Logic, Executive Functioning, Organization
As an undergraduate I took a great interest in the philosophy of logic. For a time, leading thinkers like John Stuart Mill argued that the laws of logic are psychological regularities and that to learn logic we have to study the mind. This is a position called Psychologism. The reason to take this view seriously is that it provides us with some real-world data that we could use to frame our understanding of logic. But this is also its weakness.
If laws of logic are not psychological, then we have to look elsewhere for them. Moreover, if they are not, I think this shows that the idea that we can treat mental health as an empirical question is confused. For mental health in large measure has to do with our capacity to sort through the information of our life responsibly. And if those sorting practices, logic, are not psychological, we have to look to elsewhere to provide guidance on what mental health can look like.
The best refutation of this view that I can think of comes from Husserl’s Prolegomena to Pure Logic (his only good work if you ask me).
Husserl’s Criticism of Mill and the Problem of Normativity
Here is the thought experiment that Husserl sets up. Let us assume that the laws of logic were merely an empirically observable process. If this were the case, we could (and should) study logic by studying machines, such as computers. However, we can also design these machines to miscalculate; we could easily design a calculator that produces the result 2+2=5. If reasoning were just a type of observable physical process, then this result should be considered as reasonable as 2+2=4. But it is not.
Husserl rightly noted that the reason we can distinguish between these two results is that reasoning is a normative endeavor. It is because we have norms of reasoning that we can criticize some calculations and inferences as correct and others as wrong. This means that we cannot use our observations of mental processes to define what reasoning is.
While this part of the argument is solid, it leaves us with a difficult question: what accounts for the normativity of reasoning? Husserl claimed that there were ideal laws that govern reasoning, but a similar problem can be generated for these: how do we know them?
(1) If we observe them, how can we distinguish between correct laws and incorrect laws without already presupposing the very logic we are trying to justify? If this requires higher-order logical laws to identify lower logical laws, we are in for an infinite regress.
(2) If the suggestion is that by observing them we will come to know the content of reason (which Husserl attempted to describe in his Phenomenology), then this is a relapse into Psychologism, for in this case we will conflate the norms of logic with our minds and what we are aware of.
What is logic?
Frege for his part was pretty confident that he could treat logic as part of the organization of ideal objects, like sets. In his Foundations of Arithmetic , he argued that we could generate the series of natural numbers from basic logical devices. And this would seem to show how logic shows up in working with abstract logics. Specifically, he constructed an account of numbers as sets, where each natural number is a set.
Russell sends him a note, and asks him: does the set of all sets contain itself? This is Russell’s paradox.
The story goes that this wasn’t something Frege was able to recover from.
But also, I think, in all of this, the question of what logic is gets lost. A lot of these philosophers of logic start talking about math as a way to make sense of logic. Husserl did in his calculator example. Frege did when he developed his Logicism, the idea that numbers are reducible to logic in the form of predicate calculus. It was though logic being used to explain math explained what logic is. It doesn’t.
How do we know what logic is? How can we tell the difference between proper reasoning and improper reasoning?
Husserl tries to answer it, but then we are left with the dilemma of an infinite regress or psychologism.
Here is an example to think about
Valid but All False: Good Reasoning
(1) The Sun is a ball of ice.
(2) Balls of ice are made out of coconut oil.
Therefore, the Sun is made out of coconut oil.
Invalid but All True: Bad Reasoning
(1) The sun rises in the east.
(2) January 1st is New Year’s Day.
Therefore, this is Shyam Ranganathan’s website.
I shared this on the About page when I was engaging in my mini-teach. And what these two arguments show is that good reasoning as defined by logical validity is different from an explanation in terms of our beliefs.
In the literature, an explanation by way of belief is an interpretation. I call an explanation by way of logic, explication. In my recent book, Moral Philosophy and De-Colonialism, I show how all logical errors are explainable by interpretation.
Logic as Organizational Responsibility
In my work put a lot of emphasis on the distinction between explication, which is a reasoned-based explanation, and interpretation. The difference is that interpretation trades in propositional attitudes, like belief, while explication is about the thoughts and data, understood apart from the attitudes. My suggestion is that what counts as logic is what protects our autonomy. Interpretation does not. And what respects our autonomy is an activity that we are in charge of. So logic is an organizational activity, where we get to order information we are considering.
If you want a concrete example of the difference, consider the promulgation of conspiracy theories. If you interpreted, then you would approach these theories emotionally. You would also want to watch for whether the beliefs they express correspond to your own. In this case, a person so interpreting has surrendered their autonomy to what they are contemplating. This is why people drawn to such theories can be manipulated into doing extreme and irrational things.
