The use of scientific methods and models in the philosophy of science

Abstract

What is the relation between philosophy of science and the sciences? As Pradeu et al. (British Journal for the Philosophy of Science https://doi.org/10.1086/715518, 2021) and Khelfaoui et al. (Synthese 199:6219, 2021) recently show, part of this relation is constituted by “philosophy in science”: the use of philosophical methods to address questions in the sciences. But another part is what one might call “science in philosophy”: the use of methods drawn from the sciences to tackle philosophical questions. In this paper, we focus on one class of such methods and examine the role that model-based methods play within “science in philosophy”. To do this, we first build a bibliographic coupling network with Web of Science records of all papers published in philosophy of science journals from 2000 to 2020 ($N=9217$). After detecting the most prominent communities of papers in the network, we use a supervised classifier to identify all papers that use model-based methods. Drawing on work in cultural evolution, we also propose a model to represent the evolution of methods in each one of these communities. Finally, we measure the strength of cultural selection for model-based methods during the given time period by integrating model and data. Results indicate not only that model-based methods have had a significant presence in philosophy of science over the last two decades, but also that there is considerable variation in their use across communities. Results further indicate that some communities have experienced strong selection for the use of model-based methods but that other have not; we validate this finding with a logistic regression of paper methodology on publication year. We conclude by discussing some implications of our findings and suggest that model-based methods play an increasingly important role within “science in philosophy” in some but not all areas of philosophy of science.

Appendices

Appendix 1: Naive Bayes classifier

To label papers with respect to their methodology, we used a multinomial naive Bayes classifier. Naive Bayes classifiers assign an item to a class by maximizing the following expression:

$$\begin{aligned} Pr(q_i|w_1,..., w_m) = \frac{ Pr(w_1,..., w_m|q_i) Pr(q_i)}{ Pr(w_1,..., w_m) } \quad , \end{aligned}$$

(1)

where $Pr(q_i|w_1,..., w_m)$ is the probability of the item belonging to class $q_i$ given that the item has features $w_1,..., w_m$, $Pr(q_i)$ is the unconditional probability of the class, and $Pr(w_1,..., w_m)$ is the unconditional probability of the features. Items correspond to papers, classes correspond to the two types of methods that a paper might use (model-based method vs. no model-based method), and features correspond to the number of times that a word occurred in a paper’s abstract and the number of times that a last name appears in a paper’s reference section. These numbers are integers because words can appear any number of times in the abstract and last names can appear any number of times in the reference section.

Appendix 2: Wright-Fisher model

To build a model for the cultural evolution of methods in philosophy of science, we assumed that papers are chosen to reproduce in proportion to how many papers of each type were available in the previous year. The probability that an individual of a given type—say, papers that use model-based methods—will be chosen to reproduce is given by:

$$\begin{aligned} p = \frac{ i_{t} \cdot (1+s) }{ i_{t} \cdot (1+s) + j_{t}} \quad , \end{aligned}$$

(2)

where $i_{t}$ is the number of papers of that type in generation t, $j_{t} = N_{t} - i_{t}$ is the number of individuals of the other type, and s is the selection coefficient measuring the strength of selection. Generations correspond to publication years. The parameter s is positive when selection favors the focal type, negative when selection favors the non-focal type, and zero when selection does not favor any type.

Conversely, the probability that a paper of the other type—papers that do not use model-based methods—will be chosen to reproduce is given by:

$$\begin{aligned} q = \frac{ j_{t} }{ i_{t} \cdot (1+s) + j_{t}} \quad , \end{aligned}$$

(3)

where terms are defined as before.

Further, we assume that the population of papers grows over time because papers never leave the publication record. The probability that a population with $i_{t}$ papers of a given type in generation t transitions to a population with $i_{t+1}$ individuals of the same type in generation $t+1$ is thus given by:

$$\begin{aligned} Pr(i_{t+1}|i_{t}) = { N_{t+1} - N_{t} \atopwithdelims ()i_{t+1} - i_{t} } \cdot p^{ i_{t+1} - i_{t} } \cdot q^{ j_{t+1} - j_{t} }, \end{aligned}$$

(4)

where ${ N_{t+1} - N_{t} \atopwithdelims ()i_{t+1} - i_{t} }$ is the number of combinations we can obtain by choosing $i_{t+1} - i_{t}$ individuals of the focal type in a group of $N_{t+1} - N_{t}$ individuals, $p^{ i_{t+1}-i_{t} }$ is the probability that $i_{t+1} - i_{t}$ individuals of the focal type will be chosen to enter the population, and $q^{ j_{t+1}-j_{t} }$ is the probability that $j_{t+1} - j_{t}$ individuals of the non-focal type will be chosen to enter the population. Expression (4) therefore gives the probability that a population with $i_{t}$ papers of a given type will transition to a population with $i_{t+1}$ individuals of the same type by growing from size $N_{t}$ to size $N_{t+1}$.

Appendix 3: Maximum-likelihood estimation

To estimate the strength of selection (s) for or against the use of model-based methods, we used the technique of maximum-likelihood estimation. That is, we take $\hat{s}$ be the value that maximizes the following expression:

$$\begin{aligned} \hat{s} = \mathop {{\textrm{argmax}}}\limits _{s \in [-1,1]} \quad \sum _{t=2000}^{2020} log \left( Pr(i_{t+1}|i_{t}) \right) \quad , \end{aligned}$$

(5)

where $\hat{s}$ is the maximum-likelihood estimate of selection for or against the use of model-based methods in a particular community, $Pr(i_{t+1}|i_{t})$ is given by expression (4), and the sum is over the entire time period considered here—namely, from 2000 to 2020. Note that we take the log of $Pr(i_{t+1}|i_{t})$ simply to facilitate computation, as values for $Pr(i_{t+1}|i_{t})$ can be very small. Note also that equation (5) correspond to the estimate of selection for a particular community, so $\hat{s}$ must be estimated separately for each community of papers.