Peter Smith

Problems raised by complex life cycles for standard summaries of evolutionary processes, and for concepts of individuality in biology, are described. I then outline a framework that can be used to compare life cycles. This framework treats reproduction as a combination of production and recurrence and organizes life cycles according to the distribution of steps in which multiplication, bottlenecks, and sex occur. I also discuss fitness and its measurement in complex life cycles and consider some phenomena that raise complications and difficulties for my framework.

Lockdowns and related policies of behavioral and economic restriction introduced in response to the COVID-19 pandemic are criticized, drawing on three sets of ideas and arguments that are organized in accordance with the likely degree of controversy associated with their guiding assumptions. The first set of arguments makes use of cost–benefit reasoning within a broadly utilitarian framework, emphasizing uncertainty, the role of worst-case scenarios, and the need to consider at least the medium term as well as immediate effects. The second draws on assumptions about the political value of basic liberties. The third draws on ideas about the roles of different stages within human life.

Both biologists and philosophers often make use of simple verbal formulations of necessary and sufficient conditions for evolution by natural selection (ENS). Such summaries go back to Darwin's Origin of Species (especially the "Recapitulation"), but recent ones are more compact.1 Perhaps the most commonly cited formulation is due to Lewontin.2 These summaries tend to have three or four conditions, where the core requirement is a combination of variation, heredity, and fitness differences. The summaries are employed in several ways. First, they are often used in pedagogical contexts, and in showing the coherence of evolutionary theory in response to attacks from outside biology. Second, they are important in discussions of extensions of evolutionary principles to new domains, such as cultural change. The summaries also have intrinsic scientific and philosophical interest as attempts to capture some core principles of evolutionary theory in a highly concise way. Despite their prominence, both the proper formulation and status of these summaries are unclear. Standard formulations are subject to counterexamples, and their relations to formal models of evolutionary change are not straightforward. Here I look closely at these verbal summaries, and at how they relate to formal models. Are the summaries merely rough approximations that have no theoretical role of their own? Perhaps they could operate as theoretical statements in Darwin's time, but have now been superseded by more exact treatments.

The commentaries by Dennett, Sterelny, and Queller on Darwinian Populations and Natural Selection (DPNS) are so constructive that they make it possible to extend and improve the book’s framework in several ways. My replies will focus on points of disagreement, and I will pick a small number of themes and develop them in detail. The three replies below are mostly self-contained, except that all my comments about genes, discussed by all three critics, are in the reply to Queller. Agential views of evolution, discussed by Queller and Dennett, are addressed in my reply to Dennett

Recent years have seen a renewed debate over the importance of groupselection, especially as it relates to the evolution of altruism. Onefeature of this debate has been disagreement over which kinds ofprocesses should be described in terms of selection at multiple levels,within and between groups. Adapting some earlier discussions, we presenta mathematical framework that can be used to explore the exactrelationships between evolutionary models that do, and those that donot, explicitly recognize biological groups as fitness-bearing entities.We show a fundamental set of mathematical equivalences between these twokinds of models, one of which applies a form of multi-level selectiontheory and the other being a form of ``individualism.'' However, we alsoargue that each type of model can have heuristic advantages over theother. Indeed, it can be positively useful to engage in a kind ofback-and-forth switching between two different perspectives on theevolutionary role of groups. So the position we defend is a``gestalt-switching pluralism.''.

The Pinocchio paradox poses one dialetheia too many for semantic dialetheists (Eldridge-Smith 2011). However, Beall (2011) thinks that the Pinocchio scenario is merely an impossible story, like that of the village barber who shaves just those villagers who do not shave themselves. Meanwhile, Beall maintains that Liar paradoxes generate dialetheia. The Barber scenario is self-contradictory, yet the Pinocchio scenario requires a principle of truth for a contradiction. In this and other respects the Pinocchio paradox is a version of the Liar, unlike the Barber. One wonders why some Liars would be impossible if others generate dialetheias

One version of pluralism was defended in a well-known paper by Sterelny and Kitcher. In this sense, pluralism is the view that any given selective process can be described at a variety of different levels in the biological hierarchy. On Sterelny and Kitcher’s view, one can explain giraffe necks in terms of competition among longer-necked and shorter-necked giraffes, and one can also explain them in terms of competition among the genes that lead to these differences in neck size. Although these descriptions might have different heuristic virtues, neither description has a special explanatory status that the other lacks.

