The documented origin of the scientific method

In the union between Greek and Jewish philosophy.philo-jew


“Our sight is sent upwards by light and beholds the the heavenly spheres and their harmonious movement, the well-ordered revolutions of the fixed stars, and of the planets, some always revolving in the same manner and coming to the same places, and others having double periods in an anomalous and somewhat contrary manner. Beholding the harmonious dances of all these bodies arranged according to the laws of perfect music causes an ineffable joy and delight to the soul. And the soul, feasting on a continuous series of spectacles, for one succeeds another, has an insatiable love for beholding the wonders of the universe. What often follows from beholding these wonders, is a curiosity about the nature of the stars and planets; whether they have an existence without having been created, or how they received their origin by creation, and what is the character of their movement, and by what causes everything is regulated. It is from inquiries into these things that natural philosophy has arisen. And there is no greater good that has entered into human life.” – Philo, De Opificio Mundi, 17:54


“We don’t know everything, but we know of things that contribute to the stability of the universe, unalterable laws that God has established, and these laws are accomplished always, in every instance and in every place.” – Philo, De Opificio Mundi, 19:61

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Marriage Equality and Gay Marriage

This article is a brief response to “What is Marriage?”, an article by Sherif Girgis, Robert George & Ryan Anderson, published in the Harvard Journal of Law & Public Policy, Vol. 34, p. 245, and kindly shown to me by Kevin Aldrich.

The authors provide a definition of marriage that “most people accept”, and seem to assume this definition without really defending it. They do respond to objections, but they don’t provide any solid positive reason for accepting their definition. But we’ll ignore that particular failing. What’s more interesting is that their definition, which we’ll call the Traditional Definition, seems to include gay marriage. That’s with a charitable reading. A less charitable reading of the Traditional Definition would find that there is only one possible marriage, which is a heterosexual polyamorous situtation where each man in the world is married to every woman and each woman is married to every man. How? First, let’s introduce the Traditional Definition as presented by Girgis, George & Anderson. Here goes.

Marriage involves a comprehensive union of the spouses, a special link to children and norms of permanence, monogamy and exclusivity. We can number these, and will number them in the reverse, from least relevant to most relevant requirements.

  1. Marriage involves the norms of permanence, monogamy and exclusivity.
  2. Marriage involves a special link to children.
  3. Marriage involves a comprehensive union of the spouses.

The first part of the first involvement of marriage (p. 259) is the norm of permanence, at least until death, and is not gender specific. A commitment between two friends or between a father and a son can also be permanent. Monogamy and exclusivity in this context means that each marriage is between two and only two people, and it is noted by Girgis, George & Anderson that this does not rule out Biblical polygamy, since in that case each woman would have been married to the same man, but not to each other. After all, it would seem strange to consider a traditional definition of marriage incapable of comporting to many Old Testament marriages, not to mention a large number of Muslim and other multi-partner marriages all over the world and throughout history.

The second involvement of marriage is a special link to children (p. 255-259). This link to children need not involve actually being able to have children. The authors use the analogy of a baseball team. Even if a baseball team never wins a game, it can still be considered a baseball team, because the members participate in an activity the purpose of which is to win. To adjust their analogy for the sake of a clearer connection to infertile couples, even if all the members of the team were physically incapable of scoring points, the fact that they can play the game is sufficient to consider them a team. By the same analogy, any couple that can unite bodily can be married, regardless of whether that bodily unity can possible generate children. Understood this way, although there may be an important link between the unity of bodies and children in general, specific relationships may have that no instance of bodily unity can possibly result in children and that relationship can still be a marriage. This second involvement is therefore neither necessary nor sufficient, even if it is somehow conceptually connected.

