When can we call an explanation "rational"?

There are a lot of questions involving rational judgment, rational choice, rational explanation, and so on.

At the same time, it seems that "being rational" is a guiding principle for many people.

Prior to assessing the value of rationality, I am not sure that I understand what it means when we say "this is a rational explanation."

I find it hard to distinguish the rational explanations from the rest, in real-life situations; a guiding principle on how to do so is lacking.

• What is the difference between a rational explanation and an explanation that is not rational?

• What criteria would one use to distinguish the rational from the irrational?

• When Mr. Spock says it is. He's the final arbiter of rationality. (psst! wrong universe!) (oops.) Commented Mar 22 at 22:05

One way to define rational argument is by saying that an argument is rational if it does not violate any of the Laws of Thought:

1. The law of identity `(a = a)`
2. The law of non-contradiction `(~(a and ~a))`
3. The law of the excluded middle `(a or ~a)`

in addition to this, for a rational argument to be useful in practice, a rational argument had to have a base set of axioms which everyone in the audience would accept as truth for granted. The reason for demanding axioms is that otherwise we can reason about almost anything just by carefully choosing the axioms (e.g. by assuming the conclusion is true).

However, it is not necessary for an argument to have accepted axioms for it to be a "rational argument" (argument with nonsense axioms are still rational but useless arguments). Example being, `cheese is edible` and `moon is made from cheese`, therefore `moon is edible`. This is a rational argument, but useless since nobody in their right mind would accept that `moon is made from cheese`.

Also note that not all axioms need to be explicitly listed out. Some of the more common axioms that are often accepted without being explicitly listed out are the rules of inference. Implicit axioms are the "ground rules" of a particular session of discussion.

• +1 Also consider vacuous truths, a drawback we're forced to accept as a result of our system of formal logic, wherein a conditional statement with a false antecedent becomes true. For example: If the moon is made of green cheese, then 2+2 = 5. Commented Jun 9, 2011 at 5:01
• @Ryan, thanks for your detailed answer on these formal aspects. Starting with law 1, when do you concider that two things are the same ? Commented Jun 9, 2011 at 11:49
• +1 - Lovely answer. Discussing pragmatic considerations was a nice touch. Your use of A = A, as opposed to A ≡ A has given me an idea about a meta question. Once again, great answer. Commented Jun 9, 2011 at 17:01
• @boehj Lovely ? I would say it lacks thickness ? I view is that the level of the examples that are used to illustrate the rule are at the level of the rule. Commented Jun 10, 2011 at 7:13
• @robin: Yes I think @Lie wrote a lovely answer. I don't understand your criticism of it, if indeed it is a criticism (i.e. thickness/level of the rule). Perhaps you could explain further what you mean by these things. Commented Jun 10, 2011 at 7:31

One way to answer the question (and I suspect there are many approaches) would be to define reason as the product of an instrument of rationality, i.e., a mind. What makes the question more than trivial for us, however, is that our minds are connected to bodies that interfere with reason. Emotion, instinct, and biases often dominate the function of the mind and produce various type of irrational thought.

An oddity of the human mind is that when it considers its own thoughts, it usually finds a great deal to like and when it considers the thoughts of others, it often is skeptical. I've found this can happen even when I'm in agreement with the thoughts of others! (I believe the Ontological argument is valid and so does my friend. But I think he might be wrong.) We are often over-skeptical of the ideas of others and over-confident of our own ideas.

Since every mind will be disrupted by a unique set of interference, one solution to the problem of knowing if an explanation is rational or not is to submit it to a collection of minds in some public forum (such as this one!) where it can be analyzed. Presumably the consensus of many minds will eliminate the most common forms of bias. Problems with this approach are left as an exercise for the reader!

Often we work together to form a set of rules we agree on and can apply to validate our reasoning. Remarkably, there are many overlaps between one set of rules and all other sets of rules. Therefore, over time, we've learned to use these basic rules of reason and declare that thoughts which conform to these rules are rational. You can find examples of these rules in the other answers.

