Differences between False Equivalence, Extended Analogy, Weak Analogy

In the extended analogy link, it doesn't say that "X=Y"  ("equivalent" doesn't mean "equal"). The word "equivalent" always needs some trait. I'm electrical engineer and in electric circuits when two circuits are equivalent does not mean they're the same. It means that when you apply the same voltage FOR SPECIFIC PINS, you'll have the same current. I emphasize the SPECIFIC PINS because only for two of them the voltage and current ratio will match. FOR THE OTHER PINS it will be different (although they are EQUIVALENT, they are not EQUAL). "equal" would mean "equivalent in all traits" (or for all pins, in electrical circuits). With that in mind, the two definitions (weak analogy and extended analogy) are exactly the same. 

For me to understand the difference, I was hoping for an example of each fallacy and what would it take to add, subtract or change to transition to the other two fallacies, because until now for any example I read about those three I can take the definitions of the three and see that they match.

Let's take the extended analogy where it says that reductio ad Hitlerum is a special case of extended analogy.
"My professor is making me redo this assignment. Do you know who else forced people to do things they didn't want to do? Hitler"
How is that not false equivalence? How is it not weak analogy ("forcing me to redo this assignment (or wear a mask) is as oppressing as forcing Jews to wear the David Star so you are as oppressing as Hitler")

As for the "fruitarians are as crazy as vegetarians because they both don't eat animals" which is given as an example of the extended analogy , how it does not match the False Equivalence definition? (And as I see it, there's no analogy there, it's an ad hominem (guilt by association) which one can argue it's a special case of False Equivalence). 

Or if we take the example from weak analogy:
"Not believing in the literal resurrection of Jesus because the Bible has errors and contradictions, is like denying that the Titanic sank because eye-witnesses did not agree if the ship broke in half before or after it sank." That's actually a Double Standards accusation. How is it not False Equivalence? Or Extended Analogy ("The Bible had witnesses that are inconsistent, the Titanic had witnesses that are inconsistent therefore the Titanic and the resurrection has the same degree of credibility") Where doesn't that match the Extended Analogy definition? Where doesn't it match the False Equivalence definition?

Could you think of an example of one these three fallacies that don't match the definitions of the other two? Either that or we should change the definitions to something more fitting 

The RationalWiki example goes as follows:

Person N: "Software pirates should campaign to change the law and not break it. I don't think it's ever valid to oppose the law by breaking it."
Person M: "Such a position is odious: it implies you would not have supported the women's suffrage movement."
Person N: "Are you suggesting piracy is as important as giving women the vote? How dare you!"

The mistake made by person N is suggesting that, because person M pointed out that X has something in common with Y, that X and Y are  equally significant  (this is not the case). Perhaps I shouldn't have written "X = Y" though. 

Doesn't this qualify as strawman fallacy (misrepresenting what the other person said)? 

Also the definition in rational wiki is inconsistent with what it is written in the "Form" part:
P1: A is like X in some way.
P2: B is like X in a different way.
C: Therefore, A is like B.
Isn't this what happens with False Equivalence? In all the examples I have seen, two things have SOMETHING in common and then it is implied that they are equivalent in general (or at least equivalent to the specific point in question). And isn't that what weak analogy uses?

[To Kostas Oikonomou]

Doesn't this qualify as strawman fallacy (misrepresenting what the other person said)? 

That's what I was thinking, or at least, it'd be missing the point.

Also the definition in rational wiki is inconsistent with what it is written in the "Form" part:
P1: A is like X in some way.
P2: B is like X in a different way.
C: Therefore, A is like B.

I don't see how it is inconsistent. Two things are alike in a way, thus they are said to be alike in additional ways. Software piracy and (aspects) of the women's suffrage movement involve breaking the law - so they are alike in that way - thus they are interpreted as being treated as equally significant - they are alike in another way.

With false equivalence, you're saying that because two things share a property, they are equal (I'm aware of the equivalent-equal distinction; but this is how Dr Bo defines the term). That's slightly different from this case, but there is significant overlap. And in the weak analogy, you're saying that because two things are 'alike', the property that one has is also a property the other has (except the two are not really alike).

So:

Weak analogy: X and Y are alike. X is P. Therefore Y is P (but X is not like Y at all).

Extended analogy: X is like P. Y is like P (in a different way). Therefore, X is like Y.

