What is Proof?

I was recently asked what I consider to be “proof”. This question came up specifically with respect to my blog post on why I am an atheist and not an agnostic.  So what is “proof”?

I hold that the most essential form of proof is observation -that which you can come into contact with by means of your sensory-perceptual mechanism. In other words, “proof” is generally what you can see, hear or touch. (Taste and smell would also count, but these are pretty weak senses for human beings.) There are other types of proof that are possible, but they are related back to observation.  Some things are not directly perceivable, but we know that they do exist because of how they interact with things that we can observe. We can observe the effects on things that we do observe directly, and thereby come to understand something about the imperceptible thing that was the cause.

In the natural sciences, much of what we would call proof involves observing the effects on things we can perceive by things that we cannot perceive, thereby providing evidence about the existence and nature of those imperceptible things. For instance, bacteria were first observed by Antonie van Leeuwenhoek in 1676, using a single-lens microscope of his own design. http://en.wikipedia.org/wiki/Bacteria#History_of_bacteriology  With bacteria, human beings have been able to use a device with known properties to observe what was previously unobservable. The device was something that used specially shaped glass to amplify light. We knew that when glass was shaped in certain ways, it would make something appear bigger. We then extrapolated that if we bent and shaped this glass and combined it with other bent and shaped glass -other lenses- then it would amplify even smaller things. With sufficiently powerful enough lenses, such a device would eventually amplify the appearance of things that were too small to see with the naked eye. This device was named a microscope, and when Leeuwenhoek looked through it, he saw tiny organisms that were not visible with the naked eye, which were subsequently called “bacteria”.

The atom was discovered thanks to a number of observations made by scientists:
“In the early 1800s, John Dalton used the concept of atoms to explain why elements always react in ratios of small whole numbers (the law of multiple proportions). For instance, there are two types of tin oxide: one is 88.1% tin and 11.9% oxygen and the other is 78.7% tin and 21.3% oxygen (tin(II) oxide and tin dioxide respectively). This means that 100g of tin will combine either with 13.5g or 27g of oxygen. 13.5 and 27 form a ratio of 1:2, a ratio of small whole numbers. This common pattern in chemistry suggested to Dalton that elements react in whole number multiples of discrete units—in other words, atoms.” http://en.wikipedia.org/wiki/Atom#First_evidence-based_theory

This knowledge was combined with other knowledge such as the phenomena of “Brownian Motion”:

“In 1827, botanist Robert Brown used a microscope to look at dust grains floating in water and discovered that they moved about erratically, a phenomenon that became known as “Brownian motion”. This was thought to be caused by water molecules knocking the grains about.” http://en.wikipedia.org/wiki/Atom#First_evidence-based_theory

In the case of atoms, it was observed that a certain amount of tin always combined with a certain amount of oxygen in one of two ways, suggesting that whatever the ultimate constituents of tin and oxygen were, they must be discrete units. In other words, they must consist of units that cannot be divided any further -at least if you still wanted to speak of them as “oxygen” and “tin”. This knowledge, combined with other observations, such as Brownian motion, eventually led to the widespread acceptance of the existence of atoms. We inferred the existence of something, the atom, based on things that we could observe with our inborn sensory-perceptual mechanisms (our eyes).

The Theory of Evolution is another example of how we have come to have, at the very least, a theory, that explains our origins. There is no way to directly confirm this theory by direct observation. If it is happening, evolution happens over millions of years, with parents giving rise to slightly different offspring, who then are either more or less successful at survival because of these characteristics. These offspring have more children than those without those characteristics, and this continues on and on, until the resulting organism is so different from the original ancestor that it can no longer even be considered of the same species. This theory is based on things like:
(1) Geological observations that suggest the Earth is billions of years old.
(2) Observing the fact that different members of the same species of organism have different characteristics from each others. (E.G. some people have red hair while others have brown hair.)
(3) Parents are able to pass some of their unique characteristics on to their children. (E.G. blue-eyed parents have blue-eyed children.)
(4) Some of the unique characteristics an organism has can make it more successful at surviving and reproducing than if it didn’t have that characteristic. (E.G. a bacteria might have partial resistance to penicillin, while other members of its species do not, meaning resistant ones will tend to survive and reproduce.)

