Updated Study Questions and Reading Advice

There will be extra office hours from 1:30-3:00 in the lounge of the philosophy dept on Monday, May 12. The exam will be held at the normally scheduled time, Tuesday May 13 at 9 AM in Sayles 105.

Review for Final Exam

About 3/4 of the material on the final exam will be on material that we covered after the mid-term exam. The questions will be of essay form.

The final exam will require that you concentrate a bit more on arguments that were in the textbook and readings, but not thoroughly discussed in class. I suggest rereading all the chapters in Theory and Reality that correspond to chapters we covered after the mid-term exam, with some attention to chapters 13 and 15.

Some issues to reconsider before the exam:

• What are the various accounts of laws?
• What is the principle that John Carroll uses to attack Best-Systems (BS) accounts of laws?
• How effectively do BS accounts vindicate our intuitions about physical necessity?
• What is Humean Supervenience, and what motivates it?
• What problems do chances pose for Humean Supervenience?
• What is the principal principle?
• What motivated a reformulation of the principal principle?
• What distinguishing features do necessitationists have in their account of laws?
• What is Bas van Fraassen's criticism of the necessitationist accounts?
• What is Hempel's account of explanation?
• In what ways do explanations not coincide with predictive ability?
• What is van Fraassen's account of explanation and how does it differ from accounts that tie explanation more closely to science.
• What is inference to the best explanation and how does it differ from eliminative inference that Peter Godfrey-Smith discusses?
• Why does Godfrey-Smith struggle to define scientific realism? (I.e., what is the issue that makes the definition non-trivial?)
• Why do empiricists conflict with realists?
• What options are available to reconcile empiricism with realism?
• What is van Fraassen's Constructive Empiricism, and why is it a serious problem for his account that there is no clear distinction between the observable and unobservable?
• What is objectionable about scientific realism?
• Chart out the various strategies that arise in Proofs and Refutations and discuss how they are relevant to scientific research (as opposed to informal mathematics). Any strategies that are unacceptable?
• Compare and contrast the method of proofs and refuations to Popper's method of conjectures and refutations.
• Which parts of Popper's claims about the scientific method are acceptable and which parts need to be rejected?
• How significant are the attitudes of individual scientists in judging whether their activities are scientific? (Specifically, can a scientist be dogmatic and unwilling to accept disconfirmation of his or her own hypotheses and still be scientific?) Godfrey-Smith discusses this a bit.
• What is the Duhem-Quine thesis about holism in testing, and how does it relate to Popper's methodology and to Bayesian approaches?
• Is it right to evaluate whether a theory or researcher is scientific by evaluating whether the broader research program has been making success? What does Sober say? What alternative approaches to the demarcation program are available? What is Popper's solution to the demarcation problem?
• What is the adaptationist claim? What are the Gould & Lewontin criticisms of it? What is Sober's defense of the scientific nature of adaptaionism?

Mid-Term Exam

1. Explain the problem of old evidence for Bayesianism and present what you think is the best solution for it.

2. Discuss whether Goodman adequately addresses Humean skepticism about induction.

3. Clarify which criticisms of NHST are substantive attacks on the method and which are mere caveats about potential misinterpretations of the conclusions of NHST.

4. Contrast various approaches to solving the demarcation problem, and argue for which account best resolves it.

Course Description

The goal of this course is to become involved in the central task of philosophy of science: to determine what we have to believe in order to make sense of this thing we call science. Our work this semester will involve investigating various aspects of science that bear on philosophical issues. For one, science has had some substantial success. The success of science is commonly thought to be a result of a specific technique for solving problems, the scientific method. We want to investigate whether there is a scientific method and whether scientists are doing something special or different from non-scientists. More important, we want to see whether there is a good justification for the reasoning patterns used by scientists (other than just noting their actual success). Second, science bears on questions of traditional philosophical importance like "Is there an external reality independent of conscious observers?" and "Why does the world obey certain laws?" Along these lines we will examine whether science is attempting to tell us the truth about the world, whether science gives us the real explanations for physical phenomena, and whether all science is reducible to or in some other sense strongly dependent on physics.

