Archive for June, 2009

My Refutation of the Doomsday Argument

It has been more than a month since my paper, “Past Longevity as Evidence for the Future,” appeared in Philosophy of Science. (Update, 6/29/2011: Read about my revised and expanded paper, now available online.) The most important parts of the paper present my own positive ideas on an objective means for using knowledge of the past as evidence for the future. However, part of the paper presents what is, in my judgment, a new and definitive refutation of the Doomsday Argument popularized by philosopher John Leslie. This Doomsday Argument has been debated for the past two decades in leading journals of philosophy and of science, and even discussed often in the mainstream media. It has been widely held that the controversy remains unresolved.

Therefore, when my paper was published in arguably the world’s leading journal for the philosophy of science—the other candidate for that designation is the British Journal for the Philosophy of Science—I thought that there would be a great deal of interest. However, to date, there has not been a single discussion of my paper, except by my colleague Glenn Marcus and me, anywhere on the Internet. Moreover, I have not received a single correspondence from anyone who has read the paper. In fact, as far as I know, the only people who have read the published version of the paper are Glenn and I.

I realize that it is summer, and philosophers and scientists have their own research to think about. But I am an impatient person about everything but my own slowness. Therefore, to help publicize my own work, I am here posting a brief description of my refutation of the Doomsday Argument.

There is also a second part of this post. Glenn finished re-reading the paper on Saturday, and he found an error on a side issue that is yet important, because the error is an incorrect criticism of another person’s work; therefore, I want to correct the error, and apologize for it, right away. I was incorrect in claiming that one of the derivations, by J. Richard Gott III, of Gott’s “delta t argument” commits the same basic error committed by the Doomsday Argument. Glenn pointed out to me that Gott’s derivation avoids that particular error.

Here then is the basic error in the Doomsday Argument.

(Warning: The rest of this post is a little technical.)

The Doomsday Argument relies on the equivalent of this equation, which is an attempted statement of Bayes’s theorem:



HFS = the hypothesis that the future duration of the phenomenon will be short;

HFL = the hypothesis that the future duration of the phenomenon will be long;

HTS = the hypothesis that the total duration of the phenomenon will be short—i.e., that tt, the phenomenon’s total longevity, = tTS;

HTL = the hypothesis that the total duration of the phenomenon will be long—i.e., that tt the phenomenon’s total longevity, = tTL, with tTL > tTS.

Clearly, this equation is an invalid application of Bayes’ theorem, as it conflates future duration and total duration.

Basically, that’s it! That’s the solution to a two-decade-old problem.

In my paper, I take numerical examples based on two possible corrections to this equation: considering only future durations, and considering only total durations. In both cases, I conclude that the Doomsday Argument’s claim, that there is a ‘Bayesian shift’ in favor of the shorter future duration, is fallacious. In fact, unless more information is specified, the solution to this equation is undetermined. Moreover, in many cases, the Doomsday Argument’s uniform-distribution assumption—that P(tp/tt | tt) = U(0,1) where tp = past duration and tt = total duration—contradicts the prior information.

Now to Gott. In a famous paper in Nature in 1993, Gott presents his “delta t argument” for deriving a probability distribution for the total longevity of any phenomenon, based solely on the phenomenon’s past longevity. In a follow-up discussion in Nature in 1994, Gott presents a new derivation of his delta t formula. This new derivation is widely held to be equivalent to Leslie’s Doomsday Argument; see, for example, here and here. However, now that I have identified the conflation error in the Doomsday Argument, it is obvious that Gott’s derivation is different: Gott’s derivation avoids the conflation error! Unfortunately, this obvious fact did not become obvious to me until Glenn pointed it out to me on Saturday.

Though Gott’s derivation from the Jeffreys prior avoids the conflation error I mention above, I think that Gott’s derivation is still vulnerable to other criticisms that I mention in my paper. Nevertheless, I argue in my paper that Gott’s delta t formula, with some important constraints and modifications, has validity. Indeed, in my paper, I present an alternative derivation of Gott’s formula starting from the Jeffreys prior.

