Fallacy of Semantic Assumption

July 27, 2010 9:26 AM

What kind of a logical fallacy is this?

I am having a hard time identifying what kind of fallacy this statement is, based on the fact that it seems to rely on semantic definitions.

Here it is: Man says that he is Boo and Radley, therefore he is also stating that one can be Boo and not Radley, or Radley and not Boo.

I guess the idea is that use of the word "and" means that the speaker is listing attributes separately, and so is asserting that the attributes exist independently.

I am having a hard time tagging this one. Thank you!

posted by alice_curiouse to Writing & Language (23 answers total)

Fallacy of Composition?
posted by Chocolate Pickle at 9:33 AM on July 27, 2010

Best answer: Well, Boo Radley is a Radley who is Boo and a Boo who is Radley. But there are doubtless Radleys (his parents for example) who are not Boo and there are Boos (Berry, Hoo) who are not Radleys.
posted by inturnaround at 9:43 AM on July 27, 2010 [1 favorite]

I guess the idea is that use of the word "and" means that the speaker is listing attributes separately, and so is asserting that the attributes exist independently.

"And" certainly does this (and not just in English) -- but I'm not sure why it is a fallacy per se? Something more like "this liquid is made of water and H20" might illustrate the point better; in this case the speaker would be falsely implicating that the two substances are distinct, perhaps revealing their own misunderstanding.
posted by advil at 9:49 AM on July 27, 2010

Can you give an actual example? (Like, was there an example that prompted you to ask this question?)
posted by ManInSuit at 9:53 AM on July 27, 2010

You capitalized Boo and Radley... are those proper names?

It is not possible to be two people at the same time. Assuming that to be Boo means to not be Radley, and to be Radely means not to be Boo, means the speaker is in violation of the law of non contradiction.
posted by yoyoceramic at 9:53 AM on July 27, 2010

I'm having a hard time seeing how this is fallacious. Could you give a different example?
posted by adamrice at 10:00 AM on July 27, 2010 [1 favorite]

This is not a fallacy, it is just awkward. There is a musician named Boo Radley. First name Boo, second name Radley. You would not normally say I am Boo and I am also Radley since it is so much easier and more direct to just say I am Boo Radley.
posted by grizzled at 10:04 AM on July 27, 2010

Yeah, if we're not talking about To Kill a Mockingbird, the example seems unnecessarily confusing.
posted by box at 10:04 AM on July 27, 2010

Response by poster: I see that saying a liquid is made of water AND H20 implies that water and H20 are separate things. But, how can a listener logically conclude that a speaker is making an implication because they use the word "and"?

I guess I thought that fallacies were not about interpreting what a speaker is implying unless the speaker makes a concluding statement which is not logically supported.

So, "Man says he is Boo and Radley," therefore: "Man thinks one can be Boo and not Radley" is a logical conclusion?

Sorry if I seem dense.
posted by alice_curiouse at 10:11 AM on July 27, 2010

I think what you're looking for is called the fallacy of division, which is the opposite of the fallacy of composition.

The fallacy of composition uses a part to inappropriately represent the whole. The obvious example is "All the black men I know are in prison, therefore all black men have criminal tendencies." Knowledge about a handful of people in a certain category does not necessarily give one good information about the entire category.

The fallacy of division does the opposite, in that it uses properties only properly associated with the whole and applies them to constituent parts, like so: "Black men as a population group have a 30% chance of ending up in jail at some point in their lives, therefore this particular black man does too." While the information about the whole is useful in a demographic sense, it is not a terribly good predictor of what will happen to any single individual, who may be at far higher or far lower risk for incarceration.

There are better examples out there, but I think that gets the point across. I only use race as a subject because most Americans--well, most American MeFites anyway--are pretty good at spotting fallacies having to do with it, and they're so common that they don't appear as silly as the textbook examples on the wiki page.
posted by valkyryn at 10:18 AM on July 27, 2010

In a propositional logic, if (A and B) is true, then (A and not B) is false and (not A and B) is false. And so your original proposition is invalid. However, you say that a "man" says he is Boo and Radley and that this implies that "one" can be Boo and not Radley and not Boo and Radley. If "man" = "one" then this violates the principle of non-contradiction, as yoyoceramic pointed out. However, if "man" != "one" then you can have a situation as inturnaround pointed out. But, as others have said, I think you may need to clarify where you're having an issue with this.

