Modelling the truth of scientific beliefs with cultural evolutionary theory

Abstract

Evolutionary anthropologists and archaeologists have been considerably successful in modelling the cumulative evolution of culture, of technological skills and knowledge in particular. Recently, one of these models has been introduced in the philosophy of science by De Cruz and De Smedt (Philos Stud 157:411–429, 2012), in an attempt to demonstrate that scientists may collectively come to hold more truth-approximating beliefs, despite the cognitive biases which they individually are known to be subject to. Here we identify a major shortcoming in that attempt: De Cruz & De Smedt’s mathematical model makes one particularly strong tractability assumption that causes the model to largely miss its target (namely, truth accumulation in science), and that moreover conflicts with empirical observations. The second, more constructive part of the paper presents an alternative, agent-based model, which allows one to much better examine the conditions for scientific progress and decline.

Appendices

Appendix A: Derivation of Eq. 3

According to Henrich, assuming that everyone copies the most skilled individual, population-level change in mean $z$-value, $\Delta \overline{z}$, is given by Eq. (2), that is,

$$\begin{aligned} \Delta \overline{z} = \underbrace{z_h -\overline{z}}_\mathrm{selective\;transmission } + \underbrace{\Delta z_h}_\mathrm{noisy\;interference } \end{aligned}$$

For a population with skill levels distributed according to a Gumbel distribution, we have

$$\begin{aligned} z_h = \mu + \beta (\gamma + \ln (N)), \end{aligned}$$

where $\mu$ is the mode and $\beta$ the spread of the distribution, and $N$ represents population size. Further, for $\overline{z}$ we have

$$\begin{aligned} \overline{z} = \mu + \beta \gamma . \end{aligned}$$

Finally, the transmission error is given by

$$\begin{aligned} \Delta z_h = -\alpha + \beta \gamma , \end{aligned}$$

where $\alpha$ represents imitation inaccuracy, as represented in Fig. 1. Adding all this yields Eq. (3) in the main text.

Appendix B: Relaxing D & D’s first tractability assumption

What happens if one were to relax D & D’s first tractability assumption, and concede that belief selection is subject to the same cognitive biases as imitation? Put differently, what happens when imitators not only make inferior copies, but prior to that, also select inferior beliefs to copy from? Under these conditions, the relatively simple Eq. (2) no longer applies. Instead, one would need to deploy the following equation:

$$\begin{aligned} \Delta \overline{z} = \frac{1}{n}\sum _{1}^{n} \frac{f_i}{\overline{f}}(z_i + \Delta z_i) - \frac{1}{n}\sum _{1}^{n}z_i \end{aligned}$$

(4)

So instead of having only one best belief $h$, which is copied by all, one now has several beliefs $\{i,j,\ldots ,n\}$, that all come with their own likelihood of being copied $\{f_i,f_j,\ldots ,f_n\}$, and with their own transmission bias $\{\Delta z_i,\Delta z_j,\ldots ,\Delta z_n\}$. Without making any further assumptions, there is no way of telling how $\Delta \overline{z}$ will evolve over time. In sum, the “best belief” assumption is indeed required for tractability. The only alternative for examining the effects of less selective forms of mentor selection is to switch to agent-based models (see Sect. 4).

Appendix C: Implementation of the simulations

Simulations were implemented in NetLogo (code available from the authors upon request). Simulations start with a population of $N=10,50,100,175,250,350,500, 1000$ parents, each with an initial $z$-level randomly drawn from a Gumbel[10;1]-distribution, and a population of $N=10,50,100,175,250,350,500,1000$ offspring individuals, each with an initial $z$-level of 0.

In each run, models go through two stages: transmission and replacement.

During transmission, each offspring selects—according to the learning biases defined in the main text—one agent from the parent generation, the latter acting as a cultural parent for the former. In particular, the offspring’s $z$-value is given by the parent’s $z$-value, minus the structural transmission inaccuracy $\alpha$, plus an individual error, randomly drawn from a Gumbel[0;1]-distribution.

During replacement, the offspring generation replaces the parent generation, and the average $z$-level of the population, $\overline{z}$, is measured.

Models go through 100 runs, after which the overall change in average $z$-level, $\Delta \overline{z}$, is measured. To account for stochastic variation in simulation outcomes, 1,000 iterations were performed and results were averaged across these.