Patterns, Similarity and Relevance

One of the really hard problems in epistemology is about patterns. Which patterns can be extrapolated more widely? What situations do they apply to? What situations are too different so they don't apply? Usually, there are lots of other situations or scenarios where a pattern is a pretty good or decent fit, but not a perfect fit. So then you have to consider how good of a fit is good enough. And that's hard.

This comes up with the "no evidence" issue. When people say there is "no evidence" for something, they mean that all the evidentiary patterns they're aware of don't fit well enough to count. They're looking at a bunch of evidence and patterns and deciding the fit is poor enough to dismiss them. To reasonably reach a conclusion like this, you need to be able to judge how good the fit is and how good the fit should be to count as evidence.

The same issue, in different words, is judging similarity. How similar are two things? How similar is similar enough for ideas about one thing to apply to another thing?

The same issue again, in a third set of words, is judging relevance. Which patterns are relevant to which situations? Which ideas about something are also relevant to something else?

These are some of the key issues regarding induction. Many versions of induction rely on a premise about the future (probably) resembling the past. To think about that well, you need to be able to look at two things and decide if they resemble each other – in other words, you need to evaluate how similar they are, how relevant one is to the other, how well a pattern that fits one also fits the other. In other words, induction involves thinking about patterns continuing over time, which requires an understanding of what is a pattern and what it continuing looks like (what outcomes are similar enough to count as fitting that pattern).

Induction also runs into the huge problem of figuring out which patterns will continue over time. The premise about patterns continuing is kind of missing the point. No matter what happens, some patterns will continue and others will break.

From a mathematical and logical point of view, no matter what happens, infinitely many patterns will fit what happens perfectly: they will be an exact match not merely a good fit. This raises questions about why to care about good fits at all when perfect fits are available. Why look for significant similarity or enough relevance when perfection is logically available?

Since these problems are really hard, we might like to avoid them. Are there any alternatives?

Exact Matching

One alternative, which avoids some difficulties, is exact pattern matching. When you consider if a pattern fits well enough, or two things are similar enough or relevant enough you're doing fuzzy pattern matching. That means you expect imperfect fits and consider the pattern to still have held. Alternatively, we could be much more strict, and only use exact pattern matching, so the slightest difference means the pattern broke. This avoids all the difficult judgments about whether some outcome fits a pattern well enough, or whether two things are similar enough or relevant enough.

The downside of exact pattern matching is it's so strict it's hard to do much with it. It's much more limited. Used straightforwardly, it wouldn't enable induction because real data is messy. It's unclear if it'd even work for any laws of physics because when we measure experimental results our data never 100% perfectly fits the law. There's always a little bit of experimental error or imprecision.

To use exact pattern matching more widely, you can include fuzz inside the pattern. Instead of interpreting the pattern in a fuzzy way, you can interpret a fuzzy pattern in an exact way. For example, you could say the pattern is that a constant speed multiplied by travel time always equals distance plus or minus ten percent. The plus or minus ten percent is the fuzz we're adding inside the hypothesized law of physics. That isn't how physics is normally done because we believe – I think correctly – that the fuzz is in our imperfect measurements (and in details we may have left out of our calculations, like air friction), not in the actual law of physics.

Scientists believe that two objects traveling for the same time, at the same speed, always go exactly the same distance, not random, similar distances (at least that's the "classical" perspective that's probably intuitive to readers; I'm not going to worry about quantum physics here). The view is that the exact law is actually right; it's our data that's inexact. So scientists will write laws like that as exact patterns, with no built-in fuzz, and then they will do fuzzy matching between the pattern and the data because the data isn't perfect. So they have to judge how good a fit the data is; they can't just avoid having to think about that by using exact matching. (Also, if they did put fuzz into their laws/patterns, they'd have to think about how much fuzz to put in, which is basically the same issue.)

You can also add fuzz to the data itself (margins of error or measurement precision information) rather than to the laws or the pattern matching. Then you check if the fuzzy data contradicts the exact pattern or not. If we measure 1 meter and fuzz that to the range 0.9 to 1.1 meters, then it fits the pattern if the pattern specifies any length in that range (e.g. 1.07 meters) and contradicts the pattern if the law says it should be a value outside of that range (e.g. 5 meters).

People may also add another layer of fuzz saying e.g. that they expect 99% of measurements with this ruler to be within 10% of the correct value. So there is a 10% margin of error for all measurements, and also up to 1% of measurements are allowed to contradict the pattern even after fuzzing them and we'll still say the data fits the pattern.

Fuzzing the data itself, especially when you start ignoring some contradictory data points or outliers, leads to questions about how much it should be fuzzed. Also, some patterns perfectly fit the data with no fuzzing, so why prefer patterns that require fuzzing the data? Whatever your data is, there are infinitely many patterns that perfectly fit it. This gets into issues like preferring some patterns over others, even though they fit the data less well, and how to judge how good a pattern is and how much lenience we should give it on account of it being an inherently preferable pattern. This gets into not just figuring out the right patterns or laws from the data, but also approaching it the other way around: having preferences for some types of patterns and pushing back against the data some based on those preferences. This actually contradicts one of the major talking points of many inductivists, which is that it's supposed to be about learning and extrapolating from data and letting the data guide us. If we have preferences for patterns due to abstract reasoning or inborn intuitions, and we rely on those when using an inductivist approach, then induction isn't really working as advertised.