Here then is the wrong passage from my paper:

Since the Doomsday Argument is invalid, Gott’s use of the Doomsday Argument to derive his delta t argument from the Jeffreys prior is also invalid. There is, however, a valid way to derive the delta t argument from the Jeffreys prior.

Here is how I would correct that passage:

Interestingly, Gott avoids the Doomsday Argument’s conflation error in his Bayesian derivation of his delta t formula. Gott’s version of the Bayesian equation deals consistently with total durations, and no future durations. Gott is able to do so because he assumes the Jeffreys prior as the prior for total duration. Such an option is not available for the Doomsday Argument, which is intended to hold for any prior.

There is, moreover, a way to derive Gott’s delta t formula from the Jeffreys prior without having to invoke the uniform distribution assumption; this way has some other benefits as well.

My paper then presents my derivation: I use the Jeffreys prior as the prior distribution of λ in the exponential distributions for past and future longevities. I think that my derivation is more robust and precise than Gott’s for these reasons:

    - My derivation makes explicit the assumption that there is the same, constant rate of risk, λ, per unit time, in both the past and the future—and that we have no knowledge of the value of λ. [Italicized phrase added on July 1.]. (Gott makes an assumption resembling this one in other derivations.) This assumption means that the same causal factors are present throughout the past and future, and the assumption specifies how knowledge of the past updates the probability distribution for the future.

    - My derivation removes the need for Gott’s uniform-distribution assumption, that P(tp/tt | tt) = U(0,1) where tp = past duration and tt = total duration. The uniform distribution of tp/tt is a consequence of the exponential distributions, with the same value of λ, for past and future durations.

    - In my paper, I explain that the exponential distribution for past duration actually overestimates—or places an upper bound on the possibilities of—past duration. Therefore, Gott’s delta t formula is actually a worst-case bound—worst-case, assuming that we want a long future duration—on the final probability distribution for total longevity. My derivation, which makes explicit the exponential-distribution assumption for past duration as well as future duration, thereby makes clear that the result is only a bound. That Gott’s result is only a bound is consistent with a result by Frank Coolen (“Low Structure Imprecise Predictive Inference for Bayes’ Problem” and “On Probabilistic Safety Assessment in the Case of Zero Failures”), which I discuss at length in my paper.

I hope that my alternative derivation, along with my correction and apology, will somewhat atone for my incorrect criticism of Gott’s argument.

Update, 10/6/2009:

In Pisaturo (2009), I argued that the Doomsday Argument commits the error of conflating total duration and future duration. I subsequently realized that Dieks 2007 makes a similar identification, though he presents arguments somewhat different from mine, and I should have cited this work.

Also, I stated in my post above that Gott (1994) is able to avoid the Doomsday Argument’s error of conflating future duration and total duration because Gott uses the Jeffreys prior for total duration, not future duration. Such a prior is not available for the more general Doomsday Argument. Nevertheless, an argument can be made that the Jeffreys prior should indeed be used by Gott as the prior for future duration and not for total duration. (See Caves 2000, 151 for a related argument.) If that argument is correct, and I think it is, then two errors by Gott cancel each other out. –Deleted on November 7, 2009.


Caves, Carlton M. (2000), “Predicting Future Duration from Present Age: A Critical Assessment”, Contemporary Physics 41: 143–153.

Dieks, Dennis (2007), “Reasoning about the future: Doom and Beauty”, Synthese 156: 427–439.

Pisaturo, Ronald (2009), “Past Longevity as Evidence for the Future”, Philosophy of Science 76: 73–100.

Ayn Rand’s Diagnosis of “Collectivized Rights”

Explain this contradiction.

