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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?

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3 Answers 3

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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.

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Ok, good question! My follow up questions would be then, first, do you perceive many people falling into the fallacy fallacy in response to use of argument by analogy in order to discredit any persuasiveness of the argument? Second, what if logical reasoning is argued to be something inductively understood. Then it seems that there is no special status to compare the experience of making a conclusion in a syllogism to past experiences and say that it will work the same. –  nayrb May 15 at 16:40
    
I'm sorry I don't understand your questions very well. The English is hard to follow. I don't encounter many people who don't know how arguments by analogy work... And deductive syllogisms are generally considered superior to other forms because they are truth-preserving... –  virmaior May 15 at 22:35
    
@nayrb, for what it's worth, I would partially agree with your first point -- I have frequently seen people reject strong arguments by analogy on principle, instead of taking the arguments on their own merit. But that's not the "fallacy fallacy." You commit the fallacy fallacy when you claim that a conclusion is false because an argument for it is fallacious. That doesn't follow; it is itself a fallacy. Your second point is interesting because it's pretty close to what David Hume says about mathematical reasoning! –  senderle May 20 at 12:52

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.

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An analogy directly compares two things. If all the comparisons are exact and match, and you've compared every aspect of the two things, then it's perfectly valid to say the two things are the same. Usually, however, analogies are incomplete. You can generate a virtually endless list of commonalities between apples and oranges, but a single difference is enough to distinguish them. The difficulty of verifying an analogical comparison is why they're presumed false from the start.

I also can't agree that this is anything like induction, which is based on a pattern. If you have a line of 12 items and the first 11 are fruit, you might reasonably conclude that the twelfth is a fruit as well. That doesn't mean every fruit is an apple. (And of course, the twelfth item could be a Rubik's cube or something.)

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