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June 30th, 2008 (Permalink)
Wikipedia Watch
The fact that Wikipedia is often the only source on the web for some types of information―or, at least, the only free source―is no doubt one reason why it is so widely used. Unfortunately, it is also the source for some types of misinformation. Case in point:
A doublespeak argument is a valid argument that is not the true source of the arguer's position. A doublespeak argument may be used because the true reasoning behind a position is not popular or convincing. Such an argument is fallacious because even if the argument were defeated, the arguer's position would remain.
If a "doublespeak argument" is by definition valid, then it will be a sound argument if its premisses are true. So, the only ways to "defeat" such an argument will be to show that it has a false premiss or that it begs the question. If it has a false premiss then it isn't fallacious, because the truth-value of a premiss is not usually a matter of logic. Whether a statement is true or false is usually a question for some other science, or for history. If the argument begs the question, then it is fallacious because it begs the question and not because "the arguer's position would remain", whatever that is supposed to mean.
I've never come across the term "doublespeak argument" before. "Doublespeak" refers to certain misleading uses of language, such as euphemism and inappropriate uses of jargon. So, a "doublespeak argument", if it were anything, ought to be an argument stated in doublespeak.
Here's the first example of a "doublespeak argument" given in the entry:
A tobacco company may oppose a cigarette tax because it threatens to reduce smoking and therefore reduce their profits. The company's public argument, however, may be that smokers are poorer than the general population, so a tobacco tax unfairly burdens the poor. But the tobacco company's real concern is not the well-being of the poor, evidenced by how it already addicts said poor to a costly product that will end up killing many of them. But the "hurts the poor" argument may evoke more sympathy than the "hurts our profits" argument.
Either it's true that the average smoker is poorer than the average person or not. If so, then a tobacco tax is, indeed, likely to be regressive. This is a perfectly cogent argument, and one which may sway those who oppose regressive taxes against taxing tobacco, which is no doubt why the tobacco company would make the argument. The fact that the company has its own motives for opposing the tax is irrelevant to the cogency of the argument, and to suggest otherwise is to commit a genetic fallacy.
Here's the second example:
A person may oppose the use of condoms because of a moral belief that sex should only occur between married couples for the purpose of procreation. If, however, the target of this person's arguments are people who may already be inclined to have premarital or recreational sex or may simply not agree with such moral beliefs, the condom opponent may instead argue that condoms cannot be trusted because they are not 100 percent effective in preventing pregnancy and STDs. Yet the opponent of condom use would continue to oppose condom use even if condoms were 100 percent effective, as the opponent's concern is not rooted in preventing pregnancies or making premarital or recreational sex safe.
There's no rule in logic that says that the argument you advance for a proposition has to be the source of your own belief in that proposition. It is often more rhetorically effective to take your audience into consideration and choose an argument that is likely to persuade them, even if it wouldn't persuade you. For instance, you may advance an argument whose premisses are propositions that your audience believes, though you don't. There's nothing logically wrong with doing so, and there needn't be anything ethically wrong, either. Of course, pretending to believe in the premisses when you do not is a type of dishonesty, but to think that the dishonesty of the arguer undermines the argument is, again, to commit the genetic fallacy.
Moreover, in this example the objection to the argument seems to be that even if the argument were refuted, the arguers would not stop opposing condom use because they have additional reasons for opposing it. However, there is no rule in logic that arguers have to put all of their eggs in one basket. The fact that they have other reasons for their position does not mean that their position is wrong, or that this particular argument is not a good one.
In general, it should always be kept in mind that the validity or invalidity of arguments is an objective feature, and not dependent upon who the arguer is. Thus, whether the arguer is a dishonest hypocrite is irrelevant to the logical status of the argument. Arguments are not respecters of persons.
To Wikipedia's credit, the entry has two notes at the top: one indicating that nothing in the encyclopedia links to the article, and the other pointing out its lack of source references. Both of these notes should warn readers that the entry ought to be regarded with some suspicion. The lack of source references is probably due to a lack of sources for the concept of "doublespeak argument" outside of the head of whoever created the entry. Even though anyone can edit a Wikipedia entry, not just anyone can delete an entry: you have to be an "administrator" to do so. Since I'm not an administrator, I won't be deleting it. Besides, I want to leave it as an example of why you shouldn't rely on Wikipedia.
Source: "Doublespeak Argument", Wikipedia, 6/10/2008. Note, 10/3/2016: This article appears to have been removed.