The third involvement of marriage is this bodily unity (p. 253-255). A comprehensive union of spouses. I will begin with the less charitable reading of this requirement, comparing it to the most holy of traditional Christian marriages, that of Mary and Joseph. Were Mary and Joseph validly married? Someone who had only this article by Girgis, George & Anderson would struggle to answer. As the story goes, Mary and Joseph never once had sex. If an actual instance of bodily unity is required for marriage, then Mary and Joseph were never married and Joseph was in no sense Jesus’ father. If, however, the potential for comprehensive union is all that is necessary, then, even accepting a prohibition between two members of the same sex, all that separates any two potential partners is mere ceremony. Every man and woman would have all the conditions provided by Girgis, George & Anderson for marriage. Their relationship would be exclusive and monogamous. Since every man would be married to every woman and could not be divorced, the marriage would be permenant and exclusive and monogamous (all sexual activity would occur within the one polygamous and polyandrous group and no living person can leave the marriage). The marriage is necessarily connected to the birth and raising of all children and all child-producing acts. Finally, the marriage includes all possible bodily unions. Each man alive is then effectively married to every woman, and each woman to every man.

A more charitable understanding of the text could ignore Mary and Joseph as a special case, and continue, while recognizing that maybe there are other real marriages that do not comport to the Traditional Definition of marriage. Even with this charitable reading, marriage between two men or two women can be included. What do the authors say is required for comprehensive union? According to them, the union must be sexual. Union based around tennis wouldn’t be marriage. Union around solving theoretical physics problems, another example the authors raise, involves some sought-after good, truth, even if truth wasn’t achieved, even apparently if truth is known beforehand never to be achievable without a miracle (Artie and Jughead sit down to solve a unified field theory). So long as there is a sincere desire for children from the act, it doesn’t matter if the desire is entirely unrealistic apart from a supernatural event. In fact, the sexual activity between two men or two women might produce children if a miracle occurs, and so if two men or two women enter into that relationship as a sexual relationship, then the right end of the sexual act may be children, even if that end is impossible without divine intervention. Maybe if the world had more faith, such divine intervention would occur more often.

Maybe you object and say that a sexual relationship where children are impossible (without recourse to miracles) cannot constitute comprehensive unity. If you raise that objection, the response is simple. Sterile couples cannot have children of their own without recourse to a miracle, and therefore their sexual acts are just as much instances of comprehensive unity as sex between two married men or two married women.

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The Flexibility of Natural Law

The basis of the argument is, as with all natural law arguments, simple on the face of it. The details, and replies to potential objections, can become complicated, and when I was Catholic I wrote a couple dozen pages on this form of the argument. Here I’ll just show the argument itself, cite some of my sources, and then wait for replies.

A natural law argument for the evil of an act can be represented as

(Foundational Assumption) All human actions are oriented to an intrinsic end.
(Definition) An act is evil if it is intentionally carried out in a way opposed to its intrinsic end.
(Premise 1) Act X has the intrinsic end E.
(Premise 2) Intentionally committing X in a way that frustrates E forces X to be opposed to E.
(Premise 3) A possible component C included in X entails that X be committed in a way that frustrates E.
(Prop) Intentionally including C in X forces X to be opposed to E. [Premises 2 and 3]
(Conclusion) Intentionally including C in X makes that instance of X evil. [Prop, Premise 1, Definition]

All natural law ethics use arguments similar to this, as far as I know. The problem is that many forms of natural law do not agree on the premises, especially Premise 1. They don’t agree on the good of a given act, because they find the foundations to their natural law ethics in different places. We will explore changing Premise 1 only. The argument against contraception is very simple (T for traditional, premises as above).

(TP1) Sex has the intrinsic end of procreation.
(P2) Intentionally having sex in a way that frustrates procreation forces that instance of sex to be opposed to procreation.
(P3) Contraception in sex entails that sex be committed in a way that frustrates procreation.
(TC) Intentionally contracepting during sex makes sex an evil act.

Different acts can have a lot of ends. For example, sex produces friction and that results in heat. Sex as an end of producing heat, but that’s not the intrinsic end, because that’s not why people have sex. That’s not what makes sex good. But who is to say that procreation is the intrinsic good of sex? Maybe it’s just something that comes along for the ride. It doesn’t matter if procreation is connected to evolution and is necessary for species survival, because evolution is directionless (unless we are going to include religion with our natural law).

