How Many Lumps?

Introduction: This example comes from a cartoon, entitled “Rabbit’s Kin,” featuring Bugs Bunny, starring Mel Blanc and Stan Freberg. It was put out by Loony Tunes.

Key Facts: N/A.

Text: Bugz Bunny invites Pete Puma to enjoy a cup of tea, wherein the following exchange takes place (text taken from IMDB):

Bugs Bunny: There’s nothing as sociable as a nice cup of tea, I always say. How many lumps do you want?

Pete Puma: Oh, three or four

Bugs Bunny: [Bugs bunny whacks Pete on the head with a mallet 5 times and 5 lumps appear on his head] Oh dear, I gave you one too many. Well we can fix that.

[whacks the 5th lump back in his head]


Comments: This is of course a joke.

Statements: Much of this argument has to be inferred from the context of the exchange and the actions of the character’s in question. It ends up being a simple argument with an unstated conclusion. (Bugs acts on the conclusion rather than telling us what he has inferred from Pete Puma’s answer.

[1] [I want] 3 or 4 [lumps].

[2] [Pete Puma wants 3 or 4 lumps on his head.]

Diagram: This is a simple argument.

2 ->[1].

Discussion: This raises three themes; Dialectic, Equivocation, Missing Assertions, and Playful Reasoning.

Dialectics: Bugs builds up to the punchline of this gag by questioning his intended victim (Pete Puma). It’s perversely Socratic, …which come ton think of it may be true of many of his cartoons, as well as those of Daffy Duck. Both of these tricksters consistently engage in a kind of dialogue with their adversaries and base whatever punishment they have in mind when the other party’s own choices.

Missing Assertions: Insofar as the conclusion of this argument must be supplied (using Bugs’ actions to determine the conclusion he has drawn), this is an example of a missing assertion.

Equivocation: Bugs clearly shifts the meaning of “lumps” over the course of this exchange. When he asks how many Pete Puma wants, there is a strong implication that he means “lumps of sugar.” After getting his answer, Bugs shifts the meaning to “lumps on the head.”

Playful Reasoning: This is not a serious argument, of course. It is a joke. It is accordingly cheating to use this as an example of the equivocation fallacy.

…If I doos it, I get a whippin.

I doos it!

Evaluation: The argument is of course unsound as it commits the fallacy of equivication.

Final Thoughts: Yes, this post is self-indulgent.

Not Be on a Boat

Introduction: This text is from the play, Rosenkrantz and Guildenstern are Dead, by Tom Stoppard. In this scene, the two central characters contemplate death while passing the time on a ship sailing from Denmark to Britain.

Key Facts: This is a dark comedy. The philosophical discussions between these two characters are full of absurd exchanges like this one.

Text: Really, the argument is contained in the last line (along with a missing conclusion.)

“Rosenkrantz: Do you think death could possibly be a boat?

Guildenstern: No, no, no. Death is not. Death isn’t. You take my meaning? Death is the ultimate negative. Not-being. You can’t not-be on a boat.

Rosenkrantz: I’ve frequently not been on boats.”


Comments: This is not a very serious argument.

Statements: The relevant argument would be as follows:

[1] I’ve frequently not been on boats.

[2] It is possible to not-be on a boat.

Diagram: This one is simple.

2 ->[1].

Discussion: This argument raises the following issues; Dialectics, Equivocation, Missing Assertions, Playful Reasoning.

Dialectics: Although they are not following any particular methodology, Rosenkrantz and Guildenstern are engaging in a philosophical discussion through which each builds on the other’s points to help the author make his own points. This is accordingly a kind of dialectics, albeit a comic one.

It’s tempting to say that this might not be dialectics, because Guildenstern doesn’t really build on Rosenkrantz’s point. He just denies it. Yet, the fallacy can only be understood by looking at the shift in meaning between then Rosenkrantz and Guildenstern, so perhaps it’s a failure of dialectics, which still makes it a kind of dialectics.

…I think.

Equivocation: Rosenkratz is talking about a state in which existence itself is no longer a predicate of the subject, i.e. the dead person. Guildenstern is clearly evading the point by saying he has not been on boats, i.e. that he, while still existing, simply wasn’t on a boat.

Missing Assertions: Rozenkrantz’s conclusion is not spelled out in the text of the play, but he clearly means to suggest that Rosenkrantz is wrong. So, the argument contains at least one missing conclusion.

Playful Reasoning: the actual source of the argument is of course not seriously advancing an argument here, at least not the one presented above. He is using the form of a denial to generate a joke. It is accordingly cheating a bit to use this as an example of a fallacy.