In contrast, if we took an organizational, explicatory approach, we would be responsible for how we organize the data of a conspiracy theory, and our main guardrail would be our epistemic autonomy. We have to engage in this organizational behavior without conflating what we are organizing with our contingent view of the world. For if we collapse our explanation with our outlook, then we are epistemically limited to that outlook. Put another way, we have to engage in processing information by avoiding interpretation. Logic and explication are hence generated by this responsible, autonomy-respecting approach to information.
For example, the rule of logical validity (if the premises of an argument are true, the conclusion has to be true) is one such logical rule that governs how we evaluate deductive arguments. Inductive arguments have their own specifications, as does Inference to the Best Explanation. And there could be other forms of logic too. But what they have in common is that they are all ways to organize information without collapsing into an interpretation.
The organizational approach to logic respects Husserl’s insight, which was necessary to criticize psychologism, that logic is normative. It is normative in so far as it is generated by our decision to avoid interpreting. That decision creates an obligation and constraints on how we can think.
But it also helps us avoid the Regress of assuming that there has to be a higher-level logical law we are aware of that is the criterion of lower-level logical laws. Every logical law is chosen as part of a practice of avoiding interpretation. There is no higher logical law it answers to. It also helps us avoid Psychologism for logic is nothing we observe in the contents of our mind: it’s something we create by protecting our epistemic autonomy and by organizing the contents of our mind.
This organizational approach would allow us to note that we can discover rules of inference, or ways of organizing information logically. Reason is thus mind-independent. But this discovery is made possible by our choice to be responsible with information.
Logic so understood has important implications for our executive functioning: we need it as a practice to make sure we do not lose our epistemic autonomy. Also, it has important implications for leadership. A leader has to be able to keep possibilities straight without getting confused by them. That takes reasoning.
Logic as Research Methodology
The organizational approach to logic provides a structured methodology for research. This is the fully realized version of explication.
(1) Deductive logic renders explicit reasons for controversial conclusions about first-order options.
(2) Induction—the logic of generalizing from samples—helps determine the general topic of controversy by examining a representative sample of first-order disagreement.
(3) Inference to the Best Explanation (Abduction) discerns the explanation that accounts for the first-order disagreement.
This is a method of research applicable wherever controversy is possible. It allows us to arrive at objective answers—not based on our beliefs or outlook—about the controversy. Once we reach this point, we have reason to conclude what is objectively true: it consists of the integrated findings across all three levels.
This schema is content-neutral. You can use it for the empirical sciences and philosophy alike.
Using Logic as a Research Method to Prove Logic
My thinking about logic is highly indebted to Patañjali’s Yoga Sūtra. But in order for me to have appreciated that this is what was taught in the Yoga Sūtra, I had to make a series of responsible choices to reason and explicate the text when everyone else interprets it. And so in some strange way, it’s as though I had to rediscover exactly what is taught there in order to understand what is taught there. (That actually threw me off for years when I was translating it. It was like looking at a mirror of my thinking, and at times I would get disoriented and wonder if I was projecting. I know I wasn’t because of my methodology. But it was nevertheless dizzying.) Unlike most philosophies, Yoga begins with the question of what methodology we should adopt to deal with information. One protects our epistemic autonomy (that’s Yoga) and the other leads to us being influenced by what we contemplate. My distinction between explication and interpretation is a modern retelling of that distinction.
Given my explicatory three part scheme to get to the objective truth of a contraversy, how dose logic come out as an objective truth?
In Moral Philosophy and De-colonialism, I formulate the basic first-order disagreement where logic is concerned as a disjunction between interpretation and explication. Explication, on an organizational approach to logic, is the rejection of interpretation. And hence, the disjunction is exhaustive of the two extremes. There are no further positions we need to keep track of to appreciate the breadth of the disagreement. We can, on the basis of this disagreement, at the second level, appreciate that the topic of dissent is the constraints of adequate explanation.
We can then ask which account can elucidate the disagreement. It cannot be interpretation, for interpretation will not allow us to appreciate a disagreement, as it confuses a thought with what one believes. A disagreement, in contrast, is a contradiction: it is the affirmation of something one could believe, and its denial. For this reason, dissent is always outside of interpretation. Hence, we would have to accept explication as our method of explanation, for it can elucidate the controversy as a disjunction between two incompatible models of explanation. It is, therefore, the objectively true account of explanation.
Why is this an acceptable way to reason? Isn’t this just biased? You have to assume logic to get this argument off the ground. The answer is, if bias is a prejudice, it’s a propositional attitude. But reasoning, so understood, is the rejection of propositional attitudes. So this reasoning is objective. The correct way to phrase this is that we are choosing to reason. It’s not as an assumption. It is something we do.