Sorites paradox and emergence

Question

Imagine a heap of sand where we gradually take away grains one by one. According to the Sorites logic, if taking away one grain does not stop it being a heap, then removing another grain also shouldn't. And so on, leading to the paradoxical conclusion that a single grain could be considered a heap. This is the classical example of the Sorites paradox (sorites derives from soros, Greek for heap, which was surprising because I always thought Sorites was a Greek philosopher).

Emergence argues that complex systems can exhibit new properties, or emergent properties, that cannot be fully understood by examining their individual parts alone, meaning they emerge from the interactions within the system.

Does this problem of not understanding emergent properties reduce to (I know!) the Sorites paradox? Is there any relation between the phenomena? I did a quick search and found almost no overlap in the usual sources.

Answer 1

Yes, emergent properties involve the Sorites paradox.

Intelligence is an emergent property of groups of neurons. Take one neuron away and the group of neurons still has intelligence. Keep taking neurons away and at some point we will stop saying the group of neurons has intelligence, but where is the boundary? It's unlikely that there will be any sharp divide between intelligence and non-intelligence that would be crossed by a single neuron. Rather, we will see a fading-out, as the group of neurons gradually has less and less intelligence and becomes less and less able to solve cognitive tasks.

This is the same way we resolve the heap paradox. Rather than a sharp divide where the heap is a heap until we take away one more grain and then it's not anymore, we see a fading-out, as the word "heap" gradually becomes less fitting for the diminishing pile of grains. This is the resolution offered by fuzzy logic.

In fact, Sorites-like dilemmas are ubiquitous in language. Take a chair, and add and remove atoms one at a time until the result is a tractor. At what point does it cease to be a chair, and begin to be a tractor? At no sharp point; rather, it gradually stops being a chair, and then gradually starts being a tractor. The statement, "It is a chair," has a truth value that begins at 100% and at some point starts to decline gradually towards 0%, and then the statement, "It is a tractor," has a truth value that begins at 0% and at some point starts to rise gradually towards 100%. Chairs, tractors, cats, apples - any macroscopic noun is subject to this problem. Natural language terms are usually fuzzy around the borders.

Answer 2

There are 2 types of emergence.

Strong emergence

"Strong emergence" posits the emergence of some property of a system that cannot be reduced to behaviour of its individual parts or the interaction between them. This is mostly proposed for consciousness. We don't have any verified examples of strong emergence. It seems untestable and unfalsifiable (unless, perhaps, we were to limit the definition to parts we know about, which would differentiate it from weak emergence only through an appeal to ignorance).

It indeed seems like a problem when one considers where the line must be where such emergence happens, where consciousness starts (to focus on that example), and where consciousness would cease.

The most reasonable interpretation I can imagine (for this unreasonable thing) is that if one has all the right "parts" (e.g. brain stuff), and they bump together in just the right way, then somehow, something new magically pops into existence. And then that exists distinctly from the parts (and is still connected to it in some way).

This suggests that there is some specific point where one has all the right stuff, where the last single atom added would cause emergence to happen, such that there's a sudden drastic change from merely adding that one single atom (that can't be explained merely in terms of how it affects atoms around it, e.g. for "the last straw that broke the camels back", each straw adds more and more pressure, until that pressure exceeds the weight tolerance, and that causes effects that are reducible to interaction between the individual parts - that effect emerges "weakly", not "strongly").

As mentioned above, we don't have any verified examples of this happening, and it's only really proposed for consciousness.

In theory, it seems like it shouldn't be that difficult to find that point, assuming it happens for every conscious organism born across the entire planet. Yet we haven't found such a point, and we haven't even managed to narrow down where such a point could be (except by proposing which species are and aren't conscious, which is also perfectly consistent with weak emergence).

This line of reasoning is probably one of the strongest arguments against strong emergence (along with the problem of how consciousness would interact with the brain and why the two seem so closely linked, with a change to either causing an effect in the other).

Weak emergence

"Weak emergence" posits the emergence of some property of a system that CAN be reduced to behaviour of its individual parts and the interaction between them. We can talk about some emergent behaviour of a traffic jam, but this can be reduced down to the actions of individual drivers / cars and their effects on one another. This is how we understand practically every part of the natural world.

