Rationality | Nick Byrd, Ph.D.

The Bat And Ball Problem 20 Years Later

In 2002, a chapter from Kahneman and Frederick mentioned “the bat and ball problem”.

A bat and a ball cost $1.10 in total.
The bat costs $1.00 more than the ball.
How much does the ball cost?

By 2005, Frederick’s Cognitive Reflection Test paper added the lesser known Widgets and Lily Pad problems. In the intervening 20-ish years, each paper seems to have accrued over 5000 citations.

In 2023, Meyer and Frederick published a massive follow-up paper about the first problem: 59 studies, over 73,000 participants, and more pages of Appendixes than pages in the main article. As someone studying various reflection tests and interventions, I had to take a look right away. In this post, I list five initial takeaways and two things to like about the paper.

Upon Reflection, Ep. 12: Tell Us What You Really Think

I have a question for you: “If a bat and a ball cost $1.10 in total and the bat costs $1.00 more than the ball, how much does the ball cost?“. Did 10 cents seem right? The authors of questions like this are attempting to lure you to accept this incorrect answer in order to test whether you thought reflectively when you solved the problem. However, there may be problems with this method of testing reflective thinking. So my colleagues used some underrated methods to determine the degree to which tests like this misclassify correct responses as reflective or lured responses as unreflective. I’ll read the paper in this episode.

Podcast: Play in new window | Download (Duration: 32:57 — 60.3MB)

Upon Reflection, Ep. 9: Bounded Reflectivism & Epistemic Identity

In this episode, I read one of my 2022 articles in Metaphilosophy titled, “Bounded Reflectivism & Epistemic Identity“. Does reflective reasoning help or hinder our judgment? In this paper, I take a middle view between reflectivism and anti-reflectivism that I call bounded reflectivism. The idea is that reflection is a tool that can be used to improve our judgment or for other purposes (such as to defend the beliefs that we consider essential to our identity—a.k.a., our “epistemic identity”).

Podcast: Play in new window | Download (Duration: 40:55 — 74.9MB)

What good is reflective reasoning?

Philosophers and cognitive scientists tend to think that reflective reasoning will improve our judgments and decisions. The idea reflection will lead us to test our judgments by “looking for their coherence with our beliefs about similar cases and our beliefs about a broader range of …issues” a la reflective equilibrium. This sounds intuitively plausible. But is it true? In this post I briefly present some research suggesting that reflective reasoning often, but does not always improve our judgments and decisions. Continue reading What good is reflective reasoning?

Upon Reflection, Ep. 5: Reflective Reasoning For Real People (Dissertation Overview)

Welcome to Upon Reflection. In this episode, I review the major take-aways and findings from my dissertation titled, “Reflective Reasoning For Real People”. I explain what cognitive scientists mean by terms like “reflective reasoning”, how reflection is measured empirically, how reflection can either help or hinder our reasoning, how more reflective philosophers tend toward certain philosophical beliefs, and how reflection may help us retrain our implicit biases.

Podcast: Play in new window | Download (Duration: 15:53 — 29.1MB)

The Base Rate Fallacy

Who is more likely to be killed by a police officer in the United States: a white person or a black person? You might think, “Police kill more white people than black people in the US. So it’s the white person.” That answer contains a fallacy: the base rate fallacy. This post explains the fallacy, provides some examples, and suggests how to avoid it.

50+ Philosophy Podcasts

Philosophy takes many forms. So do its podcasts. Here are some of the most popular philosophy podcasts that I have found. I listen to almost all of them, so feel free to contact me if you have questions that are not answered in each podcast’s description below.

Continue reading 50+ Philosophy Podcasts

Evaluate An Argument With Just ONE Flowchart

I love philosophy and science. I also love flowcharts because they can compress many pages of instruction into a simple chart. And three researchers from George Mason University and the University of Queensland have combined these three loves in a paper about climate change denialism. In their paper, they create a flowchart that shows how to find over a dozen fallacies in over 40 denialist claims! In this post, I’ll explain this argument-checking flowchart. First, we will identify a common denialist claim and then evaluate the argument for it. Continue reading Evaluate An Argument With Just ONE Flowchart

Sexual Harassment Accusations & The Acceptance Principle

A public figure is accused of a sexual misdeed. You know nothing about the accused besides their name and their alleged crime. And you know nothing about the accuser except their name and their accusation. Can you believe the accuser? We often learn about such sexual harassment accusations. So it behooves us to find a principled response. The Acceptance Principle suggests that we can accept this kind of accusation. Why? I’ll explain in this post. Continue reading Sexual Harassment Accusations & The Acceptance Principle

Domain-familiarity & The Cognitive Reflection Test

This week I’m commenting on Nicholas Shea and Chris Frith’s “Dual-process theories and consciousness: the case for ‘Type Zero’ cognition” (2016) (open access) over at the Brains blog. My abstract is below. Head over to Brains for the full comments and subsequent discussion.

Abstract

Type 1 and type 2 cognition are standard fare in psychology. Now Shea and Frith (2016) introduce type 0 cognition. This new category of cognition manifests from existing distinctions — (a) conscious vs. unconscious and (b) deliberate vs. automatic. Why do existing distinctions result in a new category? Because Shea and Frith (henceforth SF) apply each distinction to a different concept: one to representation and the other to processing. The result is a 2-by-2 taxonomy like the one below. This taxonomy classifies automatic processing over unconscious representations as type 0 cognition. And, deviating from convention, this taxonomy classified automatic processing over conscious representation(s) as type 1 cognition.

		PROCESSING
		Automatic	Deliberate
REPRESENTATION	Unconscious	Type 0	?
REPRESENTATION	Conscious	Type 1	Type 2

According to SF, we deploy each type of cognition more or less successfully depending on our familiarity with the domain. When we’re familiar with the domain, we may not need to integrate information from other domains (via conscious representation) and/or deliberately attend to each step of our reasoning. So in a familiar domain, type 0 cognition might suffice.

SF briefly mention how this relates to the cognitive reflection test (CRT) (Frederick 2005). There is a puzzle about how to interpret CRT responses that do not fit a common dual-process interpretation of the CRT. In what follows, I will show how SF’s notion of domain-familiarity can make sense of these otherwise puzzling CRT responses.

Image: “Wiffel ball” from Andrew Malone as modified by Nick Byrd. CC BY 2.0

Category: Rationality