#9 - Since anyone who supports the new tax plan has no

[Snomen]

Correct me if I am wrong..., so here we just denying the incorrect assumption that the author made.
Incorrect assumption: E /STP TUE
The correct answer is denial D: (denial of all; some are not ) /STP /TUE
My question is, does it mean that we can make each conditional statement incorrect by denying it or only when there is a deliberate mistake in conditional?

Thank you in advance

[Rachael Wilkenfeld]

Hi snowmen,

We aren't making any of the explicit conditionals given incorrect, we are showing that an assumption that was made didn't follow from the conditionals as given. We don't want to challenge the premises or the conditional rules we have, but we want to show that a deduction that the author attempts to make didn't follow from the premises as given.

Hope that helps!

[broth99]

Hi,

So, I have read all the comments for this question, and I understand why D is correct. However, I am not sure why B, C, E aren't possibilities ignored by the argument. I'm not sure I understand what the previous comments said about opposites and such and/or why certain answer choices aren't relevant. If someone could explain, that would be very helpful.

Thanks,
Barath

[Luke Haqq]

Hi Barath!

I'd be happy to help sort through the answer choices on this one.

To begin, we're given conditional reasoning in the first sentence, "anyone who supports the new tax plan [STP] has no chance of being elected [E]," which can be rewritten as:

STP E

Its contrapositive is:

E STP

That generic form (A B) can also be rewritten as a double-not arrow:

E STP

We're also told, "anyone who truly understands economics (TUE) would not support the tax plan (STP)," or:

TUE STP

As earlier, this is the same as:

TUE STP

Or:

STP TUE

It's possible to connect these:

E STP TUE

In other words, this is saying that if one is elected, then one did not support the plan, and if one supported the plan, then one does not truly understand economics.

The author then reaches a conclusion, "only someone who truly understands economics would have any chance of being elected." This is where the flaw comes into play. We're told in the above conditional reasoning that someone supporting the new tax plan doesn't have a chance of getting elected--support for the new tax plan is sufficient to be not elected, and it's necessary not to support it to be elected. We also know that economists won't support that new tax plan, but we don't have more from the stimulus on this front. That is, we know what happens if someone supports the new tax plan (the person becomes un-electable), and also we know that if a person is elected, the person did not support the plan.

But the conclusion is ultimately too limited. There could be others besides only "someone who truly understands economics" who might also not support the tax plan. Just because understanding economics is sufficient to establish that a person won't support that new tax plan, this doesn't prevent others who are non-economists from not supporting it as well. This is what answer choice (D) conveys: it ignores the possibility that some people who "do not support the tax plan do not truly understand economics."

With that in place, it's easier to address (B), (C), and (E). Answer choice (B) states that it ignores the possibility that some people who "truly understand economics have no chance of being elected." The stimulus is making a specific argument that imposes limits: "only someone who truly understands economics would have any chance of being elected." The stimulus is concluding that the only route to being elected is by truly understanding economics (understanding economics is necessary). That doesn't mean understanding economics is sufficient--even knowing economics, a person might have an unlikable personality, for example. So the conclusion in the stimulus isn't saying that knowing economics guarantees being elected--some may know economics and still have no chance. This is why answer choice (B) doesn't correctly describe a flaw.

Similar reasoning applies to answer choice (C), which states that the argument ignores the possibility that some people who "do not support the tax plan have no chance of being elected." As the diagrams above reflect, not supporting the tax plan is necessary to be elected (E STP ). Not supporting the tax plan is necessary to being elected, but it's not sufficient on its own to guarantee election; again such a person might be unelectable because of an unlikable personality. So answer choice (C) also isn't a flaw made in the stimulus.

Finally, answer choice (E) states that the argument ignores the possibility that some people who "have no chance of being elected do not truly understand economics." This seems less related to the conclusion. The conclusion in the stimulus is about who has a chance of being elected. Thus, failing to consider aspects of those who have no chance of being elected seems unrelated to that conclusion. If such material isn't mentioned, that omission doesn't amount to being a flaw.

[pineapplelover18]

hello! I was wondering if you guys could help me find more questions alike this one (that spell out the mistake instead of "mistakes necessary for sufficient") so I can practice? I got the diagramming flaw but I struggled with the wording to find the correct AC so I would like to practice.

[Dana D]

Hi Pineapplelover,

If you have the LR Bible or other Powerscore materials, there is an entire section on necessary and sufficient flaws in the "flaw" chapter. I would start there!

[alex.r.berson@gmail.com]

Hi there,

I was curious if there's any rule of thumb to establishing double-not arrows and double arrows. This problem tripped me up a little bit because I didn't see how the elements could chain (or not chain I should say) so I was curious if there was any tips or tricks. Thanks!

[Jeff Wren]

Hi alex,

Double arrows (also known as biconditionals) occur when each term is both sufficient and necessary for the other term. The most common wording that indicates a double arrow is the phrase "if and only if." (Of course, there are also other ways to express this idea.) These biconditional phrases actually contain two separate conditional statements in one sentence. The double arrow is simply a way of showing the two different conditional statements combined into one diagram. For example, the diagram A <- > B means both "If A, then B" and "If B, then A."

Double-not arrows express the idea that two terms never occur together (it's similar to a not equal sign). For example, the diagram A <- | - > B means that A and B cannot both occur. It is shorthand for the statement, "If A, then not B" and the contrapositive "If B, then not A." The most common words that indicate a double-not arrow are absolute negative words such as "no, none, never, cannot" or a conditional statement with the word "not" in the necessary (as shown above).

The important thing to remember is that you don't need to use either the double arrow or the double-not arrow. Each is an optional shorthand that basically expresses two conditional statements in one diagram. If you prefer, it is perfectly acceptable to write out the two conditional statements separately.

The double-not arrows were previously most useful in Logic Games, especially certain grouping games that had many conditional rules and inferences, as these shortcut symbols could save time/space rather than writing out both the rule or inference and its contrapositive.

There is a good discussion on double arrows and double-not arrows in the conditional reasoning chapter of "The Logical Reasoning Bible."