prior probability

Lon Fuller’s Speluncean Explorers

Posted on August 29, 2016 by F. E. Guerra-Pujol

In our previous post, we mentioned Peter Suber’s beautiful book on Lon Fuller’s fictional “Case of the Speluncean Explorers.” By way of background, this hypothetical case occurs in the year 4300 A.D. in the Commonwealth of Newgarth. The relevant facts and the applicable statute are as follows:

I. The Facts

The relevant facts of this fictional case are undisputed: After a massive landslide, five explorers are trapped in a remote cave with limited rations. Via radio, they learn that a massive rescue effort is underway, but as their food and water supplies dwindle, one of the explorers (Roger Whetmore), who happens to have a pair a dice with him, proposes to the others that they draw lots (by throwing the dice) to randomly determine who should be sacrificed so that the other four might live until they are rescued. After much discussion, the men apparently assign numbers to themselves and agree to roll the dice. (We say “apparently” because Fuller does not disclose any facts regarding the details of the dice throw.) But Whetmore later has second thoughts and decides to back out of the plan. The other men, however, proceed to roll the dice, and as it happens, Whetmore’s number comes up, and “he was then put to death and eaten by his companions.” (Fuller, p. 9, in Suber, 1998.)

II. The Law

The applicable laws of the Commonwealth of Newgarth simply state: “Whoever shall willfully take the life of another shall be punished by death.” The text of the law makes no mention of self-defense or the defense of necessity.

III. Issue (Question Presented)

On these facts and statutory language, are Whetmore’s companions guilty of committing murder?

IV. Preliminary Analysis

Given these facts and given the statute, this should be an easy case to decide, right? Wrong! It turns out that one can generate any legal outcome (guilty or not guilty) depending on the theoretical or philosophical framework one applies to the facts and law of this case. Worse yet, in law there is no way of testing or deciding which outcome is the “correct” one. In a future post, building on the previous work of Lon Fuller (pictured below), Peter Suber, and others, we will enter the theoretical fray and write up our own legal analysis of this famous hypothetical case.

Credit: Estate of Lon Fuller

Posted in Ethics, Law, Philosophy, Probability, Uncategorized | 1 Comment

In praise of Peter Suber

Posted on August 28, 2016 by F. E. Guerra-Pujol

We first discovered the work of Peter Suber, formerly a legal philosopher at Earlham College and now a senior researcher at Harvard’s Berkman Klein Center for Internet & Society, sometime in 2011 or 2012, while we researching and writing up our paper “Gödel’s Loophole.” (In that paper, we revisit the legend of Kurt Gödel’s alleged discovery of a logical contradiction in the U.S. Constitution; at the time, after carefully reading Suber’s excellent book on “The paradox of self-amendment” and after considering the 1933 Enabling Act that legalized Hitler’s dictatorship, we offered the following Gödelian conjecture regarding one possible constitutional contradiction: specifically, we reasoned that the logical flaw in the Constitution is that the amendment procedures set forth in Article V of the Constitution self-apply to the amendment rules in Article V themselves.) Then, a few months ago, one of our loyal readers (shout out to Craig Collins; check out page one of his thoughtful blog “100 billionth person” here) brought to our attention Douglas Hofstadter’s engaging review of a strange game called Nomic, a complex self-amendment game created by none other than Peter Suber himself. (The rules for Nomic also appear in an appendix to Suber’s paradox book.) Among other things, Nomic provides further evidence in support of our Gödelian conjecture, for this strange game contains a set of both mutable and immutable rules, and the players can eventually transform all the rules of the game over time, even the immutable ones!

But wait, there’s more … A couple of weeks ago, we serendipitously stumbled upon a used copy of another of Suber’s beautiful books, “The Case of the Speluncean Explorers: Nine New Opinions” (pictured below), and finished reading it earlier this week. In brief, Suber takes a famous hypothetical example from law, a hypothetical developed by the late great Lon Fuller–the so-called “Case of the Speluncean Explorers”–and Suber presents new ways of looking at that old hypothetical case. Suber’s book, along with Fuller’s original statement of the problem, provides a deep and engaging introduction to legal theory and the philosophy of law, so we will be blogging in greater detail about Fuller and Suber’s “Speluncean Explorers” in the days ahead. (We will then return to Kenny Easwaran’s important 2015 paper on Bayesian reasoning.)