When he discusses Osama bin Laden and Al Qaeda, Obama talks about killing or capturing them. But when he discusses Ahmadinejad, Khamenei, and the Iranian government, Obama talks about “diplomacy” and “a good-faith effort to resolve differences,” and “a new beginning.” Even in this past Tuesday’s press conference, when he finally condemned the Iranian government for oppressing Iranian protestors, Obama also spoke of “healing some of the wounds of 30 years, in terms of U.S.-Iranian relations.” And he reiterated the following:

I’ve made it clear that the United States respects the sovereignty of the Islamic Republic of Iran …

Like Al Qaeda, the Iranian government has killed many Americans, from the support of Hezbollah in its killing of 241 Marines in Beirut in 1983 to the backing of terrorism against American soldiers in Iraq.

Why doesn’t Obama speak of “a new beginning” and “healing some of the wounds” with Al Qaeda?

Evidently, Obama holds that the Iranian government is legitimate, deserving of respect, for no more reason than that it is a government, that it has total control over some territory, and (above all) that some group of people—“the Iranian people”—chose it.

In her essay “Collectivized Rights,” (1963, reprinted in The Virtue of Selfishness) Ayn Rand writes:

What subjectivism is in the realm of ethics, collectivism is in the realm of politics. Just as the notion that “Anything I do is right because I chose to do it,” is not a moral principle, but a negation of morality—so the notion that “Anything society does is right because society chose to do it,” is not a moral principle, but a negation of moral principles and the banishment of morality from social issues.

The fact that many Iranians support or tolerate the Iranian government makes the government no less evil, but rather makes those Iranians guilty too. The fact that the Iranian government oppresses those Iranians who do not support or tolerate the government makes the government’s evil even more obvious. The fact that the Iranian government controls a vast territory (with enormous oil assets) and an entire population, in a way that Al Qaeda does not, makes the Iranian government no more legitimate than Al Qaeda, but far more of a threat to America.

Just as the American military should kill Osama bin Laden on sight, so too should it terminate Ahmadinejad, Khamenei, and the rest of the Iranian dictators.

Of course, this will not happen. The sad truth is that if Obama were living in the 1930s, he would say that he “respects the sovereignty” of Nazi Germany.

This notion of “collectivized rights,” the notion that “‘Anything society does is right because society chose to do it,’” is also implicit in Obama’s domestic policy. But that is a topic for another post (or comments?).

Obama Submits to Evil

Yesterday, while thousands of Iranians were protesting, and some were being killed by Iran’s ruling tyranny, Obama was interviewed by Harry Smith of CBS News. Here is an excerpt:

Smith: People in this country say you haven’t said enough, that you haven’t been forceful enough in your support for those people on the street — to which you say?

Obama: To which I say, the last thing that I want to do is to have the United States be a foil for those forces inside Iran who would love nothing better than to make this an argument about the United States. That’s what they do. That’s what we’re already seeing. We shouldn’t be playing into that.

In other words, America should not say things bad about bad guys, because those bad guys would then say bad things about America.

In other words, not only must America refrain from taking military action against our enemies, but we must also refrain from speaking ill of them.

This mentality of Obama reveals a perverse motivation behind his praise of Iran and Islam, and his criticism of Israel. Israel, after all, is a moral nation and would never use America as a “foil.”

Throughout Obama’s presidential campaign, Obama and his current Secretary of State said that they would “restore respect for America throughout the world.” (The direct quotation is from Hillary Clinton.) Now we are seeing in concrete terms what they really meant. They seek not respect but approval—through submission to evil.

The literal meaning of the word ‘islam’ is ‘submission’, and a Muslim is ‘one who submits’. In a fundamental sense, Obama is a devout Muslim.

Obama-Care: A Tyrant’s Notion of ‘Choice’

President Obama spoke in Chicago Monday morning at the Annual Conference of the American Medical Association about his plan for health care in America. The first part of Obama’s speech was a fairly accurate litany of current problems: more than $2 trillion a year (which is roughly $7,000 per person) is spent by Americans on health care; moreover, expenditures are rising rapidly; yet the quality of care is not what it should be.