Don't Focus on Patterns

Another way to avoid these problems would be to stop basing your epistemology on patterns, amounts of similarity, degrees of relevance, and similar ideas.

What could we do instead? A lot of people, for many centuries, struggled with that. It's hard. One approach is to focus only on logic, math and deduction, but that's too restrictive to explain all of human thinking. How do you write or evaluate a song with deduction? No one knows how to do that, so that approach could only provide part of an epistemology, not full answers. (Evaluating songs with induction also sounds hard.)

Karl Popper, with the help of Charles Darwin and others, gave us a complete answer. The answer is to base epistemology on evolution instead of patterns.

This is literal and technical, not metaphorical nor saying it's close enough to fit well. Although high schools usually don't explain it, evolution is about replicators, and genes aren't the only type of replicator. Ideas are replicators too. Genes make progress when replicated with variation and selection, and so do ideas.

In high level terms, Popper said we learn by conjectures and refutations. It could also be called guesses and criticism or brainstorming and error correction.

Instead of trying to figure out which patterns fit which things in a fuzzy but good-enough way, we try to make critical arguments so we can find and reject mistakes. We should focus on looking for errors and making changes so we stop being wrong (or avoid being wrong preemptively).

Patterns, like evidence, are just one of the many tools we can think about, make guesses about, and criticize. Like anything else, they may be refuted by critical arguments, or not. In Popper's view, patterns and evidence are topics to reason about, not a fundamental part of the core method of thinking.

Instead of trying to prove how good any ideas are, or justify them, or support them, we should instead look for and reject errors. If we can't find anything wrong with an idea, that is the best scenario. As far as the primary issues go, there is no better status an idea can have than non-refuted. There are also secondary issues like we can consider how much effort we spent trying to refute an idea and differentiate between new ideas and old, heavily-analyzed ideas.

If people haven't looked for errors with an idea enough, then it can be criticized for that lack of critical investigation, which makes it unsuitable for belief and use in many contexts. How much looking for errors is enough? That depends on the idea and the context. There's no simple answer. For small ideas that aren't very important, with no special risks, a rule of thumb is to spend a minimum of 5 minutes on critical thought trying to find errors. It can help to use a literal timer and spend the 5 minutes consecutively without distractions (no multi-tasking, no social media, no going on your phone, etc.). Larger ideas merit more thought, but lots of tiny ideas get less thought (and people often don't even recognize those tiny things are ideas that could get more thought).

Overall, how much to look for errors before accepting an idea as having "no known errors" and being usable is a matter of judgment. You have to use your best judgment, and so do other people. It's common, and OK, that there's an idea I am suspicious of, but you aren't, so I analyze it more but you don't. We can disagree about which ideas to prioritize giving further scrutiny. It's actually good, overall, that lots of different people investigate lots of different things instead of everyone investigating the same things repetitively. Diversity of thought is more productive overall.

The most proper method I know is to understand that deciding how much to scrutinize an idea is itself an idea. You have an idea about how much time and effort (and what kinds) to spend trying to find errors in another idea. Your idea about how much critical thinking an idea needs can itself be criticized. If you can't find any errors, then you can use it. Ideas about when to be done investigating something are just another type of idea that follow the normal rules; they're not a special case not a special case.

Using critical thinking about ideas is the fundamental, universal method of Popper's philosophy, Critical Rationalism, and that's one of the points that Critical Fallibilism keeps. I don't think Popper directly, explicitly said it regarding this case (deciding how much to critically scrutinize another idea). But I read it as implied by what he said – he gave a universal rule and I'm just applying it to address a particular issue. Also Popper did explicitly talk about how well tested or critically analyzed ideas were: he thought that was an important thing to look at. I'm interpreting Popper, and a lot of interpretation is always needed when reading philosophers, so that's nothing unusual. There's no way to ever provide perfect clarity or write down every detail someone might wonder about. Popper wrote a lot, but even with a million books that'd just be a finite amount of information that still requires interpretation.

So focusing on criticism lets us avoid the very hard, unsolved problems (maybe impossible, but that's open to further research and debate) involved with epistemologies focused on patterns.

A lot of people claim the issues with patterns are already solved and that pattern-oriented methods work great. But none of them have ever managed to refer me to a book that explains it in a way that addresses the kinds of Popperian questions and criticism I have. My impression is that people claiming to have solutions don't understand the difficulties well enough. And many mainstream, non-Popperian experts are pro-induction but acknowledge there are significant unsolved problems with it. Also, besides failing to provide literature cites that back up their assertions, none of the people claiming the problem of induction is already solved will have an organized, lengthy debate with me to get to the bottom of the matter. At least that's my perspective on my experiences engaging in these kinds of discussions. I'm always open to debate if someone knowledgeable disagrees.