Acknowledgment: Thanks to Mitch Nelson for pointing out this entry.
Update (7/3/2008): I see that the entry for "Doublespeak Argument" is now marked as under consideration for deletion. However, it appears that it was so listed because someone saw my discussion of it and thought that the Wikipedia article was copied from me, rather than that I was quoting it for the purpose of commentary!
Mitch Nelson, who brought the article to my attention, writes:
The Wikipedia article suggests not that a "doublespeak argument" is just one of many arguments someone has, and that "even if the argument were refuted, the arguers would not stop [holding a position] because they have additional reasons for [holding] it," but rather that the arguers are making up arguments that don't even work on themselves. They're being disingenuous or dishonest about the arguments that lead to their position, and are engaging others in futile exercises. The arguer is setting people up to tilt at windmills, while leaving their true reasonings unchallenged. In order to successfully argue with such a person, one would have to ignore all the arguments they put forth and instead somehow divine their true path to their position and challenge that instead. What's being called a "doublespeak argument" at least seems like a debate tactic that should have a name so as to be identifiable, even if it's not a logical fallacy. "Smokescreen" seems closer to describing it, but "smokescreen" isn't defined this precisely.
You're assuming that the reason why you're listening to the other person's argument―let's assume it's a woman―is that you want to get her to change her mind about something. Of course, this is one possible reason why you might pay attention to her argument, but there are other reasons, including the possibility of changing your own mind. And in order for you to change your own opinion, wouldn't it be better if she tailored her argument to your existing beliefs, using premisses that you believe?
Moreover, if you put yourself in her position and assume that she has similar motives to your own, then she wishes to change your mind. That being the case, how better to do so than to advance an argument that has a chance of convincing you, even if it is not an argument that convinced her.
In my comments above, I mentioned that this type of argument could involve dishonesty if the arguer pretends to believe the premisses or to have been convinced by the argument. However, if that's what is supposed to be wrong with it, it's not a matter of illogical but of unethical argument. I'll leave it to rhetoricians interested in debate to decide whether it's worth naming for debate purposes.
Finally, from my experience, arguing with other people in order to get them to change their minds is usually a futile endeavor. Even if you succeed, you can't read their minds and few people will admit that they changed them as a result of your arguments. It's better to argue because you want to learn something from other people's arguments, which is facilitated by their paying attention to your views and adapting their arguments to fit them. Rather than being a bad thing, a "doublespeak argument" may be doing you a favor.
June 29th, 2008 (Permalink)
Check it Out
Alan Wolfe has a lengthy article in The New Republic about the influence on economics of work in the psychology of cognitive biases. In the course of the article he reviews Dan Ariely's new book Predictably Irrational, which I've mentioned here before and am in the middle of reading. Our Book Club book, Nudge, also gets a passing mention.
Here are a few miscellaneous comments on the article:
- Wolfe suggests that the results of Ariely's experiments may be misleading:
Before we start pulping all the economics textbooks, let alone rethinking a century's worth of public policy, we ought to pay a bit more attention to the actual details of Ariely's experiments. … [One] experiment involved a fairly narrow segment of the American population: all the subjects were male, young, and students. Why them and not, say, fiftysomething housewives? … He does not tell us why he chose students, but we can guess: students are plentifully available, and securing their participation is cheap. Daniel Kahneman hoped that economic psychology could figure out what it needed to study and then develop the appropriate technologies; but in reality…it works the other way. Technique comes first in the new economics, just as it did in the old, and conclusions follow. Ariely may want us to believe that his findings are startling; his methods, however, could not be more conventional. Survey researchers have been asking the same kinds of questions for ages, and psychologists have been studying students since experimental psychology was first developed as an academic discipline.
No one should underestimate the difficulty of persuading people to participate in psychological experiments. Availability is an important consideration in such research, which is one reason why psychologists continue to probe the behaviors of students, even though it has long been recognized that relying on them introduces bias into the results. At best, what we learn about some students might tell us things about all students…. At worst, and the worst is all too common, male students at MIT or Berkeley tell us only about male students at MIT or Berkeley, and perhaps not all that much about foreign students, older students, or female students.
Ariely is obligated to remind his readers, most of whom are neither psychologists nor economists, of the problems of selection bias that follow from his over-reliance on students as subjects. But he fails to do so. In fact, he does the opposite: he generalizes from MIT classrooms to humankind as a whole, and with abandon. This might be called the technique of the Big Slip, gliding imperceptibly from a controlled and artificial experiment to breathtaking generalizations about matters that have puzzled philosophers and theologians through the ages. It makes for entertaining reading. Alas, it tells us little about the kind of creatures we are.
