There are no singular facts (Questions II)

There is more to explore here, and more thoughts to test. Let’s talk more about knowledge, and take two really simples examples. We believe we know the following.

(i) The earth is round.
(ii) Gravity is 9.8 G

Our model here is one of knowledge as a set of propositions that can be justified and defended as knowledge – they can be deemed true or false, and the sum total of that body of propositions is all we know. We can add to it by adding new propositions and we can change our mind by throwing old propositions out and replacing them with new ones.

This model is incredibly strong, in the sense that it is often confused with reality (at least this is one way in which we can speak of the strength of a model – the probability p that it is mistaken for reality and not seen as a model at all), but it is just a model. A different model would say that everything you know is based on a question and the answer you provide for it — just as Plato has Socrates suggesting. We can then reconstruct the example above in an interesting way.

(i) What is the best approximate geometrical form for representing the Earth in a simple model? The Earth is round.
(ii) What is gravity on the average on planet Earth? 9.8G.

Once you explicate the question that the proposition is an answer to you suddenly also realize the limits of the answer. If we are looking for the gravity on a specific place on earth, as the top of Mount Everest, the answer may be different. If we are looking for a more exact representation of the earth with all the topological geological data exact, the round model will not suffice. Articulating the question that the proposition you say you know is an answer to opens up the proposition and your knowledge and helps you see something potentially fundamental, if it holds for closer scrutiny.

There are no isolated facts.

Facts, in this new model, are always answers to questions, and if you do not know the question you do not really understand the limits and value of a fact. This is one alternative way of addressing the notion of “a half-life of facts” as laid out by Sam Arbesman in his brilliant book on how facts cease being facts over time. The reality is that they do not cease being facts, but the questions are asking change subtly over time with new knowledge.

Note that this model is in no way a defense for relativism. It is the opposite: questions and answers provide a strong bedrock on which we can build our world, and we can definitely say that not every answers suffices to answer a question. There are good and bad answers to questions (although more rarely bad questions).

So, then, when Obama says that we need to be operating our political discussion and debates from a common baseline of facts, or when senator Moynihan argued that you are entitled to your opinions but not your own facts, we can read them under the new model as saying something different.

Obama’s statement turns into a statement about agreeing on questions and what the answers to those questions are – and frankly that may be the real challenge we face with populism: a mismatch between the questions we ask and those the populists ask.

Senator Moynihan’s point is that if we agree on the questions you don’t get to invent answers – but your opinions matter in choosing what questions we ask.

So, what does the new model suggest? It suggests the following: you don’t have knowledge. There are no facts. You have and share with society a set of questions and answers and that is where we need to begin all political dialogue. These provide a solid foundation – an even more solid foundation – for our common polis than propositions do, and a return to them may be the long term cure for things like fact resistance, fake news, propaganda, polarization and populism. But it is no quick fix.

Strong claims, but interesting ones – and ones worthy of more exploration as we start digging deeper.

Socratic epistemology, Hintikka, questions and the end of propositional logic (Questions I)

The question of what knowledge is can be understood in different ways. One way to understand it is to focus on what it means to know something. The majority view here is that knowledge is about propositions that we can examine from different perspectives. Examples would include things like:

  • The earth is round.
  • Gravity is a force.
  • Under simple conditions demand and supply meet in a market.

These propositions can then be true or false and the value we assign to them decides if they are included in our knowledge. The way we assign truth or falsity can vary. In some theories truth is about correspondence with reality, and in some it is about coherence in the set of propositions we hold to be true.

Now, admittedly this is a quick sketch of our theory of knowledge, but it suffices to ask a very basic question. Why do we believe that propositions are fundamental to knowledge? Why do we believe that they are the atoms of which knowledge is constituted?

Philosopher and historian of ideas RG Collingwood thought the explanation for this was simple: logic and grammar grew up together, as sciences, so we ended up confusing one with the other. There are, Collingwood asserts, no reasons for assuming that knowledge breaks down into propositions. There are no grounds for asserting that propositions are more basic than other alternatives. The reason we have propositional logic is just because logic is so entwined with grammar.

That leaves us with an interesting problem: what, then, is knowledge made of?

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Socrates was clear. In Plato’s Theaetetus we find the following discussion in passing:

I mean the conversation which the soul holds with herself in considering of anything. I speak of what I scarcely understand; but the soul when thinking appears to me to be just talking—asking questions of herself and answering them, affirming and denying. And when she has arrived at a decision, either gradually or by a sudden impulse, and has at last agreed, and does not doubt, this is called her opinion. I say, then, that to form an opinion is to speak, and opinion is a word spoken,—I mean, to oneself and in silence, not aloud or to another: What think you?

This idea, that knowledge may be dialogical, that it may consist in a set of questions and answers to those questions is key to open another perspective on knowledge. It also, potentially, explains the attraction of the dialogue form for the Greeks: what better way to structure philosophical debate than in the same way knowledge is structured and produced? Why state propositions, when dialogue mimics the way we ourselves arrive at knowledge?

