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.

Why I am not an Agnostic

A friend of mine asked me about being an atheist recently, and I realized that I had written very little directly on that subject, especially in recent years. I typically just refer someone to what others have written on the subject. For instance, I found “Atheism: The Case Against God” by George H. Smith to be a fairly thorough explanation, and to be largely correct, although I haven’t read it since 1994, so I don’t know to what extent I might now have disagreements with that book.

I am a proponent of Ayn Rand’s philosophy of Objectivism. I am also fully convinced that it is inconsistent to be an Objectivist and be anything other than an atheist, but that is not actually an explanation for why I am an atheist. After all, maybe Objectivism is right on that one issue, and wrong on everything else, or vice-versa, or somewhere in between. So, in my mind, simply saying: “I am Objectivist, therefore I am atheist,” is not a satisfactory explanation to give to someone regarding why I am, specifically, an atheist. In this essay, I will explain why I am an atheist, but I will do so in the context of a related issue: Why I am not an agnostic.

For me, being an atheist rests on a logical principle that is known as “the onus of proof” principle. This is generally defined as something like: “He who asserts a claim has the burden of proof.” Every statement has a truth-value. That statement can be true, it can be false, or it can be “arbitrary”. A statement is “true” if there is evidence to establish that the statement is in accordance with reality. A statement is “false” if there is evidence to show that that the statement is not in accordance with reality. For instance, imagine that person A says: “All swans are white,” and then he shows person B ten white swans to prove it. However, person B then shows person A an eleventh swan that is black, thereby establishing that A’s statement is “false”. Or, Person A says: “All men are law-abiders,” and person A shows person B ten men who are obeying the law. But, person B then shows person A an eleventh man that is breaking the law, thereby showing person A’s statement to be “false”.

It is also possible to make a statement and offer no proof regarding that statement. Such a statement is neither “true” nor “false”, but “arbitrary”. For instance, person A says: “All swans are white,” and B asks for proof, and A says: “Prove that it isn’t so.” As far as B is concerned, A has made an “arbitrary” statement. In B’s mind, there is no evidence to establish it. Notice that unlike the example above, person A did not show ten white swans to prove his statement. He just “arbitrarily” asserted it.

Another example of an arbitrary statement would be if person A says: “Portland is a city in Oregon.” Person B then asks for proof, and A says: “Prove that it isn’t so.” As far as B is concerned, assuming that B didn’t already have any independent proof of this statement, this is an “arbitrary” statement. In B’s mind, there is no evidence to establish it. (In this case, it can be established that Portland is a city in Oregon, but the evidence simply hasn’t been presented to B.)

A more common example of an arbitrary statement will be something more mystical, along these lines: Person A says: “I was Julius Ceasar in a past life.” Person B then asks for proof, and person A says: “Prove that it isn’t so.” A has made an “arbitrary” statement. In B’s mind, there is no evidence to establish it.

So, if someone asserts: “There is a little gremlin standing on my shoulder, but he is invisible, and you cannot see, hear, touch, taste, or smell him, nor can you use any sort of logical reasoning or deduction to establish that he exists, now prove that it isn’t so,” then they have violated the onus of proof principle. Their statement is neither “true” nor “false”. It is merely “arbitrary”.

How should such an “arbitrary” statement by a person be dealt with by the listener? This question depends on what you think the purpose of knowledge is. I assert that human beings use their rational faculties –that they think- in order to maintain or enhance their individual lives. Knowledge, in general terms, is about grasping causal relationships between perceived entities in order to effectively use those things to maintain or enhance your own life. For instance, people study Biology and human anatomy so that they can understand how a particular entity, the human body, works, and how it interacts with things in its environment like viruses and bacteria. This enables them to develop means of curing disease, which maintains and enhances human life. Or, we study planetary motion, which gives us the ability to understand the nature of gravity, which, thanks to Isaac Newton, gave us the law of Universal Gravitation, which eventually, along with other knowledge, let us build rockets. This allowed us to launch weather satellites that we can use to predict hurricanes. Such technology gives us the ability to evacuate cities in the path of a hurricane, thereby saving countless human lives. One last example that isn’t from the natural sciences: We study man’s fundamental nature in order to understand and grasp certain general principles of action that will enhance or maintain his life. These general principles of action for maintaining one’s life are what Ayn Rand called “ethics” or “morality”.

