Some statisticians claim that the surest way to increase the overall correctness of the total set of one’s beliefs is: never change that set, except by rejecting a belief when given adequate evidence against it. However, if this were the only rule one followed, then whenever one were presented with any kind of evidence, one would have to either reject some of one’s beliefs or else leave one’s beliefs unchanged. But then, over time, one could only have fewer and fewer beliefs. Since we need many beliefs in order to survive, the statisticians’ claim must be mistaken.

Summarize Argument
The author concludes that it is not correct to believe that the surest way to increase the overall correctness of a set of one’s beliefs is to never change the set, except by rejecting a belief when given adequate evidence against it. This is based on the author’s assertion that, if one were to follow that approach, then over time, one would have fewer and fewer beliefs. But, we need many beliefs in order to survive. (The implication is that following the approach described would threaten our ability to survive.)

Identify and Describe Flaw
The author’s premises establish that following the approach described threatens our ability to survive. But that doesn’t show that the approach isn’t the surest way to increase the overall correctness of one’s set of beliefs. Why can’t the surest way to increase overall correctness also threaten our survival?

A
presumes, without providing any justification, that the surest way of increasing the overall correctness of the total set of one’s beliefs must not hinder one’s ability to survive
The author assumes that the fact the approach described hurts our ability to survive shows that it’s not the surest way to increase overall correctness. (A) captures the author’s assumed connection between hurting survival and the surest way to increase overall correctness.
B
neglects the possibility that even while following the statisticians’ rule, one might also accept new beliefs when presented with some kinds of evidence
The statisticians’ rule does not allow for accepting new beliefs. So the author doesn’t overlook this possibility.
C
overlooks the possibility that some large sets of beliefs are more correct overall than are some small sets of beliefs
The author never takes a position on whether larger sets of beliefs are more or less correct than smaller sets. The possibility in (C), if true, would not undermine the author’s reasoning.
D
takes for granted that one should accept some beliefs related to survival even when given adequate evidence against them
The author never takes a position on what one “should” do. The argument is simply about whether a particular approach is the surest way to increasing overall correctness of beliefs. What one should believe or not believe doesn’t affect the reasoning.
E
takes for granted that the beliefs we need in order to have many beliefs must all be correct beliefs
The argument concerns the overall correctness of a set of beliefs and the need for many beliefs to survive. Perhaps some beliefs can be false within a set of many beliefs; this doesn’t undermine the reasoning.

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On the basis of the available evidence, Antarctica has generally been thought to have been covered by ice for at least the past 14 million years. Recently, however, three-million-year-old fossils of a kind previously found only in ocean-floor sediments were discovered under the ice sheet covering central Antarctica. About three million years ago, therefore, the Antarctic ice sheet must temporarily have melted. After all, either severe climatic warming or volcanic activity in Antarctica’s mountains could have melted the ice sheet, thus raising sea levels and submerging the continent.

Summarize Argument: Phenomenon-Hypothesis
The author hypothesizes that about 3 million years ago, the Antarctic ice sheet must temporarily have melted. This is based on the fact that we recently discovered 3-million-year-old fossils under the ice sheet of Antarctica. These fossils are of a kind that have only been found in ocean-floor sediments. In addition, severe climatic warming or volcanic activity in Antarctica’s mountains could have melted the ice sheet, which would have produced liquid water that submerged the area.

Identify and Describe Flaw
The author assumes there’s no way for the fossils to be found under the ice sheet unless the ice sheet was melted. This overlooks other explanations for the presence of the fossils. Perhaps, for example, the floor has shifted underneath the ice sheet, which allowed the fossils to move underneath when they were originally not underneath the ice sheet.

A
That a given position is widely believed to be true is taken to show that the position in question must, in fact, be true.
The author’s conclusion that the ice sheet must have melted is not based on the idea that this view is widely believed to be true. We don’t know whether other people besides the author believe the ice sheet melted.
B
That either of two things could independently have produced a given effect is taken to show that those two things could not have operated in conjunction to produce that effect.
The author does not assume that the melting of the ice sheet could not have been produced by a combination of climatic warming and volcanic activity. The author presents those two things as potential causes for the melting, but never suggests they were mutually exclusive.
C
Establishing that a certain event occurred is confused with having established the cause of that event.
The author’s conclusion is that a certain event occurred — the ice sheet melted. The flaw relates to the author’s failure to prove that this event happened. The author did not establish this event occurred, and does not try to reach a conclusion about the cause of this event.
D
A claim that has a very general application is based entirely on evidence from a narrowly restricted range of cases.
The claim that the ice sheet must have temporarily melted does not have “general application.” It is a claim about a particular ice sheet and that it must have melted around 3 million years ago. This does not apply to other ice sheets or other time periods.
E
An inconsistency that, as presented, has more than one possible resolution is treated as though only one resolution is possible.
The inconsistency is that we found 3-million-year-old fossils under the ice sheet, even though this kind of fossil has previously been found only in the ocean floor. The author thinks this must be because the ice sheet melted. This overlooks other explanations.

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