Beyond Popper

I was having a conversation with a friend of mine recently about the nature of knowledge. As with just about any discussion of epistemology with me, much of the conversation was about critical rationalism. In this discussion, I came to realize something. One of the key foundations of critical rationalism is the idea that no amount of evidence can prove an idea to be true, but a single piece of evidence can refute/disprove an idea. I see this as paradoxical.

For example, if I have a stone, I might form the hypothesis that the mass of the stone is 30g. To test this, I might weigh the stone. Implicit here is the idea that what is recorded from the scale is the mass of the stone. Once I read the scale, I have the following ideas:

(A) The scale says “45g”.
(B) The mass of the stone is 30g.
(C) The scale is an accurate measure of the stone’s mass.

If all three were true, there would be a contradiction, so I can conclude that one or more of my ideas must be false. The problem with falsification is that I have no logical reason to favor A & C (false hypothesis), over A & B (bad scale), B & C (bad eyesight), or others. Ultimately, I cannot refute anything with absolute certainty, so I cannot disprove.

This difficulty can be reduced by what I like to think of as the inductivist section of critical rationalism (I’ll show why in a moment). Wikipedia says that, with respect to hypotheses, “differentiation may be made on the basis of how much subjection to criticism they have received, [and] how severe such criticism has been”. In my example, none of the three ideas has been criticised, but it’s easy to imagine a scenario where the accuracy of the scale had been previously tested.

There are, unfortunately, two problems with this reasoning: (1) the scale requires evidence to test, so we still have the “which conjecture do we accept” problem at an earlier point, and (2) we still have two conjectures to decide between (A&B). What most critical rationalists will likely turn to is the difference between unsubstantiated conjectures (B) and those based on observation. It’s important to remember that hypothesis A is still conjectural, but we can grant it a sort of “natural critisism” stemming from our perception.

Here’s the rub: lending a heigher weight to any of our conjectures still doesn’t allow any refutation to logically occur. The only way to do that would be to accept something as true after enough observation, and this is exacly what everyone does (including critical rationalists), but CR brushes off as illegitimate.

At this point, one might turn to belief weights in order to avoid having to assign a binary value to a hypothesis (and the fallacy of inference). Unfortunately, any sort of updates to belief weights requires knowledge that is assumed to be true; it doesn’t actually let you move from a state of unsubstantiated conjecture to one of informed belief. In other words, it requires prior knowledge, which, as discussed earlier, we can’t logically obtain.

As an example, let’s say I have a hypothesis that a zebra exists and then I perceive a zebra. What weight do I give my hypothesis? In order to find it, I must know how accurate my perception is. For example, if hallucinating a zebra is equally probable to seeing a real zebra, there is a 50/50 chance that the zebra actually exists. But let’s say that I am not given a value for how accurate my perception is… how do I determine the likelihood of false positives, etc? The natural answer is to make a bunch of observations, and test to see if they were “correct”… except to do that, you’d need to assume the training labels (“correct/incorrect”) were true! If you want to evaluate the accuracy of the training labels, you have to assume some other input is true. The catch 22 ensures that you cannot logically produce a factual statement (even a probabilistic one) about the world without having been given other (binary) factual statements.

Unless I’m overlooking an infallible source of knowledge, I can conclude that nobody in the entire universe has any knowledge (that is, factual data) of the universe… and never will. Not even an infinite intelligence would be able to know anything about reality.

To escape this agnosticism, I might suggest that when we look like we’re doing logic, we’re actually not (at least, not formally). For instance, if the scale reads “45g”, I might simply accept that the stone is 45g and reject my old hypothesis, not through logic, but through common sense. The problem here is that common sense is a blanket term used to describe mental tasks that are easily done by people, but we don’t understand explicitly. Doing something via “common sense” is a lot like dying from “old age”; it’s just not a useful term. To make things worse, humans generally seem to reject paradox and use deduction, so we can be confident that something very close to formal logic is going on mentally.

My theory is that ideas are not evaluated based on truth, but based on the utility that comes from predictive power. Prediction, here, is based on sensory data, as opposed to objective reality. Unlike reality, we can be sure of our sensors as long as we think of the sensors as “inputs”. Let me give some examples…

I find a stone and decide to weigh it. I predict that the measured mass of the stone will be 30g. I put the stone on a scale, and it says 45g. My prediction had a significant error, so I discard it as being non-useful. Because I’d like to be able to predict the stone’s mass I form a new prediction that the mass is 45g (informed hypothesizing). I can use my memory to test the prediction… it works! This retrospective success reinforces the expected predictive power of that hypothesis. This explains why a hypothesis that matches previously observed data is granted more weight, and why one that doesn’t is discarded (falsification).

Let me give an example. Little Andrea sees a crow that is black. She conjectures that all crows are black (or more simply: “crows are black”). She sees another black crow. Prediction reinforced. She asks her mom what color crows are. Prediction reinforced. She sees a green apple (non-black non-crow). Observation is outside prediction scope; no change. At the age of 46, Andrea meets a street performer with an albino crow. Prediction failed. She notes “Oh, how strange… a white crow!” Prediction weakened slightly, but still retained, because in the vast majority of cases it’s useful to guess that crows are black. After seeing enough white crows she may reject her initial generalization and adopt a more probabilistic one (about 90% of ravens are black), but since a probabilistic idea has intrinsically less predictive power (and is harder for humans to measure*), they are under-weighted and often avoided (leading to accident fallacies and others).

I could wander from here into my theories of semantic memory, but I’ll try to stick with critical rationalism to finish my thought. When Popper started, what he sought was to step away from justification, the practice of trying to support currently held ideas. In the service of this, the claim was made that one can disprove an idea, but not prove one. Though I’ve come to reject this claim, I don’t think that critical rationalism is a bad approach.

Justificationalism comes out of a natural tendency to want to be right, and it appeals to this bias even when a more open mind might find more effective ideas. Critical rationalism avoids this by forcing each person to listen to other arguments in order to determine how they might fail.

Critical rationalism also avoids the trap of adding weight to a theory because of selective observation. For instance, if I have the theory that “proteins are a kind of enzyme”, I might seek to “confirm” it by looking for enzymatic proteins. This will bias my data set so that it appears that the idea is effective, when it actually isn’t. Critical rationalism will naturally disrupt this bias with a second bias of seeking data that doesn’t fit the theory. Because an idea that is predictive only, say, 80% of the time isn’t very useful, this bias is helpful in pushing us towards more consistently accurate ideas.

One might suggest that when people say “truth” they mean “predictive power”. If this is true, I can easily show where Popper’s ideology fails. No prediction will be correct 100% of the time; our sensors are fallible. An idea that fails shouldn’t be rejected as “falsified” if it’s still accurate almost all of the time. F=ma is still a really important piece of knowledge. In this way, induction works.

* – Probabilistic ideas work differently for different forms of memory. Associative memory, the kind of thought that we use when making split-second decisions, is very probabilistic. For example, it is easy to have a gut feeling that a deck of cards is about half black and half red. Semantic knowledge, the kind of idea that we use consciously, doesn’t work so well with such things. I cannot imagine a person being able to tell you what proportion of a pile of cards is clubs unless they do some mental math.

Photo credit: swissbones on Flickr