Julia Galef on Aumann's Agreement Theorem

I had never heard of Aumann's Agreement Theorem until now. It was published by Robert Aumann in this beautifully written three-page paper in 1976. In this video, Julia refers to this Rationally Speaking podcast. This discussion has some very useful insights into how we could better organise the global economy to serve the interests of the common good, rather than those of the wealthiest groups of people. It also offers an insight into how this Relational Semantics of Quantum Mechanics ultimately produces one single coherent model of the actual state of the world, in spite of the many possible contradictory descriptions of that state that inevitably exist within it, due to individual agents not each being in possession of the same actual knowledge. This is inevitable, because the state of the world, in this Relational Semantic interpretation, includes the state of knowledge of the individuals within it.

Aumann's definition of common knowledge is:

So Aumann takes common conscious experience of a certain event as common knowledge. This allows him to take the actual state of the physical world as something concrete and fixed, about which all observers agree, so this gives common knowledge a "ground" in empirically observed facts. When we do actual science in an actual laboratory, however, we do not have such direct access to reality. Then our different experiences in different laboratories are not identical, for obvious reasons, yet our aim is to produce together a single coherent interpretation of the physical meaning of the experimental data we obtain from our observations. The essential character of a scientific explanation is not that it is accurate, nor that it is even "objective", but rather that it explains the cause of the phenomena under investigation.

Any observation in a laboratory is made in a certain more-or-less specific context of interpretation and that interpretation of the meaning of the observation is never the subject of direct experience, but it is always mediated by other scientific knowledge. For example, measuring the voltage of an electric potential might be done by allowing a small current to flow through a known resistance, and measuring that current by observing the deflection of the needle of an ammeter. In this case, the scientific knowledge is the theory of electrical current and its effects as it moves through a coil in a magnetic field. Then, knowing the resistance R of the circuit, we can infer the potential voltage V from the current I, using Ohm's Law, which is the theory that these three quantities will always satisfy the equation V=IR. In practice, laboratory measurements are not perfectly accurate, but with careful experimental design, such measurements can often be carried out reliably to accuracies of a few parts per million. It is this background knowledge of theory and experimental design, and the practical technology of understanding and making laboratory apparatus, which we refer to as the context of interpretation of the data. And so when we say that an explanation is scientific, we use that as shorthand for the whole complex of physical theory, practical knowledge and skill in experimental design, and, when we claim to have explained the cause of the phenomena, we are using, albeit often only implicitly, this context of interpretation of the experimental data, along with logic, to reason about the causes of the phenomena under investigation, and the descriptions we give of those causes are always going to be interpreted by this background knowledge of experiment. Thus it follows that, in science, we never have empirical common knowledge, in Augmann's terms. Rather, empirical common knowledge is our ultimate objective. It is that knowledge which necessarily must exist, if the enterprise of obtaining scientific knowledge is to have any meaning at all.

Now if I have done a good enough job of explaining my reasons, you will be able to see why I answer the question Jade asks here in the negative. Because the question "Are all Ravens black?" is not in itself a test of a scientific theory. A scientific theory would be a plausible reason why all Ravens are black, and that reason would take the form of a certain set of conditions, which are the context, along with a causal explanation as to how and why those conditions necessarily give rise to the phenomenon that every Raven observed under those conditions should indeed be black. So the explanation would be composed of a number of interdependent parts, which were each, in principle, individually subject to experimental verification, and which parts combine to produce an explanation of the cause of the Ravens all being black.

So you should see that when Jade gives her thought experiments in terms of some person hiding potential experimental data, and explaining the context of that data verbally, those conditions such as: "I have a non-black thing behind my back" can be interpreted as experimental contexts that would produce non-black things in a certain (unspecified) experiment.  So you would only be interested if that process of carrying out the experiment could produce Ravens, and then you would be very interested in the conditions of the process that resulted in Ravens.

The value of experimental verification lies in the mutual confirmation of these background contexts of interpretation of measurements as they are used in scientific explanations of different phenomena. And obviously, experimental verification is more valuable when it comes from differing contexts of interpretation of the data. So, if, in another experiment, I measure the voltage by discharging some of it into a capacitor, then measuring the time taken to discharge the capacitor through a known resistance, and I can adequately explain all the ways in which my results differ from when I use an ammeter to measure the voltage of the potential, then I have more reason to believe that the explanation is independent of the particular experimental context in which it is being tested. And the more we do this, the more we see the underlying phenomena, which are the empirical grounds of our scientific knowledge, as being objectively real. But being apparently objectively real is not the same thing as being absolutely true, so we need to be prepared to have this empirical ground we construct through our shared descriptions of our personal experience change, sometimes radically, as we learn more from each other. That is the sense, then, in which common knowledge is the objective of the whole scientific enterprise, without which science would be ultimately pointless and without value.

Here is a beautifully clear introduction to the idea of hidden Markov models,
which explains how certain observations of samples can be used to infer something about an underlying event that is not directly accessible to observation. In this example, Alice has information about Bob's mood, which she can use to to infer data about the weather where Bob is, which is not something she can directly observe. So in this case, Alice is using Bob's mood as a gauge on a measurement apparatus, which is Bob!

This is, as far as I understand it, just the scientific method described by Aristotle. It fits well with Karl Popper's Logic of Scientific Discovery, because Popper studied Aristotle very carefully. See also the discussion on Integrated Information Theory and top-down development of ontologies for interpreting descriptions of subjective experience here: FT Illustrating The Problem With Modern Medicine.