The use of analogical reasoning is most certainly one of the powerful techniques used in one's daily argumentations. Great orators like Winston S. Churchill used it intelligently. An example may help clarify the point. The point he made in this beautiful analogy , " A good speech should be like a woman's skirt; long enough to cover the subject and short enough to create interest.” practically shows how effective analogies can be essential in conveying our ideas to our audiences.

However, it seem to be strongly connected to the cultural background and a common pool of ideas. Otherwise, the audience will not be in resonance with the speaker. Or are these persons simply charismatic?

Notwithstanding false analogies, analogical reasoning stands to reason. In the history of science, analogical reasoning was at the origin of a lot of scientific progress, allowing what Gentner calls structure mapping both in analogy and metaphor. For Gentner (1983), analogy is a "mapping of relations between objects, rather than attributes of objects, from base to target” (p. 168). The merit of scientific analogy is that it includes five internal structural characteristics, namely, base specificity, clarity, richness, systematicity, and abstractness (Gentner, 1982: pp. 113-115). For instance, “The hydrogen atom is like the solar system” enables understanding atoms by mapping them onto the solar system.

Gentner, D. (1982). Are scientific analogies metaphors? In D. S. Miall (Ed.), Metaphor: Problems and perspectives (pp. 106-132). Sussex: Harvester Press Ltd.

Gentner, D. (1983). Structure-mapping: A theoretical framework for analogy. Cognitive Science, 7, 155-170.

I must say thanks to all those scholars who've made responses to my questions! Your answers are really helpful, indeed. But I want to put it in an another way: What are the pitalls of analogical reasonings? Or what are the shortcomings of analogical reasoning?

I agree

Philadelphia, PA

Dear Zang and readers,

You ask whether analogical reasoning is "reasonable." Good question.

But it is not an easy question. Some analogies are exact and compelling, others vague and unconvincing. An analogy is a complex comparison, basically. Analogies exist virtually everywhere in thought. If I ask, "2 is to 4 as 4 is to ?" I think you won't hesitate on an answer, since 2/4 =4/8 (= 1/2). Or consider "London is to England as Paris is to ?" Again, I don't think anyone will long hesitate.

But on the other hand, if I ask "England is to London as the U.S. is to ?" --then you may reply in what way? If analogies are complex comparisons, then they depend on specifying the various ways in which things resemble each other. "England is to London, economically as the U.S. is to ?" gets one answer (New York) while "England is to London, politically as the U.S. is to ?" gets a different answer: Washington, D.C.

So analogies can be precise and logically compelling and sometimes they are merely suggestive and plausible --or even merely metaphorical and rhetorical as we see suggested above.

Analogies become more interesting when they are involved in creative thought and hypothesis formulation. We match up, say, two theoretical structures, as best we can and argue from the better supported to analogous features in the weaker theory that needs to be filled out with (possibly) testable subsidiary hypotheses.

For example, given the Standard Model of particle physics, in which every force is carried by a quantum particle, one may argue, well, if gravity is a force like the others, then there must be (would be) a force-carrying particle of gravity: the graviton. In effect the postulation or hypothesis of the graviton projects the structure of the successful theories of the three other basic forces in the Standard model onto an (extended or proposed) theory of gravity. Are there really gravitons? Well, no one knows, and they would certainly be hard to detect. But this is very much a live hypothesis. Stronger theoretical analogies make for live hypotheses.

Or consider historical analogies. Suppose it is suggested that "Lincoln's emancipation proclamation was much like the freeing of the serfs under Czar Alexander." Is this an interesting or helpful comparison? Well, if it is then there must be other similarities, say of cause or effect between the two historical events. Can the comparison be elaborated by bringing in similar elements of what happened in the U.S. and in Russia in the 19th century? If so, we may have an interesting analogy to explore--though it seems in this case that the analogy may quickly break down?

Historical analogies are the most interesting when there are many points of comparison that pan out, and perhaps some, a few discordant and dis-analogical elements. If the dis-analogies predominate, then we may have to take another approach. Deciding on whether they pan out is itself an historical inquiry. The question of whether there are, in fact, broadly analogous developments in differing historical periods is always interesting, because it brings us to try to fill out the analogy --or else, if the analogy breaks down, it sets us on a different approach in which the two periods or events are treated more in terms of their distinctive elements.

H.G. Callaway

I'm a little late to the party, but here's my view: yes, it is reasonable, but with a major caveat. The analogy has to be reasonable. Essentially, an analogy is a homeomorphism (homomorphism?). And just like with other homeomorphisms, we can use what is true in one space to show what is true in another.