Posted in Law, Uncategorized | 2 Comments

Two questions about degrees of belief

Posted on August 27, 2016 by F. E. Guerra-Pujol

Previously, we saw how the Bayesian notion of “degrees of belief” offers a possible solution to the preface paradox. Here, we shall consider some philosophical or epistemic objections to this idea of “degrees of belief.” In his thought-provoking and beautiful 2015 Nous paper, for example, Kenny Easwaran poses a number of open questions regarding the nature of degrees of belief, all of which (we think) boil down to the two following queries:

Question 1: What is the difference between an old-fashioned and plain and simple “belief” and a highfalutin Bayesian “degree of belief”? In particular, is there some threshold or cut-off point (say, .9 or .95 or .99) above which a degree of belief acts like a full-fledged belief? (A related question we have is this: do we even need the notion of degrees of belief? After all, isn’t a regular or ordinary belief just as subjective and susceptible to Bayesian updating as a degree of belief is?)

Question 2: In actual human reasoning and daily practice, are degrees of belief “infinitely precise real numbers” (e.g., exact numerical values ranging from 0 to 1) or “something less precise” (e.g., high, medium, and low)? In other words, can a degree of belief really be expressed in precise numerical terms, and if so, how? Aren’t we just plucking numbers out of thin air?

This second question is especially delicate. If it turns out that for whatever reason we cannot assign a precise numerical value to a degree of belief, then we won’t be able to transpose the axioms of probability into the Bayesian framework, and the Bayesian view of probability collapses like a house of cards. In any case, thus far it has taken us three separate blog posts to summarize the first three pages of Easwaran’s 38-page paper. We hope to discuss the rest of his paper in future posts (most likely after the Labor Day holiday).

Credit: Zoubin Ghahramani, via SlideShare

Posted in Bayesian Reasoning, Mathematics, Philosophy, Uncategorized | 3 Comments

The Bayesian solution to the preface paradox

Posted on August 25, 2016 by F. E. Guerra-Pujol

In our previous post, we presented Kenny Easwaran’s vivid description of the paradox of the preface. Briefly, the paradox is this: when a scholar writes up an academic paper, he would like to believe that every claim or proposition in his paper is true. But at the same, that same scholar may add a statement or disclaimer (usually in the acknowledgements section of his paper) accepting responsibility for any error or errors that may appear in the body of the paper. Hence the paradox: if all the claims and propositions in the paper are true, the statement in the preface or acknowledgements section is false; but if the preface/acknowledgements section is true, then there must a claim or proposition in the body of the paper that is false.

In the next part of his beautiful paper, Easwaran presents the standard Bayesian solution to this paradox: the ingenious idea of “degrees of belief.” Simply put, a scholar’s belief in the truth of a claim or proposition is not binary, is not all or nothing; instead, his belief in the truth of claim x or proposition y may range anywhere from 0 to 1; in other words, our beliefs may vary in degrees of strength or weakness; our beliefs may come in shades of grey. So, how does the Bayesian notion of “degrees of belief” solve the paradox? Through the axioms of probability. By way of example, let’s say a scholar has written a paper containing two claims or propositions (Claim A and Claim B)–a very short paper indeed!–and further assume that the scholar’s degree of belief in each claim/proposition is only 0.51 (i.e., the scholar believes that it is only more likely than not that each proposition or claim is true). If the truth of the first claim (Claim A) is independent of the truth of the second claim (Claim B), this strange state of affairs means that there is a high probability that at least one of the claims or propositions might, in fact, be false. (Why? Because when two probabilistic events are independent, the probability of both occurring is P(A and B) = P(A) times P(B).) This ingenious device (degrees of belief) thus solves the paradox of the preface: it is consistent for the scholar to believe in the truth of his claims and to believe that one of those claims might turn out to be false. In our next post, however, we will consider some objections to the Bayesian solution.

Posted in Academia, Bayesian Reasoning, Paradoxes, Philosophy, Truth | 1 Comment

The Paradox of the Preface

Posted on August 24, 2016 by F. E. Guerra-Pujol

Kenny Easwaran, a philosopher at Texas A&M, recently published in the journal Nous this beautiful paper on Bayesian probabilities (hat tip: Brian Leiter). Among other things, Easwaran’s paper contains the best and most succinct explanation of the “paradox of the preface” we’ve ever read. Here it is (edited by us for clarity):

Dr. Truthlove … has just written an extensively researched book, and she believes every claim in the body of the book. However, she is also aware of the history of other books on the same subject, and knows that every single one of them has turned out to contain some false claims, despite the best efforts of their authors. Thus, one of the claims she makes, in the preface of the book, is to the effect that the body of this book too, like all the others, surely contains at least one false claim. She believes that too. She notices a problem. At least one of her beliefs is false. Either some claim from the body of the book (all of which she believes) is false, or else the claim from the preface (which she also believes) is. So she knows that she’s doing something that she hates–believing a false claim. At the same time, she notices a benefit. At least one of her beliefs is true! Either the claim from the preface is true, or all of the claims in the body of the book are true.