False equivalence: X and Y are P. Therefore, X = Y.

I suppose the difference between 'weak analogy' and 'extended analogy' is that with the former, the analogues themselves are weak (because they're really not alike) while in the latter, they have something in common, but they are not alike in the way that is being suggested. Neither, though, implies X and Y are equal - only false equivalence does that.

You're right though; there is a lot of overlap between them. It might be because Dr Bo often classifies variations of the same fallacy separately if those variations are quite common. E.g. there is an appeal to emotion entry, but also appeal to anger, argument by emotive language among others. Another example: we have alternative advance and false dilemma.

Thus, some of the entries might seem redundant (from Dr Bo's point of view though, the site isn't supposed to be strictly academic but a handy resource for non-logicians, so it might make sense to document variants on the same error in reasoning separately). 

I think only one of our members (Kaiden) is trained in formal logic. The rest of us are just trying our best, lol

[To Rationalissimus of the Elenchus]

1. I'll try to explain the inconsistency:
   Definition given by RationalWiki: "the use of an analogy IS TAKEN TO BE a statement that the scenario in the analogy and the scenario in the original argument are alike in additional ways. It is a fallacy of distraction." 
   
   The example given (piracy and sufragetes) misrepresents what is meant (like Strawman) so it matches the 'TAKEN TO BE A STATEMENT" form the other interlocutor.
   
   In the Form part though, there's no relation to Strawman or misrepresentation whatsoever and instead it just matches the False Equivalence definition. So, the example given applies only the first definition but not the second. That's the inconsistency.
2. Dr. Bo mentions mentions the term 'equal' only in the Logical Form part, not in the definition. And I believe the word is misleading and what I'm saying here is prominent in every example where when someone says that person A is like person B, does not mean they are in ALL WAYS the same (like for example a doppelganger). In all the cases it is suggested that a specific trait of behavior is the same based (fallaciously) on another trait which is undeniably similar. So, nowhere is said - or rather can be said but not actually meant - to be completely equal.
3. I'm still waiting for a specific example for which only one of the definitions of the three apply and no other :)
   And as a follow-up from our previous discussion about blurry, ambiguous definitions, I sense that this is yet another case of failure to elucidate ;)
4. The good part about logic is that you don't have to have formal training. I believe logic is built into us. Surely most people a lot of times think irrationally but I believe this stems from wishful thinking (i.e emotional comfort) or missing evidence. Besides, people who first coined a fallacy weren't formally trained to identify that fallacy. "Letters were invented by illiterate" or so the saying goes, right?

About the differences between those three please read my comment above,  on the answer of "Rationalissimus of the Elenchus" 

My proposition about merging them into False Equivalence, was based on "Rationalissimus of the Elenchus"'s comment about you "clarifying some of the old definitions, and get rid of any fallacies that potentially overlap" and your comment about updating the website, here

So my proposition is that, no matter how well-known or widespread a fallacy is in the internet, your site (and book) could be consistent and provide a more clear view of fallacies. In the other thread mentioned above, the issue I and ROTE raised was also about Failure to Elucidate in the definitions of many fallacies. Those three definitions I mention here, IMO also fall under the Failure to Elucidate. And no wonder since, again IMO, they are the same. 

For the Extended Analogy you give a different definition from the one commonly used in the internet by introducing "transitivity".
 
Let's take the example given in the site is under the extended analogy . "Vegeterians don't kill animals. Fruitarians don't kill animals. Frutarians are crazy. Vegetarians are as crazy as vegeterians". This is said to be an extended analogy (although it's an ad hominem (guilt by association which also raises the question of why introducing the same fallacy under a new name when there's already one that describes it, but that's another story). Going back to your definitions it would fall under the False Equivalence definition. 

Also your example 1 would be the same as example 2 if we said:
f and g are continuous functions. g belongs in the differentiable set (as c is). Therefore f is differentiable. It's pretty similar to the False Equivalence. It is slightly different but is it that important a difference to keep them separate?

As for the third example of weak analogy, the argument is "You're selecting 3 out of 12 (but in the second case you change the way you select by introducing order) therefore you would have the same amount of combinations". Doesn't this match your definition of False Equivalence?