The core value/nature between comparisons should be same so that analogical reasoning remains at a reasonable level. That is, it is not related to the premise that a metaphor is at its fever pitch.

Now that you have further clarified your position by highlighting the downside of analogical reasoning, we are in a better position to proceed with the argument. The model of analogical reasoning usually consists of three components: a base premise, a similarity premise and a conclusion. Very often when it is not structured adroitly, analogical reasoning which is based on comparisons and associations may involve a fallacious argument which has an invalid substance. For one thing, in some cases the features of the entities making the comparison do not have a complete overlap and this results in a comparison with a weak analogical argument. Under such circumstances, the analogy is considered weak if the similarity premise does not guarantee that the expected conclusion is valid. Another thing is that the comparison may evoke what is known as Metaphoric Fallacy to a Deductive Inference involving a faulty comparison ( false analogy) and a wrong deduction or conclusion.

Philadelphia, PA

Dear Goldman & readers,

Thanks for your note on this thread.

To push the point just a bit, we might say that an analogy or an argument by analogy, is an alleged or attributed homeomorphism --and in more empirical cases it may be more of less a homeomorphism. Or perhaps we should use the term "homomorphism"? ("Homeomorphism" I understand, is a technical term of topology or of graph theory.

In any case, I suppose that it is "sameness of form" which is of interest here; "homo" = same, "morphe" = form. (I take it you don't intend to restrict us to topology or graph theory.)

For example, there are valid forms of deductive arguments, e.g., the following form, with two premises and a conclusion.

P

If P then Q,

Therefore Q.

What it means to say that the argument form is valid, (not that its sound, mind you, but valid) is that any argument of this form is valid, no matter what statements we substitute for "P" and "Q". That all such arguments are valid means that for each and any of them, if the premises are true, then so is the conclusion. (An argument is sound if it is valid and the premises are true.) One way to argue for a disputed conclusion, then is to hold that the conclusion is established by an argument (however complex) of the same form as another one already accepted and generally recognized.

Of course, we might expand things a bit beyond logic, and include arguments involving mathematical validity as well. In that kind of case we are concerned with logical plus mathematical form. This is still something pretty precise. But since mathematics is in principle incomplete one might, in unusual cases become involved with mathematical forms not accepted as valid. The mathematicians then still have work to do.

However, analogies and arguments from analogy extend into every field, and they are especially interesting when they are used to render particular hypotheses plausible. Here we are no longer depending merely on logical or mathematical form, but instead on something like similarities between the forms of theories, which may involve particular factual premises or claims. E.g., we sometimes hear things like, "the fall of the British empire was much like the fall of the Roman empire --a matter of over extension. Expand an empire to far and it eventually falls of its own weight!" Clearly, we have an analogy here, and an explanation on offer which presupposes an accepted account of he fall of the Roman empire--it fell because it became to large and the people in power could no longer keep track of or manage the affairs as needed.

Is this a good explanation? Or is it a reasonable argument by analogy, given the assumption that the Roman empire fell due to its over extension? Obviously, to answer such questions we would need to have a great deal of historical detail on hand or easily available. But my point is that arguments from analogy are often used to introduce hypotheses; and the hypotheses may be checked (at least in part) by following out the analogy suggested. It is not, certainly, that there is only ever one such argument from analogy to be considered. Where there is one plausible hypothesis available, there will likely be others as well.

Overall, arguments by analogy are plausible and reasonable --or more or less so. In less precise fields you have to get down to the details (where formalists, as it happens, don't like to tarry.)

H.G. Callaway

---you wrote---

I'm a little late to the party, but here's my view: yes, it is reasonable, but with a major caveat. The analogy has to be reasonable. Essentially, an analogy is a homeomorphism. And just like with other homeomorphisms, we can use what is true in one space to show what is true in another.

H.G. Callaway your discussion seems like a great clarification and expansion of what I was saying.

Philadelphia, PA

Dear Goldman & readers,

Thanks for your good words! Much appreciated.

H.G. Callaway

My answer is, sometimes analogies make sense, and reasoning by analogy may be valid, other times it's invalid. The trick is to inform ourselves enough to intuit when there may be pitfalls. Easier said than done.

This question leads to philosophical arguments, which by definition, can only address what our minds can comprehend. But on what tablet is it etched that our minds can grasp everything? Especially when the mind has not been educated thoroughly enough, in a given subject. Sometimes, the analogy we claim to be able to use turns out to be false. Even if we do not grasp why it is false. Even when we thought it was valid until yesterday, and then suddenly, today, we discover it to be false.

