What is meant by ‘a reason’? — Part 1
Psychology, Logic & Rhetoric
keywords: feeling, action, habit, mechanism, habit formation, nested parameters, habit taking, higher-order habit formation, the habit of habit taking, functions, higher-order functions, logic, term, proposition, argument, syllogism, enthymeme, validity, soundness, contextual relevance, rhetoric, logos, ethos, pathos, telos, Kairos, fixation of belief, stability, annealing, error correction, street epistemology
The law of mind is that feelings and ideas attach themselves in thought so as to form systems.
— C. S. Peirce, ‘Grand Logic 1893: Division III. Substantial Study of Logic Chapter VI. The Essence of Reasoning’
Logical analysis applied to mental phenomena shows that there is but one law of mind, namely, that ideas tend to spread continuously and to affect certain others which stand to them in a peculiar relation of affectibility. In this spreading they lose intensity, and especially the power of affecting others, but gain generality and become welded with other ideas.
— Peirce, C. S. (1892). The Law of Mind. The Monist
I want to try clarify some of my own confusion about the meaning of the terms “reason” and especially “a reason” from contexts such as explaining why someone holds a belief about some knowledge claim. Eventually in some follow up articles I want to examine the different senses of this term in wider and wider contexts.
Let me first talk about the terms “feeling”, “habit”, “habit-formation” (or “habit-taking”), and “the habit of habit-taking” (aka “self-organization” or “development”) for the purpose of making an analogy to our usage of the word “reason” and the phrase “a reason”.
Feeling, Habit, Habit Formation
Feeling
An isolated feeling is a difficult concept to understand because it is a mental phenomena that has abstracted away any notions of interaction with the world. Such an abstraction never truly actually exists in isolation, but rather is always occurring in the context of some outward or internal compulsion.
… imagine a person in a dreamy state. Let us suppose he is thinking of nothing but a red colour. Not thinking about it, either, that is, not asking nor answering any questions about it, not even saying to himself that it pleases him, but just contemplating it, as his fancy brings it up. Perhaps, when he gets tired of the red, he will change it to some other colour, — say a turquoise blue, — or a rose-colour; — but if he does so, it will be in the play of fancy without any reason and without any compulsion. This is about as near as may be to a state of mind in which something is present, without compulsion and without reason; it is called Feeling. Except in a half-waking hour, nobody really is in a state of feeling, pure and simple. But whenever we are awake, something is present to the mind, and what is present, without reference to any compulsion or reason, is feeling.
— C. S. Peirce, What is a Sign? (1894)
Feelings when isolated from compulsion are associated with spontaneity and chance. Through their interaction with each other and the environment they meld into various relations developing into habits. This is analogous to the process of crystallization or snowflake formation, what contemporary scientists call self-organization.
Habit
A habit can be a described as a routinized behavior (a stabilized dynamic pattern of action). Habit-formation is just the process of moving from a more spontaneous form of action towards a more routinized and functional form. Most fully formed habits usually still have a degree of adaptiveness left meaning they can be somewhat adjusted by the context in which they occur.
Nested Parameters (Mathematics)
If you remember some high school mathematics, a more formal concept that I find somewhat analogous to this context sensitivity is the idea that an equation can have parameters in addition to variables. The equation along with the parameter defines a family of equations all of the same type.
Quoting Wikipedia:
If asked to imagine the graph of the relationship y = ax², one typically visualizes a range of values of x, but only one value of a. Of course a different value of a can be used, generating a different relation between x and y. Thus a is a parameter: it is less variable than the variable x or y, but it is not an explicit constant like the exponent 2. More precisely, changing the parameter a gives a different (though related) problem, whereas the variations of the variables x and y (and their interrelation) are part of the problem itself.
When reasoning about an equation such as the simple exponential equation shown above we usually implicitly “freeze” the parameter at some value before we begin to reason about the function relation between the input and output variables. A related notion is that of “making it explicit” which can mean to narrow the scope of a reference by making definite some of the information in the implied context.
Now imagine that we had two or more parameters where each was intended to be “frozen”, i.e. applied (partial application) in a partial ordering. For example one would rarely apply a numeric argument for x in the function above before setting the parameter a. This notion of nested contexts or nested parameter hierarchies starting from upper levels and moving downward is often encountered in software code. Programming languages have concepts such as “environment”, “scope”, and “namespace” to refer to such notions. So the analogy I’m drawing here is between the concepts “making it explicit” and “actualization of a parameter”.
In the domain of habit formation we would say the habit is “actualized” by the context but there will still be some remaining context-dependence in addition to the “bottom” most specific spatiotemporal level of action.
If we were to idealize this asymptotic processes of becoming less and less spontaneous and less and less context-dependent we could imagine that it would become more and more of a dumb mechanism until it behaved in the most mechanistic or reflexive way possible. This idealization is even beyond the limited adaptability of a reflex.
