First I want to emphasize that the author of this essay (we’ll only examine the first paragraph here) has done nothing wrong. Yes, the lesson is on Logical Fallacies, but that doesn’t mean this essay is full of mistakes. The paragraph doesn’t necessarily offer the evidence to prove its argument, but neither does it draw any illegal conclusions from the evidence it does offer.
My goal in examining this paragraph is to raise your awareness of what can and cannot be proved with certain facts and claims so that you’ll be careful not to draw unwarranted conclusions in your own essays. The essay written for this class follows below. My comments are in block quotes.
Reluctance to Seek Life-Saving Mammograms
Breast cancer is the leading cancer causing death among women. It kills about 40,000 women in the United States every year. Even knowing this, women are reluctant to get mammograms for many reasons, the main reason being that they distrust the accuracy of certain statistics dealing with the results of mammograms.
This is not a logical fallacy; it’s a series of claims that don’t add up to a proof yet. 1) Breast cancer kills. 2) Women distrust mammogram accuracy. 3) Their distrust causes reluctance to be tested.
Mammograms are the best way to detect breast cancer, although they are not perfect. An estimated 28 million women have mammograms annually. 15 percent of breast cancer will go undetected, while 85 will be detected.
This is not logical fallacy; it’s a pair of statistics that don’t allow a conclusion. We can’t determine how many cancers are detected from these numbers or how many are missed.
On average 20% – 40% of cancer is missed in the first screening.
This is not logical fallacy; it’s a statistic that’s hard to reconcile with the earlier numbers. Some of the 28 million women are getting first screenings; some are being re-tested. A significant number of first screenings will miss cancer. But eventually, 85 percent will be detected.
Even though it is always better to be safe than sorry, women do not like the anticipation and anxiety that comes with getting the results of mammograms.
This is not logical fallacy; it’s a claim that hasn’t been proved yet. 28 million women, for all we know, are all the women who should be tested in any given year. Unless we know how many women would be medically advised to receive mammograms, we can’t know if 28 million is a majority or whether millions of women who should be receiving mammograms are failing to do so. More importantly, we don’t know why. Anxiety and distrust are certainly possibilities, but only possibilities.
This is especially true if the radiologist that reads that mammogram suspects that there might be something wrong. 4 to 10 percent of women’s mammogram results are found to contain some kind of abnormality.
This is not logical fallacy; it’s a recurring claim that’s beginning to sound like a conclusion. It encourages readers to believe that anxiety has been proved. The more often it does so, the closer it comes to fallacy.
These findings can lead to anything from another mammogram to a biopsy, to hopefully rule out any possibility of cancer. 80 to 95 percent of these abnormalities usually turn out not to be cancer.
Let’s do the numbers on the high side. 10 percent of 28 million mammograms (if they’re all first screenings) is 2.8 million abnormalities, 80 percent of which are not cancer, meaning 560,000 cancers detected every year, compared to 40,000 deaths per year, means that for every woman who dies from breast cancer every year, 13 women are diagnosed with cancer by mammograms and do not die. That’s a valuable statistic.
Although mammograms are not perfect, they still save 25 percent of women’s lives that are in between the ages of 50 and 69.
It’s not easy to call this fallacy because it’s not clear what we’re supposed to conclude from it, but it seems to mean that one in four women who live to be 50 will receive a life-saving mammogram. My admittedly very unscientific numbers say we prevent 520,000 cancer deaths every year with mammograms, which may be another way of saying the same thing. It’s impossible to say.
What we still don’t know is almost as important as what we do know:
1) How many women die of cancer even after positive mammograms?
2) How effective is detection at preventing cancer death?
3) How many women actually seek medical treatment after positive readings?
4) How many women suffer through false positives for every woman whose life is saved?
5) How many women who should be getting mammograms fail to do so?
6) What percentage of those women are reluctant because of fear or anxiety?
7) Is it fear of false positives or fear of true positives that makes them anxious?
ARGUMENT ANALYSIS: In no particular place does the author ask us to draw a specific conclusion that can’t be supported by the statistics. Clearly though we are meant to conclude that women who should be getting mammograms are not, and nothing in the paragraph supports that conclusion. So while the numbers could easily be used to support (but not prove) the effectiveness of mammograms in preventing cancer death, they do nothing to advance the actual thesis, that fear of the test is costing women their lives.
WHERE THE REAL FALLACIES ARE: Much of what I pretended to prove with these numbers is very, very suspect and probably contains more logical fallacies than the original article. Some percentage, probably a large percentage, of those 40,000 cancer deaths occurred to women who never got mammograms, so it’s entirely unfair to conclude we only save 520,000 lives a year. Maybe we save all 560,000 in whom cancer is detected, and the only women who die of breast cancer are those who are never diagnosed. It’s possible, and until we rule it out, claiming to have proved otherwise is a logical fallacy.
POSSIBLE APPROACH: Shannon may never have to prove that women are reluctant to get mammograms. Somewhere she’ll find a survey of women who tell the interviewers about their concerns. Even a small sample of such women prove the counterintuitive she’s identified. The more important proof is how effective mammograms are at saving lives. She hasn’t done that yet but should be able to. What she really needs is the “survival rates” for breast cancers detected early, detected late, and undetected. If early detection really does save lives, it will be easy to demonstrate the counterintuitivity of not taking a test that could prevent early death.