Ariel Jonathan Roffé

In this article, I develop three conceptual innovations within the area of formal metatheory, and present a computer program, called Reconstructor, that implements those developments. The first development consists in a methodology for testing formal reconstructions of scientific theories, which involves checking both whether translations of paradigmatically successful applications into models satisfy the formalisation of the laws, and also whether unsuccessful applications do not. I show how Reconstructor can help carry this out, since it allows the end-user to specify a formal language, input axioms and models formulated in that language, and then ask if the models satisfy the axioms. The second innovation is the introduction of incomplete models (for which the denotation of some terms is missing) into scientific metatheory, in order to represent cases of missing information. I specify the paracomplete semantics built into Reconstructor to deal with sentences where denotation failures occur. The third development consists in a new way of explicating the structuralist notion of a determination method, by equating them with algorithms. This allows determination methods to be loaded into Reconstructor and then executed within a model to find out the value of a previously non-denoting term (i.e. it allows the formal reconstruction to make predictions). This, in turn, can help test the reconstruction in a different way. Finally, I conclude with some suggestions about additional uses the program may have.

The adequacy of Elliott Sober’s analogy between classical mechanics and evolutionary theory—according to which both theories explain via a zero-force law and a set of forces that alter the zero-force state—has been criticized from various points of view. I focus here on McShea and Brandon’s claim that drift shouldn’t be considered a force because it is not directional. I argue that there are a number of different theses that could be meant by this, and show that one of those theses—the idea that drift cannot bias populations to be taken somewhere in the evolutionary space from one generation to the next—is actually false. Not only has this thesis been implicitly assumed in the discussion of the force analogy thus far, but it is also commonly found in a wider range of philosophical and biological texts. I argue that correcting this view, and the usual images associated with it, will thereby bring heuristic benefits that impact the force analogy discussion, but that also go beyond it.

En un libro reciente McShea y Brandon defienden que la diversidad y la complejidad de la vida se explican, principalmente, por la acción de un principio que llaman “la ley evolutiva de fuerzas cero” o “ZFEL”. Tal principio actuaría de un modo implícito por detrás de muchas explicaciones de la biología, pero nunca habría sido explicitado. Asumiendo que esta idea es interesante, y que los autores en cuestión tienen razón, discutiremos el modo metateórico en que presentan dicho principio, como siendo parte de la teoría de la probabilidad. Esto permite a los autores afirmar que la teoría de la probabilidad brindaría la base reductiva para toda la biología evolutiva (dado que consideran que otros principios, como el de selección natural, también serían parte de la teoría de la probabilidad). Defenderemos que, efectivamente, ZFEL no es propio de la biología únicamente, pero no por formar parte de la teoría de la probabilidad, sino por tratarse de una versión específica del principio de causa común. In a recent book, McShea and Brandon argue that the observed diversity and complexity of life are explainable by a principle they call the “zero-force evolutionary law” or “ZFEL”. Although this principle would be implicit in many explanations given by biologists, it would have never been made explicit. Assuming that this idea is interesting, and that the authors are right, we will discuss the metatheoretical way in which they present said principle, as being a part of probability theory. This allows the authors to claim that probability theory provides the reductive basis for all evolutionary biology. We will defend, in accordance with them, that ZFEL is not a solely biological principle, but not because it is a part of probability theory, but rather because it is a specific version of the principle of common cause.

In this article, we defend that incorporating a rejection operator into a paraconsistent language involves fully specifying its inferential characteristics within the logic. To do this, we examine a recent proposal by Berto for a paraconsistent rejection, which — according to him — avoids paradox, even when introduced into a language that contains self-reference and a transparent truth predicate. We will show that this proposal is inadequate because it is too incomplete. We argue that the reason it avoids trouble is that the inferential characteristics of the new operator are left unspecified, exporting the task of specifying them to metaphysicians. Additionally, we show that when completing this proposal with some plausible rules for the rejection operator, paradoxes do arise. Finally, we draw some more general implications from the study of this example.

Resumen El objetivo de este trabajo consiste en analizar las relaciones entre los modelos de optimalidad y la selección natural. Defenderemos que esas relaciones pueden dividirse en dos tipos, en tanto hay dos tipos de explicaciones seleccionistas, que llamaremos “históricas” y “ahistóricas”. Las explicaciones históricas revelan como una población dada adquiere un rasgo que es adaptativo en ese ambiente e involucran muchas generaciones, variación, etc. Las explicaciones ahistóricas, explican por qué, en determinado momento, ciertos tipos de organismos tienen un mayor éxito reproductivo que otros. Mostraremos que los modelos de optimalidad pueden jugar un rol en la determinación del explanandum de las explicaciones histórica seleccionistas, esto es, que ayudan a reconocer qué rasgos son adaptativos. Por otra parte, mostramos que los modelos de optimalidad nos permiten determinar a veces la parte del explanans de las explicaciones ahistóricas (particularmente, el concepto de fitness). Abstract The goal of this paper is to analyze the relations between optimality models and natural selection. We contend that these relationships can be divided into two kinds, as there are two kinds of natural selection explanations, which we call “historical” and “ahistorical”. Historical explanations reveal how a given population acquires a trait which is adaptive in its environment, and involves many generations, variations, etc. Ahistorical ones, explain why, at a given moment, certain kinds of organisms have a greater reproductive success than others. We show that optimality models can play a role in determining the explanandum of historical selectionist explanations, that is, they help us to recognize which traits are adaptive. And, on the other hand, that optimality models sometimes allow us to determine part of the explanans of ahistorical explanations (particularly, the concept of fitness).

This article elaborates on McShea and Brandon’s idea that drift is unlike the rest of the evolutionary factors because it is constitutive rather than imposed on the evolutionary process. I show that the way they spelled out this idea renders it inadequate and is the reason why it received some objections. I propose a different way in which their point could be understood, that rests on two general distinctions. The first is a distinction between the underlying mathematical apparatus used to formulate a theory and a concept proposed by that theory. With the aid of a formal reconstruction of a population genetic model, I show that drift belongs to the first category. That is, that drift is constitutive of population genetics in the same sense that multiplication is constitutive in classical mechanics, or that circle is constitutive in Ptolemaic astronomy. The second distinction is between eliminating a concept from a theory and setting its value to zero. I will show that even though drift can be set to zero just like the rest of the evolutionary factors, eliminating drift is much harder than eliminating those other factors, since it would require changing the entire mathematical apparatus of standard population genetic theory. I conclude by drawing some other implications from the proposed formal reconstruction.