• thanks for this answer, I definitly like it (even with the problem left as exercises) +1. for the reference to public forum and all that. I think this has an importance. I am not really conviced by your image of a "mind" separated and dominated by "Emotion and instinct" but I also think it goes into another important direction. Commented Jun 9, 2011 at 12:13
• @robin: I haven't thought it through, but it seems like most of us are far too skeptical of the rationality of others and far too trusting of our own rationality. Commented Jun 9, 2011 at 17:50
• I guess rationality can be found the other way: faith in others rationality and doubt a bout our own. Commented Jun 10, 2011 at 7:19
• Now with your last paragraph it's even better! Commented Jun 14, 2011 at 17:13

A rational explanation appeals to our critical faculties -- it does not attempt to appeal to our passions or weaknesses. Rationality involves the justification of beliefs; a rational explanation precisely gives reasons for a conviction, and these reasons are validly correlated with the inferences the argument wishes us to draw. An irrational or unreasonable argument is marked by various misalignments between the premises and the conclusions; some of these are so commonly exploited that they are classified as traditional logical fallacies.

While I am definitely a believer in clear formulations of concepts, it is undoubtedly the case that "reason" is often a likely mask for other interests. What is said to be "rational" may turn out upon critical analysis merely to be a precept of common sense without justification, or indeed someting more sinister -- a rationalization for social or psychic repression. And underneath this sort of "rationality" there is only drift; and as at the very least it is difficult to conceptually define what "pure reason" might mean (though cf. Kant) there is a certain sense in which the ultimate meaning of our "reason" may merely be a series of long errors.

This apple is a fruit, because all apples are fruit.

This apple is a fruitcake, because fruitcake can have fruit in it."

The conclusion doesn't follow from the "rule".

In real life, it might not be as glaringly obvious that something doesn't follow the rules, but it should still be apparent when you think about it. If you're not sure about something, ask for elaboration. If someone can't explain what they've said, then they either have no basis for it ("Because I said so" or "That's how I feel") or the basis is faulty. This doesn't mean that what they've said is wrong, just that they haven't rationally justified it.

• I defined the rule: The sentence `a and not a` is true for any propositions a. Commented Jun 8, 2011 at 20:01
• What about this rule: `whenever it gets cold in my office, I will whistle "Old Man River" until it gets warm`? But I think you are on the right track. Commented Jun 8, 2011 at 20:38
• @JonEricson I am almost completely sure that he mans the rules of logic, not personal rules. Commented Jun 8, 2011 at 20:45
• @Edward: I'm sure you are right. But that seems to just put off the question a bit. How can we separate rules of logic from other types of rules? (My answer is not immune from that sort of critique, by the way.) Commented Jun 8, 2011 at 21:01
• I left out evaluating the appropriateness of rules as an exercise to the reader :P
– user20
Commented Jun 8, 2011 at 21:02

I agree that a mathematical explanation that follows “the laws of thought ” is a good starting point to make a rational explanation . I don’t think it is the rules themselves but the purpose of those rules that helps us to understand what is a rational explanation. At the end logical systems are one ingredient among others to go toward a rational explanation.

A rational explanation is an explanation that is coherent with a large system of though. At some point, It is the efficiency of logic that legitimates logic and, it is the efficiency of an explanation that makes it rational.

Toward the word “efficiency” which might be a bit problematic, I would say that a rational explanation is an explanation that contributes to the agreement -association- of minds and objects. The association of my mind with the mind of those the explanation is given to, the association of objects between themselves, the association of minds between themselves...

From that point we can deduce and list several practical ingredients for a rational explanation

• Complete Logical system of rules form a good ingredient because these are self sufficiency, simple and structured. All this makes easier the association of minds but not the association of object and mind.
• A Detailed description of the objects under discussion contribute to a rational explanation. This helps creating a system of though that is more robust and hence contribute to all mentioned form of associates.
• Confrontation of the explanation with system of explanation helps association of minds and hence is a very important ingredient to a rational explanation (I guess this is what peer reviews are made for?).
• .... other propositions ?