What Obama evaded is that the American healthcare system is already essentially a socialized system.

Of the $2 trillion in spending that Obama cites, about $900 billion is spent by the federal government on ‘Health and Human Services’ (if state spending on federally-sponsored Medicaid is included) alone. And this expenditure is only partial reimbursement for the full cost of government-mandated services, so that the non-reimbursed costs must be built into the price of services charged to those in the private sector. The half of the healthcare industry outside of government’s Health and Human Services is highly socialized in the form of fascist controls: near-total control over what insurance companies must cover in their policies, control over drug companies via the Food and Drug Administration, state licensing of doctors (restricting what services non-doctors—including doctors’ assistants—can perform), malpractice court rulings that fault doctors for not being omniscient, and unfavorable tax treatment for individuals (in contrast to groups of employees) who pay for their own health insurance.

Obama bemoaned the fact that doctors have become “paper-pushers.” But that paper pushing is the filling out of government-required forms. Obama called for “medical IT” to computerize the form-filling. But why is there not medical IT already? Private, non-socialized industries already have IT.

Obama bemoaned the fact that insurance premiums have doubled over the past decade. When I was living in New York City in the early 1990s, my insurance premium increased six-fold in two years. The cause was the state government’s instituting of “community rating,” which forced insurance companies to charge premiums based solely on where I lived, regardless of my personal health. Insurance companies were no longer allowed to give me a physical exam.

Obama extolled the benefits of preventive medicine, calling for lower premiums for people who take better care of themselves and “score well” on health tests. But this practice is just what is expressly forbidden by current, community-rating laws. In California, where I now live, insurance companies are not even allowed to offer lower premiums for those who “score well” on an AIDS test:

California law prohibits an HIV test from being required or used by health insurance companies as a condition of obtaining health insurance coverage.

Later in his speech, Obama said this:

We need to end the practice of denying coverage on the basis of preexisting conditions. (Applause.)

Obama has expressed this idea before, and I have shown its absurdity before. But I will add here that this idea is the exact opposite of rewarding people who “score well” on health tests. Moreover, insurance companies are already forced to insure for some pre-existing conditions—such as AIDS—and to provide treatment for unhealthful practices such as substance abuse, thereby driving up insurance premiums for those who do not engage in unhealthful practices. So much for encouraging prevention.

Throughout his speech, Obama bemoaned dire conditions under the current system, evading the fact that these dire conditions have been caused by socialized medicine. His solution is more socialism: more violations of individual rights of life, liberty, the pursuit of happiness, and property—all in the name of sacrifice of the individual to the collective:

We are not a nation that accepts nearly 46 million uninsured men, women and children. (Applause.) We are not a nation that lets hardworking families go without coverage, or turns its back on those in need. We’re a nation that cares for its citizens. We look out for one another.

In other words: “To each according to his need.”

Yet Obama denies his socialism:

We know the moment is right for health care reform. We know this is a historic opportunity we’ve never seen before and may not see again. But we also know that there are those who will try and scuttle this opportunity no matter what — who will use the same scare tactics and fear-mongering that’s worked in the past; who will give warnings about socialized medicine and government takeovers, long lines and rationed care, decisions made by bureaucrats and not doctors. We have heard this all before. And because these fear tactics have worked, things have kept getting worse.

What is Obama’s argument that he is not advocating socialism? He has none. Instead, he appeals to ridicule, calling his opponents “fear-mongers” and saying the word “socialize” in a mocking tone, and never addressing his opponents’ arguments.

The closest that Obama comes to an actual argument that his plan is not socialism is his claim that his plan is different from a single-payer system—though his only criticism of a single-payer system is the following:

I’ll be honest; there are countries where a single-payer system works pretty well. But I believe — and I’ve taken some flak from members of my own party for this belief — that it’s important for our reform efforts to build on our traditions here in the United States.

