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.

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I am Dean Cook. I currently live in Dallas Texas.