Rather than "the Big Slip", I prefer to call it "hasty generalization". I'm not sure how big a problem this really is, as I haven't finished reading Ariely's book yet, but it is a good point to keep in mind when reading any kind of research.
- Wolfe confuses cardinal and ordinal numbers.
- Wolfe makes the following argument against federalism:
[Federalism] was enshrined in the American system of government not to extend democracy but to protect slavery, and "state's rights" has been the rallying cry of regional elites ever since. In the real world, both direct democracy and federalism further elite control, and for one obvious reason: in any kind of democracy, representative or direct, people do not themselves rule, but choose the leaders who do. The more power those leaders have, the better able they are to deliver to the people what they want.
This appears to commit the genetic fallacy in arguing against federalism based on why it was initially instituted, and guilt by association with the reference to the "rallying cry" of "state's rights". Moreover, the notion that the way to enhance democracy is to consolidate power in the federal government reminds me of H.L. Mencken's remark that "democracy is the theory that the common people know what they want, and deserve to get it good and hard."
Source: Alan Wolfe, "Hedonic Man", The New Republic, 7/9/2008
June 27th, 2008 (Permalink)
Blurb Watch: As it is in Heaven
An ad for the Swedish film "As it is in Heaven" has the blurb: "'Masterful.'-Hollywood Reporter". The only occurrence of that string of letters in the review from that publication is in the sentence: "The rest of the cast offers sterling work as a range of characters masterfully established by Pollak and his co-scriptors." (Emphasis added.) Thus, an adverb modifying "establish" becomes an adjective presumably applying to the movie itself.
The trick of turning an adverb into an adjective in an ad blurb is one I've seen before―see the previous Blurb Watches linked below. It's a quirk of English grammar that adverbs are regularly formed from adjectives by adding the suffix "ly", which makes it possible to "quote" by dropping the suffix, thus turning an adverb into an adjective. In contrast, Latin adverbs and adjectives are often formed from a stem by adding different endings, so Roman ad writers would have one less trick.
Why did the ad writer do it? The review quoted is a very favorable one, and it should have been easy to find a good blurb―for instance: "Deeply affecting…Filled with passion, humor and much sadness." Maybe the ad writer needed to keep in practice for the bad movies.
Sources:
- Ad for As it is in Heaven, Dallas Morning News, 6/27/2008
- Ray Bennett, Review of As it is in Heaven, Hollywood Reporter, 11/24/2004
Previous Blurb Watches:
- Scary Movie 4, 4/21/2006
- National Treasure: Book of Secrets, 12/28/2007
June 26th, 2008 (Permalink)
Dueling Polls
Obama holds 12-point lead over McCain, poll finds
Gallup Daily: Obama, McCain Tied at 45%
When polls get conflicting results, what can you do? How about believe the one whose results you like best, and dismiss the others? But that's confirmation bias! Try looking at other polls taken about the same time, instead.
The L.A. Times/Bloomberg (T/B) poll that shows Obama with a 12 percentage point lead over McCain was taken at the same time as two recent polls: A Gallup poll that had Obama with a 3-point lead and a Rasmussen poll showing Obama with a 6-point lead.
Two subsequent polls give similar results: the latest Gallup poll, which was the subject of the second headline above, that shows Obama and McCain tied; the other was another Rasmussen poll that has Obama with a 4 percentage point lead.
So, is it just Gallup and Rasmussen versus T/B? If you go back to just before the T/B poll was conducted, there are two polls by different pollsters: A Fox poll showing Obama with a 4-point lead and an Economist/YouGov poll giving Obama a 3-point lead.
What can we conclude from all this? If all the other polls showed Obama with a far smaller lead than the T/B poll, then the conclusion would be clear: the T/B poll would be an outlier and almost certainly wrong. For it to be correct, all the other polls taken just before, just after, and at the same time, would have to be wrong. However, there was also a Newsweek poll taken just before the T/B one which had Obama with an even greater lead of 15 points! I'm not sure what to make of this fact. One outlier is not so surprising, but two that go in the same direction is unlikely.
However, it looks as though both headlined polls are probably wrong, and that the truth is somewhere in between. Obama appears to be leading McCain, contra the current Gallup poll, but by a considerably smaller margin than indicated by either the T/B or Newsweek polls. Obama's lead over McCain in almost all of the recent polls is either statistically insignificant or just barely significant. However, except for the one Gallup poll, all of the recent polls show Obama leading, which is very unlikely to happen just by chance.
