Putting information together

Do we build theories, or weave them?

Re-Assembling Reality #23c, by Mike Brownnutt and David A. Palmer

In Essays #23a and #23b we looked at how we get information: the raw stuff from which ideas and theories are made. But, regardless of how we got it, a collection of unconnected bits of information is not — and never can be — a theory. If unconnected bits of information even get as far as being an idea, they are rarely enough to be a very interesting idea. The key issue now is therefore how we connect individual bits of information to make something greater than the sum of the parts.

There are two main ideas on how this is, or can be, or should be done: foundationalism and coherentism. They are completely different. And they are the subject of this essay.

Foundationalism

On a foundationalist view,

any statement must be justified by a more basic statement,
or else be properly basic itself.

“Properly basic” means “obvious beyond question”. Properly-basic statements are the kind of thing that no reasonable person could ever possibly dispute.

Foundationalism can be illustrated by considering a statement such as

How do I know I am in Hong Kong? Is the statement properly basic in itself? Is it obvious beyond question? No, not really. So let us go down a level.

I am in Hong Kong is justified by two more basic statements. If it is true that I am here and that ‘Here’ is Hong Kong, then it necessarily follows that I am in Hong Kong.

The claim that I am here is properly basic. It is obvious beyond question. No right-thinking individual could object to that. To remind us of what is properly basic, we can underline the statement.

But how do I know that ‘Here’ is Hong Kong?

It is obvious that the University of Hong Kong is in Hong Kong. No right thinking person would put an institution called ‘The University of Hong Kong’ in Guatemala. But how do I know that ‘Here’ is HKU?

No reasonable person would dispute that there was a sign that said HKU; I saw it with my own eyes, and I am a reliable witness. (And no honourable reasonable person would cast doubt on my solemn testimony.) It is obvious that HKU signs are in HKU; They don’t put HKU signs up in Cambridge! it is not, however, obvious in itself that I left campus. So let us go deeper.

You may wondering whether you need to plough through a blog that is going to state the blindingly obvious. But bear with me. This is the entire point of foundationalism: working down step by step, using steps that any idiot can follow, until you reach a set of statements that any idiot can accept. Within foundationalism, every statement is credible either because it is blindingly obvious to the point that no sane person could disagree, or it is directly traceable to a statement that is that blindingly obvious.

If there is any possibility of doubt (“What if you were distracted and didn’t notice the sign?”) we have to go deeper until there is no doubt. Once there is no doubt, the claim with which we started is demonstrated true. And until there is no doubt, the claim with which we started is not demonstrated true.

Foundationalism takes its name from a building metaphor: ideas are put together in much the same way as a building. We start off with the foundations, which no one can dispute (I am here, HKU is in Hong Kong, HKU signs are in HKU). Then we build up layer by layer, with each layer resting on — which is to day, logically following from — what went before.

In this view, if someone is not convinced by an argument, the way to convince them is to start by stating (or re-stating) the foundational claims: I am here, HKU is in Hong Kong… By definition, any sane person will accept these. If the person to whom you are talking to does not accept them, then either the person is insane and you give up there, or your foundational claims were not properly basic and you must keep going down until you find something which is properly basic and which they do accept. From there, you construct your case, step by logical step, until you reach your conclusion. As your conclusion follows logically from a shared foundation, they must either accept your conclusion, or admit that they have not understood plain reason.

If they have not understood plain reason, there is no point in engaging with things “from their point of view”, or trying to understand how they see things. There are an infinite number of ways they could be wrong. Why unpick an unending variety of wrong answers, when you can just demonstrate the right answer? You demonstrate the right answer, of course, by restating the foundational ideas, and then repeating the entire process, but speaking slower and louder.

If a person wants to find fault with a conclusion within a foundational system, then they must find fault in the reasoning. Once a connection between one piece of the argument and the next is broken, every conclusion that follows from it must also be discarded, unless I can find some other way of supporting the claim.

When building an argument, just like building a Lego model, each part is attached by more basic parts to some foundation. Removing the light blue arch means that the yellow cup must also be removed. (Source: Authors.)

