The Mad Scientist Problem

The Problem

Let's imagine we have a mad scientist who is performing an experiment on a caged man who is unaware the mad scientist exists. In order to get food, the man must press a button on a food dispenser. However, the dispenser is rigged to deliver a mild electric shock to the man 50% of the time. After some time, the man learns that there is about a 50% chance of shock. At this point, the mad scientist then alters the machine to deliver a shock 75% of the time without the man's knowledge. This problem has a two questions:

1. Without further button pressing, does the man "know" there is a 50% chance of shock despite the scientist's alteration?
2. After encountering higher levels of shock, when should the man move from attributing the higher rate to a streak of bad luck to "knowing" the nature of the dispenser has changed?

The Nature of Statistics

The first question is easily answered once you understand something about the nature of statistical knowledge: We are using knowledge about the past to try and predict the future. When the man claims to know there's a 50% chance of shock, he is not claiming knowledge about specific future outcomes. Instead, he is claiming knowledge about the past and using that knowledge to infer the nature of the dispenser.
Here the man is making a legitimate provisional assumption: the nature of reality is consistent. In physics, we make the same kind provisional assumptions. In fact, these assumptions have names: Uniformitarianism and Methodological Naturalism. We assume that the universe has a specific nature and it will always behave according to that nature... whatever that nature might be.
One might assert that the man really doesn't "know" the dispenser has a 50% chance of shock because its not "true" anymore. This is nothing more than an appeal to the unknown to invalidate what is known. The very same  flaw we discovered in Philosophical Skepticism.
The profound truth is that all our knowledge is based on past experience. If we allow this to cripple our knowledge of the future, we are left with nothing to work with rationally. The whole point of reason, logic & thinking is to make future predictions. Without this element, "knowledge" is useless.
The only rational answer to the first question is "yes."

Something's Up

The answer to the second question is a bit fuzzier and a little misleading. There is no specific point at which the man suddenly changes his mind about the nature of the dispenser. Rather, the change becomes increasing apparent with each successive trial. A good rule of thumb statistically is that 1000 trials offers roughly a 3% margin of error... although to be fair, there are variables in this calculation that are simply not known. Weather the man averages the last 100 trials or the last 1000 trials, he will eventually arrive at the correct conclusion: the nature of the food dispenser has changed.

The A+ Problem

As promised, here is the first example of Foundational Evidentialism in practice:

The Problem

Your child comes home and claims they got an A+ (100%) on a recent math test. Do you take their word for it or demand more evidence (e.g. the graded exam paper)? Here's the relevant evidence:

• Your child has been historically honest about their exam grades 72/75 times.
• Your child's math grades are typically C (70%) average with a standard deviation of 10%.

If this is starting to sound like a math problem, you'd be right. Typically in real life, our minds will estimate these values (and the answer) for us unconsciously and quickly. We might even include other factors we are unaware of. These subjective estimations are easily thrown off by subtle cues, childhood indoctrination, personal disposition or any degree of altered state of mind. We are using hard numbers in this example to keep the answer as objective as possible.

Cause and Effect

Establishing the accuracy of truth claims like this one requires understanding that testimony is part of a cause and effect relationship. Regardless of weather or not your child actually got the A+, you know that they did claim it. The fact that they claimed it is an effect. Our job, in this logic problem, is to establish the most likely cause of that effect. Here are the most likely causes:

• The child is lying about their grade
• The child actually got an A+

There are, of course, other possible causes... perhaps the child is being mind-controlled by invisible aliens or perhaps the child is a clone impersonator from the 4th dimension. We don't consider these possibilities. Why not? Two reasons:

1. No Knowledge. We don't exactly know anything about "invisible aliens" or "clone impersonators." We don't know anything about their likelihood as candidates for an explanatory cause. By contrast, we know a lot about the honesty of children. In this case, we even have data regarding the specific child's honesty and academic records.
2. No Positive Evidence. I happen to know a little about exobiology (alien life), "extra" dimensions and cloning. My knowledge about these related concepts tell me that these hypotheses are inconsistent with repeated observations. So, given the only evidence about these hypotheses is negative, they shouldn't be considered. It only makes sense to consider explanations with at least some positive evidence.

It's important to note that these excluded explanations are not "ruled out" per se. They are still possibilities... There's just no logical justification for including them in the reasoning process.

Abductive Reasoning

This kind of reasoning (comparing the relative likelihood of competing explanations) is called abductive reasoning. In this form of reasoning, we don't judge the likelihood of each explanation independently. Instead, we compare their relative likelihoods and proceed with the most likely explanation. Let's get to it...

Doing the Math

First, let's consider the odds that the child is lying. Calculating this value is easy, since it is practically given:

Second, let's consider the odds that the child got an A+. This calculation requires a strong understand of probability distribution functions and calculus:

At this point, it should be clear that you should ask to see the graded exam before taking your child at their word. Perhaps if the child was more honest and/or got better grades, the result would have been different. Either way, there is a clear, objective method for figuring out weather or not you should believe someone when they make a claim. That is point of this exercise.

