Introduction: This was posted to twitter on June 11, 2022. It is clearly an argument about the proper interpretation of the Second Amendment of the U.S. Constitution. Many similar arguments have been made online and in other contexts on pretty regular basis.
Key Facts: There are a few facts which might have bearing on the (de-)merits of this argument.
1: The Second Amendment reads as follows: “A well regulated militia, being necessary to the security of a free state, the right to keep and bear arms, shall not be infringed.”
2: Muskets were not the only weapons known to those writing the Second Amendment. They would of course have been familiar with canons. Muzzle-loading rifles had been used for hunting and even saw some use during the American revolution, and experimental forms of semi-automatic weapons such as the Gieardoni air rifle and the Belton flintlock had been developed by this time. Still, muskets were the predominant form of weapon used in warfare. I believe muzzle-loading rifles may have been more useful in hunting, but I am not entirely sure of this.
3: Much of the current discussion of gun control focuses on the prospect of banning assault weapons, or otherwise subjecting them to some form of stricter-than-usual regulation. What constitutes an ‘assault weapon‘ can be a difficult question. The difficulty is of course compounded by the controversial nature of the debate over gun control.
4: James Madison’s first official draft of the Second Amendment was proposed in 1789. The Second Amendment was ratified in 1791.
Text: “The Second Amendment is from 1789. So, technically, the second amendment only applies to muskets.”
Comments: I am using this as a representative sample of a broad range of arguments about the meaning of ‘arms’ by gun control advocates.
Statements: There are two statements in this argument.
 The Second Amendment is from 1789.
 technically, the second amendment only applies to muskets.
Discussion: This argument raises the following issues; Availability Heuristic, Contextualization, Hedges, Indexicality, The Masked Man Fallacy, Micro-Reasoning, Semantics.
Availability Heuristic: It appears that the author assumes that muskets were the only weapons available in 1789, or the only ones who count as far as she is concerned. Either way, it’s a problem. While muskets were certainly the most prevalent weapon used in war, they were not the only weapons available. So, the notion that the Second Amendment can apply only to muskets does not literally work, even as applied to the weapons of the day.
Most likely, this is an expression of the availability heuristic. In other words, the author is letting her sense of the weaponry available at the time be defined entirely by the weapons most talked about in history books and movies (which deal most often with warfare). She may even be aware of some of the author weapons of the era, but they do not stand out in her mind so much as muskets.
Just how much this matters is another question. Experimental semi-automatic weapons were not widely available at the time, and even rifles were not the main weapons of war as of yet. (Also, she may mean to include muzzle-loading rifles in her own use of ‘muskets.’ A distinction between a smooth-bore musket and a muzzle-loading rifle is probably not that common in modern thinking about guns, at least not amongst the general population.
This is probably a trivial mistake. Insofar as the author is most likely trying to distinguish between muzzle-loading weapons available in the founding era from some construction of ‘assault weapons’ today, a significant difference would not be hard to establish. So, if this is a problem, it is probably not a problem critical to her argument.
Contextualization: The issue here arises because of the contextualization behind the Second Amendment. It is a text written in a particular time and place, but it is also a text written with future generations in mind. We also read this text today under the assumption that it must somehow be relevant now. In effect, this is a text with a exceptionally broad context insofar as its authors clearly meant to speak to people not yet born on matters not yet coming to pass. The problem is thus a question about how to manage the logical implications of a text with different practical implications at different times.
Hedges: The term “technically” is a hedge. Its use indicates that the author sees her interpretation as narrow in comparison to conventional meaning. For reasons mentioned below, it is doubtful that her interpretation of the Second Amendment is ‘technically’ correct.
Indexicality: Part of the problem here is a problem of reference and predication. The text of the amendment refers to something by means of a term, ‘arms.’ What that term means in semantic terms, is one thing. What real-world objects may be referenced through that meaning is another. The problem here is a question of what specific things are referenced by means of the term ‘arms?’ The term carries certain notions, but the actual objects reference by those notions have changed over time.
