### Patrick Stevens

Former mathematics student at the University of Cambridge; now a software engineer.

# My objection to the One Logical Leap view

A large chunk of the reason why changing someone’s mind is so difficult is the fact that our deeply-held beliefs seem so obviously true to us, and we find it hard to understand why those beliefs aren’t obvious to others. Example:

A: A god exists - look around you; everything you see is so obviously created, not stumbled upon!
B: No, that’s rubbish - look around you, everything you see is easily explained by understood processes!

The basic problem here is that B sees things differently to A. Everything that B sees is automatically interpreted through the prism of “process that is understood”, and that is a really hard thing to convey to A. The same evidence is spun in two totally different ways, and yet people argue as if the other party were only one logical leap away from coming round to their point of view. Weirdly, I can’t find a source for that - I have heard the phrase before. In lieu of a source, I will (very briefly) summarise that viewpoint. I was under the impression that it is often trumpeted around that at the heart of every argument is one logical leap (OLL) that made that argument significantly different from the opposition, and that if one could only convey why that point was so important, then one could sway everyone to that point of view. (As I say, I can no longer find anyone saying this.) There is implicit evidence that people think in this way - the fact that when people are arguing earnestly with each other, each in an actual attempt to change the other’s mind, they usually repeat the same argument again and again, as if that were simply a killer blow. Now, quite aside from the obvious symmetry here (both sides feel that their point is the one thing that just needs to be understood), there is a deeper point to be drawn about how we think, that exposes the OLL as a fallacy.

# Ideas are not atomic

There are precious few ideas that are what I call “atomic”. An atomic idea is one that most observers will experience in essentially the same way. The idea that $1+1=2$ is the closest I can get to an atomic idea - most people, I suspect, know that numbers can be added, and for small numbers, I posit that we all think of addition in the same way. Certainly the concept of “addition” is very much observer-dependent, in that a mathematician will probably have a very different view of addition to, say, a painter - but we have all been so well drilled that $1+1=2$ that I suspect we all view it (not “addition”, but “$1+1=2$”) in the same way - as an isolated fact. By the way, the main difference in the concept of “addition” generally is, I think, that for a mathematician, addition is a small part of a much larger edifice (involving the Peano axioms and so forth), whereas I have met many people to whom “maths” is merely a collection of isolated computational techniques, for whom addition is simply an extra tool. Most ideas are not like $1+1=2$. If you were to get me to free-associate on the word “death”, for instance, my immediate reaction would probably be “bad, get rid of it”. If you were to get J. K. Rowling to do the same, you’d probably get “inevitable, must reconcile with”. (I base this on the final book of the Harry Potter series, in which a major theme is the portrayal of death as “the next great adventure”.) “Death” is a concept which varies heavily from person to person - it is not atomic. In order to change someone’s view of death, it is likely that (for most people) a large reshuffling of the worldview would have to take place - for me, you would probably have to do one of the following:

• weaken my “human life is to be desired” axiom (in the process drastically altering my aesthetic principles);

• prove to me that there was something desirable after death (in the process weakening my ultra-materialistic worldview);

• show me that there would be horrific consequences to the prolonging of life (but that wouldn’t change my view that “it would be better if we could get rid of death”).

Common to the two options that are actually changing my mind (the first and second) is the requirement that you break down a key part of my worldview. I think that this is why opinions are so hard to change - because they so quickly become very heavily bound up with the entire worldview. Few ideas have sufficient force to alter my entire model of the world (although they do exist: for me, one such idea was Cached Thoughts). The “one logical leap” in an argument is merely the global interface of a particularly large chunk of world-model - the tip of an iceberg.

At this point, I will explicitly attempt to do what I have been claiming is the impossible - to convey my worldview to you. I attempt this in order to show just how much worldview sits behind my simple opinion on the topic that “the One Logical Leap does not exist” - and how much harder than it first appears it would be to change my mind on it. I very much doubt that I will succeed in explaining my mind to the extent that I would like, for reasons explained throughout this post. Anyway, I took fifteen minutes of introspection, and here (hopefully in a reasonably logical order) are the major areas of worldview on which this article rests. I will refer to these bullet points throughout the article, and will leave out my views on mathematics and death (which have already been mentioned, but are not central to my argument). It should go without saying that these are incomplete generalisations.