In other words, socialized medicine is a good system, but such a system is too much of a change for traditionally capitalist America. In other words, Obama admits that he is a socialist, but he does not believe that Americans would accept socialism.

What then is Obama’s alternative to single-payer socialism? Here is Obama’s description:

So we need to do a few things to provide affordable health insurance to every single American. The first thing we need to do is to protect what’s working in our health care system. So just in case you didn’t catch it the first time, let me repeat: If you like your health care system and your doctor, the only thing reform will mean to you is your health care will cost less. If anyone says otherwise, they are either trying to mislead you or don’t have their facts straight.

Now, if you don’t like your health care coverage or you don’t have any insurance at all, you’ll have a chance, under what we’ve proposed, to take part in what we’re calling a Health Insurance Exchange. This exchange will allow you to one-stop shop for a health care plan, compare benefits and prices, and choose a plan that’s best for you and your family — the same way, by the way, that federal employees can do, from a postal worker to a member of Congress. (Applause.) You will have your choice of a number of plans that offer a few different packages, but every plan would offer an affordable, basic package.

Again, this is for people who aren’t happy with their current plan. If you like what you’re getting, keep it. Nobody is forcing you to shift. But if you’re not, this gives you some new options. And I believe one of these options needs to be a public option that will give people a broader range of choices — (applause) — and inject competition into the health care market so that force — so that we can force waste out of the system and keep the insurance companies honest. (Applause.)

To many people, who do not understand political freedom, Obama’s proposal sounds appealing. After all, Obama is offering more choice, more options, more competition, right?

Perhaps the evil of Obama’s plan is more apparent in this analogy:

So we need to do a few things to provide a desirable wife to every American man. Now, if you don’t like your wife or you don’t have any wife at all, you’ll have a chance, under what we’ve proposed, to take part in what we’re calling a Wife Exchange. You will have your choice of a number of different women, provided by the government.

Again, this is for men who aren’t happy with their current wife. If you like what you’re getting, keep it. Nobody is forcing you to shift. But if you’re not, this gives you some new options. And I believe one of these options needs to be a public option that will give men a broader range of choices.

Oh, and by the way, your current wife will also be made available for other men to choose, as part of their ‘public option’. After all, the government does not create new women out of thin air, any more than it creates new doctors. But don’t worry, we’ll pay her (with your tax money). And if other men choose her, you’ll still be able to share her.

Does that analogy make the meaning of Obama’s plan clearer?

Obama has a tyrant’s notion of ‘choice’. In a free society, individuals engage with each other when such engagement is by mutual consent. A man and woman marry when both the man and the woman choose each other. A purchase is made when the purchaser and the seller agree to the terms of the sale. An employee works for an employer when they both choose such an arrangement and agree to terms.

Obama, on the other hand, wants to give people the option to be served by doctors, in part paid for by taxpayers and in part not paid for at all, even when those doctors and those taxpayers choose not to do so of their own free will. Obama would abolish the principle of trade by mutual consent, and replace it with one party’s choice to coerce the other.

“If you’re not happy with your current cotton-pickers, whom you have to pay, we’ll provide you with the choice of free cotton-pickers.”

This notion is a tyrant’s notion of ‘choice’. This mentality is the mentality of America’s President.

See also:

Immoral, Impractical Socialized Medicine

Obama Seeks “Cure for Cancer”

Fascism: Controlling Capitalists, for Socialist Goals

The Tyrant’s Lies Against Capitalism

The Fraud of “Interdependence”

Now is the Time to Strike Iran

The current rioting in Iran over Iran’s sham presidential election (in which all candidates were approved by the religious Guardian Council, ultimately selected by the religious Supreme Leader Ali Khamenei) provides a good window of opportunity for a military strike by the U.S. and Israel against Iran. Of course, this won’t happen.