All of these observations suggest that, given sufficient time, one organism can be the ancestor of organisms that would be considered a completely different species, and that this occurs because of changing environmental conditions.

Proof of things that we didn’t observe by observing other things, and recognizing that there is a relationship, is not limited to the natural sciences. For instance, in a murder trial, all of the evidence that is presented is something that the judge and jurors can observe directly with their eyes and ears. For instance, the prosecution can present finger prints that were lifted from the murder weapon, and explain the chain of custody of the object such that no one had touched the murder weapon since it was discovered at the scene. Or, the prosecution can explain how each gun barrel leaves unique markings on the bullet when it is fired, and that the markings on the bullet found in the victim matches the markings on a bullet fired through the weapon by a ballistics expert.

Witness testimony can also establish other facts for the jury, such as if someone saw the accused walk into the victims house, and then heard a shot ring out. In that case, the jurors are relying on the eye witness’s observations, which are generally going to be believed, unless it can be show that the witness had some bias to lie or some mental problem that makes them unreliable. Even testimony such as someone seeing the victim and the accused in a heated argument a few days prior to the murder can be evidence, based on what we know about human nature. Human beings tend to do things because they have a motive for doing so, and if the accused hated the victim, then that would suggest he might have killed the victim. This recognition of human behavior is also based on observation.

What is the method of relating the things that we observe and then concluding the existence of something that we didn’t observe? The method of logic provides us with guidance in this area. Logic generally takes two forms: the inductive and the deductive. In deductive logic, we mentally place a specific instance into a general category or principle. It is reasoning from the general to the specific. For instance: All men are mortal. Socrates is a man. Therefore, Socrates is mortal. “All men are mortal” is a general category or principle. Socrates is shown to be a specific instance of a man, and therefore everything that is known to be true about all men is true with respect to Socrates, i.e., that Socrates, just like all men, is mortal.

Deduction is a means of coming to have knowledge that doesn’t depend on direct observation of the conclusion, but the conclusion is based on other direct observations. In the case of the Socrates syllogism, you didn’t observe Socrates being born, growing old, and then eventually dying, but you were able to conclude without such direct observation that he is mortal -that Socrates will eventually die. What is the evidence for this?  One such fact is that every other man who is known to have lived eventually died. You then assume that since Socrates is in this category of “men”, that he has the same characteristics as other men, and is therefore mortal.

The above discussion of deduction leads to the other major form of logic. Where did the “all men are mortal” part of the Socrates syllogism come from? This is a complicated subject, and is not even fully agreed on today, but, in general, such knowledge is gained by observing a sufficient number of concrete examples of a thing and then generalizing that all members of that category possess that characteristic. For instance, it is impossible to actually observe all men and see that they are mortal, but you observe enough examples that you can eventually conclude that “all men are mortal.” The problem is that this can lead to generalizations that are erroneous. An example of this is the generalization: “All swans are white.” You observed numerous examples of white swans, and you conclude that they are all white. But, one day, you discover a bird that is morphologically the same as white swans, but it has black feathers. How do you know when you have a valid generalization versus an invalid one? I would like to know the answer to that one myself. In general terms, I think that if you are clear about the nature of the thing, and your purposes when you generalize, then it is possible to come up with valid generalizations. So, in the case of the invalid statement “all swans are white,” if you were clear about what a swan is and also about why the color of swans matters to you, then you probably wouldn’t make such a generalization in the first place. I cannot even think of a situation where it really matters whether swans are black or white. If you regard swans as a food source, then their color makes no difference. If you simply think swans are beautiful and graceful, then I think that belief applies to both colors. For my purposes here, the minutia of valid induction can be put aside. The point is that you generalize, or induce, by observing a sufficient number of examples to reach the generalization. Induction ultimately depends on your observations -on what you can perceive with your senses.

Someone might claim that they have a means of gaining knowledge other than through observation or logical reasoning, but I am aware of no such means. However, if they can provide me with proof, then I am open to hearing what they have to say. I just don’t know how you provide proof without proof, which seems to be what they are claiming.