It is worthwhile taking a moment here. In one way this all seems so evident: of course we ask ourselves question to know! That is how we arrive at the propositions we hold true! But this is exactly where we need to pause. The reality is that the leap from questions and answers to propositions is uncalled for, and a leap that fools us into believing that questions are merely tools with which we uncover our propositions. Shovels that shovel aside the falsity from the truth. But knowledge is not like nuggets of gold buried in the earth – knowledge is the tension between answer and question in equilibrium. If you change the question, the balance of the whole thing changes as well – and your knowledge is changed.

As an aside: that is why, in belief revision, we often are interested in generating surprise in the person whose views we want to change. One way to describe surprise is as the unexpected answer to a question, that then forces a new question to be asked and the network of questions and answers is then updated to reflect a new belief – a new pair of questions and answers.

This minority view is found again in people like RG Collingwood who writes extensively about the fundamental nature of questions and it has been explicated at length by Jaako Hintikka who in his later philosophy developed what he called Socratic epistemology. In the next couple of posts we will examine what this could mean for our view of the conscious mind, and perhaps also for our view of artificial intelligence.

I think it will allow us to say that the Turing test was the wrong way around: that the questions should have been asked by the human subject and the computer to the test leader. It will also allow us to understand why human questioning is so surprisingly efficient, and why randomly generating queries is a horrible way to learn any subject. Human questions shape the field of knowledge in an interesting way, and we see this in the peculiar shape of human go games in the overall game space of go, but equally in the shape of human knowledge in chess.

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When new models for learning are devised they are able to explore completely different parts of the problem space, parts you don’t easily reach with the kinds of questions that we have been asking. Questions have a penumbra of possible knowledge, and I suspect – although this will be good to explore further – that our ability to question is intrinsically human, and perhaps in some sense even biological. Here I would point to the excellent work of professor Joseph Jordania on questions and evolutionary theory, in his work Who Asked The First Question?.

This is an area of exploration that I have been mining for some time now with a close collaborator in professor Fredrik Stjernberg, and we are getting ready to sum up the first part of our work soon, I hope. It is not just theoretical, but suggests interesting possibilities like dialogical networks (rather than adversarial ones) and a science of possible categories of questions and ways to ask new questions, or better questions.

Computational vs Biological Thinking (Man / Machine XII)

Our study of thinking has so far been characterised by a need to formalize thinking. Ever since Boole’s ”Laws of Thought” the underlying assumption and metaphor for thinking has been mathematical or physical – even mechanical and always binary. Logic has been elevated to the position of pure thought, and we have even succumbed to thinking that is we deviate from logic or mathematics in our thinking, then that is a sign that our thinking is flawed and biased.

There is great value to this line of study and investigation. It allows us to test our own thinking in a model and evaluate it from the perspective of a formal model for thinking. But there is also a risk associated with this project, a risk that may become more troubling as our surrounding world becomes more complex, and it is this: that we neglect the study of biological thinking.

One way of framing this problem is to say that we have two different models of thinking: computational and biological; the computational is mathematical and follows the rules of logic – and the biological is different, it forces us to ask things about how we think that are assumed in computational thinking.

Let’s take a very simple example – the so-called conjunction fallacy. The simplest rendition of this fallacy is a case often called ”Linda the bank teller”.

This is the standard case:

Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.

Which is more probable?

Linda is a bank teller.

Linda is a bank teller and is active in the feminist movement.

https://en.wikipedia.org/wiki/Conjunction_fallacy

What computational thinking tells us is that the first proposition is always more probable than the second. It follows from the fact that the probability p is always bigger than the probability p x q if either probability is less than 1.

Yet, a surprising amount of people seem to think that it is more likely that Linda is a bank teller and active in the feminist movement. Are they wrong? Or are they just thinking in a different mode?

We could argue that they are simply chunking the world differently. The assumption underlying computational thinking is that it is possible to formalize the world into single statement propositions and that these formalizations are obvious. We thus take the second statement to be a compound statement – p AND q – and so we end up saying that it is necessarily less probable than just p. But we could challenge that and simply say that the second proposition is as elementary as the first.

What is at stake here is the idea of atomistic propositions or elementary statements. Underlying the idea of formalized propositions is the idea that there is a hierarchy of statements or propositions starting from ”single fact”-propositions like ”Linda is a bank teller” and moving on to more complex compound propositions like ”Linda is a bank teller AND active in the feminist movement”.

Computational thinking chunks the world this way, but biological thinking does not. One way to think about it is to say that for computational thinking a proposition is a statement about the state of affairs in the world for a single variable, whereas for biological thinking it is a statement about the state of affairs for multiple related variables that are not separable nor possible to chunk into individuals.

