Why is argument by analogy invalid?

Question

There is a well known fallacy called the "argument by analogy" fallacy. As I understand it, the fallacy occurs in a situation where someone makes a reasonable comparison between two situations and then concludes a one-to-one correspondence (or greater correspondence than warranted) between the two situations.

I think there is a strong case to make that most reasoning and knowledge, if not all reasoning and knowledge, is inductive. But what is inductive reason but argument by analogy? For instance, we say we know that the sun will come up tomorrow. Why do we know this? Well, if we think back to all our experiences where we go to bed when it is dark, we wake up and find the sun rises again. Today, before we go to bed at night, we say it will rise tomorrow because we infer it will be like the situations we've had before.

Why is inductive reasoning allowed as an argument but argument by analogy is not?

Answer 1

The reason why argument by analogy could be called invalid hinges on a technical definition in formal logic. Viz., "invalid" means not attaining to formal validity either in sentential logic or one of the many types that depends on it (e.g. deontic logic, modal logic).Thus, the following argument is invalid:

(1) If Japan did not exist, we would not have hello Kitty.
Ergo, (2) the earth orbits the sun.

The conclusion is true. The premise is true. But the argument is not valid.

A second example:

(1) If the earth orbits the sun, then there are aliens living in my basement. 
(2) the earth orbits the sun  
Therefore, they are aliens living in my basement.

This is valid. But one of the premises (i.e. (1)) and the conclusion are false.

Arguments by analogy cannot be valid. Instead, they can be strong or weak depending on how convincing they are. The same is true of inductive arguments.

The distinction has to do with what an argument can accomplish. A valid deductive argument is "truth-preserving" meaning that if its premises are true, its conclusion is necessarily true. A strong inductive argument is not truth-preserving, it just more or less probably true. Thus, the belief (seen here as a conclusion reached on looking at a large amount of evidence) that there are only white swans had a good degree of support but its conclusion turned out to be false. It didn't mean the argument for the claim was weak -- just that it was a type of argument that is always defeasible.

Invalid is not a bad thing for inductive and analogy arguments. It's just part of the nature of the beast.

Answer 2

It isn't always invalid. The analogy of Riemann surfaces and number fields (finite extensions of the rational field) proved very useful, and one might hazard a guess that it was one of the roots of the grand synthesis between number theory and geometry achieved by the Grothendieck school in the theory of schemes.

Also, there appears to be an analogy between prime knots and prime numbers as speculated here

Given this, one might suggest the inconsiderate and rigid use of 'fallacies' as a fallacy itself; one should instead regard it perhaps as a rule-of-thumb in which the exceptions to the rule are as interesting as when the rule holds. If not more so. In Poetry of course, arguing by analogy is the rule - ie simile, image & metaphor - rather than the exception.

So perhaps, one can say that schemes were a poetic fancy that proved useful. Shelley - the English Poet & pamphletist - in his defence of Poetry also noted this factor of poesis in mathematics and the sciences; and it is why Arendt & Scheler consider man as homo faber, man the fabricator, the maker & creator.

Answer 3

There is a wonderful irony about anybody claiming that arguing by analogy is fallacious, because calling an argument fallacious is itself an analogical claim - it amounts to saying that the argument is defective because it is similar in relevant respects to other defective arguments.

There are other problems with your question. The question title says "invalid", but your first sentence talks about "fallacy". These are quite different things. An argument being invalid is neither necessary nor sufficient for it being a fallacy. "Valid" is not an evaluative term that means an argument is strong or cogent, it just means it is impossible for the premises to be true and the conclusion false. Likewise "invalid" does not mean an argument is weak or fallacious, it just means it is logically possible for the premises to be true and the conclusion false.

All non-deductive forms of reasoning (inductive, abductive, analogical, ...) are invalid, because it is possible for their premises to be true and their conclusions false. It does not mean these forms of reasoning are weak or fallacious. But no matter how cogent they are, they will never be valid.

More generally, my advice is stop fussing about fallacies. It is a foolish modern obsession to hunt for fallacies everywhere and it brings little illumination. When you hear people using the word fallacy in every other sentence and asking, what fallacy is this? then you know you are dealing with novices and wannabes. Real logicians seldom use the term, except for clarification.

Answer 4

It’s not correct to say that an analogical argument is strictly inductive. Rather, it is abductive (there is a critical distinction between the two, c.f., Peirce). We apply abduction because “man is an analogist and studies relations in all objects” (Emerson).

An abductive argument (CP 5.189) is not valid because its goal is to give justification for further pursuit, that is, to determine the truth that is in the future. The logic depends on esthetic and ethical judgments and in that it is the commens making such choices, it is unsound but not invalid.

As for a direct answer to your question of why induction is allowed but not analogy, look to reasons given for why casuistry is accused of being a form of chicanery and not “a problem-solving endeavor, seeking to interpret and resolve practical issues of the day” (Miller). There is a quality to good metaphor making that is embedded in culture but culture has its own rules, too.

"In like manner, the memorable words of history, and the proverbs of nations, consist usually of a natural fact, selected as a picture or parable of a moral truth. Thus; A rolling stone gathers no moss; A bird in the hand is worth two in the bush; A cripple in the right way, will beat a racer in the wrong; Make hay while the sun shines; 'T is hard to carry a full cup even; Vinegar is the son of wine; The last ounce broke the camel's back; Long-lived trees make roots first; — and the like. In their primary sense these are trivial facts, but we repeat them for the value of their analogical import. What is true of proverbs, is true of all fables, parables, and allegories." ~ Emerson, Nature

Answer 5

The reason I think arguing by analogy is improper is that by definition, when you claim that two things/situations are analogous, they are literally different, but the person you're disagreeing with has to agree that they're analogous to the same extent, and that's unlikely to happen, (particularly if it weakens the other's position).

As proof of this, you may notice that any analogies you come up with are perfect representations of the thing being discussed that clearly illuminate the central issue, whereas your opponent's analogies are invariably twisted misrepresentations of half-truths that totally miss the point.