On theory and observation (6): Public events and the two generals’ problem

Public events
In our series about theory and observation (as well as in the philosophical literature dealing with this question), the truth is that most of what we have said is more about theory than about observation (perhaps with the only exception of our third entry). Philosophers of science have devoted a lot of effort to explain what is what makes theoretical concepts theoretical, and what is what we gain from that, but there are not so many philosophical explanations of what is what makes observational concepts observational, or by the way, what makes of a particular action an act of observation. After all, it seems that the answer to this question is trivial, and the problem (if there should have to be one) seemed to be for most philosophers that no observation is ‘pure’, but all of them are ‘theory laden’. I feel a little bit perplexed by this fixation with the problem of theory-ladenness, because it presupposes that we have a clear idea of what something like a ‘completely theory-free’ observation would be. This is perhaps an effect of a bad influence from some philosophical systems like classical empiricism, according to which all knowledge comes from ‘pure sense data’: mere sensations of color, sound, etc., not categorized in any way by our minds, and which later our intellect connects in ways that depend on one ‘theory’ or another. But ‘primary sensations’ or ‘sense data’ are just fictional entities: it is not only that nobody has ever seen (or heard, or felt) one, but I would dare to say that nobody has ever imagined how such an entity would look like.

Most discussions about observation within traditional philosophy of science (and this was in the end the official stance of ‘logical positivists’) is that ‘observation’ has to be taken as a primitive term, in the sense that real scientists simply know ‘by acquaintance’ (to use Bertrand Russell wording) what to make an observation is, and we philosophers have basically nothing to add to that. Probably one of the most sophisticated views on the question was Otto Neurath’s idea of protocol sentences: the statements with which the experimenters describe what they see in their labs, and that don’t have any kind of Cartesian certainty, because scientists may have been wrong in thinking that they have seen something in particular, or may have described it in a wrong way, so that protocol sentences are, for Neurath, essentially revisable (instead as the permanent and indubitable building blocks of the edifice of scientific knowledge, as previous empiricists seemed to have assumed). But this, however sophisticate it looks in comparison with the theory of sense-data, still leaves us without the feeling of having captured something sufficiently interesting from a philosophical point of view about the notion of empirical observation.

Public events
Source: Wikimedia Commons

I think that something a little bit deeper can be grasped by reflecting on a well-known paradox of game theory: the two generals’ problem. The problem consists in two armies, before the time of radio communications, having to decide the precise moment of a concerted attack on the enemy (whose own army lays between the other two ones), a strike that (in the ideal situation assumed by the argument) will succeed if and only if both allied armies charge exactly at the same time. How can the two generals agree on a particular moment? General A can send a message to general B, but the messenger can be captured by the enemy, preventing that B receives the message. To assure that this has not happened, B has to send a new messenger to A confirming that he has got the first message. But how can B be sure that A has got his (i.e., B’s) response? A should have to send a new messenger to B confirming that he got B’s message… and so to infinity. This problem relates to the problematic concept of game theory known as common knowledge: something is common knowledge within a group not just if every member of the group knows it, but also if everyone knows that everyone knows it, and if everyone knows that everyone knows that everyone knows it, etc., etc. But is this just not too much knowing for our human, limited minds? The two generals’ problem illustrates this difficulty by associating each recursive step in the definition of common knowledge with the physical process of sending a new confirmation message from one general to the other. Real common knowledge of the fact ‘we must attack at 3 o’clock’ requires the sending and receiving of an infinite number of messages, which is just impossible, and hence, real common knowledge (which is a necessary assumption for the existence of an equilibrium in many games) cannot exist in the real world, or so the argument goes.

What makes this paradox interesting for our philosophical quandary about observation is the fact that the generals would not have encountered that problem if they were not physically separated, or if they had benefited from modern telecommunications: there is something in face-to-face communication that makes, in almost an automatic way, that one knows that the other knows that you know that he knows, etc., what has been told. If one general says to the other ‘we shall attack at 3’ and the other just says ‘OK’, that’s all that is necessary to agree… and to know that they have agreed. The economist (and Nobel laureate) Paul Milgrom suggested four decades ago a way in which an event can, so to say, trigger this automatic common-knowledge production without the need of sending an infinite series of messages. He defined something as a public event just if everybody knows that, if it happens, it is impossible (within a specific spatio-temporal context, and perhaps within a group of people with some special training) that someone ignores that it has happened. Public events allow dispensing with an infinite series of new physically existing pieces of information about what others know, and replace it with just a logical inference, in the same way as we know that there are infinite natural numbers without the need of counting them all. Instead of ‘public’, we might use terms like notorious, evident, obvious, patent, or the like. The pronunciation of the phrases in the physical conversation the generals might be having in the face-to-face case would be an example of such notorious events (actually, real languages are so that possible ambiguities in the emitted sounds tend to be minimized, at least for the native speakers).

This idea of publicity is an essential, or even one of the most essential aspects, of observation. It is essential at least if we consider ‘observation’ not just in the solipsistic way in which a living being can interact with its environment and hence needs to get some reliable information about it, but in the way in which we take observation as a fundamental building-block in the process of communication-mediated interaction with other beings (and in particular, in that interaction that we call ‘scientific research’, but, in truth, this is just a small application of a more day-to-day concept of ‘public observability’). As it is clear by our example of the two generals, observation as the perception of public events (in Milgrom’s sense) is essential for communication, not only because most communication is about those types of events, but because communication consists in the production and reception of a specific set of that type of events (it is what we call ‘talking’ or ‘writing’). Communication would not exist if there were no public events, and hence, we can affirm (in a Kantian voice) that the existence of Milgromian public events is a condition of possibility of communication itself. That we are speaking to each other counts as a philosophical demonstration that some public events exist, and hence, it counts as a proof that the world is necessarily observable.

Of course, this does not entail that everything in the world is accessible to observation, only that something is observable (in this technical sense that there are some facts that, once they happen, it is -almost- impossible not to realize that they have happened, at least for people with the adequate training and sensory capabilities). What it does entail is that observation being unavoidably theory-laden cannot prevent communication in a ‘radical’ way, leading us to an ‘absolute relativism’ or something like that: Copernican and Ptolemaic astronomers may certainly (as Thomas Kuhn suggested) ‘see different worlds’ when they look at the same stars, but at some point there must be something (no matter how they call it, or how they interpret it) that they are seeing in the same way. What they can do starting from that ‘common base’ is of course not guaranteed by any transcendental structure of the world, or something; but what is guaranteed, if they are just speaking to each other, is that there must be some description of what they are seeing that is ‘neutral enough’. Science has done a lot in the last centuries thanks to this ‘observational basis’, what perhaps only means that we have been lucky so far, and does not entail that our luck will last forever: perhaps we are reaching the limits of what can be known from observations in some areas of knowledge (or not), but probably there is still a lot of progress to be made in many other areas. So, let’s keep observing our common world.


Milgrom, P., 1981, “An Axiomatic Characterization of Common Knowledge”, Econometrica, 49, 219 22.

Zamora Bonilla, J., 2017, Sacando consecuencias, Tecnos, ch. 2.

‘On theory and observation’ series:

(1): The theoretician’s dilemma
(2): The Ramsey sentence
(3): Scientists selling lemons, a game-theoretic analysis of how scientific facts are constructed
(4): Sneed’s structuralism and T-theorecity
(5): Testing theory-nets

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