# When can we call an explanation “rational”?

There are a lot of questions involving rational judgment, rational choice, rational explanation, etc... And at the same time, it seems that "being rational" is a guiding principle for a lot of people.

However, I am not sure that I completely understand what it means when we say "this is a rational explanation." Even putting aside the value of such a principle, I find it hard to distinguish the rational explanations from the rest in real-life situations, particularly when the situation requires a guiding principle.

Hence my question: 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?

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. – Cody Gray Jun 9 '11 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 ? – robin girard Jun 9 '11 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. – boehj Jun 9 '11 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. – robin girard Jun 10 '11 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. – boehj Jun 10 '11 at 7:31

An argument or explanation is rational if it contains two things:

• No factual errors. For example, saying

All circles are square.

Is false because we have facts (in this case, the definition of a circle) that directly contradicts that statement.

• No fallacies For example, saying

All round things are circles, because all circles are round.

Is false for two reasons. While we have documented facts to directly contradict this statement, the focus on the word 'because' reveals this argument to be a form of the Sweeping Generalization or Accident.

If an argument or explanation lacks factual errors and fallacies, then we can safely say that it is rational and logical.

• Is this statement rational: "I like coffee."? It does not seem particularly rational, but I don't see how it fails either test. – Jon Ericson Jun 8 '11 at 20:35
• That is a statement, instead of an argument or explanation, and therefore these criteria do not apply to it. I am not sure if opinions can have any measure of rationality applied to it, can they? – Edward Black Jun 8 '11 at 20:39
• How about "I like coffee because it's bitter"? I suggest that the original questioner would like to differentiate "opinion" from "reason" and this answer isn't much help there. – Jon Ericson Jun 8 '11 at 20:57
• That's a perfectly rational explanation, assuming all coffee that you drink is bitter. – Edward Black Jun 8 '11 at 21:06
• Ok. "And I don't like beer because it's bitter." Assuming both are true and I'm not equivocating on the word bitter: it seems my taste in beverages is irrational, but does not break either rule. – Jon Ericson Jun 8 '11 at 21:18

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.

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. – robin girard Jun 9 '11 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. – Jon Ericson Jun 9 '11 at 17:50
• I guess rationality can be found the other way: faith in others rationality and doubt a bout our own. – robin girard Jun 10 '11 at 7:19
• Now with your last paragraph it's even better! – robin girard Jun 14 '11 at 17:13

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. – Lie Ryan Jun 8 '11 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. – Jon Ericson Jun 8 '11 at 20:38
• @JonEricson I am almost completely sure that he mans the rules of logic, not personal rules. – Edward Black Jun 8 '11 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.) – Jon Ericson Jun 8 '11 at 21:01
• I left out evaluating the appropriateness of rules as an exercise to the reader :P – Matthew Read Jun 8 '11 at 21:02

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 ? – robin girard Jun 9 '11 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 ? – robin girard Jun 9 '11 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" ? – robin girard Jun 9 '11 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. – Michael Dorfman Sep 30 '11 at 13:46

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 on 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 ?

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.