We shall have more things to say about this original paper in the days ahead …

Posted in Academia, Bayesian Reasoning, Paradoxes, Philosophy, Truth | 3 Comments

Visualization of the argument for free trade/open borders

Posted on August 23, 2016 by F. E. Guerra-Pujol

Hat tip: Landon Schnabel, via Twitter.

Posted in Economics, Law | 6 Comments

Facebook 101

Posted on August 22, 2016 by F. E. Guerra-Pujol

This fall, we are teaching a large undergraduate survey course (n > 800) on “the legal and ethical environment of business.” Instead of trying to cover everything, we will focus instead on the founding and subsequent explosive growth of Facebook–as depicted in the bestseller “The Accidental Billionaires” by Ben Mezrich (pictured below) and the movie “The Social Network”–in order to explore various areas of the legal and ethical environments of business, including such areas as the law of contracts (think of Facebook’s “terms of use”), intellectual property (think of Facebook’s logos, brand, and “Like” symbols), choice of business entity (think of Facebook’s evolution from a two-man partnership into a Florida limited liability company before incorporating in the State of Delaware), and many other relevant legal and ethical topics, such as the ethics of Facebook’s privacy policies. Although the Professor is not a big fan of Facebook, we think our focus on the founding of Facebook makes good sense for several reasons. First of all, our target audience consists of undergraduates, most of whom use some form of social media to connect with the wider world, and furthermore, it was a motley crew of college students who ended up creating one of the most successful Internet platforms in the world today. Mark Zuckerberg literally changed the world, so why not learn from his successes … and from some of his mistakes?

Posted in Ethics, Law, Uncategorized | 1 Comment

The Simple Sabotage Field Manual

Posted on August 20, 2016 by F. E. Guerra-Pujol

Via kottke, we found this 20-page government-issued, World War II era guidebook called the Simple Sabotage Field Manual. University administrators and business managers take note, here is tip #3:

Organizations and Conferences: When possible, refer all matters to committees, for “further study and consideration.” Attempt to make the committees as large and bureaucratic as possible. Hold conferences when there is more critical work to be done.

Use at your own risk

Posted in Uncategorized | Leave a comment

The spatial physics of cancer cells

Posted on August 19, 2016 by F. E. Guerra-Pujol

Jammed Cells Expose the Physics of Cancer https://t.co/TakGY21ev0 pic.twitter.com/mpMqxV08Lp

— Quanta Magazine (@QuantaMagazine) August 18, 2016

Posted in Nature, Science, Traffic | Leave a comment

Ethical machines (part 3 of 3)

Posted on August 18, 2016 by F. E. Guerra-Pujol

In our previous posts, we presented Brett Frischmann’s novel idea of a Reverse Turing Test, i.e. the idea of testing the ability of humans to think like a machine or a computer. But, how would we create such a test? For his part, Frischmann proposes four criteria (pictured below, via John Danaher) for creating a Reverse Turing Test. Here, we consider Frischmann’s fourth factor: rationality. ((His first two criteria–mathematical computation and random number generation–do not appear to carry any moral significance, while his third criterion–common sense or folk wisdom–seems better suited for Alan Turing’s original test rather than a reverse one.))

By rationality, Frischmann means instrumental or ends-means rationality. Consider the rational actor/utility-maximization model in economics (homo economicus) or the assumption of hyper-rationality in traditional (i.e. non-evolutionary) game theory: “I know that you know that I know …” Many human decisions, however, are often emotive or irrational in nature, such as falling in love, overeating, suicide, etc. Given this disparity between machine-like rationality and human-like emotions, we should in principle be able to create a Reverse Turing Test to measure how rational or machine-like a person is. The more instrumental and less emotional a person is, the closer he or she would be to passing Frischmann’s hypothetical Reverse Turing Test.

Does the rationality component of the Reverse Turing Test have any ethical implications? John Danaher thinks so: “This Reverse Turing Test has some ethical and political significance. The biases and heuristics that define human reasoning are often essential to what we deem morally and socially acceptable conduct. Resolute utility maximisers few friends in the world of ethical theory. Thus, to say that a human is too machine-like in their rationality might be to pass ethical judgment on their character and behavior.” (See his 21 July blog post.) We, however, are not so sure what the ethical implications of Frischmann’s rationality criterion are. John Rawls’s famous “original position” thought-experiment, for example, is premised on the rational actor model, and theories of consequentialism (such as rule-utilitarianism) form a major tributary in the infinite river of moral philosophy. In other words, to the extent machines are far less emotional and more instrumentally rational than humans, might machines potentially have a greater ethical capacity than humans?