What's the moral of this story? Here are a couple:
- The importance of the margin of error (MoE) in polls is highlighted when you look at how contemporary polls can vary. Any poll can be expected to be off by as much as its MoE, and most of the polls cited above are consistent with one another when that fact is taken into consideration. Thus, no individual poll is likely to be precisely correct.
- The difference between the headlined T/B and Gallup polls is much greater than their MoEs, which means that they are inconsistent. As explained in the Resource linked below, one out of twenty polls can be expected to be off by more than the MoE. Given the frequent occurrence of political polls nowadays, especially during a presidential campaign, it shouldn't be surprising that every so often you see an outlier―of course, two similar outliers at almost the same time is surprising, as mentioned above. To spot such an outlier, compare it with concurrent polls. This again emphasizes the importance of looking at multiple polls.
Source: "2008 National General Election: McCain vs Obama", Pollster
Resource: How to Read a Poll, Fallacy Watch
Update (7/1/2008): Since the above was written, five new polls have been released―see the Source above, which has been updated to include the new polls. A new Gallup poll shows Obama with a five-point lead, and a new Rasmussen one has him ahead by six points instead of the previous four. Also, a new Economist/YouGov poll has Obama with a two-point lead. In addition, there are a couple of polls from pollsters that we haven't seen before: both a Democracy Corps poll and a Time magazine poll show Obama with a four-point lead.
All of these different polls make it highly likely that Obama has a genuine lead, though it's a single-digit lead, as opposed to the double-digit leads of the T/B and Newsweek polls, and probably a low single-digit lead. Almost none of the polls is statistically significant on its own, but the similar results reinforce one another. What was wrong with the two double-digit polls, I don't know, but it's clear now that they are outliers. Either there was some kind of systematic error involved, or coincidentally biased samples. It will be interesting to see the results of future L.A. Times/Bloomberg and Newsweek polls.
June 24th, 2008 (Permalink)
"Textbook Ambiguities"
Linguist Arnold Zwicky has an interesting post with the above title on types of ambiguity. When I first read the title, I thought that it was about ambiguities found in textbooks. However, none of the "in-the-wild" examples are from textbooks; rather, what Zwicky means by a "textbook" ambiguity is one that is "just the sort" that is found in textbooks, that is, a "textbook" ambiguity is a paradigmatic one, which is fit to be a textbook example. I don't know whether Zwicky intended his title to be ambiguous, but I thought it amusing that a post on ambiguity should have an ambiguous title.
Zwicky's post is slightly linguistically technical, so here are some terminological notes and comments on the article:
- "Lexical ambiguity": the kind that occurs in the fallacy of equivocation.
- "Syntactic ambiguity": also known as "amphiboly", which underlies the fallacy of the same name.
- A number of the examples are scope ambiguities―the source of scope fallacies―and Zwicky uses brackets in much the same way as I use parentheses to indicate scope.
- "Distributed reading": Wide scope.
- "Narrow reading": Narrow scope.
- The Anscombe Society example is a "textbook" example of a scope ambiguity. By the way, the Anscombe Society is named for the philosopher Elizabeth Anscombe, an important interpreter of the famous linguistic philosopher Ludwig Wittgenstein.
Source: Arnold Zwicky, "Textbook Ambiguities", Language Log, 4/4/2008
June 19th, 2008 (Permalink)
"100 Years" of Propaganda
Here we go again. The liberal group MoveOn has a new video that shows an infant boy with his mother, who says:
Hi, John McCain, this is Alex, he's my first. So far, his talents include trying any new food and chasing after our dog. That, and making my heart pound every time I look at him. So, John McCain, when you said you would stay in Iraq for 100 years, were you counting on Alex? Because if you were, you can't have him.
There's a minor factual error in this ad in that McCain never said that he "would" stay in Iraq for a century; rather, he said that the U.S. "could" end up staying there that long.
This ad is similar to the earlier DNC one―discussed in the Resource "Updates" below―in so far as it doesn't come right out and claim, falsely, that McCain is suggesting a century-long shooting war in Iraq. However, the protective reaction of the mother towards her child suggests that's what he meant.