Evaluation: The argument is unsound because it commits the fallacy of equivocation.

Final Thoughts: Sometimes, the best* examples of a given fallacy are made up for humorous purposes.

* Admittedly, this would be for an ironic value of ‘best.’

Wisdom of the Oompa Loompas

Introduction: This argument is a (hopefully) well known part of the movie Willy Wonka and the Chocolate Factor, which was produced in 1971. In this film, the Oompa Loompas, mysterious workers at the chocolate factory sing a number of songs amounting to criticism of the children featured in the story. Each of the Oompa Loompa songs effectively points out the misconduct of an individual child and makes a case for changing that behavior.

This particular passage is the tune the Oompa Loompa’s sing at Violet Beauregarde, a girl who obviously likes her gum.

Key Facts: It’s worth considering that the Oompa Loompas play the role of a chorus in much the same manner that the convention was used in old Greek theater. In this case, they deliver a moral lesson which not only speaks to the characters in the story but also echoes lessons many parents might have given their own children.

Text: Here tis!

“Gum chewing’s fine when it’s once in a while
It stops you from smoking and brightens your smile
But it’s repulsive, revolting and wrong
Chewing and chewing all day long
The way that a cow does.”


Comments: I got nuthin!

Statements: In the following, statement 5 is rewritten so as to spell out the comparison. Statement 6 is the implied conclusion of the entire argument. It comes very close to matching statement 1, but it also entails the negative implications of chewing too much, which is of course the main thrust of the moral lesson.

[1] Gum chewing’s fine when it’s once in a while.

[2] It stops you from smoking.

[3] (It) brightens your smile.

[4] It’s repulsive, revolting and wrong chewing and chewing all day long.

[5] [Cows chew gum all day long.]

[6] [Gum should be chewed in moderation.]

Diagram: the diagram for this argument seems pretty straight-forward to me. Two reasons to say gum chewing is okay in moderation and one to show that it’s bad to chew gum too much. These two combine together to suggest a general proposition about doing the one and not the other.

Note that an alternative approach might be to spell out a more explicit negative statement about the need to avoid excessive gum chewing. This would perhaps capture the immediate significance of the lesson directed at Viola in the wake of her blueberry gum fiasco, but it has the down-side of complicating the signifcance of the counterpoint (that gum chewing is good when done in moderation), so I have opted here to treat the point as a more general lesson. Either approach seems plausible to me.

Discussion: This argument raises the following themes; Analogy, Appeal to Emotion, Causation, Missing Assertions, Moral Reasoning, Voicing.

Analogy: The Oompa Loompas compare shewing gum to the behavior of a cow chewing cud. Whether or not this is a good reason to avoid chewing gum is another question.

Appeal to Emotion: The main thrust of the analogy to cows chewing cud appears to be an appeal to emotion, in this case disgust.

Causation: Both statements 2 and 3 suggest a causative relationship between chewing gum and some desirable effect. Whether or not these claims are justified is open to question, but they are sufficient to suggest that this argument involves a degree of causal reasoning, unsupported as the argument is in it’s current form. (Damned Oompa Loompa’s never cite any peer-reviewed papers!)

Missing Assertions: As is common in a great deal of reasoning, the actual conclusion of this argument is unstated in the original song. There are a couple different ways to think about what that final conclusion would be, but in its original form, the implications are left unstated.

Moral Reasoning: As the argument in question here is about how people (and in particularly children) should moderate their gum-chewing, it raises familiar questions about what it means to say that someone should or should not do something.

In this tune as well as the others, the Oompa Loompas seem to emphasize the negative effects of the behavior in question which suggests that this argument might be best construed in consequentialist terms. They are suggesting that excessive gum-chewing will make someone look foolish, or at least cowlish.

Voicing: The Oompa Loompas effectively serve as a kind of Greek chorus, announcing the moral significance of events taking place in the larger story. Their message thus seems to express a normative stance intended for the movie audience. When Viola and the others produce arguments expressing their own views on these topics, they appear to be voicing the imagined voices of children in need of correction. The events of the story then reveal the foolishness of their actions, and the Oompa Loompas arrive to drive the point home with a specific moral lesson. That moral lesson is a real lesson directed at children who may be trying to decide how to deal with issues such as how much gum should I chew.

Evaluation: I’m not going to do a complete evaluation here, but I will mention a couple of specific themes.

