Logical Reasoning

PT21 · S2 · Q21 If a mechanical aerator is installed

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If a mechanical aerator is installed in a fish pool, the water in the pool can be properly aerated.

Conclusion (therefore)

Any fish in John's fish pool will not thrive.

Evidence

Without properly aerated water, fish cannot thrive.

Intermediate Conclusion (So)

John's pool is not properly aerated.

Evidence (since)

John's poll does not have a mechanical aerator.

If a mechanical aerator is installed, the water can be properly aerated.

Evaluate

Whenever we're doing Flaw or Parallel Flaw and the argument has any conditional logic in the evidence, then we immediately suspect that the argument will commit some conditional logic flaw, i.e. use a rule in an illegal backwards or negated fashion (also known as confusing Necessary with Sufficient).

When we look at the move from the Intermediate Conclusion to the Main Conclusion, the logic seems sound:

Without proper aeration → fish can't thrive + J's pool is not properly aerated. ---------------------------------------- in J's pool, fish can't thrive

So the error must be elsewhere. What about the move from the first couple facts into the Intermediate Conclusion?

mechanical aerator → properly aerated + J's pool has no mechanical aerator ---------------------------------------- J's pool is not properly aerated

Ah, here's the problem! The author is doing an illegal negation. We were told "If mechanical aerator, then properly aerated", and the author is making it seem like . We're not allowed to make that move.

A mechanical aerator is identified as one sufficient means for proper aeration. It's not indicated as the only possible means. John might lack a mechanical aerator but have some other means of getting his pool to be properly aerated.

Goal

The structure of the argument is pretty complex, because the author pairs up a fact and a conditional to get to the Intermediate Conclusion. And then the author pairs up that Intermediate Conclusion with another conditional to get to the Main Conclusion.

But the flaw is simply that the author does an illegal negation with one of his conditionals. So we can probably start by just seeing whether each answer is committing an illegal negation. If there's more than one doing so, then we'll worry about the more complicated structure of the argument.

21.

Which one of the following arguments contains an error of reasoning that is also contained in the argument above?

Correct
If alum is added to
Why this is right
This answer has the illegal negation we were looking for, right out of the gate. We're given this rule: If alum is added, brine can replace water. Then the author reasons: Paula no add alum, so brine can't replace water The rest of the argument ends up being structurally similar, where the author then uses that erroneous intermediate conclusion to pair up with another conditional rule to derive the main conclusion. But we really didn't need to even worry about that, since this is the only answer that replicates the illegal negation flaw of the original argument.
Skill tested: Parallel Flaw · how this choice captures the argument's function is the move to repeat next time.
82% picked this
If pectin is added to
No Illegal Negation
The first two sentences may look like an illegal negation of each other, but they are just two separate conditional rules. An illegal negation means that the author provides a rule and then her reasoning involves thinking through the rule in a reversed or negated fashion. ILLEGAL NEGATION If x, then y. Since Tony is not x, he must not be y. NOT AN ILLEGAL NEGATION If x, then y. If not x, then not y. The second case is just two conditional rules. They would actually create a bi-conditional relationship between x and y. The first case is a rule followed by reasoning, by an attempted application of the rule. This answer just gives us "If P is added, jam will gel" and then gives us a second rule, "if P (or some other setting agent) is not added, jam will not gel".
2% picked this
If stored potatoes are not
No Illegal Negation
We're given a rule, "If P's aren't exposed to E, the P's won't sprout". An illegal negation would say, "Sara's P's have been exposed to E, so her potatoes will sprout."
6% picked this
If a carrot patch is
No Illegal Negation Valid Logic
We're given a rule, "If CP is covered with mulch in the fall, then C's can be left until spring". An illegal negation would sound like, "Thus, since Kevin did not cover his CP with mulch, his C's cannot be left until spring". But the conclusion is saying "Since he did cover, his C's can be left". It's a valid application of the rule.
5% picked this
If tomatoes are not stored
No Illegal Negation Valid Logic
We're given a rule, "If T's aren't stored in a dark place, their seeds may sprout." An illegal negation would sound like, "Therefore, since Maria's T's are stored in a dark place, their seeds will not sprout." But the conclusion says that Maria's T's aren't stored in a dark place, so this is an accurate application of the rule.
5% picked this

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