“Free Will” and “Determinism”

I was thinking about the “determinism versus free will” debate yesterday, and I had a couple of thoughts that I thought might help in this debate. I am aiming my thoughts at people who are generally secularists and who look for naturalistic explanations for all phenomena.

First, I think it’s useful to think about things that clearly *are* determined. These are all non-living things, some of which are man-made and some of which are not. Examples include: billiard balls on a pool table that bounce when struck by other billiard balls, water reacting to a pebble being thrown in it with waves, the planets moving in orbit around the sun, a mouse trap when it is set and then sprung by a mouse, a basket ball that is dropped from a height and then repeatedly bounces -but less and less until it comes to a stop, and a rube goldberg machine. Both a proponent of determinism and an opponent of determinism will agree that all of these things are completely “determined”. These things possess no “internal will” that causes them to act as they do.

Second, it is also useful to look at the human mind to see if all of our mental actions are the same in terms of “level of choice”. Internal introspection of your own mind is the only way to really do this. There are certain “mental behaviors” or “mental actions” that seem less “chosen” than others. Normally, your emotions typically just react to external stimuli with very little or no ability on your part to avoid feeling those emotions. You feel anger, hatred, sadness, or happiness in reaction to certain perceived events seemingly “automatically”, like a mousetrap going off. At any given moment, your emotions seem closer to the examples of non-living things that are determined. If you are a man interested in women, and you see a woman with a certain body shape, size, and age-range, who behaves in a certain way, you feel a certain amount of romantic desire for her. If you are a woman with a child, you will normally feel fear if you see your child facing some sort of danger -or you will feel hatred or anger for the source of the danger towards your child. If someone tries to rob you with a gun, you will feel fear or anger. If someone you care about dies, you feel sadness. In all cases, you have little choice about the feelings that you feel at that moment. Your actions with respect to those feelings appear to be more under your control, but not the feelings themselves. Over time, your emotional reactions to certain things seem like they change. If you see someone you were romantically involved with several years after you broke up, you may no longer have the same romantic feelings you once had for them, or not to the same degree, but this happens over time. At any given time, one’s emotions are more fixed. (Some psychological schools seem to be based on the assumption that your thoughts can change your emotions over time, so if you change your thinking, which is under your control, then you will eventually change your emotions, but that is beyond the point here.)

But, when it comes to certain tasks, your ability to mentally solve problems seem less “automatic” than your emotions. For instance, if you are a physicist trying to solve a complex math problem, you actually have to sit down and work on the math problems. If you are a doctor trying to diagnose a patient’s illness, you actually have to draw on your store of knowledge and try to come up with a diagnosis. If you are a computer programmer, you actually have to sit down and try to figure out what data structures and if-then-else statements will solve the problem you are trying to solve. If you are a lawyer, you have to think about the facts of the case, and then go research the law and try to determine what legal precedents the facts of your case fit into. If you are a structural engineer, you have to decide what are the requirements of your building, such as: What will it be used for? How many people will use it? etc. Then you actually pick construction materials, work out the load requirements, etc. This applies equally to “blue collar” occupations. If you are a taxi cab driver, and your fare wants to get to the airport from downtown in less than 30 minutes, you have to consider the time of day, the traffic conditions, which roads are under construction, possibly consult maps, and mentally devise a route. In all of these cases, the mental activity involved is not nearly as “automatic” as when you feel an emotion. They all involve thinking to solve the problem of human survival.

Now, I think that a dedicated determinist is just going to say that all of these examples of thinking are “illusory” examples of choice because at some “lower level”, we are all just made up of some substance(s) that appears wholly determined. For instance, he will say on the molecular level, an atomic level, or a subatomic level, you are actually determined. He says this with the following reasoning: Your brain is made of nothing but molecules (or atoms). Molecules are entirely determined. Therefore, your brain is entirely determined. In other words, your mind is actually just a more complicated example of things like the mousetrap discussed above. My concern with that sort of reasoning is that it basically says: what you perceive as reality is not really reality at all. “Reality” is the molecular level, and the world that you perceive is nothing but an illusion. But, if you cannot count on what you perceive, including your perception of the choice to think, then I am not sure that any sort of knowledge of the molecular level, or any other level, is actually possible. Without knowledge, life would seem to be, as Hobbes said in another context, “nasty brutish and short”.