The constancy of the speed of light. That defies analogies, if one pretends to explain the phenomenon (verified through experimentation) with classical physics analogies.

Quantum entanglement. That too defies any analogies. And yet, evidence of its veracity is piling up.

I think the problem with analogies is that they assume that there must be "self-evident truths." Hey, this works this way, so that must too. Cave canem.

Philadelphia, PA

Dear Manfredi & readers,

Thanks for your comments on this thread.

Well, of course, some people may think there are absolutely self-evident truths and then also argue using analogies. This is mostly beside the point.

Whether or not anyone believes in self-evident truth, though, making good use of analogies in argumentation presupposes that one is up on the basics in a given field. No one is going to take a hypothesis very seriously if it is proposed in ignorance of basics. But by the same token, criticism of arguments from analogy based in a particular field will be very difficult for outsiders to evaluate --who don't have the relevant facts at hand.

I suspect, from your examples that you don't really have a firm grasp of what it means, in an empirical field, to argue for a hypothesis on the basis of an analogy from some well established theory. So far as I know, and understand, the constancy of the speed of light was not proposed on the basis of an argument from analogy. Instead it entered special relativity as a postulate invoked to explain known facts. Make this assumption and the facts fall in place.

If arguments from analogy are sometimes useful to proposing hypotheses, if does not follow that every hypothesis must be arrived at in the same way. You seem to make an assumption to the contrary, but without any argument.

Much the same point goes for quantum entanglement, though, in that case, it is more a matter of an implication, drawn out by Einstein, first termed "spooky action at a distance," as a reductio ad absurdum of the supposed completeness of QM-- and later simply accepted as a consequence of QM. There is no thesis on this thread that everything is based on arguments from analogy--if anything is. Rather you have brought the straw-man in that you criticize.

Strictly, in arguments from analogy based on analogous structures and empirical theory, there is no such thing as "validity." Validity pertains to deductive arguments. But we do not deduce hypotheses. There is only greater or lessor plausibility, differing degrees of liveliness of hypothesis. Hypotheses need to be tested empirically. An untested hypothesis is still merely a hypothesis. So it is, for instance with the graviton as the supposed force-carrying particle of the gravitational field. If the gravitational field is (sufficiently!) like the fields of the Standard Model then there would have to be a force-carrying particle. Of course, it is not that the force-carrying particles of the Standard model are exactly alike, and the accepted variations of the forces, fields and particles of the Standard Model leave some room for variations in proposed graviton hypotheses. Where there is one compelling argument from analogy, there will likely be others, too. But in any case, argument from analogy is often quite creative and useful.

H.G. Callaway

---you wrote---

I think the problem with analogies is that they assume that there must be "self-evident truths." Hey, this works this way, so that must too. Cave canem.

HG Callaway, I don't think there is anything terribly controversial in what I wrote.

I suspect, from your examples that you don't really have a firm grasp of what it means, in an empirical field, to argue for a hypothesis on the basis of an analogy from some well established theory. So far as I know, and understand, the constancy of the speed of light was not proposed on the basis of an argument from analogy. Instead it entered special relativity as a postulate invoked to explain known facts. Make this assumption and the facts fall in place.

So for example, in the Michelson (originally) and then later Michelson-Morley experiments, the constancy of the speed of light came as a big surprise. At least, at first. The experiment was more likely expected to show how fast the earth revolves around the sun, i.e. the earth's tangential velocity in its orbit, using arguments that made sense in classical physics. And yet, oops, wrong. (And special relativity theory is subsequent to these experiments. It derives, in part, from them.)

And for that matter, even Einstein, when confronted with quantum entanglement, showed great skepticism. Because he used the analogy of information having to travel infinitely fast, for this phenomenon to exist. He used an analogy with a model of space that we knew, at the time. Who is to say that analogy is valid? These things cannot be assumed to be self-evident.

Strictly, in arguments from analogy based on analogous structures and empirical theory, there is no such thing as "validity." Validity pertains to deductive arguments. But we do not deduce hypotheses.

I'm trying to parse this. Einstein objected to quantum entanglement, because it seems to require information to travel through space infinitely fast. He was assuming space to be as he had imagined it to be. Analogy: if this were a vehicle, or a photon, traveling between points A and B, then for the two objects to come to the same state would take at least x many msec/sec/hours/years. Instead, the state changes instantly, for both.

His analogy, it does seem, was not valid. I'm not sure how else to express this.