Looking at language, the building metaphor of foundationalism crops up everywhere. Having laid the groundwork, we build our case. We construct an argument, only to have someone demolish it. If someone wants to knock down our case, they might try to undermine a claim, deconstruct our argument, or show it to be baseless, unfounded, unsupported. If we cannot buttress our ideas with further support, we may see our argument crumble or even collapse. All of this language is the language of buildings.

Within a foundationalist picture, when you know a fact, you are certain of that fact. It is true, and it is demonstrably true. The reasoning by which you got to knowledge of the truth can be followed objectively by anyone else. Foundationalism (if it works) therefore leads to objective, demonstrable, certain knowledge of the truth. How could it be any other way? Within this system, any method of putting ideas together which is subjective, or indemonstrable, or uncertain is a poor reflection of what can properly be called knowledge. Maybe it could be called a belief, or a hope, a hunch, a suspicion, a conjecture. But it is not worthy of the term knowledge.

Foundationalism and four-year-olds

Unfortunately, foundationalism meets its kryptonite in the form of four-year-old children. Foundationalism rests on the notion of “a thing which is obvious beyond question.” And anyone who has spent any time with a four-year-old child will know that, for a four-year-old, nothing is obvious beyond question: on any topic, whatever answer you come back with, it is always possible to ask “Why?”

It starts well enough:

I am in Hong Kong.
Why?

You can answer that. But by the end it gets tricky:

There are signs on campus exits.
Why?
What do you mean, “Why?”? Because that’s the rules.
— Why?

There never comes a point when a four-year-old child ever feels the need to say “Oh,OK. That seems reasonable.” There is always another “why?”

Have the greatest enlightenment philosophers been defeated by a child? is this a problem that they somehow overlooked? They did not overlook it, and they would argue they are not defeated by it.

The claim of foundationalism is that properly-basic statements are things that no reasonable person could ever possibly dispute. And if a four-year-old child disputes what is obvious, then all this shows is that four-year-old children are not reasonable people. And, frankly, that is a claim that all reasonable people can agree with. So the foundationalists are safe.

Still, it it plants a question in our minds: what if four-year-olds are on to something?

Coherentism

But let us play at being four years old for a moment. Let us see where it gets us.

I say that there are signs on the campus exits. But are there signs on all of the campus exits? And, if so, how do I know?

Well, yes there are signs on all of the campus exits. And I know this because the regulations require there to be signs. And this is a place that follows the regulations.

But how do I know that? Guatemala doesn’t follow regulations.

It may be true that Guatemala doesn’t follow regulations. But that is hardly relevant because I’m not in Guatemala! I’m in Hong Kong!

Oh dear.

It would be nice if there were statements that were obvious beyond question. Not just beyond the questions of your own unimaginative soul; beyond question by anyone, in any context, from any culture, at any time. There are some things that might be obvious to a white, male, middle-aged, middle-class academic — starting with the self-evident necessity of drinking tea, and working up from there. But what seems self-evident to one person is very often not self-evident to another.

Within a foundationalist system, we said that a claim is only demonstrated to be true once there is no doubt. And until there is no doubt, the claim with which we started is not demonstrated true. If we allow that the doubts of people who see the world differently to me — the doubts of a four-year old, or a Nigerian, or an old woman , or a Buddhist — count as bona fide doubts, then there will always be doubt. If the explanation satisfies a Buddhist, it may no longer satisfy me. And if there will always be questions, then no claim can be demonstrated to be true within a foundationalist framework.

How an we salvage the ability to meaningfully engage with truth in any way? If it is hard — if not impossible — to come by self-evident truth from which we can establish a common foundation, then our reasoning either leads to an infinite regress or — more often — to circularity. Within a foundationalist view, circular reasoning is an abomination. Within a coherentist view, circular reasoning is accepted as necessary. And this acceptance is not some furtive, embarrassed admission of logical failure, which they hope you will not notice. No. If circularity is necessary, they go all in and proudly embrace it:

“We can voice our ultimate convictions only from within our own convictions…Any inquiry into our ultimate beliefs can be consistent only if it presupposes its own conclusions. It must be intentionally circular… Logically, the whole of my argument is but an elaboration of this circle.” [1]

Yes. At least, that is what coherentists are saying. Given the choice between being circular and being silent, coherentists chose circularity. Foundationalists still say that circularity is not OK. At all. Because, they say, accepting circularity will lead to the end of reason, knowledge, and all civilisation.