What sets up the state space we are asked to predict is the premises, and they define the state space we are asked to predict as one that contains facts about someones activism. The premises determine the chunking of the state space, and the proposition ”Linda is a bank teller and active in the feminist movement” is a singular, elementary proposition in the state space set up by the premises — not a compound statement.

What we must challenge here is the idea that chunking state spaces into elementary propositions is the same as chunking them into the smallest possible propositions. For computational thinking this holds true – but not for biological thinking.

The result of this line of arguing is intriguing: it suggests that what is commonly identified as a bias here is in fact just a bias if you assume that computational thinking is the ideal to which we are all to be held — but that in itself is a value proposition. Why is one way of chunking the state space better than another?

Another version of this argument is to say that the premises set up a proposition chunk that contains a statement about activism, so that the suppressed second part of ”Linda is a bank teller” is ”and NOT active in the feminist movement” and cannot be excluded. That you do not write it out does not mean that the chunk does not automatically contain a statement about that as the second chunk and the premises set that up as the natural chunking of the state space we are asked to predict.

The real failure, then, is to assume that ”Linda is a bank teller” is the most probable statement – and that is not a failure of bias as such, but an interesting kind of thinking frame failure; the inability to move away from computational thinking instilled through study and application.

It is well-known that economists become more rational than others, that they are infected with mathematical rationality through study. Maybe there is this larger distortion in psychology where tests are infected with computational thinking? Are there other biases that are just examples of being unable to move from the biological frame of thinking?

On not knowing (Man / Machine III)

Humans are not great at answering questions with “I don’t know”. They often seek to provide answers even where they know that they do not know. Yet still, one of the hallmarks of careful thinking is to acknowledge when we do not know something – and when we cannot say anything meaningful about an issue. This socratic wisdom – knowing that we do not know – becomes a key challenge as we design systems with artificial intelligence components in them.

One way to deal with this is to say that it is actually easier with machines. They can give a numeric statement of their confidence in a clustering of data, for example, so why is this an issue at all? I think this argument misses something important about what it is that we are doing when we say that we do not know. We are not simply stating that a certain question has no answers above a confidence level, we can actually be saying several different things at once.

We can be saying…
…that we believe that the question is wrong, or that the concepts in the question are ill-thought through.
…that we have no data or too little data to form a conclusion, but that we believe more data will solve the problem.
…that there is no reliable data or methods of ascertaining if something is true or not.
…that we have not thought it worthwhile to find out or that we have not been able to find out within the allotted time.
…that we believe this is intrinsically unknowable.
…that this is knowledge we should not seek.

And these are just some examples of what it is that we are possibly saying when we say “I don’t know”. Stating this simple proposition is essentially a way to force a re-examination of the entire issue to find the roots of our ignorance. Saying that we do not know something is a profound statement of epistemology and hence a complex judgment – and not a statement of confidence or probability.

A friend and colleague suggested, on discussing this, that it actually makes for a nice version of the Turing test. When a computer answers a question by saying “I don’t know” and does so embedded in the rich and complex language game of knowledge (as evidenced by it reasoning about it, I assume), it can be seen as intelligent in a human sense.
This socratic variation of the Turing test also shows the importance of the pattern of reasoning, since “I don’t know” is the easiest canned answer to code into a conversation engine.

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There is a special category of problems related with saying “I don’t know” that have to do with search satisfaction and raise interesting issues. When do you stop looking? In Jeremy Groopman’s excellent book on How Doctors Think there is an interesting example of radiologists. The key challenge for this group of professionals, Groopman notes, is when to stop looking. You scan an x-ray, find pneumonia and … done? What if there is something else? Other anomalies that you need to look for? When do you stop looking?

For a human being that is a question of time limits imposed by biology, organization, workload and cost. The complex nature of the calculation for stopping allows for different stopping criteria over time and you can go on to really think things through when the parameters change. Groopman’s interview with a radiologist is especially interesting given that this is one field that we believe can be automated to great benefit. The radiologist notes this looming risk of search satisfaction and essentially suggests that you use a check schema – trace out the same examination irrespective of what it is that you are looking for, and then summarize the results.

The radiologist, in this scenario, becomes a general search for anomalies that are then classified, rather than a specialized pattern recognition expert that seeks out examples of cancers – and for some cases the radiologist may only be able to identify the anomaly, but without understanding it. In one of the cases in the book the radiologist finds traces of something he does not understand – weak traces – that then prompts him to do a biopsy, not based on the picture itself, but on the lack of anything on a previous x-ray.

Context, generality, search satisfaction and gestalt analysis are all complex parts of when we know and do not know something. And our reactions to a lack of knowledge are interesting. The next step in not knowing is of course questioning.

A machine that answers “I don’t know” and then follows it up with a question is an interesting scenario — but how does it generate and choose between questions? There seems to be a lot to look at here – and question generation born out of a sense of ignorance is not a small part of intelligence either.