In this blog, I want to share my first cognitive science paper on the relationship of reasoning and logic. This is my term paper in the course CHP 395: Thinking and Reasoning @UIUC. I have to admit that the title here is for eye-catching purposes. Technically, consciousness is different from awareness and logicalness is restricted to the alignment with classical first-order logic.
[main argument] humans are sometimes unaware of whether their cognitive products align with classical first-order logic
In this paper, I will argue that humans are sometimes unaware of whether their cognitive products align with classical first-order logic. Classical first-order logic is a logical system favored by many as the unique normatively correct account of deductive reasoning [1]. However, daily human cognitive behaviors don’t align completely with this normative model (Evans, 2013). For example, people have a cognitive bias to judge the validity of an argument based on their existing beliefs than on the validity or invalidity of the argument itself, termed “belief bias”. Based on some empirical results and further discussion, I would like to argue further that, humans not only have behaviors misalign with this model but are also sometimes unaware of this misalignment. It is also worth mentioning that although awareness is not a straightforward concept, I will use its daily meaning only for argument. The words “cognitive process”, “entailment”, and “thinking” are interchangeably used. The words “cognitive product”, “conclusion”, “judgment”, and “decision” are also interchangeably used.
We first define logicalness for cognitive processes based on conditionals in classical first-order ****logic. In this logic, the conditional is assumed to be truth-functional and equivalent to material implication. A material implication $p \to q$ being true means that q is true whenever p is true. In classical logic, when this conditional is true, p is allowed never to be true and q is allowed to be true even when p is false. A cognitive process involves serval changes in the mental state of the individual. We can model transitions between the semantic content of different mental states as inferences in logic, called logical entailment [2]. A logical entailment from semantic content M1 to M2 aligning with the classical logic is defined as the consequent holds in every model in which the antecedent holds. This is true if and only if the conditional $M_1 \to M_2$ is a logical truth in classical logic. A process aligns with the classical logic if and only if all transitions do. In this paper, for the sake of brevity, cognitive processes that align with classical logic are called logical, while all the others are called illogical.
Now I want to connect the logicalness of processes with their products. From the same mental state, one can perform many different logical cognitive processes. Define a statement be logical if it does not contradict any statement that is derivable from that starting mental state via any logical cognitive process. All statements that are not logical are called non-logical. A mental state will not logically entail some conclusions that are contradictory to each other by definition, therefore all conclusions that are achieved via logical cognitive processes are logical. Our definition aligns with our intuition. It is worth mentioning that the choice of words "non-logical" and "illogical" are just to indicate whether the subject is a process or the product of a process. They carry no semantics but the opposite of "logical" in the corresponding context.
In the next session, I’ll use some empirical results to show that in some cases most people arrive at a non-logical conclusion and then justify their decisions.
Firstly, people sometimes make non-logical decisions. The famous experiment exemplifying such “sometimes” is the Wason selection experiment given in the account of dual-process theory (Wason, 1968). The Wason selection task is essentially a hypothesis-testing task using classical first-order logic as the normative reference of deductive reasoning. The participants had no training in logic and none was provided by the experimenter. This choice is part of the paradigm “derives from a logicist tradition in philosophy and psychology which assumed that logic must be built into the mind to allow rational thought to take place”. (Evans, 2013).
The following is the setting for illustration: “There are several doors, each displaying only one side to you at a time. Each door has a word of color on one side and a Greek letter on the other. The exposed sides to you are ‘green’, ‘blue’, ‘pi’, ‘sigma’, and ‘yellow’ respectively. Letters and colors can be on either side. Now you are given a statement: ‘If the door has the word ‘green’ on one side, no matter whether displayed or not, it must have the letter ‘pi’ on the other side’. Note that it is not a biconditional claim. Now you need to pick a minimum number of doors that you have to open to decide whether this statement is true or false with 100% confidence after opening them.”
Let’s analyze the problem and fit it into our logical entailment framework. The statement is a universal statement, which is true if and only if all possible instances that can falsify it do not hold. We can symbolize the hypothesis as a material implication $p \to q$, where p: has “green” on one side and q: has “pi” on one side. An instance falsifies a material implication if and only if “p and not q” is true on it. All possible instances that can falsify the hypothesis are those that may have “p and (not q)”. Excluding instances that “(not p) or q”, we get a collection of doors, which is the two showing “green” and “sigma”, that can lead us to claim the truth of the hypothesis with full confidence. When the settings are so novel and abstract to naive reasoner, we can assume they have no prior belief affecting it and most of them share the same semantic content for this problem in their mental state. As our analysis shows, the starting mental state can entail the statement: “To decide the truth of statement we at least but also only need to open the ‘green’ and ‘sigma’ door”.