As I said about the previous DNC ad, this contextomy has been fact-checked so many times now that MoveOn must know that the ad is misleading. Moreover, they include the "100 years" quote in context on a separate "substantiation" page, together with a second quote explaining the original remark:
We've got to get Americans off the front line, have the Iraqis as part of the strategy, take over more and more of the responsibilities. And then I don't think Americans are concerned if we're there for 100 years or 1,000 years or 10,000 years. What they care about is a sacrifice of our most precious treasure, and that's American blood. So what I'm saying is look, if Americans are there in a support role, but they're not taking casualties, that's fine. We're in Kuwait now. As you well recall, we had a war, we stayed in Kuwait. …
I assume that MoveOn expects that most people won't actually check the so-called substantiation of the ad, which does the opposite of substantiating it. This is the sort of thing that gives propaganda a bad name!
Sources:
- "Not Alex" Ad, MoveOn
- Substantiation of "Not Alex" Ad, MoveOn
- Jim Rutenberg, "Taking On McCain for a Comment on the War", New York Times, 6/19/2008
Resources:
- The "100 Years" War, 4/2/2008
- Updates, 4/30/2008
June 16th, 2008 (Permalink)
Headline
Wang hurt in Yanks' blowout win
June 12th, 2008 (Permalink)
Update
A couple of years ago, I wrote an entry about the International Astronomical Union's debate about redefining the word "planet" to exclude Pluto (see the Resource below). In the end, the IAU decided to introduce a category of "dwarf planet" that would include Pluto and a few other known solar system objects. I criticized this decision on the grounds that, as defined, the categories of "planet" and "dwarf planet" were disjoint, which goes against the usual meaning of "dwarf" and is, therefore, likely to be confusing. I argued, instead, that a new term should be introduced for the new category, such as the suggested "pluton".
Now, the IAU has introduced the new term "plutoid" instead of "pluton". While this is progress in the right direction, it is not what I had in mind. The IAU is keeping "dwarf planet" and a "plutoid" is defined as a transneptunian dwarf planet, that is, a dwarf planet whose orbit is beyond Neptune's. This means that Pluto itself is a dwarf planet, along with Eris, but excluding Ceres whose orbit is in the asteroid belt. It is expected that more plutoids may be discovered in the outer solar system, but that Ceres is the only dwarf planet within Neptune's orbit.
The new term "plutoid" has the objectionable feature that its definition makes reference to position in the solar system. How, then, is the term to be extended to dwarf planets outside the solar system? Is "plutoid" limited to objects within the solar system, or are all dwarf planets outside the solar system plutoids because their orbits are beyond Neptune's? If the former, then the only plutoids are, by definition, within our solar system, and the term is parochial. If the latter, then the only non-plutoid dwarf planet is Ceres. Why not just replace the misleading phrase "dwarf planet" with "plutoid"?
I assume that there must be some reason for this decision, but I can't see what it is, unless it's a way station on the path to replacing "dwarf planet" with "plutoid". If so, why is it necessary to make the change in stages? Perhaps it's a committee compromise that's trying to satisfy everyone, but will really make no one happy.
Source: "Plutoid chosen as name for Solar System objects like Pluto", International Astronomical Union, 6/11/2008
Resource: Headline, 8/17/2006
June 7th, 2008 (Permalink)
LSAT Logic Puzzle 4
The following puzzle is based on a type of question which, as I understand it, is no longer used on the LSAT. However, I think that it makes a puzzle that should be of special interest to Fallacy Files readers. Consider the following premisses:
All unripe fruit is inedible, and no greenhouse fruit is now ripe, but some bananas are now edible.
Which of the following statements follows validly from the above premisses? Only one statement follows logically, and each of the others commits some fallacy. For extra credit, identify the fallacies committed by the other statements:
- Some greenhouse fruit is now edible.
- Some bananas are unripe.
- All ripe fruit is edible.
- Some bananas were grown outside.
- No bananas are not now unripe.
June 4th, 2008 (Permalink)
Fallacy Files Book Club: Nudge,
Part I: Humans and Econs,
Chapter 1: Biases and Blunders
This is the chapter of Nudge in which authors Thaler and Sunstein ("T&S", for short) explain all of the cognitive biases that they advocate using to paternalistically nudge people in the right direction. They begin and end the chapter with an optical illusion: in the first section of the chapter (pp. 17-19), T&S show a highly deceptive optical illusion and, in the final section (pp. 37-39), they discuss how a different optical illusion is used to encourage drivers to slow down on a dangerous curve. So, the point of these examples seems to be that the biases they will discuss in the chapter are like optical illusions and, like such illusions, can be used to "nudge" people to do the right thing. T&S are not the first to use optical illusions as an analogy for cognitive biases. Massimo Piattelli-Palmarini uses it in his book Inevitable Illusions, and refers to biases as "cognitive illusions" throughout.