Masked Man fallacy: Probably the biggest problem with this argument is its confusion of reference by intension with reference by extension. The relevant term in question is ‘arms.’ What the author asks us to consider is the fact that this term was used in 1789 to refer to a much narrower category of weapons than we could use it for today. She concludes from this that the term applies only to that narrow range of weapons from 1789 rather than the full range of arms presently on the market for civilian gun ownership. In so doing, she derives a conclusion about intensional meaning of ‘arms’ from the extension of the original reference to muskets.
This seems like the opposite of the usual form of the masked man fallacy. This fallacy treats two terms as equivalent in meaning if they refer to the same actual things even when the equivalence is not known to a given subject (e.g. Lois Lane knows Clark Kent is in New York because she knows Superman is in New York and we know that Superman is really Clark Kent). In the case of this argument by contrast, a broad intension is denied, because of a limited initial extension (to muskets only) in its initial reference whereas there is nothing in the semantics of the term that suggests it must be so limited. Those who wrote, debated and ratified the Second Amendment may not have known about an AR-15, but we have no reason to believe its characteristics would not have qualified as a form of ‘arm.’ The direction of the inference is unusual for an application of the masked man fallacy, but the author is still confounding reference by intension with reference by extension.
Micro-Reasoning: It is probably safe to say that some of the problems mentioned here are directly due to the brevity of the argument.
Semantics: The argument is explicitly about the meaning of the text in question, and many of the problems mentioned here are also a function of questions about meaning.
Evaluation: Insofar as the argument commits the masked man fallacy, or something very close to it, this argument is unsound.
Final Thoughts: There are of course many different variations on this argument, some of which may avoid the problems outlined above. What we know is what was written at the time and what weapons were in use at the time. How those who wrote it might assess the costs and benefits of the Second Amendment today is an entirely different question. It might be fair to suggest that the difference between guns in 1989 and guns today should lead us to recalculate the costs and benefits of the Second Amendment. What doesn’t work is an argument deriving a narrow intention from the general terminology based on a factual comparison between the weaponry of 1789 and that available today. You could say; “things have changed and so we should rethink this.” What you can’t say with reasonable force is that the framers meant for the Second Amendment to apply only to the weapons generally available at the time.
Introduction: Marjorie Taylor Greene is a a U.S. Representative for Georgia District 14. She is also a known advocate of several conspiracy theories, and an advocate of Second Amendment rights. At some point in time, she posted this video explaining her views on a mass shooting that occurred in Las Vegas. (Note: This appears to be a re-post by someone else; I still haven’t tracked down the original.) At some point, she also published this article republished by the Way Back Machine, in which she provides more detail (though not much more in the way of evidence) on her views about the subject.
Key Facts: The shooting in question occurred on October 1st, 2017. It was carried out by Stephen Paddock. He fired over a thousand rounds of ammunition into a music festival on the Las Vegas Strip, killing 60 people and wounding 867 others before killing himself. (I’m just going by Wiki here.) Although some sources have made assertions about the subject, at present, police have drawn no substantial conclusions about his motives for the shooting.
Text: Here is the full text of the video clip. Obviously, some of the text below is not part of the actual argument.
“Hey Friends, I’ve got a question for you. How do you get avid gun owners and people that support the Second Amendment to give up their guns and go along with anti-gun legislation? How do you do that? Maybe, you accomplish that by performing a mass shooting into a crowd that is very likely to be conservative, very likely to vote Republican, very likely to be Trump supporters, very likely to be pro-Second Amendment, and very likely to own guns. You make them scared, you make them victims, and you change their mindset, and then possibly you can pass anti-gun legislation. Is that what happened in Las Vegas? Is that why, um, the country music festival was targeted? Because those would be the people, that would be the ones that we would relate to? Are they trying to terrorize our mindset, and change our minds on the Second Amendment? Is that what’s going on here? I have a lot of questions about that. I don’t believe Steven Paddock was a lone wolf. I don’t believe that he pulled this off all by himself, and I know most of you don’t either. So, I am really wondering if there is a, there’s a bigger motive there, and does it have to do with the Second Amendment, because what’s the best way to control the people? You have to take away their guns. So, that’s just my question today. This is Marjorie Greene with American Truth Seekers.”