Tasks and Evaluations

Your grade for the course will be determined by these factors:

1. You will turn 5 short papers on topics discussed early in the course worth 10% each.

2. You will take a mid-term exam or write one longer paper for worth 20% of your final grade.

3. There is a comprehensive final exam worth 30% of your final grade.

Grue

A thought on the nature of the Grue Problem: One commonly understood lesson of Goodman's case is that science requires some sort of priviledged set of predicates, for which we have no direct empirical evidence to rule out. Assuming this is correct, the remaining problem is to make clear how projectible predicates fit with the rest of our commitments. For example, we would like to know what makes these predicates special. Is it due to features of human psychology? Because of some aspects of 'reference' (how language distinguishes objects in the physical world)? Also, we would like to understand the natural kinds that exist in special science. Are they not really natural kinds, but just act effectively like natural kinds in the circumstances in which we typically find ourselves?

Review of First Class on Bayesianism

The example in class was intended to serve two functions. The first was to highlight, and prepare you for the fact that we typically do a poor job of determining the probabilities of different propositions. One problem is that we easily get mixed up about the probability of H assuming that E is true, P(H/E) with the probability of E assuming that H is true, P(E/H). In science it often turns out that we have information about the second, but what we want to know is the first. So we need to be able to calculate the first using the second plus other information. This is what Bayes' theorem lets us do. There are a variety of ways we can get the wrong answer. One way is to think that P(H/E)=P(E/H). This is such a glaring mistake that it doesn't show up too often, but it can happen more often when precise numbers are not being used. For example, you might mistakenly reason that if P(H/E) is high, then P(E/H) is high too. Another way to get the wrong answer is to use the wrong information or ignore relevant information that Bayes' theorem tells you you need. Ignoring base rates is an example of this problem.

The second lesson of the medical example was to show you an example where applying Bayes' theorem gives you the correct answer for the probability you are (rightly) interested in. The numbers are all objective numbers that you can read off of frequencies observed in nature: what the population is, how many people have the disease, and how accurate the test is. This is important because later, we will examine cases where we want to use Bayes' theorem to calculate the value we are interested in, P(H/E), but where we don't really have sufficient objective probabilities to plug into the formula. Once you see these cases, you might be led to think that Bayes' theorem can't help--that it is just a formula where you plug in made up numbers and hence get a contrived answer. Seeing this one example shows that at least in some very important practical examples, there is a number we are interested in, there are objective facts out there we can measure, and Bayes' theorem is the right formula to let us calculate what we want to know.

A third lesson was that the notion of chance in some situations is conceptually shaky. Naively, we think the chance that Jill has the disease is an objective fact about Jill. There is a sense in which this is true. Jill either has the disease or doesn't. If she does, then the chance she has it is 1. If she doesn't the chance that she has it is 0. There is another sense in which we want to attribute a non-trivial chance to her having the disease. We might think that Jill is a teen-ager, that 1% of teen-agers have the disease and that there is nothing special about Jill that is relevant to her having the disease. In such a case we would be tempted to assign Jill a 1% chance of having the disease, and to conceive of this chance as a fact about Jill. However, it is conceivable that if we took more (potentially accessible) information about Jill, then we could potentially apply information about the prevalence of the disease in certain sub-populations. Knowing the additional facts might lead us to rationally assign a different chance to Jill. This in itself doesn't show anything wrong with the idea that the chance of the disease is an objective property of Jill, because more information about Jill might give us more information about the objective chance Jill has. The problem is that in the limit as we gain maximal information about Jill, we will come to know a fact about Jill, whether she has the disease, and this will tell us either that her chance of having it is 1 or 0. The moral to draw is that chance in the way we have applied it to Jill is an epistemic creature. It has a non-trivial value (the chance is somewhere in between 0 and 1) only due to our ignorance of the facts. The chance is relative to some set of facts. Take into account different facts about Jill and one will arrive at different chances. This lesson is not merely theoretical. In practice, we often have samples with large numbers of people, but only small numbers of sub-populations. Should you treat Jill as a member of the larger population where the larger sample size gives you more reliable information about Jill qua person, or should you treat Jill as a female teenager where the smaller sample gives you less reliable information but where the sample is better matched to Jill's situation? Trade-offs must be made based in part on the particular details about the sample size as well as off-hand guesses about how relevant the additional facts are to predicting the disease incidence.