Rather, the natural place to look for the intrinsic end of an act is something that is generally entailed in each act by each actor, and something connected to what people generally want. Most times, food provides nourishment, so it seems that nourishment is the intrinsic good of eating. Regularly and intentionally eating while frustrating that intrinsic good is called bulimia, and natural law arguments would find bulimia to be immoral.

Most sex isn’t going to produce children, and producing children may not be in each individual’s best interest. Sex doesn’t generally result in babies. It only does so on the off chance (that’s why it has to be committed over and over). Also, having sex without having children doesn’t mean that you are “doing it wrong”. So sex can be seen to have a different intrinsic purpose. Maybe the purpose of sex is romantic pleasure for all partners involved. We’ll call this RP1. In that case:

(RP1) Sex has the intrinsic end of romantic pleasure for all partners involved.
(P2) Intentionally having sex in a way that frustrates pleasure for all partners involved forces that instance of sex to be opposed to that pleasure.
(P3) Contraception in sex does not entail that sex be committed in a way that frustrates romantic pleasure for all partners involved.
(RC) Intentionally contracepting during sex does not necessarily make sex an evil act.

There’s a very simple natural law argument (probably more in line with Hobbs’s ideas about natural law, or other non-Thomistic natural law theories). Its conclusion is that contraception isn’t intrinsically evil. It’s at worst morally neutral.

So that we don’t lose sight of what I’m arguing: I’m not arguing that contraception isn’t evil. I’m arguing that natural law by itself is too flexible to show that contraception is evil. Revelation, in the form of religion or some other source, is necessary in order to determine what the intrinsic ends of a given act are.

Natural law arguments, without the Catholic religion or some Christian religion to definitively reveal the intrinsic ends of human activity, tend to conclude that nothing is wrong with contraception.

The Natural Law Tradition in Ethics, Stanford Encyclopaedia of Philosophy

Beis, Richard H. “Contraception and the Logical Structure of the Thomist Natural Law Theory.” Ethics 75.4 (1965): 277-284.

Grisez, Germain Gabriel. Contraception and the natural law. Bruce Pub. Co., 1964.

Pakaluk, Michael. “Is the New Natural Law Thomistic?.” The National Catholic Bioethics Quarterly 13.1 (2013): 57-68.

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Probability of the Physical Resurrection

It is a Christian belief that Jesus came back from the dead (McGrew & McGrew, or as I will refer to the article, {\rm McGrew^2}). Some claim that the resurrection has significant historical evidence, great enough to compel a rational person to accept it as an historical fact. If something is an historical fact, then it happened physically, at some time and in some location. Maybe Jesus’s resurrection is not an historical fact, but rather a religious fact or some mystical experience. We can figure out the probability of it being an historical fact, but not of it being a mystical experience.

Let’s consider the physical resurrection. How unlikely is it? It’s hard to say with great precision, but an estimate can be made about how likely it is for a person to come back from the dead by known natural causes. It’s possible. A person is, physically speaking, the sum total of his atoms in a particular arrangement. Let’s say that each atom or molecule in this person’s body has nine indendent degrees of freedom (3 vibrational/velocity-components, 3 rotational, 3 translational). When he dies, let’s say some large fraction of his body is reduced to what can be approximated as an ideal gas. Let’s say 10^{26} molecules.