Comments: What makes this argument interesting is the constant hedging. Greene is doing her best to put forward ideas without taking responsibility for them. The end result is quite a study of rhetorical manipulation and general evasiveness.
Statements: I found it really hard to dissect the statements in this argument, mainly because Greene is waffling her way through it. It’s normal to rephrase a rhetorical question as a statement for argument analysis, but it isn’t normal to deal with an argument that is so thoroughly saturated with them (along with other forms of innuendo). It seems somewhat unfair to Greene to just pretend her questions are statements, but it’s also unduly generous to pretend they are just questions. She is riding the fence line on just how much she wants to assert, and that poses a problem for how to interpret her approach to this.
I wanted to preserve some elements of the contextualization strategies here as I do think they are critical to the argument.
I am designating some the contextual information Greene presents with capital letters in place of numbers. Note also, that a rather large portion of this argument consists of rhetorical questions. I have added square brackets to the periods I used to replace what would normally be question marks to indicate which statements were originally phrased as questions.
[A] Hey Friends, I’ve got a question for you.
[B1] How do you get avid gun owners and people that support the Second Amendment to give up their guns and go along with anti-gun legislation?
[B2] How do you do that?
 Maybe, you accomplish that by performing a mass shooting into a crowd that is very likely to be conservative.
 [Maybe, you accomplish that by performing a mass shooting into a crowd that is] very likely to vote Republican.
 [Maybe, you accomplish that by performing a mass shooting into a crowd that is] very likely to be Trump supporters.
 Maybe, you accomplish that by performing a mass shooting into a crowd that is] very likely to be pro-Second Amendment.
 [Maybe, you accomplish that by performing a mass shooting into a crowd that is] and very likely to own guns.
 You make them scared.
 you make them victims.
 you change their mindset.
 [if you do this,] then possibly you can pass anti-gun legislation.
 [That is] what happened in Las Vegas[.]
 [That is] why, um, the country music festival was targeted[.]
 Those would be the people, that would be the ones that we would relate to[.]
 [They are] trying to terrorize our mindset, and change our minds on the Second Amendment[.]
[11 and 12] [That is] what’s going on here[.]
[C] I have a lot of questions about that.
 I don’t believe Steven Paddock was a lone wolf.
 I don’t believe that he pulled this off all by himself.
 I know most of you don’t either.
[D] I am really wondering if there is a
 there’s a bigger motive there.
 [It has] to do with the Second Amendment.
 because what’s the best way to control the people[.]
 You have to take away their guns.
[E] So, that’s just my question today.
[F] This is Marjorie Greene with American Truth Seekers.”
Diagram: This took a lot more judgement calls than I like making, but here is the diagram.
Discussion: This argument raises the following themes: Accusatory Question, Anaphoric Pronouns, Argument from Incredulity, Burden of Proof, Double Negation, Gish Gallop, Hedges, Innuendo, Passive Voice, Provincialism, Redundant Assertions, Rhetorical Question, Straw Man, Unsupported Assertion.
Accusatory Question: Several of Greene’s questions effectively make an accusation for which she presents no evidence. By treating these as rhetorical question, as above, they are transformed into statements for which the evidence is questionable at best, but the rhetorical strategy is worth keeping track of in itself. Statements 10, 11, and 12 are the more obvious examples of this gambit.
Anaphoric Pronouns: A couple of sections of this argument turn on the use of anaphoric pronouns (i.e. pronouns that refer to a previously named entity. At least a couple of these are free-floating anaphors, i.e. pronouns used without a clearly established referent. We have a generalized “you’ in statements 1-9, for example, which seems to suggest that these are tactics anyone could use to manipulate others, but she is probably suggesting that someone in government (or more likely, an abstract government entity) is actually doing this. The ‘they’ in statement 12 would refer to the participants in some unspecified conspiracy, but once again Greene avoids telling us who it is that she is talking about. The “You” in statement 15 would of course refer to Greene’s friends (as mentioned in A), which in this case probably means something more like her fans and/or those who agree with her on this and similar topics. “Them” in statements 6-8 clearly refers to the conservative crowd referenced in statements 1-5.