The Three Branches of Evidentialism

If we work with the definitions of truth and knowledge as laid out in previous posts, then we begin to see an epistemology form that looks a lot like evidentialism. Evidence can be strong or weak with respect to a conclusion just like we can have varying degrees of certainty with respect to our knowledge. A perfect fit.

In philosophy, it generally goes uncontested that beliefs should be supported by evidence. It doesn't really make sense to have it any other way. But isn't there a problem here? Don't our beliefs about evidence have to be supported by evidence also? We could be stuck here forever wondering about how to justify the evidence for the evidence for the evidence for the evidence of something. No matter what we do, true justification is out of reach... or is it?

Philosophers have thought about this "infinite chain of evidence" problem. However, there are varying positions available on how to solve it.

Philosophical Skepticism

In this view, no belief is truly justified. This position essentially gives up on trying to justify any belief at all because it claims the problem is unsolvable. This position is useless to me. If justification is impossible, what's the point of even thinking about all this stuff? I need a system that helps me form beliefs as accurately as possible... not one that prevents me from forming any at all... or worse, makes belief arbitrary.

Coherentism

In this view, the beliefs at the end of the chain are justified if they all harmonize and make sense together. While this does solve our "infinite chain" problem, it creates another. This easily allows for beliefs that have no basis in reality. I can come up with a complex set of coherent beliefs about the intricacies of what happens to me after I die... but that doesn't mean those beliefs are true. If we don't have assurances that those beliefs are true, they cannot be justified. Having assurance of truth is, after all, what justification is all about.

Foundational Evidentialism

In this view, the beliefs at the end of the chain are justified when they are "self-evident." In the most common form of Foundational Evidentialism (aka Foundationalism), self-evident beliefs are formed directly from our senses. When we hear a bird or see a sun-rise, these things are self-evident.

This system ensures that our beliefs will be based in reality because sensory perception is the foundation for all other derivative beliefs. This also solves the "infinite chain" problem by ending each chain in something seen, heard, touched, smelled, tasted, etc.

Our method of justification, then, is to start with the truth claim and work logically backward toward the self-evident observations that justify it. It also gives us a means of discovering (unclaimed) truth, which is the same method in reverse: Start with self-evident observations and work logically forward toward the truth. This is the foundation of the scientific method and science has proved its usefulness time and time again.

In the next post, we'll examine a few examples and see how Foundational Evidentialism is used in practical, everyday situations.

Three Working Definitions of Knowledge

Knowledge is a little more difficult to pin down than truth. Understanding what knowledge is begins with its definition and one's theory of knowledge is guided by this definition. Remember, "knowledge" is just a word... not a metaphysical thing that's "out there somewhere." We ought to select a definition that's useful to us and easily communicated.
Here are the three major definitions I have ran into:

Absolute Knowledge

(Championed by Immanuel Kant & Philosophical Skepticism)
Knowledge is only that which we know to be true with absolute, 100% certainty. I haven't really found this definition to be useful, since (under this definition) no one "knows" anything. Knowledge is an impossibility; metaphysically unreachable for any mind with limited knowledge. This is easily demonstrated through a syllogism:
Premise 1) Human minds have limited knowledge.
Premise 2) What one does not know may render prior knowledge incorrect.
Conclusion) Humans can't know anything.

Kant readily accepts this conclusion. This doesn't lead me to think I can never know anything. Instead, it leads me to look for a better definition. Perhaps a more useful one?

Contextual Knowledge

(Championed by Ayn Rand & Objectivism)
Knowledge is only that which we know to be true with absolute, 100% certainty as framed in our knowledge context. This definition is a little more difficult to grasp and requires further explanation.
This model disregards that which is outside our knowledge and evaluates certainty only in the context of existing knowledge. For example, in the context of Newton's observations, Newton had certain knowledge that F = ma described the relationship between force and mass. In the context of Einstein's observations, Einstein had certain knowledge that F = ma was wrong and that  described the relationship between force and mass.
According to this model, both men had certain knowledge about force in the context of all their knowledge. I find this aspect of the definition difficult. I have found it a complex en-devour to communicate well with others using this definition of knowledge. This is because what is certainly true for one person may be certainly false for another. To me, this takes away from the intuitive objectivity of knowledge. If something is certainly true, it must be true for all observers.

Uncertain Knowledge

(Championed by Evidentialism)
Knowledge is that which we know to be true with varying degrees of certainty. No knowledge is ever 100% certain (unless one is omniscient.) In this view, knowledge exists in a spectrum of certainty rather than as an absolute. For example, we may know that things that are almost certainly false (a man flying without the aid of technology), things that are unlikely to be true (me winning the lottery), things that could be true or false (even number of grass blades in my yard), things that are likely to be true (me waking up tomorrow morning), and things that are almost certainly true (Einstein's general relativity).
Like Rand's model, we use the context of our observations and existing knowledge to reach conclusions about new observations. However, because of man's limited knowledge, everything we know is regarded with some degree of uncertainty... however small.

If you haven't already guessed, I favor this definition of knowledge. It is the one I will be using throughout the remainder of my discussion of epistemology... Unless you can convince me a different definition would be more useful and easily communicated?