Are You Sure?



“Ignorance is bliss.”

“A little bit of knowledge is a dangerous thing.”

Not exactly, these aphorisms both depend on context.

Ignorance might be bliss if you do not know about the child next door that is very sick. This bit of ignorance would save one a little emotional upset. Ignorance would not be bliss if you had cancer and had no idea. Even delayed knowledge leading to delayed treatment would be harmful.

A little bit of knowledge can be a dangerous thing if again you knew you had cancer, but had no idea of how to deal with it. This would cause you a great deal of emotional and physical pain. But, a little bit of knowledge about the weather  might not matter a whole lot. If you know it is going to rain today and take an umbrella with you, you are less likely to get wet, but you need not know why it is going to rain today. Whether it is connected with a cold or warm front does not matter as far as getting wet is concern.

Socrates claimed that all he knew was that he did not know. This is certainly overblown, since he had a lot to say in Plato dialogues, even if he could never define such important terms such as good, virtue, and beauty, leaving Plato to develop his theory of forms, which does not help a whole lot. But, nonetheless, it is good to be aware of what you do not know. This could be in order to seek greater knowledge or not acting on the little bit you may have.

You could say ignorance and knowledge are opposites. If knowledge can be defined as justified true belief, would that not make ignorance unjustified false unbelief. This would take us into the realm of epistemology (theory of knowledge), which believe it or not is rife with difficulties, but I will save you from any of this in this blog.

I will state that most of us are ignorant about vast realms of knowledge. In addition to this, most of are knowledge is second hand, third hand, or more handed.

We only have direct knowledge of things we have direct experience with, and even then we may be mistaken.

Some of the knowledge we have is second hand from another person. Here we have to rely on the accuracy of the information and the quality of the experience from the person we are getting it from.

Third hand knowledge is all most of us have of science, history, and even the news. Most of us get are scientific knowledge from secondary sources like popular science books or documentaries. Here we are getting reports of experiments that may be done by someone other than the author or presenter. Historical knowledge is even more so because the writer or presenter in case of an actual historian is reporting his or hers interpretation of the primary sources, which may not have been first hand documents or artifacts. For the person not working from primary sources there is another remove from actual first hand knowledge, which makes this fourth hand knowledge. News can be secondhand knowledge if the reporter is giving his or hers experience of the event. But, most of the time it is at least third hand knowledge and maybe more.

A good deal of knowledge takes other knowledge to become such. Maybe, practically all knowledge takes some background knowledge to be obtained. Scientific knowledge is one example. In an experimental setup one might need to know how to operate the lab equipment, what previous runs of the experiment were, any background theory, some mathematics, and about the materials used. Of course, different experiments require their own unique set of background knowledge. Map reading is another example. One has to know what the symbols stand for in order to make use of a map to navigate from one place to another. There are many many other situations that could be shown, but I think you probably get my point. But, if you are ignorant of the necessary knowledge to understand a situation you will be ignorant of that situation as well.

Now, ignorance should not be considered pejorative. The Oxford English Dictionary defines pejorative as: “The fact or condition of being ignorant; want of knowledge (general or special).” So one who is ignorant should not be considered stupid. They may have the obligation to know, so morally speaking, they are in error, but not stupid. So saying that someone is ignorant could be saying that the individual just does not know. Of course some people do use the term ignorant as a pejorative. Now, if you call someone an ignoramus, that can be considered very insulting. Actually I feel stupid people should be given a break as far as their ignorance is concerned because they may not have the necessary intelligence to understand a situation in the first place.

What about certainty? Not a chance. This is qualified by things that are so close to certainty that it would be irrational not to believe. Will the Sun keep on rotating,  so that the it, if it is not cloudy, will rise above the horizon? You bet, at least I would. But, I feel that all one’s beliefs should be open to challenge. Again there are some beliefs which one cannot imagine enough of challenge to change that believe. This I call firm belief. And personally, I operate on the principle of reasonable doubt. If I believe something beyond a reasonable doubt, I deem that is enough to act on it, if other reasons do not interfere with the act. This is part of the pragmatic side of myself.

Skepticism has had a long and varied history. One such skeptic was the ancient Greek Pyrrho, made popular by his follower, Sextus Empiricus. They were mainly theory skeptics. They accepted perceptions to a degree, maintaining that they were mainly reliable. But, anything beyond perceptions, such as an explanation for why the Sun rises, were rejected. The motivation for this was that by being skeptical of all reasons, they could could gain peace of mind. This, anyway, is my understanding of them. If this actually gave them their sought after peace of mind, I do not know.