Statement 2: As part of a lesson directed at children this is an odd point to make at the very least, but presumably it could be interpreted as a claim relevant to the conduct of adults which would also be a concern to children. Either way, we could ask whether or not chewing gum actually stops people from smoking. That those trying to kick a smoking habit often chew gum in place of it would seem to suggest that there may be some connection here, at least in this specific context, but it is by no means clear that gum chewing in general serves to keep people from smoking,

Statement 3: I am not at all sure that this statement is true, either in general or in specific contexts such as right after a meal.

5->4: This inference is questionable at best. Presumably, the point of the analogy is to suggest that one would not wish to behave as a cow does, but it isn’t clear that there is any objective reason for this preference. Neither is it clear that moderate gum-chewing would be any less comparable to chewing cud than constant gum-chewing. Arguably this is a pretty naked attempt to trigger an emotional reaction.

Final Thoughts: The temptation to finish with an Oompa Loompa tune about good reasoning is very strong here, but I am going to show restraint, and I think the Oompa Loompas would be proud of me for doing so.

King’s Pushback

Introduction: This is part of an article entitled, “The Real Reasons All the Top Chess Players Are Men,” written by Wei Ji Ma. It was published in Slate Magazine on December 11th. In this piece, tries to counter a common claim that men are inherently better at chess than women by considering a number of social factors which Wei argues could better explain known disparities between the number of successful men and women participating in competitive chess.

Key Facts: The Cable Series, “The Queen’s Gambit,” features a story-line in which a woman fights her way up the ranks of professional chess to become the world champion. When the Queen’s Gambit was released, it triggered a wave of discussions about the gap between men and women in the top ranks of chess competition. Several voices argued that the women are under-represented in chess championships for reasons of inherent inability. The author of this argument makes a case for social construction as a more likely cause of the difference. The passage below focuses specifically on the impact of the belief in inherent ability on the social construction of gender differences relevant to competitive chess.

Text: “The idea that innate chess ability is critical for success—rather than a commitment to studying the game to get better and better at it—might itself keep the participation gap wide in the first place. Andrei Cimpian, Princeton University philosopher Sarah-Jane Leslie, and colleagues studied 30 academic disciplines in the U.S. and found a strong negative correlation between the pervasiveness of innate-ability beliefs and the proportion of female Ph.D.s. Moreover, very young children already internalize beliefs that men are more brilliant than women. A 2017 study showed that 6-year-old girls in the U.S. are already less likely to believe that members of their gender are “really, really smart,” and that they begin avoiding activities that are said to be for children who are “really, really smart.” There we have it: a shockingly early start for the participation gap in chess.”


Comments: To fully assess the value of the original argument, the passage above would have to be considered alongside Wei’s account of several other confounding variables which might explain the relative lack of successful women in competitive chess, as well as his critique of the case made for inherent ability. Doing so would of course put the analysis beyond the scope of a simple exercise. So, we are just dealing with this passage here, but that does touch upon questions as to how one might best think of the specific conclusion to be drawn from this specific passage. It should be kept in mind that Wei isn’t trying to settle the whole issue in this one passage; he is using it to establish one point in a larger argument.

Statements: This argument is pretty straight forward. I have omitted a hedge from the first statement.

[1] “The idea that innate chess ability is critical for success—rather than a commitment to studying the game to get better and better at it— …keeps the participation gap wide in the first place.

[2] Andrei Cimpian, Princeton University philosopher Sarah-Jane Leslie, and colleagues studied 30 academic disciplines in the U.S. and found a strong negative correlation between the pervasiveness of innate-ability beliefs and the proportion of female Ph.D.s.


[3] Very young children already internalize beliefs that men are more brilliant than women.

[4] A 2017 study showed that 6-year-old girls in the U.S. are already less likely to believe that members of their gender are “really, really smart,”

[5] [The same study showed that] they begin avoiding activities that are said to be for children who are “really, really smart.”

[6] There we have it: a shockingly early start for the participation gap in chess.

Diagram: The argument appears to produce three separate inferences in serial form with the final conclusion being the first sentence.

Discussion: The main themes associated with this argument would include; Begging the Question, Causation, Hedges, Statistics.

Begging the Question: There is at least one way of reading the first inference which would render it a circular argument.

Causation: The essential point of the argument is to assign a causative factor to the gender disparities in chess. This passage of this article makes the case that belief in innate talent creates a self-fulfilling prophesy, depressing interest in chess by women reducing expectations for their performance. These two studies cited may not be sufficient to demonstrate the social expectations outlined in these studies, though they are probably sufficient to undermine the case for innate ability as a sufficient explanation in it itself.