On a side note: The demonstrative ‘that’ in “[11 and 12] [That is] what’s going on here[.]” is a bit ambiguous. I take it to refer to events as described in both statements 11 and 12, though it could refer to either one individually.
Argument from Incredulity: Statements 13 and 14 both present refusal to believe a proposition (the notion that Paddock acted alone) as evidence for its opposite. This is the argument from incredulity. As, Greene is actually suggesting a lot more specific than that he had help, this raises other problems as well (straw man concerns and burdens of proof).
Burden of Proof: Taylor uses double negation to assert a few unspecified assertions about possible conspiracies (e.g. statements 13 and 14). In effect, saying that paddock did not act alone is what she offers in place of a clear theory as to who helped him and what evidence she has for this. Significantly, this is one of the few areas where Greene does not disguise her assertions as question, but she still gives herself cover by hiding a specific assertion in the negation of its opposite. Arguably, it would be on her to spell out the assertion she means to make and provide evidence for it. Instead she merely uses the argument from incredulity to deny the negation of her unspecified accusations.
Double Negation: As mentioned above (in Burden of proof), Greene denies that Paddock acted alone in order to suggest that he had help. This helps her evade the need to make specific assertions as to what help he had, but to the point at hand, her argument turns on double negation.
Gish Gallop: For a short clip, Majorie Taylor Greene does incude an awful lot of objectionable material in here. I think it would be fair to call this a Gish Gallop.
Hedges: Greene uses words like “Maybe” (statements 1-5) and “possibly” (in statement 9) to avoid committing to her assertions. She tells us that she is “wondering” about this. Like her use of rhetorical questions and her use of double negation, these hedges enables her to evade responsibility for anything she gets wrong. If her accusations are clearly disproven, then she may of course say that she was only raising the possibility. In effect, she is using this language to avoid taking responsibility for the argument she is making.
Innuendo: This isn’t the most technical term, but all this adds up to an argument that works by innuendo. Greene implies a great deal more than she asserts.
Passive Voice: One of the advantages of passive voice is that you can use it without a ‘by-clause’, thus avoiding the need to specify who is actually carrying out the action in question. You see this in statement 11, talking about why the country music festival “was targeted” without saying by whom. Clearly, Greene does not mean Paddock alone, but she never tells us who else might be involved. Along with all the other hedges, her use of passive voice here enables her to skip that piece of information.
Provincialism: Greene’s statement 16 could be viewed as a appeal to provincialism. (Alternatively, it could be an appeal to popularity – i.e. the Bandwagon fallacy – but if I had to make a call, I would say that it’s bandwagon.) She appears to be trying to generate the impression that people in her own circles would certainly share her views on this topic.
Redundant Assertions: There are a few redundant assertions here, some such as statements 11 and 12 which appear to be repeated with different wording, and some (statements 1-5) which occur which several different propositions within one whole statement are spelled out individually. None of this is a problem with Greene’s reasoning, but it could trip up someone doing an argument analysis (fingers crossed).
Rhetorical Questions: As noted repeatedly above, Greene uses a lot of rhetorical questions. Statements 9-12 in the list above were actually phrased as questions. She begins with a question, repeated twice, and ends by saying that she is raising questions. Somewhere in the middle, Greene suggests that she is actually raising questions. It seems best to treat this as acknowledging some level of doubt, but Greene is in effect making an argument here. She is suggesting that the scenarios (or something like them) she raises are actually the case. Combined with her use of double-negation to affirm some unspecified scenario other than the prospect that Paddock acted alone, her use of rhetorical questions adds up to an argument in favor of some unspecific conspiracy theory.
In any event, the questions mentioned above have been rewritten as statements here.
