Last updated on 22 Jun 2018
In his classic work A System of Logic, which set up so many of the issues and problems of the modern field of the philosophy of science, John Stuart Mill wrote:
Not a trace of the properties of hydrogen or of oxygen is observable in those of their compound, water. [Bk III ch VI §1]
and drew from this the conclusion
This explains why mechanics is a deductive or demonstrative science, and chemistry not. In the one, we can compute the effects of combinations of causes, whether real or hypothetical, from the laws which we know to govern those causes when acting separately; because they continue to observe the same laws when in combination which they observed when separate: whatever would have happened in consequence of each cause taken by itself, happens when they are together, and we have only to “cast up” the results. Not so in the phenomena which are the peculiar subject of the science of chemistry. There, most of the uniformities to which the causes conformed when separate, cease altogether when they are conjoined; and we are not, at least in the present state of our knowledge, able to foresee what result will follow from any new combination, until we have tried the specific experiment.
If this be true of chemical combinations, it is still more true of those far more complex combinations of elements which constitute organized bodies; and in which those extraordinary new uniformities arise, which are called the laws of life. All organized bodies are composed of parts similar to those composing inorganic nature, and which have even themselves existed in an inorganic state; but the phenomena of life, which result from the juxtaposition of those parts in a certain manner, bear no analogy to any of the effects which would be produced by the action of the component substances considered as mere physical agents. To whatever degree we might imagine our knowledge of the properties of the several ingredients of a living body to be extended and perfected, it is certain that no mere summing up of the separate actions of those elements will ever amount to the action of the living body itself. [pp371f]
Here we have Mill’s statement of the basic problem, long before Lewes had coined the term “emergence” in 1875. “No mere summing up” of the to-be-reducing properties will give you the to-be-reduced properties. What does this mean?
Mill had a name for this, one not nearly so memorable: concurrence of causes [Bk III chapter X, §4], and he wrote
When the laws of the original agents cease entirely, and a phenomenon makes its appearance, which, with reference to those laws, is quite heterogeneous; when, for example, two gaseous substances, hydrogen and oxygen, on being brought together, throw off their peculiar properties, and produce the substance called water; in such cases the new fact may be subjected to experimental inquiry, like any other phenomenon; and the elements which are said to compose it may be considered as the mere agents of its production; the conditions on which it depends, the facts which make up its cause.
The effects of the new phenomenon, the properties of water, for instance, are as easily found by experiment as the effects of any other cause. But to discover the cause of it, that is, the particular conjunction of agents from which it results, is often difficult enough. In the first place, the origin and actual production of the phenomenon are most frequently inaccessible to our observation. If we could not have learned the composition of water until we found instances in which it was actually produced from oxygen and hydrogen, we should have been forced to wait until the casual thought struck some one of passing an electric spark through a mixture of the two gases, or inserting a lighted taper into it, merely to try what would happen. Besides, many substances, though they can be analysed, cannot by any known artificial means be recompounded: Further, even if we could have ascertained, by the Method of Agreement, that oxygen and hydrogen were both present when water is produced, no experimentation on oxygen and hydrogen separately, no knowledge of their laws, could have enabled us deductively to infer that they would produce water. We require a specific experiment on the two combined. [p440]
Mill’s argument here is simple. No knowledge of the properties of the parts (hydrogen and oxygen) would give us a knowledge by deduction of the properties of the whole (H2O). But something happened since Mill. Quantum mechanics and the periodic table happened. Now we can predict, to a high degree, what the properties of compounds are, depending upon our computational capacities (and I mean that literally – the capacities of our computers). For example, we often predict the microstructure of water itself just from a knowledge of the affinities and bonds of the H2) molecules (e.g., Paricaud et al. 2005). A philosophical argument can sometimes be overtaken by science and advances in computation.
So Mill’s point is that this is difficult, but not an in-principle impossibility. The properties of water are surprising to us based on what we know about hydrogen and oxygen in 1843, and due to limitations in what we can work out from them. It reminds me a little of this recent comic:
Of course Aragorn cannot do this (without some serious time on a supercomputer, anyway), but hey, it can be done. So if the wetness of water is a surprise, it is because we have some threshold for expectations of unsurprising and surprising results. What is this?
The surprisal value of a sequence (pieces of information in order) is roughly the inverse of expectation that it would occur by chance (see here). It is a measure of the amount of information expressed by a particular outcome, measured in bits (the negative logarithm of the probability of that event or sequence), given a distribution of outcomes and their probabilities. Now the surprisal of water having, say, a viscosity of some type, is relative to the framing assumptions we have for the ways elements interact when combined. It depends rather crucially on what we know and can work through.
If you only know the observable properties of these elements, then the idea that two gases would form a liquid at room temperature is surprising. The subjective surprisal value is high because the subjective probabilities are low. But once you understand the strong and weak bonds of these elements, and you have sufficient computational capacity to work out how these properties play out in large ensembles, you can predict the structure of water right down to the surface tension when impurities occur, and so even the biological properties of water. Once you have a fully formed quantum theory of the elements, then the liquidity of water is not longer a surprise, just a matter of working through the objective probabilities.
If one can derive a macro phenomenon from micro properties through theoretical deduction, then the emergence is simply subjective surprisal. So the remaining argument for objective emergence is, in my view, the downward causation argument, which I’ll address in the next post.
Mill, John Stuart. 1974. A System of Logic, Ratiocinative and Inductive: Being a Connected View of the Principles of Evidence and the Methods of Scientific Investigation, Books I–III. Edited by J. M. Robson. Vol. VII, Collected Works of John Stuart Mill. Toronto, Buffalo NY, London: University of Toronto Press/Routledge & Kegan Paul.
Paricaud, Patrice, Milan P?edota, Ariel A. Chialvo, and Peter T. Cummings. 2005. From dimer to condensed phases at extreme conditions: Accurate predictions of the properties of water by a Gaussian charge polarizable model. Journal of Chemical Physics 122 (24):14.