I think it's difficult to find math examples analogous to real-life weak analogies because in real-life examples the analogy usually involves inconsistency in motivation of an action or the result of the action, while math are pretty much firmly defined (and there is no motivation or consequences that in real-life are the crucial game changer). A real-life weak analogy would be "Forcing me to wear masks is like Hitler forcing the Jews to wear the Star of David". The weak analogy doesn't stem from the different way it is happening (forcing a mask around the face vs stitching a star of david on the sleeve) as it is in the 3-element-unordered-set vs 3-element ordered list. It's in the motivation and multifaceted consequences of each action. 

What you define as extended analogy would be a clear definition and would clearly emphasize the transitivity element present which distinguishes it from the other two fallacies (False Equivalence and Weak Analogy), but I don't think it is the same "extended analogy" that is referenced usually in the internet. It's a different fallacy - "Transitivity Fallacy" perhaps?

So in conclusion, after reading your post I would say that Weak Analogy is still the same as False Equivalence and we could add an Extended-Transitive fallacy as a new fallacy if we had to, but that way of fallacious thinking doesn't really happen in real life examples. Or maybe I'm wrong. Do you have any Extended Analogy real-life example in mind that makes it worthy to trouble our brain with yet another term?

I think that it doesn't technically matter to give precise names to fallacies, but I think that identifying the underlying issue would help in learning, or in knowing what went wrong. Imagine you got this question wrong:

1. f(x)=sqrt(x) and g(x)=x^2. Is f(g(x)) differentiable? 
Answer: Yes because the composition of differentiable functions is differentiable.

What went wrong? both functions are continuous. Perhaps you also recognized that g is differentiable and thus deduced that f must also be differentiable. This is a false equivalence. You don't have to technically know that that's the name of the fallacy, but recognizing the form of the logic is very helpful. Now, suppose that you got this problem wrong:

2. True/False: if g is continuous and g(f(x)) is continuous, then f is continuous.
Answer: True because f and g(f(x)) have the same domain, and g(f(x)) and g are continuous.

Consider these two functions: f(x) =1 if x>=0 and f(x)=-1 if x<0. g(x)=1 for all x. Then g is continuous, g(f(x))=1 which is also continuous, but f is not continuous at 0.

What went wrong? here's the logic: f is like g(f(x)) in some way. g is like g(f(x)) in some other way. Therefore, f is like g. This is an extended analogy.

For the last one, the logic could be as follows: A is similar to B where B is the set of all 3-element subsets of a 12-element set. C is similar to D where D is the set of all 3-element lists out of a 12-letter alphabet. Then A is similar to C. This one is just wrong and it happened because of a weak analogy. A and C are very disimilar but there is an illusion of similarity precisely because combinatorics is hard in my opinion.   

Final comment: I hope these examples provide real-life examples. We should recognize that fallacies do intersect. Some false equivalences are weak analogies, and some weak analogies are extended analogies. I don't think that it is necessary to memorize names, or to even classify fallacies. I think that the important part is to sort of see what went wrong when we got something wrong. Does knowing names or classifying types of thinking helpful? I guess. 

Notes: this is just my understanding of the fallacies so I could be wrong in my analysis. This is how I interpret them to try to develop the examples: 

1. To say that two statements are logically equivalent when they're actually not and from there deduce more things is to commit a false equivalence. The mechanism for this fallacy is noticing a shared characteristic between two statements, giving them the illusion of equivalence, and assume actual equivalence. Thus, one may think that whatever applies to one of them must also apply to the other.

2. If we assume that the "is like" relation is transitive when it actually isn't, then we would commit the extended analogy. The mechanism for this fallacy is to assign the relation "is like" to different statements in such a way that the relation changes meaning but assume preservation of meaning. 

3. When we either argue from analogy but the analogy is not apt, or misuse concepts (like in combinatorics), we would commit a weak analogy. The mechanism for this fallacy could be either misunderstanding or not considering more things that could make the analogy too disimilar from the statement that you want to either prove or disprove.

Well, I think that arguing that math problems are like real-life fallacies is a weak analogy . :)
My initial question and analysis (check my comments to Rationalissimus of the Elenchus if you like) was related to real-life examples to which all definitions of these three fallacies apply. So either they are the same (and we should simplify them into one), or change the definitions. If one cannot easily find real-life examples for the fallacies, then something stinks with those fallacies. 

I like math and that's were I feel most comfortable but sure there's real-life examples I bet. I don't see why not. But anyways, you made me think and I liked the challenge.