Probability Axioms and the Dutch Book Argument

What is the status of the probability axioms? Think of the probability axioms as a minimal number of rules that codify relations among the probabilities of logically related statements. They are formal definitions that implicitly characterize probability. Any set of quantities that satisfy all the deductive consequences of the axioms, deserves the name probability. The axioms, or laws of probability, are not necessarily statements about the physical world. They are like claims of geometry that connect the concepts of line, plane, intersection, etc. without necessarily having any physical objects that exemplify the concepts.

The axioms of probability were developed to formalize a theory of chance, in part to help people improve their gambling skills. The idea is that some kinds of (random, chancy, uncertain) phenomena in the world follow patterns that we can fruitfully study. After studying gambling for a long time, we conclude that our best predictions of the outcomes of roulette wheels and dice, etc. is to assign to each chance-setup (like a throw of a die) a set of pairs, where the pair is an outcome and a special number called the chance. For an ordinary die toss, we the set is {(1,1/6), (2,1/6), (3,1/6), (4,1/6), (5,1/6), (6,1/6)} meaning there is a 1/6 chance of rolling a 1, etc. We find that our best way of making bets uses the laws of probability to build on the knowledge we have of single chance events. For example, we can calculate that the chance of rolling a pair of dice and getting a sum of five is 1/9. These numbers that we have theorized, the chances, obey the laws of probability. Because the theory of chance is our best theory of gambling, we take the chances as expressing a significant quantity in nature. And because the chances satisfy the laws of probability, they are one kind of probability.

A task that has apparently nothing to do with gambling, is determining how strongly people should believe various claims, prescribing rational constraints on belief. For a long time, we humans believed that it is irrational to believe a contradiction, to believe (A & not-A), no matter what the statement A is. Philosophers' theories about rationality was restricted to a binary paradigm, in which you either believed A or you didn't, and so to show that someone was irrational, you had to find a contradiction among these beliefs. For example, that someone believed A and disbelieved, but also believed that (not-A or B).

A deficiency in this account of rationality is that it is silent on issues of partial belief or uncertain belief. Thus, there are some potential advantages to modeling rational belief in terms of a strength or degree of belief. Because the axioms of probability were ordinarily interpreted as a theory of propensities and chance-outcomes, it is somewhat surprising that the axioms can also serve as a central part of a normative theory of belief, a theory of rational belief. If you are developing a theory about rational belief that covers partial beliefs or degrees of belief, then you would think that there ought to be rules that say when a belief pattern is irrational. The notable fact is that these rules turn out to be the same rules that govern dice. In this sense, the use of the probability axioms is not trivial.

The Dutch book argument is the most prominent argument for why we ought to constrain our degrees of belief by the laws of probabilty. First, we assume that it makes sense to talk of precise degrees of belief. These degrees of belief are often called credences. Second, we assume that degrees of belief are closely related to actions that you are willing to take, in particular a hypothetical willingness to bet in certain ways. (This does not require too much of a stretch to accept, because you might say that part of what it means for you to believe in "It will rain tomorrow," to degree 0.89, is for that belief to in some way be connected with your behavior regarding rain. Simply, that you will want to take an umbrella with you tomorrow, that you will not claim that it is 100% certain that it will rain, etc.) Third, it is provable that if your willingness to take a bet is determined by your degrees of belief on particular propositions (ignoring the rest of your beliefs) and your degrees of belief don't obey the laws of probability, then there will exist aset of bets such that you will be willing to accept each bet, but where the net effect of accepting all the bets makes you a guaranteed loser.

With these three assumptions, the Dutch book argument is that (1) if it can sometimes be rational for your degrees of belief to violate the laws of probability, then it can sometimes be rational for you to accept a set of bets that guarantee a loss. (2) It is never rational to willingly accept a guaranteed losing bet. Thus, it is never rational for your degrees of belief to violate the laws of probability.