In the end, a more exhaustive account of relevant studies would be needed to account for all the variables.

Hedges: Notice that the opening lines of this argument use the phrasing “might be” in setting up the case that belief in innate ability constitutes a self-fulfilling prophesy. Most likely, this reflects the nature of the publication. In effect, the author is turning out a quick response to the topic at hand rather than the results of exhaustive research. The hedge this reminds us that his conclusions are tentative at best, offered as food for thought rather than as a final verdict on the topic at hand.

In omitting the hedge from the wording of the first statement, I am treating them more as a kind of affect display than a feature of the statement in question. Some might disagree with this approach, suggesting that the actual question is merely whether or not belief in innate ability MIGHT deter women from participating in chess. This would water the topic down to the point of being pointless, so I think it better to treat the claim in question as a solid assertion of the link, and the presence of the hedge as indicating something about the relative confidence of the author rather than as a feature of the claim in question.

Statistics: The argument refers to 3 separate findings from 2 separate studies. Whether or not these are enough to establish the truth of the author’s conclusion is something of an open question. Barring specific questions about the data in the study and/or the conclusions drawn from it, a reader might still be justified in wishing to consider additional variables. Still, the studies cited above do seem to provide some reason to believe, as Wei does, that belief in innate ability is itself a factor in the gender disparities present in competitive chess.

Evaluation: I am just going to comment briefly on each of the 3 inferences in this argument.

4->3: Here the author is essentially taking a specific study, to the effect that young girls already equal intelligence with gender, to demonstrate a larger claim that young children generally show this belief.

One might raise some questions as to whether the study in question demonstrates that female children are coming under the influence of stereotypes at age 6 or simply becoming aware of innate differences. Few social scientists at this point would entertain the latter option, and the authors appear to take it as axiomatic that belief in gender disparity is a stereotype, but as this author of this argument uses the study to show that social construction is the cause of gender disparities in chess rather than innate ability, this builds a degree of circularity into the argument, at least as applied to this first inference.

At least as stated, the inference from 4 to 3 appears to be invalid. Additional information may change this, but the information is not present in the immediate argument presented above.

3+5->6: Statement 3 is a general claim about the early impact of belief in gender stereotypes dealing with intelligence and statement suggests that at least one study shoes that girls as young as 6 begin avoiding activities they associate with it. Statement 6 attributes gender disparities in relevant activities to these factors.

The premises certainly do make a plausible case for the conclusion. How convincing one finds that case is another question. It would be reasonable to ask for consideration of additional variables, some of which are dealt with in the rest of the article and/or even to look for more exhaustive studies on the topic at hand. Of course, it would also be reasonable to expect of someone holding out for such information that they would look at the research in question if it was offered. If that is too time consuming, then it might well be argued, the material at hand ought to be sufficient for at least a tentative conclusion.

Note that the circularity mentioned in the first inference based on the study of young girls is less relevant to this inference insofar as the observation that girls begin avoiding tasks associated with innate intelligence does establish a behavioral impact of the belief in question. Whether or not there might be some case for the accuracy of such beliefs, the case for a behavioral impact of such beliefs is supported by the study.

2+6->1: This inference combines the case for early avoidance of intellectual activities by girls as a result of stereotyping with a parallel observation about a relative lack of adult female participation in scholarly fields strongly associated with innate ability to make the case for belief in innate ability as a deterrent to female participation in chess.

As with the previous inference, the argument makes a plausible case. Whether or not it is convincing is another question.

Final Thoughts: Overall, I do find this to be a persuasive argument, but I believe at least part of this is due to the fact that I am inclined to accept the assumptions of a social constructivist position at the outset. As a case in favor of such a position, and against the view that there are innate differences between boys and girls on skills relevant to chess, I think it is still sufficient to establish the relevance of at least one competing variable, the reaction to belief in innate differences has an impact on human behavior. To rule out any underlying innate difference probably just takes more than you can accomplish with the paragraph above and many even with the article from which it is drawn.

Michael Moore’s Thoughts on Snipers

Introduction: On January 18th, Michael Moore posted a tweet widely regarded as a comment on Chris Kyle and on the movie Sniper depicting Kyle’s service in the military. Given Moore’s status as a left wing activist and critic of the Iraq War, it should come as no surprise that he would object to a film that seems to portray Kyle as a hero. Moore seems to suggest that Kyle is nothing of the kind, eve going so far as to imply that Kyle is in fact a coward.