1. Thought is computation, mainly oriented around pattern-matching and caching

2. There is a correct answer to essentially every question - we just don’t have the computational power (in our brains or otherwise), or are not using it correctly, to answer them

3. The process of speech is literally the process of sharing thoughts (to a lesser extent, my non-rent-paying belief that the mind is an entity that is distributed across multiple brains, as Hofstadter outlines in his book I Am a Strange Loop)

4. There are low- and high-bandwidth ways to share thoughts (one-way blog posts are not high on the list of effective thought-sharing means), but we only really use low-bandwidth ones

5. The mind is a vast collection of models of the world, constantly reaching consensus to provide a single contiguous model

6. Humans are very bad at evaluating new ideas, and most of the thought happens below the level of consciousness

7. For most people, argument is a battle to prove yourself right

Of course, my statement of these aspects of my worldview is really inadequate - a soundbite summary of a seething mass of thought (viewpoints 4 and 5). As an exercise to the unusually-interested reader, you might find it interesting to go back and see where these views appeared implicitly up to now. I have tried to make this post as non-circular as I can, but it was harder than I expected to express that “the worldview is tightly bound up and hard to express”. Now that I have these viewpoints explicitly labelled, I can outline my argument properly.

• People think in “one logical leap” terms - that is, they believe that B is only one short step of understanding away from coming round to A’s viewpoint

• Worldviews are very hard (and therefore slow) to convey, because although we can share thoughts (viewpoint 3), we can’t do it anywhere near fast enough (viewpoint 4) to put across what we call “a viewpoint” but is really a truly massive edifice (viewpoint 5)

• People therefore receive novel thoughts slowly enough that they have time to pattern-match some standard answers to them (viewpoint 1), and thereby avoid dealing with the “logical leap” the other party is trying to convey

• Unless A is very careful, B will interpret A’s argument as an attack on B’s own worldview (viewpoint 7) and is thus incentivised to find objections

• Hence, it is extremely hard to change a worldview.

• What I think of as “an obvious idea” is only obvious to me because that’s how my pattern-matcher works (viewpoints 1 and 5)

• To change your pattern-matcher sufficiently to view my idea as “obvious” is to alter your worldview

• Therefore, my “obvious idea” is outlandish to you, unless our worldviews are sufficiently well-aligned already.

An atomic idea, of course, doesn’t suffer from this problem - it is seen by everyone in the same way, so it can just be packaged up and spoken, and understood as it was intended. Now, a single idea can be so powerful that it reshapes my worldview; or many different small, nearly-but-not-quite-atomic ideas relating to the same worldview can be presented, with my worldview adapting to accommodate these (viewpoints 1, 5 and 6); or I suppose I could maintain some kind of cognitive dissonance where an idea doesn’t fit on top of my regular worldview, but I don’t really count this as a good solution. But when conveying ideas, people don’t use this fact-which-is-so-obvious-to-me, that it is hard to persuade people because the task is huge. (I hasten to add, by way of example, that it only became obvious after the considerable change in worldview brought about by reading most of LessWrong.) People almost invariably present to me a single idea without the supporting worldview (and of course I include myself as “people”, but I do try to ameliorate the effect) - and then the idea has no worldview to slot into when it arrives in my brain, so I unconsciously and consciously find ways to reject it. To defeat this effect is the essence of a pretty big chunk of rationality - learning to recognise when you’re automatically rejecting an argument, and stopping yourself - but that’s a post for another time.

# What to do with this information

You may well say, “That’s all very well, but what difference does it make?” - and that’s a very natural question to ask, because (in my experience) the balance of probability suggests that you don’t have the worldview which would make it obvious (and after all, you’re reading this blog post to learn about my worldview). Over so short a period as the last few months, it has become a part of my worldview that people really don’t like to evaluate arguments - probably because to do so means the other person has “won”, as there’s a reasonably effective social norm against adapting your view in response to evidence or argument. There are two very simply-stated ways you can use what I’ve been trying to convey of my worldview:

• Notice when you’re rejecting an idea on worldview-incompatibility grounds, so that you can actually think about it rather than letting your already-stored model of the world decide for you

• When you are trying to convey a point, and you have the luxury of time, give much more justification than you think should be necessary, and remember, when the other person is obtusely refusing to absorb your idea, that it’s probably because you aren’t conveying enough background-idea. Yes, it may be very hard and time-consuming to do enough of this - but at least it stops you from unconsciously or consciously thinking that the only reason the other person isn’t taking in your idea is that ey’s stupid - and in my experience, that seems to be a major driving force behind the development of discussions into proper angry rows.

# Post Scriptum

This is far from the most coherent work to flow from my pen, I realise - it’s an oddly hard thing to construct a cogent discussion on, because the argument is itself that the argument is hard to put across. My usual structure for an argument would be something like “Statement of argument, evidence, expound”, but here my evidence is part of the statement of the argument, and my “expound” is also “evidence”. That throws the whole structure into disarray. Ah well - let it stand as a key example in favour of the argument.