Probability Terminology

• 'Probability' is the most general term, standing for anything that plays the role of probability as defined by the probability axioms, including all the probability-related notions below.
• 'Chance' refers to probabilities that exist in the actual world or some idealized situation, like dice throws or coin-flips. Chances do not include degrees of belief.
• 'Propensity' refers to a chance in the world that is unanalyzable or irreducibly probabilistic. Some people think unstable atoms exemplify propensities to decay. It is something of an understatement to say that not everyone believes propensities exist.
• 'Frequency' refers to the ratio of actual outcomes. The frequency of heads in a series of coin flips is the number of heads that appeared divided by the total number of flips. Philosophers distinguish 'actual frequencies' from 'hypothetical frequencies' when they talk about chancy phenomena in the context of hypothetical possibilities, like "If I flipped this coin a million times, the frequency of heads would likely be...."
• 'Stochastic' refers to probabilistic transition. One says that a law of nature is stochastic if the law uses probabilities in a non-trivial way to describe how things evolve.
• 'Credence' and 'degree of belief' are equivalent. They refer to the degree of confidence one has about the truth of a certain proposition. These terms are used in contexts of idealized rational agents.

Bayesianism

It is important to note that everyone agrees that Bayes theorem is true, in the sense that it follows from the axioms of probability theory. That's why it is called Bayes' theorem. The contentious claims that Bayesians make fall into two categories. First, they assume that the overall framework of talking about degrees of belief (credences) makes sense as an idealization, and that such talk can be justified as a theory of rationality. Second, they argue the specific claim that the rational response to learning that a proposition E is true, is to conditionalize on E. The way this contentious claim about the rational reaction to evidence relates to Bayes theorem is that one almost always uses Bayes theorem to determine the new degree of belief one should have. Specifically, the new degree-of-belief, P', in hypothesis H (after E has been learned) should be set to equal the old degree-of-belief, P, (before E has been learned) of how likely H is, assuming that E. Saying this in symbols, P'(H) = P(H/E) = P(E/H)*P(H)/P(E). This means the new degree of belief in H is just the old degree of belief in H multiplied by the number P(E/H)/P(E).

What about confirmation? A simple Bayesian theory of confirmation is that E confirms H if and only if the ratio P(E/H)/P(E) is greater than 1. Whenever the ratio is greater than one, the evidence has boosted the confidence that you ought to have in H. E disconfirms H if and only if the ratio is less than 1 because in that case, learning E lowers your confidence in H.

A more sophisticated Bayesian theory of confirmation could claim that E confirms H relative to a competing hypotheses, J, if and only if E boosts P(H) more than P(J). Specifically, P(E/H)/P(E) > P(E/J)/P(E). This captures the idea that confirming a hypothesis is a matter of making the hypothesis more plausible than alternative hypotheses. This incorporates the idea of eliminative inference, that the a theory is confirmed when competing theories are disconfirmed (or at least not confirmed as much).

Review for Mid-Term Exam

You should be able to explain the traditional problems of induction and confirmation including Hume's problem of induction, Goodman's old riddle, Goodman's new riddle, Hempel's paradox of the ravens. You should be able to explain each of these and explain the resolution proposed by each author.

For Bayesianism, you should know Bayes' theorem, be able to explain what a Bayesian believes about confirmation and rationality. You should be able to show how a Bayesian would resolve (or fail to resolve) the traditional problems of induction. You should be able to identify positive features of the Bayesian approach that make it superior to an approach like Hempel's. You should be able to explain the arguments leveled against the Bayesian theory of confirmation and explain which problems the Bayesian can overcome.

You should be able to explain what NHST is, and categorize all the arguments against it in terms of how devastating they are to the NHST advocate. You should be able to show how a Bayesian would approach the same data that the NHST procedure addresses. You should be able to argue about the deficiencies of Bayesianism in treating the inference to p(H/E), i.e. in what ways it is relative to an (mostly unconstrained) weighted choice of alternative hypotheses.

A useful task for you is to identify which criticisms truly identify NHST as essentially (intrinsically) flawed, which criticisms are merely against the ease with which erroneous interpretations or inferences can be made, which criticisms are against the ease with which cheating can occur, and which criticisms are substantially off-base.