Naively, we might imagine that reflexes are immutable. In reality, however, most reflexes are flexible and can be substantially modified to match the requirements of the behavior in both vertebrates and invertebrates.
— Wikipedia, “Reflex”
Higher-Order Habit Formation
Now we can shift the usage of the word “habit” to refer in a more higher-ordered (recursive) manner with the concept of “the habit of habit-taking”. This first occurrence of the word habit having a more general reference since it includes the lower-order habits as inputs and outputs. Other general terms that refer to the same or similar ideas (at least in certain contexts) are “Evolutionary Development”, “Growth” and “Learning”.
Higher-Order Functions
A similar concept to this second-order form of habit that shows up in lambda calculus and computer programming languages is the concept of a higher-order function. In much of high school and undergraduate mathematics functions operate on sets of numbers. But in functional programming, functions are more general in that they can not only map between sets of numbers but also between sets of functions.
The higher-order function, map (“apply to all”), transforms a unary function into a n-ary function. This is similar to using a control flow loop that applies the unary function to an element of a sequence at each iterate. In mathematical “mapping” notation we can represent this function as mapping the unary function f to the n-ary function f_n as follows:
Alternatively in Haskell the map's type signature would be notated as follows:
map :: (a -> b) -> [a] -> [b]To give a specific example, suppose using the Scheme programming language we describe the list '(0 5 8 3 2 1) and we were to define an anonymous function (i.e. nameless) that just increments by 1, (i.e., “(lambda (x) (+ 1 x))”). In Scheme we can simultaneously define this nameless function, transform it into an n-ary function by passing it to map, and then apply it to a list literal (as shown below). First in lets notate map in mathematical barred arrow map notation.
We define the following literal list “g := (0, 5, 8, 3, 2, 1)” that we will use as input. So, notating function application as juxtaposition we have “map g ⇒ (1, 6, 9, 4, 3, 2)”.
In the Scheme programming language calling map on x+1 and a list literal would read as follows:
; Apply anonymous square function to each item of '(0 5 8 3 2 1)
(map (lambda (x) (+ 1 x))
'(0 5 8 3 2 1))
⇒ (1 6 9 4 3 2)
Alternatively we could apply it to a not a literal but a variable which would just return the transformed function itself. The lingo in the programming world is to call these more powerful functions “higher-ordered functions” from an analogy to higher-order logic.
So what about “the habit of habit-taking”? In the same way that a higher order function like map transforms functions (and data) into other functions (and data), higher-order habit formation is like a process directing the more specialized habit formation processes. This is just our life long processes of psychological development, a form of self-organization in which we stabilize habit upon habit.
An important difference between normal habit-formation and higher-order habit formation seems to be that learning occurs throughout a person’s life and never completely settles down the way many specific habit-formation processes do.
Logic
Before moving on to the context of the phrase “a reason” in everyday conversation, let me make some remarks about an old taxonomy through which it is helpful to view these concepts.
Syllogistic
In syllogistic logic (i.e., Aristotelean logic) there is a classic trichotomy of:
- term (e.g., “man”)
- proposition (e.g., “Socrates is a man”)
- argument (e.g. “All humans are mortal. Socrates is human. Therefore, Socrates is mortal.”)
A term is a class of individuals similar to the concept of a set. We should note here that importantly a term can have a emotive connotation, but often does not in these simple syllogism examples.
Symbols are of three classes: terms, which call attention to things or quasi-things; propositions, which declare facts; and arguments, which profess to enlighten us as to the rational connections of facts or possible facts. — C. S. Peirce, 1899–1900 [c.] | Notes on Topical Geometry
A proposition is a composition of terms fused together with a copula, “is”. The function of the copula is to link the subject and predicate together. The objects in the third category, arguments are composed of a sequences of propositions (specifically a series of premises followed by a conclusion). The simplest categorical syllogism is the three-line syllogism as shown in the example for argument above and diagrammatically below.
The term “Socrates” is entirely contained with the term “Man”, and the term “Man” is entirely contained within the term “Mortal”. “Man” is known as the middle term for it mediates between the minor and major terms. This topological relation is probably why we intuitively understand this syllogism type (Barbara, AAA-1) to be valid.
When we use variables instead of words for our terms we are reasoning hypothetically (assumed validity).
These three categories of the syllogism have fundamentally different properties. Terms are associated with possibility, propositions are the “truth-bearers” and are associated with actuality, and arguments are associated with necessity (e.g. “logical necessity”).
Why do I bring this up? I want to clarify what we mean when we use the words/phrases “to reason” and “a reason”. When we talk about “a reason” like it is a proposition it can be confusing because not every proposition can be a reason.