Within a coherentist approach

a collection of statements is justified if it is coherent.

No one single statement is justified, or justifiable, or even meaningful on its own. Rather, a collection of statements which make up some consistent whole collectively help to justify each other.

Instead of working with foundationalism’s metaphor of a building, coherentism picks up the metaphor of a piece of fabric. In a garment, which thread is the most important? Or which is even indispensable? None of them.

Coherentism. Each thread is part f the fabric because it is being held by the other threads. Remove one thread, and the others are held in place by… the others. (Source: arbyreed via flickr.)

If one thread is removed, the weave becomes a little less neat, but the garment does not fall apart. The whole is weakened, but no part fails completely. Some threads may be mere embellishments at the periphery, while others run though the garment from end to end. But no one thread is indispensable. And no one thread is irreplaceable. A hole, once made, can be darned or patched. One might remove the left sleeve wholesale and then either decide to sew on a sleeve from a different garment, or else decide that the shirt can be worn with only one sleeve. One might even cut off the right sleeve for no reason other than symmetry.

So, too, is our manner of reasoning. One piece of an argument might be unpicked, but the remainder holds together sufficiently well that the story as a whole remains coherent: fetal recapitulation of an organism’s evolutionary history, if true, would seem to support evolution; but, if it’s not true, we can forget about it. A thread, once removed, can be replaced by another: the beaks of Darwin’s finches turn out not to provide evidence of speciation; but it doesn’t matter because we now have genetic evidence for speciation. A hole can be patched: the experiment does not align with theory because of a glitch with the data recording, or anomalous local circumstances, or an incompetent experimenter; one of a thousand other possibilities which seem more likely than the theory as a whole being wrong.

Ironically, coherentism (despite its name) allows the simultaneous use of multiple, mutually incoherent systems.

While Newtonian mechanics is great at describing the world at human scales, it was found to utterly fail to describe the world at the atomic scale. Quantum mechanics was then developed which, while great at the atomic scale, utterly fails to describe the world at human scales.

Did we say that the foundations of Newtonian mechanics had been undermined and the entire theory should therefore be discarded? No. We cut the sleeves off the Newtonian shirt and said that Newtonian mechanics was now a t-shirt, good for covering our (macroscopic) torso. Quantum theory provided a pair of gloves gloves to cover our (microscopic) hands. And while neither the shirt nor the gloves are currently able to cover our (mesoscopic) elbows, we hope that one day a connection between the two can be made. Until then, we are glad that we at least have something to wear, even if we are slightly embarrassed that the parts of our outfit clash.

Newtonian mechanics is coherent within the domain where we use it. Quantum mechanics is coherent (by its own standard of what that means) within the domain where we use it. Each theory is incoherent with respect to the other. And we are OK with that. Because we believe that a garish mismatched outfit is better than no outfit at all.

At the risk of pushing the analogy much too far, the final decision to throw the shirt away (if that decision is ever made) is broadly one of personal choice (because the shirt looks untidy and improvised). You will almost certainly discard the shirt long before the action is forced upon you by the fact that the garment has failed to function as a shirt. Even should the fabric become so worn that it must finally be discarded as a shirt, parts of the garment might still find use as painting overalls or rags.

To draw this back to an example from science, the Linnaean system of classification (genus, species) was developed in a framework of fixed species. Indeed, Linnaeus held that such classification would not make sense if the species were not fixed. With the rise of evolution, the fixity of species was rejected. Still, the Linnaean system which had been developed to talk about (fixed) species was repurposed (albeit sometimes problematically) for an evolutionary framework.

Looking at language, just as there are common marks of foundationalism’s building metaphor, the fabric metaphor of coherentism also crops up everywhere. We weave together an argument, ensuring no one loses the thread of what we say. We tie up the loose ends so it all hangs together, only to watch someone unpick the ideas, and we see the entire argument unravel. All of this language is the language of fabric.

