is obviously better.”
One might worry that this premiss assumes too much and is in fact inconsistent with what proponents of the Likelihood Principle accept. After all, Howson and Urbach (1996, 214) say that stopping rules do matter in some cases. Later in their book, they give an example of what they take to be an informative stopping rule and then remark (366): “Hence, the stopping rule is not necessarily uninformative, but as this example suggests, normally it would be. This concession should not be misunderstood. It does not mean that the scientist’s intention to stop the trial at a particular point is of any inductive significance.” With respect to my reconstruction of the argument from intentions, Howson and Urbach are being too charitable. A pair of experiments that differ with respect to their stopping rules in the manner suggested by Howson and Urbach’s example also differ with respect to the distribution of individuals in a population being sampled. And it is the latter difference that matters for those who endorse the Likelihood Principle. Hence, Howson and Urbach’s remarks are no threat to premiss [A1] in my reconstruction.
The notion of evidential value needs to be treated carefully in order to allow for the possibility that different epistemic agents might draw different conclusions from experiments with identical evidential value. For example, the agents might have different initial credences or they might deploy different rules of inference. But for present purposes, common sense should suffice.
Howson and Urbach (1996, 212) tell a similar story. However, they do not draw attention to the issues that I care about in this paper.
By saying that Sally and I have all the same initial opinions, I mean to imply at least this much: that we have exactly the same credences and exactly the same credence update rules. That Sally and I share all of our initial opinions will be an important stipulation in the arguments considered later on.
One objection that may occur to the reader is the possibility of so-called natural experiments. Plausibly, one may respond to the objection by treating a natural experiment as a found object that is repurposed in some way, like a piece of driftwood that is used, without modification, as a wine rack. See Korman (2015, 155–156) for discussion.
Philosophers have also debated what it is that makes something a member of a specific artifactual kind Hilpinen (2011). In addition to already-cited papers by Thomasson, see Schwartz (1978) and Kornblith (1980). Taking a page from the metaphysics of personal identity and personhood (especially Thomson 2008), one might hope that the features—whatever they are—that serve to distinguish different kinds of artifact will have a close connection to what makes something an artifact in the first place. For example, Kornblith (1980, 112) writes, “At least for the most part, it seems that what makes two artifacts members of the same kind is that they perform the same function.” If so, one might hope that having a function is part of the correct account of what it is to be an artifact. But again, experiments have functions, so accounts that treat function as central to being an artifact should count experiments as artifacts.
The claim that creative intentions matter according to the naïve view is supported by psychological work on mereological composition (for which, see Rose and Schaffer 2015, and Korman and Carmichael 2017) and on artifact categorization judgments (for which, see Bloom 1996; Malt and Sloman2007; Barrett et al. 2008; Chaigneau et al. 2008; Chaigneau et al. 2016; and Volume 4, Issue 3 of the Review of Philosophy and Psychology).
At this point, one might wonder whether Platonism with respect to experiments offers any positive reason for thinking that [B1*] is true or whether it merely cuts off an argument against [B1*]. Plausibly, an experimentalist’s intentions matter with respect to which experiment she selects to perform. But that isn’t enough to secure the claim that intentions have independent ontological significance. There are two separable questions here. First, one might wonder whether the intentions that matter with respect to which experiment one selects to perform ever matter independently with respect to which experiment one actually performs. If the identity of the experiment one performs supervenes in the right way on what one actually does, then the intention to select one experiment rather than another will not matter independently. One plausible consequence of such a view is that an experimentalist might perform an experiment different from the one she selects to perform. For example, a male researcher might intend to replicate an experiment on some laboratory rats first conducted by a female colleague but fail to actually replicate the experiment because he is unaware of the fact that male experimenters cause rodents to experience higher stress levels (for which, see Sorge et al. 2014). He selects the same experiment to perform, perhaps borrowing “aboutness” in the way Pollard (2007) suggests we borrow reference in mathematical discourse. But he does not perform the same experiment. (An interesting question here is how to distinguish between performing a different experiment correctly and performing the same experiment incorrectly.) Second, one might wonder whether there is any experiment that simply could not be performed—even accidentally—without having some specific intentions regarding how to perform it. A stopping rule is an intention regarding how to conduct an experiment, not an intention about what experiment to conduct. But it is hard to see how such an intention could be necessary. For any case in which an experimentalist intends to sample in a given way, it seems that we can imagine an experimentalist who samples in the same way without reflecting on her experimental design. For example, we might imagine an experimentalist who samples until she gets bored.
Returning to the referee’s question: I am not sure whether Platonism about experiments provides any positive reason for thinking that [B1*] is true. I am, at a gut level, inclined to think that Platonism about experiments favors proponents of the Likelihood Principle. But I have not been able to produce any arguments for the claim that Platonism about experiments entails [B1*] that I find satisfying.
In earlier writings, Dodd says that a musical work is a type of sound-sequence-occurrence, but his later writing implicates (at least) that he has not changed his view: sound-sequence-occurrences are performances.
I am quoting Dodd here except for relabeling the propositions. In doing so, I am adopting his use of “so” instead of using a line representing “therefore” as in previous arguments.