I agree with previous comments about homomorphisms, although analogy in natural language is more flexible than a structure preserving mapping in mathematics. Analogy can be very useful as a means of discovery; insights in one domain can transfer to some extent to another. Transfer of techniques in mathematics and scientific disciplines is arguably a very powerful discovery methodology. As H.G. Callaway observes, the limits of analogy have to be testable hypotheses; you cannot assert a homomorphism as the basis of a rigorous argument (since that would beg the question).

Akramul states:

The main problem with deduction is the premises. A lot of time we use premises which are not perfectly sound, and thus end up in paradoxes.

Well said! That's exactly how we end up with paradoxes. A paradox appears to be something illogical, only because our logic has not been informed correctly. Zeno's paradox of a possibly finite result, in an infinite series of sums, comes to mind.

To me, this is equivalent to using an analogy improperly. One is postulating that two situations are similar enough, such that the results of one should equally apply to the other. When in fact, that is simply untrue. Just because adding an infinite series of apples into a basket will result in an infinite number of apples in that basket, does not mean that a runner can never finish his/her race.

But, a priori, these things are not always obvious. So, that's my refrain. Math and physics, and the hard sciences in general, have to prove the veracity of what they state. Just stating something is insufficient, no matter how much logic one might throw at it.

We need to find a replacement for three-tyred static syllogism.

Philadelphia, PA

Dear Manfredi & readers,

Once again, you seem to simply fail to understand what is involved in arguments from analogy. What is true is that analogies can be valid, e.g., in precise mathematical or logical cases, they can be suggestive and productive, when they produce live and fruitful hypotheses, and of course, they can be misleading, too. You write of "using analogy improperly," and perhaps you should reflect on what it means to use analogy properly? What would that mean on your account?

You say, in "using analogy improperly" that "One is postulating that two situations are similar enough, such that the results of one should equally apply to the other." But this would seem to be a general description of any argument from analogy, good, plausible or implausible. But if some arguments from analogy are misleading then it does not follow, of course that they all are.

Consider again, Is it true that the gravitational field is sufficiently similar to the 3 other fields of the Standard Model that, since Quantum field theory requires a force-carrying particle for each force, then it is a reasonable hypothesis that there is a force-carrying particle for the gravitational field? Notice that this is a different question from asking whether the graviton, the proposed force-carrying particle for a quantum field theory of gravity actually exists. But the graviton shows up as a postulate of various attempts to extend the Standard Model to include gravity.

At points you seem to simply confuse the evaluation of a hypothesis as worth pursuing with the empirical confirmation of the hypothesis. "Math and physics, and the hard sciences in general," you write, "have to prove the veracity of what they state. Just stating something is insufficient, no matter how much logic one might throw at it." But as I've pointed out, proposing a reasonable hypothesis, whether by an argument from analogy or otherwise, is simply not the same thing as empirically confirming it.

You seem to risk simple verificationism. But often enough a claim is put forward long before anyone figures out how to test it! Such was the case, for instance with gravitational waves. They were first predicted in 1916, as an implication of Einstein's GR. Empirical confirmations came only much later. Equally, black hole solutions to Einstein's field equations came very early, and at times this implication was even disputed as a genuine consequence of GR. Empirical evidence and confirmations came only many decades afterward. So it is with reasonable hypotheses sponsored by arguments from analogy: we cannot equate the reasonable character of a hypothesis with the confirmation of the hypothesis. This would make nonsense of yet-to-be-tested hypotheses on the growing edges of any science--where the analogical arguments are many and varied.

H.G. Callaway

---you wrote---

To me, this is equivalent to using an analogy improperly. One is postulating that two situations are similar enough, such that the results of one should equally apply to the other. When in fact, that is simply untrue.

HG Callaway, you ask

You write of "using analogy improperly," and perhaps you should reflect on what it means to use analogy properly? What would that mean on your account?

Examples abound, as we tend to do this all the time. The problem is, "use properly" is not necessarily obvious at the outset. Take criminal law, when someone has been found guilty, and is being sentenced. Is this not done by analogy, to previous cases? Isn't that what judge and jury have to decide, as imprecise/subjective as that process might be?

So instead, if we take examples from math and science, the adequacy of the analogy becomes much more definite, at least, within the scope of what we know. I can pose a simple problem. If it takes me x hours to travel from NYC to Chicago at a certain average speed, how long would it take at twice that speed? Within certain limits, limits which were unknown to Isaac Newton, that problem by analogy is easy enough to solve. Outside those limits, the low speed analogy begins to fall apart. You ask, "is it reasonable to use the low speed analogy?" And I answer, within certain parameters, "No!"