Both choices are non-logical. The setting I gave is an equivalent setting to the original. Assuming we will get effectively the same result as the original experiment, most people will choose the ‘green’ door and several people will choose the ‘green’ and ‘pi’ door. The tendency to choose ones that are mentioned, in this case, the ‘pi’ door, is termed “matching bias”. Note that people do not necessarily interpret the conditional as a material implication. However, in all other interpretations, the way to falsify the conditional can only be more than “p and not q”, which only leads to more doors to check. Both of the common choices miss the “sigma” door and contradict the logical conclusion, therefore non-logical. There is some other evidence too. Following the Wason selection task, according to Evans (2013), subsequent studies on conditional inference on its own suggested that people commonly endorse two classical fallacies: Denial of the Antecedent (If p then q, not-p, therefore not-q) and Affirmation of the Consequent (If p then q, q, therefore p). Another line is the study of belief bias, which won’t be covered to avoid redundancy with literature. In summary, they all support our claim that people sometimes make non-logical cognitive conclusions.
The reason to mention the selection task specifically among this evidence is mainly for my next argument: If people make a non-logical conclusion, they sometimes justify it. This time we turn to a variant of the Wason selection task. The hypothesis becomes “every door with a ‘green’ on one side will not have a ‘pi’ on the other side.” Now the correct answer should be the ‘green’ and ‘pi’ door, and most people did get it right. It’s believed that their choices are affected by matching bias and this bias happens to turn a hard problem into an “easy” one, at least easy to get the right answer. Inspired by this mystery phenomenon, Wason and Evans (1975) later did a follow-up experiment. They gave participants both the hard affirmative and easy negative version and asked them to write verbal justification. No matter what order they gave the two questions, they found strong matching bias on both tasks and the participants always gave a justification consistent with their choices. That means, even when they received the easy negative version first, most people still make a non-logical conclusion in the hard version and subsequently justify it. Although they are asked to justify, they could have realized their decision are non-logical when they are giving justification. The consistency between judgment and justification suggests they simply can justify their non-logical conclusion whenever they want to. Their justifications are just rationalization, according to Evans and Wason (1976).
In the following session, I claim that if in some cases most people who arrive at a non-logical cognitive conclusion subsequently justify it, then humans are sometimes unaware of whether their cognitive products are logical.
Firstly, if humans are always aware of whether their conclusions are logical, then people who reach non-logical conclusions know they are non-logical. This implication is straightforward since the consequent is a special case of the antecedent.
Secondly, if people who reach non-logical conclusions know they are non-logical, most of them will not subsequently justify them. Most people want to appear logical and rational. And if people want to appear logical and rational, they will likely not justify a statement that they know is non-logical. Justifying a statement that they know is non-logical suggests incoherence, which further suggests being irrational. Justifying a statement that they know is non-logical suggests being illogical. If people justify a statement that they know is non-logical, it appears illogical and irrational. To appear as the opposite, they will likely not justify it.
We begin with the setup of defining what it means by a process is illogical or its product is non-logical in our discussion. With this language, we discuss two versions of the Wason selection task to lay down empirical common ground. Then we briefly discuss how this piece of information implies our statement that humans are sometimes unaware of whether their cognitive products align with classical first-order logic.
An implication is that, by further claiming the meaning of being “illogical” on humans as sometimes performing illogical thinking, we may further extend our conclusion to say “Humans are Unconsciously Illogical” because to have a non-logical cognitive result you must have illogical thinking. However, such discussion is outside of the scope of this paper.
Cited as:
Zory Zhang. (Dec 2023). Humans are Unconsciously Illogical. Zory Zhang’s Blog. https://zoryzhang.notion.site/Humans-are-Unconsciously-Illogical-4fdbad16b3c74ddeb25e8832432b0e41?pvs=4.
Or
@article{zory2023illogical,
title = "Humans are Unconsciously Illogical",
author = "Zory Zhang",
journal = "zoryzhang.notion.site",
year = "2023",
month = "Dec",
url = "<https://zoryzhang.notion.site/Humans-are-Unconsciously-Illogical-4fdbad16b3c74ddeb25e8832432b0e41?pvs=4>"
}