If any of the Iranian rioters are in fact champions for freedom instead of merely supporters of an alternative dictator, nothing would inspire them more than an attack now on Iran’s nuclear facilities and other military installations. Even better would be a concurrent attack on and/or seizure of Iran’s oil assets.

Because Israel and the U.S. have waited so long to attack Iran’s nuclear facilities, the outcome of such a targeted strike is uncertain. But now, with Iran’s government distracted with the riots, the chance for total success is greatest. And we have nothing to lose. Any damage we can inflict on Iran now will be moral support for any good people in Iran.

If Iran tries to respond militarily against us, now is the time that we can fight—and win—an all-out war with Iran with the least risk of casualties to Americans.

Of course, the U.S. government will not strike Iran. Instead, somewhere down the road, many Americans, Isrealis, and innocent Iranians (such as there are) will be killed. Instead of our striking when our enemies are weak, our enemies will strike us when we are weaker and they are stronger.

The Mission of Public Schooling

My friend Scott Soodek wrote this to me recently:

I attended both of my daughter’s graduations this week. One got her Masters in Literacy from Hunter College (CUNY) and the other a BFA in Interior Design from Pratt Institute. The tone and content of the message from the speakers at each graduation was so contrasting, that it took me by surprise.

At the Pratt graduation, the speakers were Judy Collins, Richard Serra, Tommy DiPaola. All are artists whose message was now that you have accomplished this great task, let your creativity be your guide, carve out your own niche in the world of art and design. You have the talent, use it to become successful.

At the Hunter graduation, the speakers were Chuck Schumer [U.S. Senator from New York], Hilda Solis (Secretary of Labor) and Scott Stringer (Borough President of Manhattan). Their message was now that you have accomplished this great task, go out into the communities that you came from and give back. Fight for the poor, the downtrodden, the people who don’t have a voice. I didn’t hear one sentence uttered about making your own way and becoming a success.

I thought the difference between the artists and the government was striking.

Hunter College is “the largest college in the City University of New York (CUNY) system.” The message of Hunter’s commencement speakers is an accurate account of the mission of public schooling (and of most non-profit schooling), from kindergarten through graduate school. The model product of public schooling is Barack Obama.

See my refutation of The Collectivist Notion of “Giving Back to Society”.

Congratulations, Scott, to your daughters and to you and your wife.

Remembering D-Day

On D-Day, sixty-five years ago today, the United States and its allies Great Britain, Canada, Free France, Poland, and Norway invaded Normandy; thus began a campaign to liberate France and other nations of Europe from Nazi Germany.

On this one day, more than 1,400 American soldiers, and more than 6,600 Allied soldiers in total, were killed. But the U.S. and its allies won the day, and the War.

Here is a video interview of Arthur Seltzer, a brave American who fought for freedom on Omaha Beach on D-Day.

Between June 6 and the end of August, 1944, more than 20,000 Americans were killed in this invasion.

In the Pacific theater, against Japan, no such massive invasion was necessary, for one reason: America dropped atomic bombs on Japan. For an account of the great saving of American lives by America’s use of this great weapon, see this excellent video by Bill Whittle.

Today is also the birthday of another American hero, from the American Revolutionary War: Nathan Hale.

Debunking Obama’s Praise of Islam

See the Charlotte Capitalist’s excellent refutation of Obama’s praise of Islam in Obama’s Cairo speech on Thursday, June 4.

Night of the Living Dead Auto Company

General Motors is now dead. The company’s corpse will be owned and driven mainly by the bad guys who destroyed the U.S. auto industry: government and the labor union.

As reported in The Wall Street Journal (see the first link above), the U.S. government will own 60%, the Canadian government will own 12.5%, and a United Auto Workers union health-care fund will own 17.5%. That leaves only 10% for existing bondholders, the only rightful owners in the lot.

The corpse of General Motors will not run on the principle of trade, but on the expediency of coercion. Instead of trading with investors, it will feed on taxpayers.

Generations ago, General Motors was a great American company. Its corpse is one of the most un-American entities on the globe.