The simplest approximation to be made involves calculating the difference in probability function between an ideal gas and a person, and we can do this via Boltzmann’s entropy equation for entropy, considering the entropy of a dead person compared to the entropy of a live person:

S = k_B \log \Omega

Where \Omega is the number of microstates that correspond to the “macrostate” of “being alive” or “being dead”. For the ideal gas, we can use the Sackur-Tetrode equation, assuming the volume of, say, a sealed tomb near the first temple period. I’ll approximate the volume as {\rm 1000 \; m^3}. We also take for the internal energy 9/2 k_B T (assuming equipartition for the gas) and k_B is Boltzmann’s constant:

S_{\rm dead} = k_BN \log \Bigg[ \Big(\dfrac{V}{N}\Big)\Big(\dfrac{4 \pi m k_B T}{Nh^2}\Big)^{3/2} + \dfrac{5}{3}\Bigg]

where m = {\rm 3 \times 10^{-23} \; grams} is the average molecular mass, taken here to be the mass of a water molecule and h is Planck’s constant. We will assume that the temperature in the room is about 300 K. Our approximation for the entropy of a dead person is about S_{\rm dead} \approx 3 \times 10^{11} \; {\rm erg/K}. S_{\rm alive} will be crudely approximated by approximating the number of microstates that corresponds to “being alive” as \approx 1, and so S_{\rm alive} \rightarrow 0, at least compared to the value of S_{\rm dead}. So:

S_{\rm dead} - S_{\rm alive} = k_B \log \Big(\dfrac{\Omega_{\rm dead}}{\Omega_{\rm alive}}\Big)

And the probability is then:

P_{\rm resurrection} = \dfrac{\Omega_{\rm alive}}{\Omega_{\rm dead}} = \exp\big(-S_{\rm dead}/k_B\big) = 10^{-10^{27.4}}

But this is only for one attempt, one roll of the dice. We can roll the dice a whole bunch of times, over and over. Let’s say that the molecules completely re-arrange themselves over the average time it takes a molecule of the dead person to get from one end of the tomb to the other, assuming random diffusion. The diffusion equation is:

\dfrac{\partial \\\phi}{\partial t} = D \nabla^2 \phi

Which can be solved by taking the size of the room as the scale length, L and \tau is the time it takes for the system to get rearranged:

\dfrac{\phi}{\tau} = \dfrac{D\phi}{L^2}

And so for a diffusion coefficient for oygen-air D \approx 0.2 \; {\rm cm^2 s^{-1}}, the time-scale to reset is about \tau = L^2/D \sim 1 \; {\rm day}, or faster if warmer (although the entropy also increases in such a case).

In order for this to be likely to happen by the known laws of nature, we would have to wait 10^{26} times longer than the age of the universe.

Virtually any explanation is more likely than that Jesus came back from the dead through the known laws of nature. This means that, among other possibilities, there are either unknown laws of nature that make it more likely for people to return from the dead, or some supernatural force or entity has the capability and desire to raise at least one person from the dead. Since there is no good evidence* for either of these alternatives, it seems best to conclude that the resurrection of Jesus is at most a spiritual resurrection, and not a physical resurrection.


We can do a very simplistic Bayesian analysis, given my prior and using the hand-wavy probabilities of {\rm McGrew^2}. We find that the probability for a miraculous resurrection ({\rm R}) vs. no miraculous resurrection ({\rm \lnot R}), given the facts of the matter, {\rm F}, and background information, {\rm \chi}:

{\rm P(R | F \& \chi)} = \dfrac{{\rm P(F \& \chi | R) \, P(R)}}{{\rm P(F \& \chi|R)P(R)+ P(F \& \chi|\lnot R)\,P(\lnot R)}} \approx 10^{44} \times 10^{-10^{27.4}}

\approx 10^{-10^{27.4}}

The probability for the resurrection is effectively completely unchanged by the available evidence, as unlikely as it is to have happened by chance.

*What does this “no good evidence” even mean?

All I mean by this is that I personally am not aware of any other value to set my priors, because I don’t know what other mechanism to use in order to estimate these priors. How likely should I think it is that someone resurrects before I look at the evidence? It seems best to compare to the physical principles that we know now, and treat the resurrection as a thermodynamic miracle that requires evidence. Even if someone thought that all physical events are enacted by God, this would suggest that God’s behavior is so orderly that him deviating from this order would be just as likely as a thermodynamic miracle.

