All assignments will be posted here. For reference, the main assignments for the course will be as follows:
Three problem sets covering material from the textbook. (I may add a fourth, depending on whether I think additional practice is needed.)
Problem set 1 will be posted below on Thursday 15 October and will be due at the start of class on Wednesday 28 October.
Problem set 2 will be posted below on Thursday 29 October and will be due at the start of class on Wednesday 18 November.
Problem set 3 will be posted below on Thursday 14 January and will be due at the start of class on Wednesday 27 January.
A short (1000–1500 words) midterm paper. The assignment will be posted below on Friday 18 December, and the paper will be due at the start of class on Wednesday 20 January.
A slightly longer (1500–2000 words) final paper. The assignment will be posted below on Thursday 21 January, and the paper will be due at 23:59 on Sunday 28 February. (Note: the assignments will be designed in such a way that you can, if you like, treat writing the midterm assignment as a way of writing a rough draft of the final paper, one that you'll revise and expand based on my feedback.)
Due at the start of class on Wednesday 28 October, via email. (If you complete the problems on paper, you can email a photographed/scanned copy.)
First, prove General Additivity using only the Komologorov axioms along with Finite Additivity (Extended) and Equivalence.
Hint: use the logical fact that P v Q is equivalent to (P & Q) v (P & ~Q) v (~P & Q).
Then, complete the following problems from the "Exercises" section at the end of Chapter 2 of Fundamentals of Bayesian Epistemology:
Problem 2.5
Problem 2.7
Note: you may use a probability table in your proof. (If you'd like an extra challenge, you can also try building a proof directly from the axioms along with the derived principles listed in Section 2.2.)
Problem 2.9
Problem 2.10
A solution set for Problem set 1, with explanations of how to think through the problems, is available here.
Due at the start of class on Wednesday 18 November, via email. (If you complete the problems on paper, you can email a photographed/scanned copy.)
Complete the following problems from the "Exercises" section at the end of Chapter 3 of Fundamentals of Bayesian Epistemology:
Problem 3.3
Problem 3.5
Problem 3.7
Problem 3.14
Hint: it will be much easier to see how to answer part (a) if you keep in mind the fact you're being asked to prove in part (b).
A solution set for Problem set 2 is available here.
Due at the start of class on Wednesday 20 January, via email.
Think of this as a way of writing a draft of your final paper, one that you'll revise and expand based on my feedback. (Your final paper won't be required to be a revised and expanded version of your midterm paper – you can write an entirely new paper if you like. But you will be allowed to submit a revised and expanded version of your midterm paper as your final paper.)
You have two options:
Develop an argument on a topic of your own choosing (though see the below caveats), and present that argument in a paper of 1000–1500 words. (If you need to make the paper longer in order to present your argument adequately, that's fine. But remember: the final version, which you'll submit at the end of February, must be no more than 2000 words.)
Caveat 1: your argument must be responsive to at least one of the papers we've discussed in class, and you must, in the course of your argument, demonstrate your understanding of some argument from that paper. (You might, for instance, give your own argument against a thesis that's relied on by some theorist, but if you do so, you must also explain what role, exactly, that thesis plays in the theorist's own argument.)
Caveat 2: if you do decide to work on a topic of your choosing, I'd like you to run your idea by me first – you can either send me an email, or we can set up a short meeting via Webex.
Below you'll find a selection of passages from some of the papers we've read up to this point in the term. Choose one of these passages and explain as best you can, in a paper of 1000–1500 words, what's going on in it.
You should explain just what the author is saying in the quoted passage (taking care to explain unfamiliar or technical terminology) and why they say it, including what role the passage is playing in the author's overall argument for the position they're defending. You should also spend at least some time evaluating the author's argument as you've laid it out.
If, in order to make sense of a passage, you need to introduce or refer to other aspects of the author's position, or to some aspect of the position the author is criticizing, then you should do so. You should also raise critical questions about the author's position, insofar as you need to do so to defend or motivate aspects of your interpretation. But you should not attempt to introduce or explain aspects of the author's position that don't bear upon the interpretation of the passage – all such discussion is irrelevant to the task you're being asked to carry out.
Regardless of which of these two options you choose, you should feel free to make use of the course notes, etc., to help you make sense of the material you're discussing.