On preview: I'm still not seeing your issue. "Man says he is Boo and Radley" does not imply that "Man thinks one can be Boo and not Radley." That's an inference that you, or the listener, are making and incorrectly attributing to the original speaker. "Man says he is Boo and Radley," if true, only implies that "Man says he is Boo" and "Man says he is Radley" are both true.
posted by fryman at 10:21 AM on July 27, 2010 [2 favorites]

Best answer: But, how can a listener logically conclude that a speaker is making an implication because they use the word "and"?

I'm still not sure if I understand (and I don't think there is a fallacy here), but inferences like this are explicitly non-logical, in the sense that standard logical representations of meaning from the early to mid 20th century typically don't capture them. But what people infer goes beyond this kind of logical meaning pervasively. Here's one way of sketching why: (A and B), where A=B, entails A, so why would someone say the longer/more complex (A and B) when they could just say A, or just B? They must not be aware that A=B, and therefore believe that the two propositions are separable. This is basically an application of "Gricean reasoning" (specifically the maxims of manner and quality) on top of logical meaning, discussed in the link in my previous post.

In a propositional logic, if (A and B) is true, then (A and not B) is false and (not A and B) is false. And so your original proposition is invalid.

The original statement isn't translatable into propositional logic; it requires modal operators. It would really have to be something like (exists x A(x) and B(x)) --> (possible(exists x A(x) and not B(x)) and possible(exists x B(x) and not A(x))). This proposition is true on some models, unlike the corresponding classical attempt at a translation.
posted by advil at 10:39 AM on July 27, 2010

Best answer: The initial statement can be rephrased more generally as:

"There exists an object X such that isA(X) and isB(X)"

("isA" and "isB" are predicates, or functions that "return" true or false for a given object.)

This first statement does not imply

"There exists an object Y such that isA(Y) and NOT isB(Y)"

One can easily find a case for which the first statement is true and the second is not. As mentioned above: X="the liquid in this cup", isA = "is water", isB = "is H2O." Both isA(X) and isB(X) are true. But there is no Y for which Y is water but Y is not H20.

It's an odd sort of fallacy, in that I'm not sure it's common enough to have a name. I don't see why the first statement would imply anything about the "independence" of isA and isB at all. It is easily disproven by writing it out formally, however.
posted by whatnotever at 10:39 AM on July 27, 2010 [1 favorite]

Response by poster: I think I'm getting closer to understanding, but I'll use another example because I think the proper noun /name thing is making things (more) weird.

PROPOSITIONS: This liquid is made of water. This liquid is made of H20.

These statements are true and non-contradictory.


PROPOSITION: This liquid is made of water and H20.

This statement is false because its grammer implies that water and H20 are separate. It is contradictory because of it's grammatical structure.


PROPOSITION: Henry says that this liquid is made of water and H20,
CONCLUSION: therefore Henry thinks that water and H20 are two different things.

This statement could be true, but is not necessarily true, so it is not a logical conclusion.



Did I get it?
posted by alice_curiouse at 10:55 AM on July 27, 2010

Proposition 2 is not false or contradictory, just redundant.
posted by ook at 10:58 AM on July 27, 2010 [2 favorites]

Best answer: I think you're inserting an unnecessary intermediate in the form of "man," and I don't know that there's generally a name for thinking that a person is committing a certain kind of fallacy.

For example,

Premise: There exist things that are both Boo and Radley.
Conclusion: There exist things that are Boo and not Radley.

is a fallacy. There's probably a specific name for it, although I don't know what it is (I disagree with valkyryn about it being a fallacy of division). It's possibly a fallacy of propositional logic, although that's more of a general term, and it doesn't seem to fit into any of the specific subtypes listed there. (None of the subtypes listed go into the "for all" and "there exists" bits of formal logic.)