Consider again, Is it true that the gravitational field is sufficiently similar to the 3 other fields of the Standard Model that, since Quantum field theory requires a force-carrying particle for each force, then it is a reasonable hypothesis that there is a force-carrying particle for the gravitational field?

Of course it appears to be a "reasonable hypothesis," as long as we don't make a religion out of it. By analogy, it appears okay. In fact, that's my main objection to those who claim that this is "nonsense." They are not equipped to proclaim what is "nonsense," not yet! None of us are.

The point is, "reasonable," at the outset, does not mean "valid." Only experimentation will determine the adequacy of that analogy. Not logical tours de force.

At points you seem to simply confuse the evaluation of a hypothesis as worth pursuing with the empirical confirmation of the hypothesis. "Math and physics, and the hard sciences in general," you write, "have to prove the veracity of what they state. Just stating something is insufficient, no matter how much logic one might throw at it." But as I've pointed out, proposing a reasonable hypothesis, whether by an argument from analogy or otherwise, is simply not the same thing as empirically confirming it.

I don't think I'm confusing anything. The original question:

Is analogical reasoning reasonable?

And my answer continues to be, it may sound reasonable, at the outset, but may instead be proven fallacious. Meaning, no, that analogy is not reasonable (and perhaps, who knew?). In the criminal law example, people can argue both sides "until the cows come home," and continue to insist "it is reasonable" for the rest of time. In the quantitative sciences, eventually reality will rear its ugly head.

Philadelphia, PA

Dear Manfredi & readers,

Well, I guess we have your answer. Arguments by analogy for the plausibility of a hypothesis are not reasonable.

It seems though that you simply equivocate on what it is that a "reasonable argument" is supposed to accomplish. We cannot define a reasonable hypothesis as one which will be finally proven. There is no way to know which hypotheses will turn out correct before hand. People try them out, develop them and look for ways to test them.

Also, there is no way to know which hypotheses will end up in unending arguments or disputes --before hand. That is why reasonable hypotheses are part of science even if they will in fact never be proven--in which case, they are eventually given up and enter into the history of science.

A more basic difficulty in your argument is that you seem to be adverse to unconfirmed hypotheses however they are arrived at.

As it happens, though, the science and scholarly disciplines are full of yet to be tested and confirmed hypotheses, from string theory to gravity as a quantum field theory, to loop quantum gravity, etc and on to, say, theories of the location and identity of the original speakers of the reconstructed proto-Indo-european language. If you are not comfortable with this, then I see little sympathy with the growing edges of the sciences and scholarly disciplines.

My view is that there is better and worse among even untested hypotheses, and that we can sometimes tell the difference.

See:

Chapter Abduction, Competing Models and the Virtues of Hypotheses

H.G. Callaway

---you wrote---

And my answer continues to be, it may sound reasonable, at the outset, but may instead be proven fallacious. Meaning, no, that analogy is not reasonable (and perhaps, who knew?). In the criminal law example, people can argue both sides "until the cows come home," and continue to insist "it is reasonable" for the rest of time. In the quantitative sciences, eventually reality will rear its ugly head. .

HG Callaway, thank you. We are on the same page now.

A more basic difficulty in your argument is that you seem to be adverse to unconfirmed hypotheses however they are arrived at.

Indeed. That's why I keep de-emphasizing clever things the ancients might have said, if the only support for that idea was that it was uttered by someone. Just because someone proclaims something, using his/her own internal logic, does not make it correct. And yes, it's a well-known banality. Analogies are always going to be risky and tend to be flawed, one way or another. Use them, but carefully, knowing the risks.

Also, there is no way to know which hypotheses will end up in unending arguments or disputes --before hand. That is why reasonable hypotheses are part of science even if they will in fact never be proven--in which case, they are eventually given up and enter into the history of science.

I could not have said it better myself!

Philadelphia, PA

Dear all,

Are we agreed, now, that analogical reasoning is (at least sometimes) reasonable, in arriving at hypotheses?

It is not that no one thinks there are no examples of poor or misleading analogies.

H.G. Callaway

Philadelphia, PA

Dear Salustri & readers,

Thanks for the reply.

H.G. Callaway

Analogy-based reasoning between pattern A and B must be satisfied by:

1, The cause-effect law of A and B is similar in logic;

2, The true-valued function, of cause is the continious true-valued function who valued on interval [-1,+1], and its 1-order derived number till n-order derived num ber of A and B is similar, if they exists;

3, The bigger n is, the more similarities between A and B exists.