Whatever the truth (or knowledge) connection amounts to, rules such as "Believe p just in case p is true" won't serve as the kind of means for pursuing truth that we are looking for, as such rules don't offer enough guidance as to what exactly it is that one should do in order to believe the truth. What we are looking for is something by means of which true belief and knowledge can be obtained. … Now, the problem for the Über-rule view is that an Über-rule just doesn't seem like the kind of rule that can offer genuine guidance. For one, it cannot even be expressed as a set of finite, informative generalisations. (Lasonen-Aarnio, "Higher-order evidence and the limits of defeat", pp. 333–334)
Every plausible story I've been able to come up with is generalizable: it applies just as well to an agent's conclusions about what's rationally required in situations other tan her own as it does to conclusions about what's required in her current situation. For example, take the universal-propositional-justification story I've just described. However it is that one reflects on a situation to determine what it rationally requires, that process is available whether the situation is one's current situation or not. The fact that a particular situation is currently yours doesn't yield irreproducible insight into its a priori rational relations to various potential attitudes. (Titelbaum, "Rationality's fixed point", p. 276)
Doxastic justification requires basing one's beliefs on evidentially relevant factors. So if Sam's belief in M is doxastically justified in Case 2, it must be because the basis for his belief in M—his higher-order evidence from Alex—is evidentially relevant to M. But Proxy does not predict this. After all, in Case 2, as in Sleepy Detective, Sam already knows what his first-order evidence is. Proxy says that when one has the relevant first-order evidence, higher-order evidence is not at all evidentially relevant to one's first-order beliefs. So if we want to capture the asymmetry between Case 1 and Case 2, we must allow that higher-order evidence cab rationally affect first-order beliefs in ways other than by Proxy. (Horowitz, "Epistemic akrasia", p. 731)
Anti-reliability higher-order evidence situations are misleading in a non-accidental way: rationality and accuracy are anti-correlated. So being akratic in such situations can be rational, precisely because it does not suggest that one's beliefs are inaccurate. In fact, given that one must expect from the outset that one's belief will be accurate only if it's irrational, akrasia is rationally required. (Christensen, "Disagreement, drugs, etc.: From accuracy to akrasia", p. 416)
What should be your credence that it will rain tomorrow, given that Sherlock is the true expert and that many people will use umbrellas tomorrow? Answer: your credence should be rather high. And it should not in general equal Sherlock's unconditional credence that it will rain. For the information that many people will use umbrellas tomorrow provides strong evidence that it will rain tomorrow. This suggests that your conditional credence should not equal Sherlock's credence that it will rain. Rather, it should equal Sherlock's credence that it will rain conditional on (at least) the information that many people will use umbrellas tomorrow. (Elga, The puzzle of the unmarked clock and the New Rational Reflection principle, p. 135)
In Drug, if 'E; and I am not drugged; therefore, p' is a form that my reasoning to p must take in order for me to keep my belief, then it's true that my belief that p cannot be properly based. But the problem is that this is not a form my reasoning must take, because my reasoning doesn't need to involve the belief that I am not drugged. To see this, think about what reasoning from one's evidence E to p amounts to: it's to believe that p because one takes E to support p. No step in the reasoning has to mention anything about whether one is drugged. (Ye, "Higher-order defeat and intellectual responsibility", p. 10)
Due at the start of class on Wednesday 27 January, via email. (If you complete the problems on paper, you can email a photographed/scanned copy.)
Complete the following problems from the "Exercises" section at the end of Chapter 4 of Fundamentals of Bayesian Epistemology:
Problem 4.2
Problem 4.3
Problem 4.4
Note 1: your proofs shouldn't appeal to Venn diagrams or probability tables -- you should appeal explicitly to the probability axioms and the Ratio Formula (and to the various other principles we've shown to be entailed by those principles).
Note 2: as mentioned at the start of the "Exercises" section, you can assume that the credence distributions you're working with satisfy the probability axioms and the Ratio Formula.
A solution set for Problem set 3 is available here. Please let me know if you notice any errors.
Due at 23:59 on Sunday 28 February, via email. (If you'd like more time than this, get in touch with me and we'll make arrangements.)
You have two options:
Develop an argument on a topic of your own choosing (though see the below caveats), and present that argument in a paper of 1500–2000 words.
Caveat 1: your argument must be responsive to at least one of the papers we've discussed in class, and you must, in the course of your argument, demonstrate your understanding of some argument from that paper. (You might, for instance, give your own argument against a thesis that's relied on by some theorist, but if you do so, you must also explain what role, exactly, that thesis plays in the theorist's own argument.)
Caveat 2: if you do decide to work on a topic of your choosing, I'd like you to run your idea by me first – you can either send me an email, or we can set up a short meeting via Webex.
Below you'll find a selection of passages from some of the papers we've read during the term. (Most of these are just the passages from the midterm paper assignment, but I have also included a new passage from Schoenfield's "An accuracy based approach to higher order evidence".) Choose one of these passages and explain as best you can, in a paper of 1500–2000 words, what's going on in it.