However:

Premise: John states there exist things that are both Boo and Radley.
Conclusion: John believes there exist things that are Boo and not Radley

While this is also a fallacy, I doubt that there's any specific name for "given that John has stated A, John believes B, where B is a fallacious conclusion from A due to fallacy X." If anything, it's simply a non sequitur, but that's independent of the particular fallacy X one assumes John uses to reach B.

As further evidence for this being a simple non sequitur, note that the conclusion about John's belief in B may be invalid even if A->B itself is valid. Consider the following:

Premise: There are 896 apples in barrel A, and 1012 apples in barrel B.
Conclusion: There are more apples in barrel B than in barrel A.

Obviously valid. But instead, consider:

Premise: John states there are 896 apples in barrel A, and 1012 apples in barrel B.
Conclusion: John believes there are more apples in barrel B than in barrel A.

Invalid: John may be very very bad at math and think that 896>1012; alternately, John's statement may not represent his true belief, i.e., John may be lying.

Thus, whether A->B is valid or invalid (and if invalid, regardless of the name of the particular fallacy involved), "John states A"->"John believes B" is a non sequitur; we do not have enough information to determine John's belief about B.
posted by DevilsAdvocate at 11:04 AM on July 27, 2010

Proposition 2 is not false or contradictory, just redundant.

Agreed. Similar statement seen in the wild: "Them good old boys were drinking whiskey and rye." While it's long bothered me that that line is redundant, I never took it to mean that Don McLean was describing something logically impossible.
posted by DevilsAdvocate at 11:17 AM on July 27, 2010

Best answer: PROPOSITION: This liquid is made of water and H20.
This statement is false because its grammer implies that water and H20 are separate.

The way its usually characterized is that the statement itself is literally true, but because of the way it was structured, it implies something that is false.
posted by advil at 11:28 AM on July 27, 2010

Response by poster: This was a magical, awesome conversation. Thank you, everyone!
posted by alice_curiouse at 11:30 AM on July 27, 2010

The problem here isn't logical; it is a language problem.

PROPOSITION: This liquid is made of water and H20.

You could break this down two ways:

a (We already know that) water and H₂O are the same thing.
b The liquid is water.
c The liquid is H₂O.

or

w (We already know that) water and H₂O are the same thing.
x The liquid is water.
y The liquid is H₂O.
z H₂O is not the same as water.

If you hold that the second reading is correct then the proposition then z contradicts w. That's just a contradiction, not a logically fallacy.

Logical fallacies occur when we arrive at incorrect conclusions from our premises. Here, we are either looking at a true statement (if we accept the first reading) or a false statement (if we accept the second reading). There is no premise or conclusion here, just a statement.

The trouble is that language is really messy, with annoying things like implications. Not only is there an implication, but you are using two different words to refer to the same thing.
posted by ssg at 11:49 AM on July 27, 2010 [1 favorite]

I'm reminded of a problem where someone says "one of my children is a boy" so what are the odds that their other child is a boy? A lot of people think 0% because they assume that person talks like a real person and not like a logic puzzle construct.
posted by RobotHero at 2:41 PM on July 27, 2010

The problem here isn't logical; it is a language problem.

Indeed. I'll suggest that perhaps the Gricean maxims may be relevant here. (aside: I learned about these from Dinosaur Comics)

The point is that in common conversation, people generally adhere to these maxims and, moreover, assume that other people are also adhering to the same standards. My interpreation is this: When someone says "There exists something which is Boo and Radley.", we as listeners assume that the speaker is adhering to the Maxim of Manner and not telling us redundant information. If all things Boo were also Radley or vice versa, then telling us both facts would be redundant. It should suffice to tell us only the more specific fact.

But again, these are linguistic principles, not logical principles. And, these maxims are merely a framework to help understand how discourse is formed, not immutable laws of nature.
posted by mhum at 7:02 PM on July 27, 2010 [1 favorite]

it's just fails logically.

A simple contradiction: I am a human and a man.
i can be human without being a man, but i cannot be a man without being human.
humanity does not depend on manhood, but manhood depends on humanity.
posted by subarctic_guy at 2:28 AM on July 28, 2010