With a foundationalist approach, appeal is made to a set of universally accepted facts from which arguments can be built. By logically building up from certainty, everyone can arrive at an agreed version of certain truth. Unfortunately, foundationalism fails if one cannot find sufficient universally accepted facts.

Coherentism has the advantage that it does not appeal to universally accepted facts. A claim which is not obvious in itself is lent weight by the ideas around it, which are lent weight by the ideas around them, and so on, in some virtuous — albeit ultimately self-referential — cycle. The down side of this is that having a coherent worldview is no guarantee than your worldview bears any resemblance to reality.

Which shall we choose?

Foundationalists will tell you that coherentism is useless.

Coherentists will tell you that foundationalism is useless.

We have argued (in Essay #10) that both universal and particular statements have their place. But then, on closer inspection, we concluded that most so-called “universal” statements (so beloved by the Enlightenment) are not (strictly) universal. They can be considered universal for practical purposes, within the limited context under consideration.

We also argued (again, in Essay #10) that both objective and subjective statements have their place. But again, on closer inspection, we concluded that most so-called “ objective” statements (so beloved by the Enlightenment) are not (strictly) objective. They can be considered objective for practical purposes, within the limited context under consideration.

Given this background, we may not be totally surprised to see what happens when we look closely to foundationalism (beloved as it is by the Enlightenment).

We stated above that, on the foundationalist view

any statement must be justified by a more basic statement,
or else be properly basic itself
(i.e. obvious beyond question to all reasonable people).

We have established that it is difficult, if not impossible, to find statements which are beyond question by all reasonable people, without begging the question regarding who counts as “reasonable”. We therefore face a choice, in direct analogy to the one we faced with “universal” and “objective”:

Option 1: We can hold on to the strict definition of “foundational”, and admit that we cannot construct any arguments which are genuinely foundationalist.

Option 2: We can ignore the strict definition as unhelpful and apply the term “foundational” to things which are as good as foundational for all practical purposes.

And again (as with Essay #10) by “all practical purposes” we mean “the purposes about which I care right now.”

So when I talk to my son and insist he should wear a jacket because it is snowing outside, I will freely admit that there exist cultures and contexts in which reasonable people may laugh at the thought of having to wear jackets just because it is snowing. But, for all practical purposes, in the context of the conversation with my son, I treat the claim that “you need to wear a jacket when it is snowing” as obvious beyond reasonable dispute. If my son objects, I simply repeat, more slowly and more loudly: “It is SNOWING! Put. A. Jacket. On!”

When we redefined “universal” and “objective” for pragmatic reasons, we faced counter-intuitive results, such as finding nominally “universally” true statements which are untrue most of the time. Similarly, if we redefine “foundationalism” along pragmatic lines, we must face the possibility that we might have “foundational” statements which (far from being beyond dispute for all reasonable people) have been disputed by most people, at most times, in most places.

If a person says “I do not want a cup of tea,” they are either wrong (so they do really want a cup of tea) or they are unwell (so they do really need a cup of tea). This is self-evidently true to all reasonable people. (Source: Authors. See also: George Mikes [2].)

When we redefined “universal” and “objective” for pragmatic reasons, we found this to appeared unproblematic in a narrow context. But we found that, as the context became broader, we had to either roll with the problems that arose, or else face the specific or subjective nature of the claims. Likewise, as long as a man is in England, the claim that there is always time for a cup of tea can be treated as though it were a foundational truth. The claim does not need to be defended. It would be disputed only by madmen (who would no doubt be brought to their senses by a brew). In France, the same man could treat there is never a bad time for a good wine as a foundational truth. While this could be done for pragmatic purposes — it would be an utter waste of time to explain to an Englishman why tea is good — it must be recognised that as soon as multiple cultures come together, we are thrust into reckoning with the coherent nature of our worldviews.

This dynamic plays out in science. A physicist at a conference in which everyone holds to the Copenhagen interpretation of quantum mechanics can (and arguably should) use a phrase like “the wave-function collapsed” without fear of contradiction. But in a conversation with adherents of Bohmian mechanics, they must be more circumspect: “If one adopts a certain view of the wave-function, then one can consider the wave function as having collapsed.” And still they may expect, if the meeting draws its attendees sufficiently broadly, that a theorist could jump up and object: “One cannot consider any such thing!”