You should explain just what the author is saying in the quoted passage (taking care to explain unfamiliar or technical terminology) and why they say it, including what role the passage is playing in the author's overall argument for the position they're defending. You should also spend at least some time evaluating the author's argument as you've laid it out.
If, in order to make sense of a passage, you need to introduce or refer to other aspects of the author's position, or to some aspect of the position the author is criticizing, then you should do so. You should also raise critical questions about the author's position, insofar as you need to do so to defend or motivate aspects of your interpretation. But you should not attempt to introduce or explain aspects of the author's position that don't bear upon the interpretation of the passage – all such discussion is irrelevant to the task you're being asked to carry out.
Note: If you like, you may choose to complete this assignment by revising and explanding your midterm paper, taking into account my feedback. But you also have the option of writing a completely new paper.
Finally, you should feel free to make use of the course notes, etc., to help you make sense of the material you're discussing.
Whatever the truth (or knowledge) connection amounts to, rules such as "Believe p just in case p is true" won't serve as the kind of means for pursuing truth that we are looking for, as such rules don't offer enough guidance as to what exactly it is that one should do in order to believe the truth. What we are looking for is something by means of which true belief and knowledge can be obtained. … Now, the problem for the Über-rule view is that an Über-rule just doesn't seem like the kind of rule that can offer genuine guidance. For one, it cannot even be expressed as a set of finite, informative generalisations. (Lasonen-Aarnio, "Higher-order evidence and the limits of defeat", pp. 333–334)
Every plausible story I've been able to come up with is generalizable: it applies just as well to an agent's conclusions about what's rationally required in situations other tan her own as it does to conclusions about what's required in her current situation. For example, take the universal-propositional-justification story I've just described. However it is that one reflects on a situation to determine what it rationally requires, that process is available whether the situation is one's current situation or not. The fact that a particular situation is currently yours doesn't yield irreproducible insight into its a priori rational relations to various potential attitudes. (Titelbaum, "Rationality's fixed point", p. 276)
Doxastic justification requires basing one's beliefs on evidentially relevant factors. So if Sam's belief in M is doxastically justified in Case 2, it must be because the basis for his belief in M—his higher-order evidence from Alex—is evidentially relevant to M. But Proxy does not predict this. After all, in Case 2, as in Sleepy Detective, Sam already knows what his first-order evidence is. Proxy says that when one has the relevant first-order evidence, higher-order evidence is not at all evidentially relevant to one's first-order beliefs. So if we want to capture the asymmetry between Case 1 and Case 2, we must allow that higher-order evidence cab rationally affect first-order beliefs in ways other than by Proxy. (Horowitz, "Epistemic akrasia", p. 731)
Anti-reliability higher-order evidence situations are misleading in a non-accidental way: rationality and accuracy are anti-correlated. So being akratic in such situations can be rational, precisely because it does not suggest that one's beliefs are inaccurate. In fact, given that one must expect from the outset that one's belief will be accurate only if it's irrational, akrasia is rationally required. (Christensen, "Disagreement, drugs, etc.: From accuracy to akrasia", p. 416)
What should be your credence that it will rain tomorrow, given that Sherlock is the true expert and that many people will use umbrellas tomorrow? Answer: your credence should be rather high. And it should not in general equal Sherlock's unconditional credence that it will rain. For the information that many people will use umbrellas tomorrow provides strong evidence that it will rain tomorrow. This suggests that your conditional credence should not equal Sherlock's credence that it will rain. Rather, it should equal Sherlock's credence that it will rain conditional on (at least) the information that many people will use umbrellas tomorrow. (Elga, The puzzle of the unmarked clock and the New Rational Reflection principle, p. 135)
In Drug, if 'E; and I am not drugged; therefore, p' is a form that my reasoning to p must take in order for me to keep my belief, then it's true that my belief that p cannot be properly based. But the problem is that this is not a form my reasoning must take, because my reasoning doesn't need to involve the belief that I am not drugged. To see this, think about what reasoning from one's evidence E to p amounts to: it's to believe that p because one takes E to support p. No step in the reasoning has to mention anything about whether one is drugged. (Ye, "Higher-order defeat and intellectual responsibility", p. 10)
Even if the calibrationist thinks that Aisha receives self-locating evidence on Monday, the update procedure that maximizes expected accuracy in response to that self-locating evidence is not the one that has her conditionalize onf the self-locating propositions she learns. It is, rather, one that has her conditionalize on the non-self-locating proposition that she learns such-and-such self-locating proposition upon undergoing her learning experience on Monday. And this, as we saw, yields steadfastness. (Schoenfield, "An accuracy based approach to higher order evidence", p. 704)