It seems that you are really asking what we mean by "rational". Now we mean a lot of different things in different contexts. Regarding the expression "rational explanations", we might say that it is in fact a pleonasm. An explanation is something that purports to give reasons why a given proposition is true. At least in one sense, "rational" just means "relating to reasons", and in this sense all explanations would be rational, i.e. reason-giving.

Now another use of "rational" is to evaluate a piece of reasoning; in this sense it means something like "correct according to a standard, principle or rule". An explanation (which by definition purports to be rational) can be irrational if it fails to satisfy the standard. To say that a given account of p which refers to a consideration is rational would be to say that p is justified by the consideration. "Be rational!" is a guiding principle which instructs you to follow the rules of logic or epistemology and to be maximally coherent. Presumably everyone is guided by the goal of being rational, though some manage better than others.

• Thanks for you answer. My question focuses on rational explanation. I think there can be non rational explanation. An explanation of an idea is a proposition that describes the interation of the idea in question with the rest of our thinking system. We can imagine any interation, even the craziest don't you think ? Commented Jun 9, 2011 at 11:19
• the question that I asked about a rational explanation could be asked about "logic" "epistemology" "marximally coherent" "reason". It is interesting to try to give words that have similar function in your thinking system be it does not really tell about how the function works ? Commented Jun 9, 2011 at 11:24
• Finally, I like the idea of maximising "coherence", +1 for that. I think it tells something, not all, about rationality that could be examine further. Do you know what the phylosophical tradition calls "the common sence" ? Commented Jun 9, 2011 at 11:26

To evaluate a rational explanation, I think it's important to distinguish correct from rational. A rational explanation is one which given a series of premises leads to an unequivocal conclusion.

```Socrates is a man.
All men are mortal,
therefore Socrates is mortal.
```

This also happens to be correct, but if I wanted to, I could make the following rational argument:

```Dogs like chicken.
Spot is a dog,
therefore Spot likes chicken.
```

It's rational because the conclusion is undeniable if its premises are sound. Of course, they're not since perhaps some dogs might actually detest chicken (though not likely), however a rational argument is not necessarily correct. If I wanted to, I could arrive at the conclusion that the earth is round because Spongebob Squarepants is square, and while that conclusion might be correct, it's definitely not rational.

• There are technical terms that are used to maintain the distinction between what you are calling "rational" and what you are calling "correct": an argument is valid (or cogent) if its conclusion necessarily follows from its propositions according to the canons of logic; it is sound if (in addition) its propositions are factually true. Commented Sep 30, 2011 at 13:46

'Rationality' in its broadest sense is puzzle solving. I mean this in the 'jigsaw puzzle' sense: any rational argument is going to take a number of disconnected ideas and observations and then draw connections between them, putting them in particular relationships to each other until a greater picture emerges. For instance, we see a number of objects fall and we create (rationally) an overarching picture of gravitational attraction; we get tricked by someone a number of times and generate (rationally) an image of them as a jerk. We think of something as being 'rational, then, when the overarching picture that emerges makes sense to us: seems cohesive, and coherent, structured, and generally 'right'.

Irrationality, by contrast, is like jamming jigsaw puzzle pieces together willy-nilly: colors don't blend, lines don't connect, gaps and overlaps appear. It violates our sense of continuity, and triggers our biases towards consistency and completeness.

Of course in real life we don't have have the picture on the puzzle box to test our puzzle-solving against. We are stuck making the best picture we can, and then comparing/contrasting it with pictures that other people develop from the same mental pieces. In that sense it isn't an either/or (rational/irrational) distinction; it's a continuum in which some arguments are more rational than others on some dimensions, while other arguments may be more rational on other dimensions. It's important to understand what mode of rationality someone is using — according to Habermas, there are at least four: teleological, normative, dramaturgical, and communicative — and how that mode might be appropriate to the discussion at hand.

I would understand this as a false framing of the nature of explanations.