Another great skeptic was David Hume. His main bug-a-bear was cause and effect. He maintained that just because we see events that occur in constant conjunction there is not any way that one can actually determine whether one cause the other. This puts induction, a prime way of understanding, under a cloud. Again, pragmatism comes to the rescue. While one cannot be sure that one thing caused another, it is often useful to act on the knowledge in question if there is enough evidence to think it so.

But, skepticism is used in modern times as a method of challenging belief with empirical evidence and coherent reason; although, there is plenty of challenges to such a scheme under the study of epistemology. But, I find this to be a reasonable approach. For a defense and exploration of this view of what gives us knowledge see Susan Haack’s Evidence and Inquiry: A Pragmatist Reconstruction of Epistemology. The best way to know about how the world (universe) works is to approach it with scientific study. Of course, us nonscientists and scientists, when not actively doing a scientific study, use what tools we have available. See what the facts are and use rational thought to figure out what something means and how to act about it. This is often a useful way to approach life.

Some think that there is certainty in logic and mathematics. This is only so when you work from an agreed upon set of axioms (premises) and definitions, and that the system so worked is consistent. A problem with this is Godel’s incompleteness theorem, which states that any formal system powerful enough to produce arithmetic, if consistent, is incomplete. So if your system is said to be powerful and consistent, it is incomplete. In Godel’s proof, which is quite ingenious, which I will not bother you with, he says that there are truths which are seen to be true, but cannot be proved within the system. So if one comes across such a truth, one is obligated to add it as an axiom to the system. So what was thought to be certain contains uncertainties.

This state of affairs has shown itself in set theory, which is used as a foundation for the study of mathematics. The issue in set theory is the truth of the continuum hypothesis, which was stated by Georg Cantor in his work on infinite sets. At the risk of being a bit technical, Cantor found that some infinities were bigger than others. He understood that some infinities were equal such as the set of even numbers and the set of natural numbers. But, the real numbers he determined contained more numbers than the integers. His hypothesis, which seems like more of a question to be answer, is that there are no infinite sets with a number of elements in between the set of integers and the set of real numbers. From the standard axioms of set theory this cannot be answered. In other words, the hypothesis is independent of these axioms. There are additional axioms that have been suggested that would show the truth or falsity of the hypothesis, but mathematicians working in the field cannot agree on the added axioms. Needless to say, mathematics, which maybe surprising to some, can be a contentious field.

So much for mathematical certainty. The same thing can be shown with logic in a different way. Logic based on Aristotle’s working out of logic back in the day, accepted the law of the excluded middle. This is that something is A or not-A. But, if you exclude this premise, you can still develop a consistent system of logic. Matter of fact, in quantum mechanics, it is thought that the law of the excluded middle does not apply.

Some philosophers (Willard O. V. Quine anyway) contend that there is no sharp dividing line between analytic truths (such as logic and mathematics) from synthetic truths arrived at by experience. George Lakoff and his collaborators posit that all knowledge is lodged in bodily experience. From there they say that metaphors lead to new knowledge. I do not buy into their whole theory, but it is an alternative view. Both of these views let one get on with gaining knowledge, but not certain knowledge.

With scientific knowledge there is no absolute certainty, which does not mean that it cannot be trusted. Technology based on science proves this. But, all scientific theories are open to challenge. It is just them some are more open than others. Some are so well confirmed by experiments and other evidence that they can carry on as truth. To say that something is just a theory in science missuses the term.

The dig that creationists use against evolution is just such an example. Evolution, besides quantum and relativity theories, is the most tested theory in science. There is plenty of evidence for the theory of natural selection, and not one bit of counter evidence to show that it is wrong.

Speaking of quantum and relativity theories, these are the most accurately measured theories in the whole of science. Does this mean that the theories have all the answers in their respective fields? No, it does not. In particle physics where the quantum rules there are plenty of questions to ask. The search for supersymmetry, if it is to be found, awaits future particle accelerators. Dark matter and dark energy are huge mysteries waiting to be fit into relativity theory. And the marriage of the two theories is being sought in various versions of quantum gravity.

So there is plenty of uncertainty in our knowledge of things. There are uncertainties in everyday life; there are uncertainties in the news; there are uncertainties in history; there are uncertainties in science; and there is even uncertainties in logic and mathematics. Where does this leave us? Without any knowledge? No. We have plenty of useful knowledge (there is pragmatism again). But, it is incumbent on us to know we have uncertainties in our knowledge, and it is incumbent upon us to seek out further knowledge when that is called for. My advise is to have a questioning attitude when approaching things in life.

As a parting shot, I will mention truth. This concept is even more debated than what constitutes knowledge. Without truth knowledge would be a mirage. In everyday life it is not hard to define truth. It is that which agrees with the facts. I will leave a more through look at truth for a future blog.


Baxter is uncertain. “Are you going to take my seat?”

2 thoughts on “Are You Sure?

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