Enthymeme
This is because when we use the phrase “a reason” we usually seem to be referring to a complex statement with the word “because” in it. But this turns a simple statement into what rhetoricians call an enthymeme, i.e. a compressed syllogism. It is essentially a collapsing of an argument into a single complex proposition along with some unstated/implied statements. When the statements that make up an enthymeme are forced to be explicitly expressed only in their minimal propositional form like “Socrates is a man” then it will have at minimum two premises and a conclusion (i.e. a sequence of propositions or an argument). Here is an example of an enthymeme:
“Socrates is mortal because he’s human.”
The complete formal syllogism would be the classic:
All humans are mortal. (major premise — unstated)Socrates is human. (minor premise — stated)Therefore, Socrates is mortal. (conclusion — stated)
— from Wikipedia Unstated premise
Now, when we use the phrase “to reason” we are talking about comprehending or producing an argument not a simple proposition. And when we say “a reason” in informal conversation contexts we are usually talking about a compressed syllogism (enthymeme) and thus a sort of disguised argument. So “a reason” never refers to a simple proposition. It is more about the relation between simple propositions. (You probably already intuitively knew that, but there it is.)
Validity, Soundness, Contextual Relevance
Of course we know that the phrase “a reason” doesn’t just mean a valid argument. If we widen the scope of the meaning just a little we can include not just the form but the content and context. That is when we say “a reason” or “an argument” are we referring to the inferential form, factual content or the context (possibly all three) of that sequence of simple propositions? By context I mean the contextual relevance.
An argument can be invalid, valid or sound. Validity means that the argument form (the abstract relations between the propositions in an argument) conforms to some conventionally accepted form of inference (e.g. BARBARA). A more formal formulation of the definition of validity is that an argument is “valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false.”
Soundness means that all the premises are true in terms of their reference to real world objects (usually outside of the logical system) and that at the same time the argument form is still valid. So soundness presupposes validity and also has to do with the reference to the “real world” objects. (semantics)
So validity is about the “valued” or accepted forms of relations between propositions (analogous to how syntax is about internal relations), soundness includes this but is also more importantly about the reference to the real world or “truth” (analogous to semantics) and we could add a final dimension of the relevance of the argument to the context (analogous to pragmatics).
So it is often the case that we mean one, two or all three of these conditions when judging “a reason” or “an argument” as good or bad.
Rhetoric
We come, therefore, to this, that logic treats of the reference of symbols in general to their objects. In this view it is one of a trivium of conceivable sciences. The first would treat of the formal conditions of symbols having meaning, that is of the reference of symbols in general to their grounds or imputed characters, and this might be called formal grammar; the second, logic, would treat of the formal conditions of the truth of symbols; and the third would treat of the formal conditions of the force of symbols, or their power of appealing to a mind, that is, of their reference in general to interpretants, and this might be called formal rhetoric.
— C. S. Peirce, 1867 | On a New List of Categories | W 2:57; CP 1.559
Logos, Ethos, Pathos
Rhetoric is the art of persuasion. Compared to logic it is a more general discipline and it is closer to the domain of practice and action, i.e., less theoretical and abstract. As a result the meaning of “a reason” is now widened to any communication that convinces you of a belief whatsoever. In this context, in addition to striving for something like scientific and logical truth (see correspondence theory of truth) that perfectly describes nature or “carves nature at its joints”, we have additional purposes in mind. This is due to the additional constraints that come with a more “real world” or action-oriented perspective like ethical value (e.g., bioweapons), efficiency of application (actionable knowledge) and memorability (mnemonics). The theoretical subdisciplines already adopt some relatively rhetorical modes already, for example mathematical elegance aka the aesthetics of logic (aesthetic constraints on logical norms).
An attempt to classify communicative purpose could be (1) to inform, (2) to effect practically, and (3) to impress an aesthetic feeling, and these imply many other subgoals. For example to effect practically the communicatee needs to remember the communication (mnemonics) and to be able to apply it easily (actionability).
In rhetoric there is a traditional triadic taxonomy of terms taught to students first coined by Aristotle of logos, ethos and pathos. Additionally Aristotle also used the concepts of kairos and telos. All of these rhetorical strategies can be thought of as “a reason” that you came to a belief although it is a less common usage than the sense strictly constrained to the logical domain.
Logos — appeal to logic.
Logos is the organization, content and reasoning of a text. This is basically the structure and information of the content of the text without the social or emotional sentiment.
Ethos — appeal to credibility.
Ethos is the credibility and character of the author. Although people often talk about the fallacy of attacking the author’s character (ad hominem), it is not very well understood how important it is that our interpersonal trust and our trust in institutions be valid.
Pathos — appeal to emotion.
Pathos is associated with the audience’s emotions and aesthetic sensibilities. One might include in this category the stylistic devices and even the medium itself.