Randall’s Aristotle, Chapter VII, “The Heavens”

I have been reading Aristotle by John Herman Randall, Jr. (1960 Columbia Press).  Chapter VII, “The Heavens” discusses Aristotle’s cosmology. It really hit home for me why the Catholic church took so much offense from Galileo and other 16th/17th Century natural philosophers saying that the Earth was not the center of the universe, that the Earth revolved around the sun along with the planets, etc.
The church had adopted Aristotle’s ideas by that time, and that included the notion that as you traveled out away from the Earth, you would approach divine perfection.  Unlike Plato who thought that such divine perfection existed in some other realm, Aristotle said such perfection was the outermost layer of the Universe.  As evidence of this perfection, it was pointed out that the stars moved in an apparently unchanging circular pattern through the night sky, and such circular motion was considered “divine” or “perfect”.  The stars, unlike the planets, exhibited this circular motion because they were closer to perfection.

As the Church became increasingly Aristotelian, it would have adopted the notion that this outer realm of the universe was where the divine resided, rather than in some “other realm” outside the universe as a more Platonic Christianity would hold.  However, the natural philosophers of the 16th/17th century began to show that the rest of the universe operated in accordance with the same natural laws as the ones operative here on Earth, and that the Earth revolved around the sun.  This would have started calling into question the whole scheme in which the Earth is at the center, and “imperfect”, while as you moved out away from the Earth, you approached “perfection”, and a different set of natural laws from the ones on Earth.  But, if the Church had already rejected the Platonic notion of the divine in another realm, and the divine also didn’t exist in this universe, then that would tend to suggest that it didn’t exist anywhere.  It wasn’t just a question of Astronomy for the Church, it literally called into question it’s most fundamental tenants.

Carl Sagan’s “Cosmos”

I am currently watching Carl Sagan’s “Cosmos” on Netflix. I recall seeing bits and pieces of this throughout the 1980’s on PBS, but I was basically too young to follow it in great detail (I am only 38). It is a journey through intellectual history, with an emphasis on Astronomy and Physics, with a little Philosophy thrown in for good measure. I think that it is, overall, a very good series.

Episode 7, “The Backbone of Night” was an especially interesting episode since it seems to present a slightly different interpretation from how I have heard most Objectivists interpret the history of Ancient Greece, which tends to focus on Aristotle. Sagan agrees that the Ancient Greeks, especially the Ionians, were the birthplace of the scientific method of observation and experimentation. But, he goes on to say that there was another strand of thought running through Ancient Greece centered in Pythagoras, which deemphasized experimentation and observation in favor of “deduction”. (I think Sagan even used the word “deduction” to describe the Pythagoreans.) This ultimately led to a mystical world-view (or was based in a mystical world-view), which was expressed in the ideas of Plato. Interestingly, he even says that this Pythagorean worldview took reason out of the hands of the Ionian merchants and artisans –practical men concerned with ideas- and put it into the hands of the elite slaveholders, which was more consonant with the ownership of slaves. This was because the Pythagorean system emphasized the mind over the body, and “the body” was associated with the physical labor of the elite’s slaves. (I assume because the slaves would be viewed as less than fully rational manual laborers who merely used their bodies.)

Sagan then goes on to say that Plato’s ideas were basically adopted into Christianity. (Sagan hasn’t come out and said he’s an atheist, but he all but says so at various points in the series.) Sagan then essentially says that the early flowering of “expermentalism” in Ionia was suppressed by the Pythagoreans and later Plato, and that Aristotle was essentially no better than Plato. It wasn’t until the Enlightenment that the “Ionian world view” was rediscovered, or so says Sagan. What I found interesting is how much he deemphasized the philosophy of Aristotle in the episode be implying that it was just a sort of outgrowth of Plato. Possibly this is due to the fact that the Catholic Church adopted Aristotle after the Renaissance, along with the Aristotelian notion that the Earth was the center of the universe, although, in fairness, the notion that the Earth was the center of the universe predates Aristotle. This might lead most to believe that Aristotle is to blame for the troubles of Galileo, Copernicus, and various other natural philosophers near the Enlightenment era.