There wouldn't really be a problem of the line where this emergence happens, of where consciousness starts (to take the same example as above). A weakly emergent consciousness would be reduced down to the various parts of your brain.

If one part of your brain stops functioning, you might lose consciousness if it's a "critical" part, or you might only lose the ability to do whatever that part of the brain did. We have lots of examples of that, of people suffering brain injury or brain disease and losing their memory or empathy or reasoning ability, as a result of damage to corresponding areas of the brain.

So it's clear that we can be conscious with only a part of the human brain, and there are various other species that demonstrate similar mental capabilities despite having much smaller and simpler brains (and we might suppose that they're conscious too, as we suppose other humans are conscious).

This can be broken down probably to the formation of just a single neuron that formed due to a mutation and had some useful function, and it fits perfectly well into the evolutionary model that explains the formation of complex life.

We may not quite have figured out when and how it came to be that species gained awareness. But it seems reasonable to suggest that the state of being aware is complex process that consists of many parts and that there are varying levels of awareness (a bird and a baby both probably have less awareness than a human adult), which would make sense if this emerged weakly.

Answer 3

There is an overlap between the two ideas, but it is one that does not shed light on either.

The SP relates to the impossibility of drawing a definitive dividing line on a path between two extremes that differ essentially by some quantity alone. For example, when does a large number become a small one? When does a heavy weight become a light one? Where is the dividing line between gas guzzlers and fuel efficient cars? Emergence relates to a change in properties other than quantity alone. Sure, quantity comes into it, but the change in quantity itself is not the main issue.

Answer 4

The sorites paradoxon and the phenomenon of emergence belong to quite different disciplines.

• The words and concepts of our language are man-made. The contents of our words are not discovered in nature but determined by the speakers of the language.

  Sorites shows that some words lack sharp boundaries but are fuzzy. In addition, the scope of the word may vary a bit from speaker to speaker.

• Emergence is a phenomenon which we discover and observe in nature. It is a fact, independent from human language.

  Emergence is a universal phenomenon. From a scientific point of view it is the phenomenon of structure building, on all scales from molecules along biological organisms to star formation.

Hence I do not see any relation between the sorites paradoxon in language and the concept of emergence from natural philosophy and science.

Answer 5

Thanks for this interesting and clear question.

I will start by noting that a heap is a most simple form of structure: elements are randomly stacked upon one another, without strong connections between them. The structure is, therefore, very weak. It can be disposed of by just kicking at it. A heap is not much of a structure, it lies at the low end of structures, as far as complexity is concerned.

Is a heap a case of emergence? Yes, but it's a very, very simple case, simplistic really. A heap is very limited in what it can do. It cannot fly or swim, for instance. Yet it can do a few things that individual grains of sand can't do, like block a vehicle, and in that sense I suppose one could say things like "a heap of sand emerged next to the kid as he started to dig into the beach".

One could consider a heap as emergent, though it seems a borderline case because barely structured at all.

Does this means that any and all forms of emergence can be seen as particular cases or instances of the Sorites paradox? Not really, for the already mentioned reason that a heap is barely a structure at all, as interactions between elements remain very weak.

A better metaphor would be some bona fide structure, like a house, a car or a boat. So the question would become: at what point does a house stops being a house, when you take out one piece of it at a time?

Unlike heaps, real structures have a function, which one can use to define them. Considering that a house primarily functions as a shelter, I would say that once you take out the roof, it ceases to offer shelter and thus stops being a house and becomes "a house in construction" (or in demolition).

So in this more canonical example of emergence, we have a system (the house) providing a function (shelter) that none of the building component can offer on its own. And it's all about how the roof interacts with the walls, within the "house system": the roof needs to be supported by walls, and in turns it will protect the walls e.g. from rain.

In conclusion, there's indeed no particular point at which a heap ceases to be a heap if you take out its composing sand grains one by one, because a heap is a mere addition of components, without a clear function. In case of a functional structure, it ceases to be it when rendered dysfunctional. If I sold you as "a car" a terminally broken wreck, you'd have good reasons to feel conned. A wreck is not a car anymore. So the Sorites paradox is more manageable when speaking of functional structures.