A number of recent discussions have argued that George Price's equationfor representing evolutionary change is a powerful and illuminatingtool, especially in the context of debates about multiple levels ofselection. Our paper dissects Price's equation in detail, and comparesit to another statistical tool: the calculation and comparison ofaverage fitnesses. The relations between Price's equation and equationsfor evolutionary change using average fitness are closer than issometimes supposed. The two approaches achieve a similar kind ofstatistical summary of one generation of change, and they achieve thisvia a similar loss of information about the underlying fitnessstructure.

The last Episode wasn’t about logic or formal theories at all: it was about common-or-garden arithmetic and the informal notion of computability. We noted that addition can be defined in terms of repeated applications of the successor function. Multiplication can be defined in terms of repeated applications of addition. The exponential and factorial functions can be defined, in different ways, in terms of repeated applications of multiplication. There’s already a pattern emerging here! The main task in the last Episode was to get clear about this pattern. So first we said more about the idea of defining one function in terms of repeated applications of another function. Tidied up, that becomes the idea of defining a function by primitive recursion (Defn. 27).

In the section ‘Further reading’, I listed a book that arrived on my desk just as I was sending IGT off to the press, namely Church’s Thesis after 70 Years edited by Adam Olszewski et al. On the basis of a quick glance, I warned that the twenty two essays in the book did seem to be of ‘variable quality’. But actually, things turn out to be a bit worse than that: the collection really isn’t very good at all! After I sent my book to press, I gave a paper-by-paper review on my blog, at http://logicmatters.blogspot.com. It is probably more fun to chase up the reviews ‘in the wild’, so to speak, starting from the entry for May 14, 2007. But here they are wrapped up into a single document, only marginally tidied. Some of the points made here should help further explain and support the general line on the Thesis taken in..

Our last big theorem – Theorem 6 – tells us that if a theory meets certain conditions, then it must be negation incomplete. And we made some initial arm-waving remarks to the effect that it seems plausible that we should want theories which meet those conditions. Later, we announced that there actually is a consistent weak arithmetic with a first-order logic which meets the conditions (in which case, stronger arithmetics will also meet the conditions); but we didn’t say anything about what such a weak theory really looks like. In fact, we haven’t looked at any detailed theory of arithmetic yet! It is high time, then, that we stop operating at the extreme level of abstraction of Episodes 1 and 2, and start getting our hands dirty. This Episode introduces a couple of weak arithmetics, before we tackle the canonical first-order arithmetic PA in the following instalment. By all means skip fairly lightly over some of the more boring proof details! But it is certainly worth getting just a flavour of how these two simple formal theories work

odel’s Theorems (CUP, heavily corrected fourth printing 2009: henceforth IGT ). Surely that’s more than enough to be going on with? Ah, but there’s the snag. It is more than enough. In the writing, as is the way with these things, the book grew far beyond the scope of the lecture notes from which it started. And while I hope the result is still pretty accessible to someone prepared to put in the time and effort, there is – to be frank – a lot more in the book than is really needed by philosophers meeting the incompleteness theorems for the first time, or indeed by mathematicians wanting a brisk introduction. You might reasonably want to get your heads around only those technical basics which are actually necessary for understanding how the theorems are proved and for appreciating philosophical discussions about incompleteness. So you need a cut-down version of the book – an introduction to the Introduction! Well, isn’t that what lectures are for? Indeed. But there’s another snag. I haven’t got many lectures to play with. So either (A) I crack on at a very fast pace (hard-core mathmo style), cover those basics, but perhaps leave too many people puzzled and alarmed. Or (B) I do relaxed talk’n’chalk, highlighting the really Big Ideas, making sure everyone is grasping them as we go along, but inevitably omit important stuff and leave quite a gap between what happens in the lectures and what happens in the book. What to do? I’m going for plan (B). But then I ought to do something to fill that gap between lectures and book. Hence these notes. The idea, then, is to give relaxed lectures, highlighting Big Ideas, not worrying too much about depth or fine-detail (nor even about getting through all of the day’s intended menu of topics). These notes then expand things just enough, and give pointers to relevant chunks of IGT. Though I hope these notes will be to a fair extent be stand-alone, and tell a brief but coherent story read by themselves: so occasionally I’ll copy a paragraph or two from the book, rather than just refer to them..