Note: I’m going to go out on a limb with this post. I may have no clue what I’m talking about and be completely unqualified to write about this stuff, but I’m trying to do something different for me and grow. Let me know if you’d like to see more or less of this.
“Since [the 19th century], cognitive scientists have established three robust facts about human reasoning. First, individuals with no training in logic are able to make logical deductions, and they can do so about materials remote from daily life. Indeed, many people enjoy deduction, as shown by the worldwide popularity of Sudoku problems. Second, large differences in the ability to reason occur from one individual to another, and they correlate with measures of academic achievement, serving as proxies for measures of intelligence. Third, almost all sorts of reasoning, from 2D spatial inferences to reasoning based on sentential connectives, such as if and or, are computationally intractable. As the number of distinct elementary propositions in inferences increases, reasoning soon demands a processing capacity exceeding any finite computational device, no matter how large, including the human brain.”
Definitions and Caveats
There is a lot to digest in this quote. I admit that I don’t fully understand it despite several readings. I will nevertheless try writing about it to see if I can write my way toward understanding.
Before beginning, I’d like to offer some definitions for people like me who have modest vocabularies. Any definitions I provide come from the linked Wikipedia entry in each bullet below.
- A cognitive scientist studies “the mind and its processes” and “examines the nature, the tasks, and the functions of cognition.”
- Cognition is “the mental action or process of acquiring knowledge and understanding through thought, experience, and the senses.”
- Deduction is a process of deductive reasoning, which involves the linking of premises and conclusions.
- I believe “2D spatial inferences” refers to spatial intelligence, which “deals with the spatial judgment and the ability to visualize with the mind’s eye.”
- Sentential connectives are the grammatical usage of logical connectives in language to connect ideas or statements. Examples are words like “and,” “or,” “if…then,” “however,” etc.
- “Computationally intractable” involves “problems that can be solved in theory (e.g. Given large but finite time), but which in practice take too long for their solutions to be useful.”
- In the context of this quote, Johnson-Laird is referring to computational complexity theory, which “focuses on classifying computational problems according to their inherent difficulty and relating those classes to each other.”
- It touches on “NP-completeness,” something I studied in my computer science program almost two decades ago (sad face) and have since forgotten (sad face). According to Wikipedia, “NP (for nondeterministic polynomial time) is a complexity class used to describe certain types of problems. Informally, NP is the set of all decision problems for which the instances where the answer is ‘yes’ have efficiently verifiable proofs.”
- Basically, the idea is that computationally tractable problems are ones that can be solved by algorithms using reproducible step-by-step processes. The amount of time it takes to solve problems also plays into this complexity.
- Inferences are “steps in reasoning, moving from premises to conclusions.” So “distinct elementary propositions” must be the number of premises that can be used in the inferring process.
Phew! Let’s begin.
Philip Johnson-Laird’s name is one that keeps coming up in my reading about mental models/frameworks, the functioning of the brain, and cognitive processes. I’ve seen enough people pointing to him as a reference that I’ve realized the need to read his work. There is a ton of free material available on his website, though much of it is deep and dense.
The “three robust facts about human reasoning” are important to me because I am trying to develop an understanding of rationality versus emotionality in decision-making and daily living. Antonio DaMasio’s quote from Descartes’ Error: Emotion, Reason, and the Human Brain particularly struck me: “We aren’t thinking machines. We are feeling machines that think.”
“First, individuals with no training in logic are able to make logical deductions, and they can do so about materials remote from daily life. Indeed, many people enjoy deduction, as shown by the worldwide popularity of Sudoku problems.”
This is comforting because it demonstrates that all normal human beings are able to be logical, including the people that drive us crazy. And children. And our enemies. I feel a sense of peace and relief knowing logic can help me find common ground even with the most difficult people I’ll ever meet. Furthermore, it is comforting to know that logical deduction can be a source of joy if presented in the right context (Sudoku).
Logic may also be intuitive or ingrained in human nature. Perhaps I’m reading too much into this aspect of Johnson-Laird’s quote, but if we need no formal training to make a logical deduction, then perhaps it is natural in relation to the cognitive functions of the mind. I’ll have to do some research as to whether cognitive function is learned or the product of evolution or something else.