If the purpose of knowledge is to allow human beings to understand laws of nature, i.e., causal relationships, then any assertion which is not backed up by proof or evidence is an attempt to get people to act on ideas that have no established connection to reality. Acting contrary to the facts in this way is typically not life-enhancing. It is more likely to lead to self-destruction. For instance, if I decided that I could flap my unaided arms and fly like a bird, then went to the roof of a building and jumped off, that will likely end badly for me. This is why it is important that all ideas, statements, and assertions be established in your own mind to be in accordance with reality before you act on them.

The onus of proof principle is the primary reason I self-describe as an “atheist”. When someone makes any statement, I expect proof, if I don’t already have it. Thus, if someone says: “There is a god,” I want proof, just like if someone said: “There is a little green man on Mars.” It just happens to be that within our culture, belief in some sort of god is so common that there is a word for what I am: “a-theist”. But, I am also “a-little-green-man-on-Mars”(ist). (If the majority of the human population were “atheist”, then there probably wouldn’t even be a word for it. That would just be considered “normal”.)

I once explained this “onus of proof” basis for being an atheist to someone who was generally a “secular humanist”, and he said that sounded like “agnosticism”. I must disagree. Let’s look at the definitions of “atheist” and “agnostic” found via a “define: atheist” and “define: agnostic” in Google’s search engine:

Atheist: a person who disbelieves or lacks belief in the existence of God or gods.

Agnostic: a person who believes that nothing is known or can be known of the existence or nature of God or of anything beyond material phenomena; a person who claims neither faith nor disbelief in God.

My interpretation of these two contrasting definitions is that agnosticism says: “I don’t know if there is a god or not, so I am not going to take a position one way or the other.” But, the truth-status of every assertion of fact matters, if you want to live. Imagine if this were done in some other area, such as if you worked at a construction site. If someone said: “There is a crane about to drop a ton of bricks on you,” the truth or falsity of this statement matters. If you look up and don’t see any crane or bricks, then you’re going to think: “This person is a liar. I am going to distance myself from him and not listen to him.” You might also investigate why he said that. Perhaps you will discover that you were standing on a hundred dollar bill you had dropped, and he wanted you to move so that he could get it without telling you the real reason. This says something about his character.

On the other hand, if you look up and see that there is a ton of bricks about to fall on you, then you will take action: you will get out of the way. (In that scenario, you’re more likely to take that person’s word for it, and jump out of the way. But, after the fact, if you see that he was lying, then, if you want to live, it will affect your opinion of him, and how you deal with him -or don’t deal with him- in the future. My point here is that the truth-status of his assertion matters to your life.)

Imagine what agnosticism would mean to your life in practice. Imagine that an advocate of Sharia Law came to an agnostic and said to her: “God says all women should wear a burka.” Is the agnostic going to think: “I don’t want to take a position on this, so I’ll cover my head half of the time, and not cover it the other half of the time,” or: “I will just cover half my head”? The agnostic can’t say: “Prove that there is a god, and until you do, I am going to disregard everything you say on this subject,” because that would be taking a position. If she does that, then she isn’t actually an agnostic in that situation. She is an atheist. Whether she wants to use the word “agnostic” to describe herself to others is a different issue, but in her mind the truth-status of the assertion matters to her, and she refuses to act on arbitrary assertions. She is an atheist, at least on that issue.

I suspect that there are several reasons why most secularists tend to want to self-describe as “agnostic” rather than “atheist”. “Atheist” is synonymous with “immoral” in our culture because most people believe that any sort of respect for the rights of others must necessarily rest in religious faith. (“Religion” and “morality” are synonymous in many people’s minds, although I don’t think that is correct, if morality means “principles of action necessary for living your life”.) Agnosticism also seems more “reasonable” or “middle of the road”, and our culture tends to promote “the golden mean” between two “extremes” as an ideal, but it is not actually more reasonable. Not if you care about living, because that is why we must adhere our minds to reality on all issues.

Ayn Rand Lexicon on “arbitrary“.