Deutsch (1991) provides an alternative approach to resisting the argument from creatability: reject the inference from [H1] to [H2]. Deutsch argues that the creation of a melody (a musical work) or a story (a work of fiction) does not require bringing anything into existence. He writes (221): “To be in a position to (literally) create a thing is to be in a position to stipulate rather than merely describe what the thing is like.” Deutsch’s paper is very interesting, but at the end of the day, I agree with Brock (2010, 343) that “Deutschian creation isn’t a kind of creation at all; causal creation is the only variety of genuine creation.” And hence, I think that Deutsch’s strategy is not a good one.
Since I think that the best option at this point in the dialectic is to reject [NAA], I have to dispute at least one premiss in each of the three arguments I suggested earlier in support of [NAA]. In the first argument, I deny the premiss [E1] that abstract objects are eternal. In the second argument, I deny the premiss [F2] that abstract objects are not sensitive to causal influences. In the third argument, I lean toward rejecting [G2] and saying that while experiments and other abstract artifacts are not located in space, they are still artifacts. However, I sometimes think that there are abstract objects that do have spatial locations. For example, one might think that a set of concrete objects is itself an abstract object that is located in the fusion of the spaces occupied by its members. If so, then I could retain [G2] and understand experiments to be spatially-located abstract artifacts. But along this route, I worry that the term “abstract object” becomes too mysterious—too unmoored from its history to do any work.
Brock (2010, 339) writes, “Creationism about fictional characters seems to be the orthodoxy in philosophical circles today.” He then goes on to quote extensively from contemporary philosophers endorsing the orthodox view. These include van Inwagen (1977), Salmon (1998), Thomasson (1999), and Soames (2002).
Of course, criticisms have been raised against abstract creationism. However, criticism of abstract creationism has (as far as I know) focused mainly on its application to fictional characters, and fictional characters may very well behave differently from experiments and other alleged examples of abstract artifacts. For two very different and interesting criticisms of abstract creationism with respect to fictional characters, see Brock (2010) and Vecsey (2014). See Friedell (2016) for a response to Brock.
I do not want to dwell on them, but there are some disanalogies between the referee’s hat case and cases involving experimenters with different intentions. First, no one initially thinks that hat color is epistemically relevant. But many people have thought and still think that stopping rules are epistemically relevant. Second, it seems initially plausible that hat color is metaphysically relevant to what experiment one performs. But the opposite is initially plausible with respect to creative intentions.
Korman discusses arbitrariness arguments in Chapter 8 of his book. He considers arguments having to do with artifacts in Chapter 8, Section 4.
Conservatism is the thesis that there are ordinary objects—such as tables, chairs, trees, and dogs—but no extraordinary objects—such as trogs, incars, and snowdiscalls. Hence, Conservatism is a middle position between various forms of Eliminativism—which reject some ordinary objects—and various forms of Permissivism—which accept some extraordinary objects. See Korman (2015, 23–25) for further discussion and references.
Korman appeals to creative intentions in order to resist an argument from arbitrariness that he attributes to van Inwagen (1990). Van Inwagen writes (126): “Pick up a lump of clay and knead it into some complicated and arbitrary shape. Call anything essentially of that shape a gollyswoggle. Did you bring a gollyswoggle into existence? I should think that if our sculptor brought a statue into existence, then you brought a gollyswoggle into existence. ‘Statue-shaped’ is a less definite shape predicate than ‘gollyswoggle-shaped’, and one we have a use for, and our sculptor intended to produce something statue-shaped while you, presumably, did not intend to produce anything gollyswoggle-shaped. But these facts would seem to be irrelevant to any questions about the existence of the thing produced; if you can make a statue on purpose by kneading clay, then you can make a gollyswoggle by accident by kneading clay. But if you can make a gollyswoggle by accident by kneading clay, then you must, as you idly work the clay in your fingers, be causing the generation and corruption of the members of a compact series of objects of infinitesimal duration. That is what seems to me to be incredible.”
In reply Korman writes (153): “The fact that many have set out to make statues, while no one has ever set out to make a gollyswoggle, is an ontologically significant difference between statues and gollyswoggles, and thus the differential treatment is not arbitrary.” However, following Saenz (2015), Korman does not appeal to creative intentions to ground the properties that distinct, co-located objects have. See Chapter 11, Section 3 of Korman’s 2015 book for details.
The distinction between dialectical and intrinsic senses of begging the question are due to Korman (2015, 28–29).
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Acknowledgements
Thanks to Sam Fletcher, Konstantin Genin, Daniel Malinsky, Conor Mayo-Wilson, Greg Gandenberger, Noel Saenz, Jonah Schupbach, and Kristin Seemuth-Whaley for comments on earlier drafts. Special thanks to Dan Korman for reading and criticizing multiple drafts, for helping me refine the arguments, and for motivating the project with his own excellent work.
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Livengood, J. Counting experiments. Philos Stud 176, 175–195 (2019). https://doi.org/10.1007/s11098-017-1011-5
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DOI: https://doi.org/10.1007/s11098-017-1011-5