The alternatives, new physics and divine free action, are difficult to incorporate into any Bayesian analysis. How do I include new physics? What processes should I invoke to estimate my probabilities? How do I include divine free action? By what method do I estimate the chance that God will decide to resurrect people? Stan says he came back from the dead and that he’s the son of God. Because of his special relationship with God, he claims it’s more likely he came back from the dead already. How do I determine the prior probability that Stan came back from the dead, before looking at the evidence? Do I assume his claim is true? If I assume it’s true, then why bother claiming that the resurrection is decisive evidence for the claim? If I assume at the beginning that his claim is likely false, then I’m back with the calculation above. Besides, why would God want to kill his own son? How am I going to psychoanalyze the Creator of the Universe?

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Predictions Intelligent Design Supposedly Makes

The speculation is that intelligent design makes predictions that turn out to be right so far. Casey Luskin makes this claim. Let’s not worry toomuch about what intelligent design means. For now, it means that some intelligence made the basic kinds of life on earth, and these kinds have diversified through evolution, but evolution is not able to take one kind into another kind. The four predictions are:

Predictions of Design (Hypothesis) [emphasis mine, redacted for simplicity]:

(1) Natural structures will be found that contain many parts arranged in intricate patterns that perform a specific function.
(2) Forms containing large amounts of novel information will appear in the fossil record suddenly and without similar precursors.
(3) Genes and other functional parts will be re-used in different and unrelated organisms.
(4) Much so-called junk DNA will turn out to perform valuable functions.

I’ll briefly say why I either don’t understand how these connect to intelligent design or, in the case of (1) I’ll say how I don’t understand the prediction at all.

(1) has terms I don’t understand. What do “natural structures” mean? What would be an example of something that is not a “natural structure“? How many parts is “many parts“? How can I tell an intricate pattern from a non-intricate-pattern? Is repeatability sufficient, or do I need something else to establish intricacy? Finally, either the patterns or the parts need to have a specified function. How can this be detected? The language seems to imply some sort of purpose. How could a purpose be observed?

(2) has a couple confusing terms. What makes information novel? What’s an example of information thats not novel? How fast is suddenly? How similar do similar precursors have to be? We can set aside these ambiguities, and make assumptions about the meaning of (2), especially since it seems to have quite a bit in common with an old argument. It seemed at one time from the fossil record that species would not change for a great deal of time, tens of millions of years, and then within a few million years the change would be rapid, and then would slow down again. Stephen Gould posed a theory about how this could be called Punctuated Equilibria. More recently, measured rates of genetic mutation seem to coincide with changes observed in the fossil record, once factors such as migration and the destruction of fossils over time in various layers. Currently there is not much consensus that this is very different from what evolution predicts.

(3) is exactly what you’d expect from evolution also.

(4) I’m not sure what Junk DNA means, even after reading through the Wikipedia article some, and I assume valuable means valuable for the sake of survival. Here’s what I speculate it means. Evolution driven by random mutations and natural selection predicts that there should be large portions of DNA in any organism that, if removed or changed, do not significantly affect its chance at survival. It seems as though there are no such large sections of DNA. This failed prediction would be a difficult problem to resolve for evolution by natural selection and random mutations alone. Maybe there’s another mechanism?

Even if this really is a problem for evolution, I don’t see how it helps Intelligent Design. An example. Atlas Shrugged is intelligently designed. Atlas Shrugged contains all sorts of unnecessary information. I can cut pages out of the book and the story is not significantly changed. There’s an example of intelligent design containing junk. Why wouldn’t the presence of unread DNA indicate either that the designer wanted to protect us better from harmful mutations, or maybe that the designer was very wordy?

I don’t think any of these four predictions really are predictions for intelligent design (except maybe the first one; I can’t understand it at all). Even if true, they wouldn’t be very convincing to me, or I suspect most scientists, that there is an Intelligent Designer.

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