Rational explanation is a tool used to justify preferring one value over another. Rational explanation assumes the existence of value systems and can be thought of in a way similar to water piping.

The rationality of an explanation is the degree to which the pipes are water tight (leaking analogous to irrationality), while the water is analogous to a particular value or desire.

All explanations are attempting to justify channeling a specific value to a specific action. All explanations fall on a spectrum of rationality to this end.

I personally think a rational explanation has more to do with objective truth rather than with "reality" itself. And what is objective truth but no more than an agreement between 2 or more people?

Look at the COVID pandemic, for instance, back in the day we would've explained this situtation as a punishment from God, but today science tells us that god has nothing to do in the equation, yet, science keeps reinventing itself everyday, what we today take as truth tomorrow we might see it as false.

Therefore a "rational argument" depends on the person who receives and aproves the argument rather than the logic behind it. If I tell a person with little knowledge of physics that gravity is a force that pulls me to the ground, he might consider my argument rational, if I tell the very same thing to a scientist, he might correct me by saying that I am pulling the ground as well according to Newton's formula. Therefore my argument would be irrational for him, but then comes Einstein, saying that gravity it's not about attraction but rather a diformation of space itself and that bodies just travel along with it, he might then be told that more likely an "artistic idea than actual science" as he was actually told at first.

You can understand my explanation then why "rational" depends HEAVILY on the subject.

Also... rationality it's always relative to the subject, all humans, therefore are rational up to their respective circumstances.

This is more of a historical-rhetorical observation than succinct answer, already provided by "Laws of Thought" reply.

Let's ask first, what is an irrational explanation? Not merely illogical or nonsensical. It may be purely emotive. "Because we MUST!" It may take the form of a "because" and refer to a "cause" that is not falsifiable. "Because I want it." It may even take the form of a chant. "USA! USA! USA!" Perhaps the most common form, which combines all these is the appeal to authority. "Because... everyone does it, Aristotle proved it, God commands it, it was always thus, etc.

According to the work of Walter Ong, Eric Havelock, and other classicists, this was the common form of knowledge transmission in oral society, specifically, the Homeric tradition. Values, codes, and knowledge had to be "memorized" in poetic form, commands,rhymes, and "sayings," because that was the only way to store culture and pass it on. Much like our first interlocutions with children.

The prerequisite of "reasoning," then, is writing. The shift from oral, Homeric culture to the Greek's unique phonetic alphabet turned words into preserved, visual objects, no longer actions and events in flux. Court oratory, proclamations, drama, histories, dialectic could all be "written down" like pinned specimens, preserved, examined, debated.

This "visualizing" of speech came alongside the visual demonstrations of geometry, where "reasoning" from common axioms was carried out visually with line and compass to "show" what follows from coherent "ratios." Similar "lines" of proportional reasoning could be followed in the developing "logoi" of written arguments. (See Plato's Phaedrus for contemporary thoughts on the matter.)

This, anyway, is Havelock's thesis pertaining to the cultural trauma of alphabetized speech and the origins of Plato's "rational" attacks on the poets and Homeric tradition, with their appeals to heroism, authority, tradition, and other forms of "irrational" persuasion. I, for one, find it quite compelling and illuminating.

So, "rational" explanations are a type of rhetoric and persuasion. They appeal to commonly accepted axioms and a coherent development of "ratios" and symmetries, not unlike geometrical theorems. They may retain, but supersede, oral appeals to memorization, rhyme, emotion, authority. They may be deductive or inductive, factual or not. But they must cohere proportionally within an implied whole, such as "the universe," as in a visual demonstration of the Pythagorean theorem outlined in the sand.

Rational explanations follow from a specific set of axioms plus rules to go from step to step. In a sense, reasoning rationally (or logically) is a way of thinking that guarantees you that everything is consistent, subject to the set of axioms.

Of course, this assumes that you believe there is some kind rationality in the Universe which has not been proven so far. What scientists or philosophers really believe is that there are principles or laws of the Universe.