Likewise, the dynamic also plays out in religion. An evangelical Christian in a bible study with other evangelical Christians can reasonably assert, “Jesus said ‘I am the light of the world’,” and treat the basis for this claim (“because the bible says he did”) as beyond dispute in that context and not needing further justification. There is no shame in acting (in that context) as though a foundational framework applied. They should, however, be aware that, when talking to people from a wider range of world views, a Zoroastrian might be a reasonable person, and nonetheless ask for justification beyond, “The bible says so.”

The paradox of coherence

Imagine you are talking to two scientists, each with a particular theory which they want you to adopt.

For each phenomenon which you raise, the first scientist provides a comprehensive explanation for how their theory can account for observations:
Why does iron expand when it melts?
My theory explains that.
Why does water expand when it freezes?
My theory explains that.
Why are women inferior to men?
My theory explains that too.
Why did my credit card get declined?
Yes, my theory can account for everything.
Everything hangs together. The theory is the epitome of coherence.

The second scientist’s theory is, by contrast, utter rubbish:
Why does iron expand when it melts?
Yes, I can answer that.
Why does water expand when it freezes?
Not sure. My theory says it should contract.
Why are women inferior to men?
Um. As a rule, I’m not sure they are.
Why did my credit card get declined?
I… I’m sorry. I really have no idea.

All other things being equal, which theory would you trust? Obviously, you trust the one which is inconsistent and full of holes. Because the world is complicated, and our minds are rather limited. And it is frankly a miracle that we can get a handle on anything, let alone everything. So if a theory is perfectly coherent it rather gives the impression that the person selling it may not be being utterly honest about things.

It is rather like two countries which hold elections, and the leader of one country is elected with 68% of the vote in their favour, while the leader of the other country is elected with 99% of the vote. You can be pretty certain that the first leader has, in reality, a higher level of popular support than the second.

Consider a religious religious person who is asked how they can explain their belief in both pre-destination and free will. They look uncomfortable and admit, “I don’t know. I really don’t see how it can work.”
Consider, then, a materialist who is asked to explain free will in a deterministic universe. They boldly respond: “There is no free will. We have an illusion of free will. But we are not — we cannot be — free.”
The materialist’s view is more coherent. And yet we suspect that, even on a coherentist view, the high level of coherence which their view has does not necessarily speak in its favour. Conspiracy theories often suffer from a similar problem: they are coherent, but they are too coherent.

One can trivially make a theory coherent by simply insisting that everything which doesn’t fit is ignored, irrelevant, or excised. Coherence reigns supreme. But, like a dictator reveling in their resounding election victory, this will not do.

At the other extreme, one can accept that anything goes. Let our theory reject causality, and teleology, and observational rigour. Incoherence is king. But, like a madman claiming victory because no-one voted for him, this also will not do.

Somewhere in between is a complex story in which a genuine effort is make to reconcile irreconcilable ideas, but which accepts that there are some bits that, with the best will in the world, do not seem to fit together. This is the “68% vote” that we feel may be plausible. There is, of course, no hard demarcation which says within these bounds is a believable level of (in)coherence. There is certainly no way to claim an optimal level of incoherence. And different people will find different levels of (in)coherence credible.

In science, some people find the paradoxes of quantum mechanics proof that the theory is wrong, while others believe they provide an acceptable level of mystery. In religion, some people find the purported co-existence of human suffering and divine love to be unacceptable, while others accept that God’s ways are higher than our ways. In elections, two independent observers may variously conclude that the 90% turnout was a sign of massive popular engagement, or a sign of coercion.

This does not mean that any of these people are irrational, or naive, or ignorant. It does not mean that we cannot or should not seek to get a handle on the world as it presents itself. Rater, it means that we should engage in science, religion, and politics with compassion; accepting that there is no view which is universally obvious to all reasonable people. And that makes life difficult. But such is the way of things.

References

[1] Polanyi, M. (1958). Personal Knowledge. pp 267, 299.

[2] Mikes, Georges (1970). “Chapter 5: Tea” in How to Be an Alien: A Handbook for Beginners and Advanced Pupils. Penguin.

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