The natural world may also follow enough logical reasoning those of us with “no training in logic” are able to find and observe it. Something as simple as “what goes up must come down” is nearly always true in the human experience. Whether we can explain them or not, we are bound by natural, observable law.
Johnson-Laird cites “the development of mathematics, science, and even logic itself” as evidence of human beings having “the seeds of rationality within them.”
“Second, large differences in the ability to reason occur from one individual to another, and they correlate with measures of academic achievement, serving as proxies for measures of intelligence.”
What he’s saying here is that our academic achievements are the measures of our intelligence. These achievements are good indicators of our capability to reason and use logic to our advantage. Therefore, someone with few academic achievements is capable of using and understanding logic, but doesn’t take advantage of the capability.
Simple enough, right?
To me, this is the whole point of Nassim Taleb’s thesis in his book Fooled by Randomness. One might mindlessly wander through life achieving moderate or high levels of success completely by coincidence. In his book, he describes a high-risk trader who makes millions betting on third-world currency, only to lose it all due to the willfully-ignored volatility of those currencies. Apparently, sudden huge losses are common in the world of trading.
Success and the ability to reason are two independent domains. One can be highly successful without reason and one can be highly reasonable and achieve no success. Therefore, we should not look to success as an indicator of an ability to reason. One should, instead, look at success through the lens of academic achievement and reason the way toward awareness of life’s inherent volatility.
“Third, almost all sorts of reasoning, from 2D spatial inferences to reasoning based on sentential connectives, such as if and or, are computationally intractable. As the number of distinct elementary propositions in inferences increases, reasoning soon demands a processing capacity exceeding any finite computational device, no matter how large, including the human brain.”
Let’s remove some of the detail and 50-cent words in this section. The essence of this third “robust fact about human reasoning” is that human reasoning is generally so complex that it exceeds the capabilities of any computer or brain.
Johnson-Laird follows this sentence by stating that our understanding of human reasoning has changed significantly since the 1980s and that he has an “alternative theory” to the idea “that our ability to reason depends on a tacit mental logic, consisting of formal rules of inference akin to those in a logical calculus.” His alternative theory demonstrates that “difficulties exist for mental logic” and that “logic alone cannot characterize rational reasoning.” Furthermore, “we withdraw valid deductions when brute facts collide with them.”
Johnson-Laird is one of the leading researchers behind the notion of mental models, which is my primary interest in reading his research. He says, “When humans perceive the world, vision yields a mental model of what things are where in the scene in front of them. Likewise, when they understand a description of the world, they can construct a similar, albeit less rich, representation — a mental model of the world based on the meaning of the description on their knowledge.”
Peter Senge devotes a chapter to mental models in his book, The Fifth Discipline, emphasizing systems thinking. He states, “Two people with different mental models can observe the same event and describe it differently, because they’ve looked at different details and made different interpretations.” If our biases and worldviews/beliefs affect the selection of details we use in our own personal “logical calculus,” then we are not only irrational/illogical in many cases, but we create a complexity far too great for any reasonable modeling or understanding outside our own heads.
How could any of us possibly outline the axioms we’ve developed that determine the worthiness of observations and inputs? This, to me, is what makes human reason “computationally intractable” because our determination of worthy information in our mental models is so selective. Without an inhuman level of objectivity, the complexity of our logic is indeed too great for any algorithm or simulation. How could anyone determine which scenarios and outputs are “silly” (to use Johnson-Laird’s term)?
So, my momentary conclusion after thinking about this for a bit is that humans are absolutely capable of logic, selectively engage this ability, and only do so in a way that is inexplicable from an objective/mathematical modeling point of view because it most likely cannot be objective outside of an academic context. Obviously, I’m not an academic and there’s much more context to Johnson-Laird’s ideas beyond this single article beyond my understanding, but I feel okay with my interpretation.
What do you think? Do you have different conclusions or interpretations of the quote? Perhaps you know more about Johnson-Laird’s work and intention. If that’s the case, please share!