Key Facts: It’s worth noting that much of Hollywood’s portrayal of snipers would fit more in line with Moore’s comments in this instance. Snipers usually make their way into a film as a menace to the heroes, or as complex characters with a deeply ambivalent sense of their own role in combat. It is only in more recent depictions that they have begun to occupy the relatively more straight-foreword role of heroes in films such as Blackhawk Down.

Text: Here is a screenshot of the tweet.



Band of Brothers – Where Are We?

Introduction: This is a scene from the HBO mini-series, Band of Brothers (2001). It takes place in Part 2, “Day of Days” at about the 13 minute mark. In this scene, two paratroopers (Lieutenant. Winters and Private Hall) have just linked up following a night drop into enemy territory during the invasion of Normandy. The following conversation occurs as they look for other U.S. soldiers and try to get their bearings while attempting to evade German defenses.

Key Facts: Different companies within the drop force were supposed to be dropped into different locations. for a variety of reasons (not the least of them being fire from German anti-aircraft guns), many seem to have missed the mark. Lieutenant Winters is from Easy Company (so he is not in D-Company or Able Company).


1) Lieutenant. Winters: “Aren’t you D-Company?”

2) Private Hall: “Able Sir.” (pause) “Guess that means one of us in the wrong drop-zone, sir.”

3) Lieutenant Winters: “Yeah, or both of us.”


Comments: The actual reasoning here is fairly simple, and this is one case where the conventions of argument analysis may lend themselves to unnecessary complication. So, let’s just get on with it.

Statements: We must add two missing assumptions, and each step of the reasoning will require some degree of rewriting to bring out the reasoning. Leaving out the problematic missing assumption, I would suggest the following propositions (each presented in bold).

1) [Missing Assumption: Lieutenant Winters is in Easy Company.]

2) Statement Two: [Private Hall is in Able Company.]

3) [Missing Assumption: Easy Company and Able Company have different drop zones.]

4) [Either Lieutenant Winters or Private Hall are in the wrong place.]

5) [Either Lieutenant Winters or Private Hall, or both of them, are in the wrong place.]

Discussion: This is a pretty simple exercise in reasoning. It touches upon dialectics, the reconstruction of missing assumptions, and the fallacy of false alternatives.

Dialectics: The argument illustrates dialectics insofar as the men cooperate to arrive at a common understanding of the issue.

Missing Assertions: Lieutenant Winters’ membership in Easy Company remains unspoken as it is obvious to both parties, as is the assumption that each of the companies in question has a different drop zone. It’s tempting to suggest that Private Hall makes a more serious assumption over the course of the discussion. In the second line, he infers from the fact that each was intended to land in a different drop zone that one of them must be out of place. This might be taken to assume that at least one of them must have landed in the right place. Alternatively, Hall makes no such assumption and the problem arises with his inference that one of them is in the wrong place. His account of the situation would then be incomplete, but it wouldn’t be erroneous. In keeping with the principle of charity, I would suggest going with the latter option as Hall’s specific wording does not commit him to the specific mistake in question.

False Alternatives: Whether it arises in an assumption or an inference, Lieutenant Hall’s conclusion fails to address the possibility that both he and Lieutenant Winters had landed in the wrong place.

Diagram(s): It isn’t clear to me that a visual diagram of the reasoning here is all that necessary or helpful, but for the sake of consistency I thought I should attempt it. After toying with a couple options, I am opting to suggest two simple models, one representing the Reasoning of Private Hall and one that of Lieutenant Winters.

Evaluation: Barring significant revelations from historical specialists, I think we can assume that premises 1, 2, and 3 are true, which leaves the inferences for us to evaluate. Assuming a literal interpretation of statement 4, support the inference in Private Hall’s reasoning would be weak at best, leaving an unsound argument. Support for the inference in Lieutenant Winter’s reasoning would seem to be deductively valid, though perhaps one could find a fiddly argument to bring it down to a rating of strong. In either event, Lieutenant Winter’s reasoning appears to be sound.

Final Thoughts: This kind of reasoning is more common in real life than it is in logic textbooks. The two men build on each others’ statements to achieve a common understanding. In the final turn, Lieutenant Winters does not so much tell Private Hall that he has made a mistake as simply suggest a better conclusion. As the narrative unfolds, Hall introduces a potential mistake and Winters simply sets it aside. As a food-for-thought kind of question, one might follow this example by asking students to think about the the varieties of context in which bypassing criticism would be more wise than direct confrontation. Conversely, one might ask if there are contexts in which direct criticism would be more useful.