Straw Man Argument: I’m not real sure about this one, but there is at least one sense in which Greene’s argument could be seen as resting on a straw man. Al though it appears that the police treat Paddock as a lone actor, the notion that his actions are not the result of a conspiracy to take away guns from American citizens simply does not rest on the notion that Paddock acted alone. Any number of scenarios involving additional parties would fall far short of the conspiracy Greene is suggesting.
Unsupported Assertion: Greene makes a unsupported assertions in this argument. She provides no evidence, for example, for her assertion that Paddock did not act alone (statements 13 and 14). She also suggests (in the form of rhetorical questions in 10, 11, and 12) that the country music festival was targeted for purposes of undermining gun-owners rights. Phrasing these as questions helps to diffuse the expectation that evidence should follow, and one does. Statements 16 and 17 are also unsupported. All of these assertions are just as controversial as the conclusion of her argument, and at least as questionable as to their truth values. It isn’t simply that these are starting premises; the problem in each of these cases is that the notions Greene puts forth fly in the face of the currently common take on this event, and she makes these assertions without offering any evidence in support of them.
Voicing: In statements 13 and 14, Greene is effectively voicing the stance of her presumed opposition. She does so for the purpose of refuting them, of course, but it’s worth keeping in mind that she is conjuring a definite sense of her political opposition for the moment. That opposition is of course present by implication not only in the dialogue over what happened in this shooting, but also in the story itself, as the presumed source of the conspiracy she wants us to believe was behind the attack. In rejecting their views, she is of course also rejecting the politics of the conspiracy. Given her assumptions about the conspiracy, calling it out and rejecting the views of those who deny the conspiracy is performatively fighting against the conspiracy, even against the shooter insofar as she hopes to defeat his presumed goals. She doesn’t hit this theme that hard, but the implication is probably part of the appeal of her position, and part of what makes it so hard to reason with people like Greene.
1-5 -> 9: Statements 1-5 each rely on an intuitive sense that an attack on gun owning conservatives might cause them to change their minds on the Second Amendment. I do wonder what social psychologists might say on the subject (particularly as regards dissonance reduction theory), but these statements seem plausible, and I think they do add up a general sense that such an event could (hypothetically) help someone who wants to restrict the rights of gun owners which is the point of statement 9. Push comes, to shove, this sub-theme strikes me as a marginally sound argument.
6-8 -> 9: This is just a more abstract argument about psychological impact. It’s vague, at best. There is a certain intuitive appeal, but its’ not clear how all this works. I don’t find this sub-theme convincing, though my concerns are mild at worst. It just isn’t clear that people would respond to such a traumatic event by changing heir views on gun ownership and gun rights. It is at least as likely that they will respond by adopting conspiracy theories and using those theories to double-down on their defense of gun ownership.
This really isn’t where the real problems in Greene’s argument reside, but if I have to make a call, I’d say this one is unsound.
11 -> 10. Statement 10 is a proposition about what actually happened. Statement 11 is a statement about the affiliation of people targeted. the one does not add up to the other. This is unsound because the inference itself is weak at best.
13+14 -> 10. This one is unsound because 13 and 14 are unsupported. Also, the prospect that Paddock may have had help from someone does not add up to evidence for the kind of conspiracy she is asserting. This argument fails on both the truth value of its premises and the logic of inference. Unsound. Really unsound.
15 -> 10. This is an appeal to provincialism fallacy. Unsound.
16=19 -> 10: Each of the assumptions of this argument is unsupported and unlikely to be true. Hence, the argument is unsound.
9+10 -> 12. If we assume 9 and 10 are true, then 12 logically follows. The problem is of course the fact that there is no reason whatsoever to believe that statement 10 is true. The argument is unsound, which is putting it mildly.
Overall: This argument is about as bad as they get.
Final thoughts: This is how conspiracy theory works in terms of rhetoric and reasoning. It is a great study in the means by which a demagogue (or a wannabe demagogue) makes accusations without taking responsibility for them.
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.
 “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.
 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.
 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,”
 [The same study showed 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.
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.