My understanding is that while Aristotle was a student of Plato, he was much more interested in experimentation and observation given his belief that the essences that form the basis of mental concepts exist in each concrete thing, rather than in some other realm. I am no expert in classical philosophy, but this is my general understanding. At any rate, the “Cosmos” series is extremely interesting, and I recommend that you watch it if you haven’t ever seen it.

The Movie “Agora”

Agora makes some fairly easy observations about the nature of faith and how it necessarily leads to force, and usually outright violence, but that is not what I want to focus on here. I think that an even greater truth is revealed by this great movie. It is an exploration of the nature of evil men, and how they survive and thrive with the assistance of good people. Just so that the reader is clear, when I say “good”, I mean that the ultimate standard of the good is man’s life. That which promotes his life is good. Furthermore, all things created by men should be judged by this standard, if living is one’s goal. An automobile is good if it serves the purpose of transportation of human beings in the most efficient manner possible. A house is good if it serves the purpose of habitation. A philosophy is good if it serves the purpose of guiding human beings in living their lives. Similarly, all men should be judged by this standard. A man is good if he strives to produce the values necessary for living. (For more detail about life as the ultimate standard of value, consult the works of Ayn Rand.)

The movie is set near the end of the Roman Empire. Christianity is on the cusp of becoming the dominant philosophy of the time, and society and government is disintegrating. In Alexandria, the pagans and a few Christians still continue to study the works of the Ancient Greek philosophers and scientists. Hypatia is a female natural philosopher teaching the ideas of Ptolemy: that the Earth is the center of the universe, and that the Sun and the Planets revolve around the Earth in complicated epicycles. (This notion was later enshrined by the Catholic Church and it wasn’t seriously challenged until the 1500’s.) At the beginning of the movie, Hypatia is a believer in the Ptolemeic system, but, throughout the movie, she begins to doubt this system of planetary motion, and even conducts scientific experiments to test some of the objections that are raised against the modern, heliocentric view of the solar system.

There are two major plot threads running through the movie, and Hypatia’s struggles to understand the nature of our solar system is one of them. In and of itself, this plot thread would have made an excellent movie. The author of the script goes even deeper than this, however, by skillfully interweaving another thread into the plot. This second thread involves the struggle between the remaining secular elements in Ancient Alexandrian society, and an increasingly dominant, and emboldened religious group. The secularists are represented by Hypatia, the natural philosopher, and her student and suitor, Orestes. At the beginning of the movie, Orestes is still her student, and he rather casually notes that the planetary system proposed by Ptolomy seems rather silly. It is this initial criticism of Ptolomy by Orestes that plants the seed of doubt in Hypatia’s mind, and leads her to begin rethinking the entire system of planetary motion.

The men of pure faith are represented in the movie by two characters: Ammonius, who is a classic “rabble rouser” and street thug, prone to acts of violence, and Cyril, the Bishop of Alexandria, who is motivated by power-lust. However, the movie makes it clear that by themselves, Ammonius and Cyril would not have been able to unleash the death and destruction that they bring. Better men like Orestes choose to compromise with them out of political and social expediency over the years, and thereby lend them an aura of social and political respectability, which eventually results in the best person being held in subjugation by the worst people, with the worst possible result.

Since it is historical fiction set prior to the fall of the Roman Empire, and the advent of one of the darkest periods in human history, one should not expect a happy ending in Agora. But, bad things happen to good people in (good) fiction for a reason, and it is very important that the reasons in Agora be understood by all of us.

The Incest Taboo

I am just finishing up the 30th Anniversary edition of Richard Dawkin’s “The Selfish Gene”. (I believe that I have already finished the original edition, but the 30th ed. has two extra chapters.) Taken purely as a text on evolutionary biology (and nothing more philosophical than that), it is an excellent work. I will probably have more to say about it in a formal book review once I finish it, but I wanted to note one fact that I discovered that I found very interesting. If correct, I think it gives a definitive and rational answer to the question: why not have sex with your relatives?