Kairos — appeal to the contingent aspects of the context.
Kairos is associated with how appropriate to the contingent context a text is. This would be things like the specific timing, or specific setting, etc. This also would be related to concepts such as chance and synchronicity.
Telos — appeal to purpose.
Telos is the goal, intension and purpose of the text.
The Fixation of Belief
The Scottish philosopher Alexander Bain (1818–1903) defined belief as “that upon which a man is prepared to act”. In what way do reasons bring us from a state of doubt to a state of belief?
The analogy I want to draw here is between ideas from metallurgy such as heat treatment and specifically annealing and between our habit and belief formation processes. This frames a good belief as a stable one. Belief is a state of comfort while doubt is a state of irritation. The method of science, empiricism and doubt, as opposed to methods such as authority and tenacity, works in a way analogous to how metallurgists’ heat treatment methods such as annealing work.
Heat treatment involves the use of heating or chilling, normally to extreme temperatures, to achieve the desired result such as hardening or softening of a material.
— from Wikipedia, “Heat Treating”
annealing — heat (metal or glass) and allow it to cool slowly, in order to remove internal stresses and toughen it.
— Definition from Oxford Languages
That is argument, doubt and empiricism are like annealing in that they ensures you don’t get stuck in a relatively local minima and can move beyond those towards relatively more global minima. This seemingly paradoxical fact that the best method of belief formation works by indirectly moving away from an optima in order to, in the end, get much closer than you would have otherwise is shown below in the graph illustrating simulated annealing an abstract method that is conceptually similar to the physical annealing process.
Argument as Habituation, Reason as Developmental Evolution
So how do the ideas expressed earlier about habituation and these logical concepts correspond to one another? Well the ideal limit of a specific habit’s formation process would be like a simple proposition in that it would be a singular action. The habit-formation process would be like an argument that moves you closer to a stable belief.
The habit of habit-taking could be described as our developmental impulse to use “reason in general” and become thus more and more reasonable. Another way of describing this is as growth of our error-correcting powers towards a more metastable and antifragile organization. Here are the correspondences between what we have covered in (1) psychology, (2) syllogistic logic, and (3) rhetoric.
- Logic
Term
Proposition
Syllogism
Reason
Conclusion - Psychology
Feeling
Habit (fully mechanized)
Habit Formation
Higher-order Habit Formation
Stable Belief - Rhetoric (this is the best fit I could come up with)
Kairos
Pathos
Ethos
Logos
Telos
Street Epistemology
I became curious about this definitional question while thinking about Socratic method-style conversations that are centered around the interlocutors method of coming to the belief (particularly epistemology) rather than the belief itself.
An epistemological method such as the method of deferring to an authority or the scientific method can be thought of as a kind of higher-order argument (i.e. a template for inquiry). So it seems that one should be able to think about this subject of “what is a reason?” even more broadly. One can do the same with soundness (facts) and relevant contexts too, but doing so one will run into many dead-ends such as propositions whose truth value we are very uncertain about (relating to soundness/factuality) and even contexts whose relevance we are uncertain about.
In such a style of conversation the point is to only think about the acceptability of “a reason” or “an argument” hypothetically in order to have one question your values about the different methods of coming to a belief. It asks one to use doubt hypothetically (e.g., “imagine you learned that that reason was an invalid reason”) and see how it affects one’s belief. If throwing away what was thought to be a primary reason doesn’t in fact move a person on some scale then it wouldn’t be true to say that it was really a reason affecting that person’s belief.
This hypothetical “throwing away” or “hypothetical refutation” of a person’s primary reason in order for them to sense its effect on their feeling of belief is a way of making the method of doubt explicit but at the cost of being a purely theoretical exercise (which can be misleading).
We can think of this in relation to our earlier example of “freezing” the different nested strata of a parameter hierarchy in that it is like a hypothetical simultaneous “freeing up” and ignoring of the former constraint of the actualized parameter on your belief. If this constraint was the primary effective information in holding your belief, this new freedom should affect one’s confidence in that belief.
In doing this one will desire to eventually by the agitating feeling of doubt and uncertainty come back to a state of belief through the search for an alternative stabilizing reason. We can think of this as moving one’s attention “horizontally” towards reasons of the same level of abstraction. But if one were to yield to further doubt it might involve moving “upwards” toward a higher-order reasons, basically higher-order methodologies or templates. Of course the feeling of yielding to the compulsion of reason (e.g., the rhetorical or logical force) is this explicit process happening in a relatively less explicit and more natural manner.
❧ — arisbe.carrd.co — ❧
- Wikipedia, “Reflex”, “Parameter”, “Validity (logic)”
- Math Insight, “Function Machine Parameters”
- Wikisource, C. S. Peirce, “The Fixation of Belief”
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