The biases that T&S discuss are the following:
- Anchoring (pp. 23-24): When you estimate some quantity, you will tend to "anchor" your estimate to some other number―even a completely unrelated number. In other words, the estimate you give will be partially determined by the anchor. For example, a charity will probably get bigger donations if they provide a check-off box for $100 rather than $10, even when those who donate choose the amount themselves instead of checking the box. The higher anchor will tend to produce higher donations.
- Availability (pp. 24-26): You tend to estimate the probabilities of types of event based on "availability", that is, how easy it is to recall or imagine such an event, which is the basis for the anecdotal fallacy. As a consequence, you will tend to overestimate the likelihood of "man bites dog" events―which are reported as news―and underestimate the probability of "dog bites man" events―which aren't reported.
- Representativeness (pp. 26-31): You tend to judge how likely it is that a thing belongs to a certain class based upon a stereotype of the class, which is thought to be the psychological source of both the conjunction fallacy and the hot hand fallacy. T&S give the example of the "Linda problem" (pp. 26-27), which itself is a kind of stereotype of the conjunction fallacy, despite the fact that it's an outdated example.
- Overconfidence (pp. 31-33): Overconfidence is the tendency to overestimate your abilities or chances. This is the "Lake Wobegon" effect, where most people are convinced that they're above average.
- Loss Aversion (pp. 33-34): People tend to be more bothered by the loss of something than they are pleased at its gain, which leads them to be willing to sell something only at approximately twice what they would pay for it.
- Status Quo Bias (pp. 34-35): Judging from the examples that T&S give, this seems to be a fancy name for laziness, that is, your tendency to accept the current situation even if it could be changed with minimal effort. T&S give the example of magazine subscriptions that automatically renew, so that effort has to be expended to cancel the subscription. As a result, more subscribers will continue to subscribe out of inertia than would renew their subscriptions if it took some effort. T&S refer to "choices" that require effort to change as "default" choices, and many of the nudges that they will recommend involve setting such defaults paternalistically.
This chapter raises a couple of additional doubts in my mind, though perhaps they will be laid to rest later in the book:
- One of the characteristics of optical illusions is their persistence, for instance, the illusion at the beginning of the chapter persists after you recognize that it is an illusion. However, I don't think that many cognitive "illusions" are like this, because they will go away when you learn to recognize them as biases. I wonder if T&S aren't again using a misleading analogy to suggest that debiasing is impossible, or perhaps they are led astray by the analogy themselves to ignore the possibility of debiasing.
- I wonder about the ethics of nudging as opposed to debiasing. The optical illusion example at the end of the chapter seems morally unobjectionable. However, some so-called psychics use optical illusions to bilk people, and other con artists take advantage of all of the biases. Is the only difference between a libertarian paternalist and a con artist that the former has your best interests in mind and the latter just wants to get your money? Isn't there something morally objectionable about treating people not as rational animals, as Aristotle defined them, but just as animals to be herded this way and that?
Source: Massimo Piattelli-Palmarini, Inevitable Illusions: How Mistakes of Reason Rule Our Minds (1994).
Previous Installment: Introduction
Next Installment:
Chapter 2: Resisting Temptation
Answers to LSAT Logic Puzzle 4:
- Invalid: existential fallacy. Since the premisses do not tell us that there is greenhouse fruit, it is possible that there is none. The only class the premisses tell us is nonempty is the class of edible bananas, but they are not greenhouse fruit.
- Invalid: "some are/some are not". Since some bananas are now edible and all edible fruit is ripe, it follows that some bananas are now ripe. However, it does not necessarily follow that some are not ripe, for it may be that all are.
- Invalid: illicit conversion. "All edible fruit is ripe" follows from the premisses, but to infer that "all ripe fruit is edible" is an invalid conversion.
- Valid. "All unripe fruit is inedible" means that all edible fruit is ripe. Given that no greenhouse fruit is now ripe it follows that no greenhouse fruit is now edible. Since some bananas are now edible it follows that some bananas are not greenhouse fruit, hence they were grown outside.
- Invalid: Negative conclusion from affirmative premisses. Eliminating the double negative, the conclusion is that no bananas are ripe. The only premisses relating bananas and ripeness are: "all edible fruit are ripe" and "some bananas are edible", which are both affirmative.