In chapter 6, titled “Genesmanship”, it discusses, on page 99, and in an endnote on that page, the high probability of brother-sister matings leading to serious genetic diseases for their children. In fact, the footnote says that each person caries, on average about 2 recessive “lethal genes” per person. The gene is “recessive”, which means it doesn’t manifest itself unless you get a copy from both your mother and your father. Normally, because of out-breeding (non-relative breeding), a child will only get one recessive of any given lethal gene, so he will be safe. But, since brothers and sisters have a high probability of getting the same lethal gene from their parents, the chance of a child from a brother-sister breeding getting two copies of the same recessive lethal gene turns out to be about one in eight. That means if you have 8 children, you are likely to have at least one child with a serious genetic problem that will result in early death. (I was vaguely aware of the fact that this was the reason that brother-sister breeding was bad, but I had no idea the probability of death for their children was that high.) To draw an analogy, a brother-sister breeding would be like taking a revolver with 8 chambers, putting a bullet in one of the chambers, and then playing “Russian Roulette” with your kid.

To me, this had to be a major reason for the “incest taboo” in most human cultures. (I say most, because there are examples of brother-sister breeding, such as the Pharaohs in ancient Egypt.) Pre-historic people probably would have “quickly” noticed that brother-sister breeding led to the death of more children than non-brother-sister breeding. (When I say “quickly”, I mean over the course of decades.) (And, yes, I am assuming that people want to have children, but even the minority of people who don’t are going to be raised in a cultural environment that views brother-sister breeding with great revulsion for this reason, and are therefore probably going to view it with revulsion themselves.)

FYI-Dawkins seems to suggest that this fact would lead to an “instinctive” revulsion by people against incest, but I regard human beings as a “tabula rasa” at birth, and I am not sure that this is consistent with the idea of “tabula rasa” at birth, so I think the taboo would have arisen through observation, not due to any sort of “innate knowledge”. (I will probably have more to say on “instincts” and the idea of “tabula rasa” when I write a book review of “The Selfish Gene”.)

The New Psychology of Time

This was an interview of Stanford Professor Philip Zimbardoon on NPR’s “Think”, which is broadcast in the Dallas area. (The podcast is available at http://www.kera.org/audio/think.php.)

This professor seems to be studying an interesting and important aspect of the human mind, which is the capability for long-range planning and thinking. He seems to take the position that this is a skill that must be developed rather than an automatic function, which I agree with. He noted his work with inner-city youths to teach them how to think long-range, which illustrates that it is a skill that must be learned. Another interesting statement by this professor was when he noted that school students need to be taught how to engage in long-range planning, and that this skill is one of the things that distinguishes (most) adults from children –as well as what distinguishes (most) modern men from primitive man. I also agree with this. He said something to the effect of: schools should teach children how to meditate on taking long-range action, which I took to mean: visualize a goal, then think about what they need to do to achieve that goal, and (presumably) take action to achieve that goal. If only Texas schools spent time teaching children this skill, instead of wasting time on that meaningless minute I’ve spoken of before.

Iron Age Coup D’Etat

PBS had an interesting episode of NOVA last night about “bog bodies” that date back to Iron Age Ireland and England -which was around 350 B.C. Occasionally, in the bogs of those countries, a mummified body will be found because the plants in the bogs secret a substance that preserves flesh in a similar manner to how leather is tanned. The bog bodies usually show evidence of having been intentionally killed or murdered, such as having their heads bashed in, and having been stabbed fatally. The other interesting thing noted was that the bodies usually show evidence of having been people who would have been of high social standing.

There is some debate as to why these people of high social rank were killed and put into the bogs, but as soon as I learned that they were people of high social standing, I thought “coup d’etat”. Later in the show, there was a suggestion that these people may have been tribal chieftains, which strengthens my thinking on this subject. These killings may have been how people in a tribal society, which has no concept of elected government, deposed of a leader. If they had had a concept of elected representatives, then they simply would have voted for a new leader, but since they would have had no concept of that, the only way to get rid of their leader would have been to kill him, probably instigated by the leader’s “political rivals”. They noted that the killings were usually brutal, which suggested that they weren’t just ritualistic, but I think the brutality would make sense. If hard times had fallen on the tribe, and the leader was regarded as responsible, then brutally killing him for tribal resentment that may have built up over many years, would make sense.