#23 - Linda says that, as a scientist, she knows that no

[Jeff Wren]

Hi maeve,

This question (and my explanation) involves formal logic. For more information on formal logic, check out chapter 13 of "The Logical Reasoning Bible."

First, let's examine the stimulus to determine what exactly the flaw in the argument is.

You correctly diagrammed the premises of the argument.

Scientists (crossed out) Appreciates Poetry
Scientists Logical

While "most" is not reversible, "most" includes the inherent inference "some," which is reversible, so we know that:

Scientists < some > Logical

We can the combine our "some" statement with our "no" statement in one diagram, placing our linking term "scientists" in the middle:

Logical < some > Scientists (crossed out) Appreciates Poetry

Using the "some train" (as described in the "The Logical Reasoning Bible), the inference that we can logically make is:

Logical < some > (crossed out) Appreciates Poetry

In plain English, this means that some logical people do not appreciate poetry.

However, the actual conclusion states that some people who appreciate poetry are illogical, which would be diagrammed:

Appreciates Poetry < some > (crossed out) Logical

Hopefully you spot the crucial difference in which term is positive and which term is negative. This conclusion is not valid based on the premises.

Answer B contains the exact flaw as the stimulus, which is why it is the correct answer.

You correctly diagrammed the premises.

Fathers (crossed out) Wants children eat candy before bedtime
Fathers Adults

From the "most " statement, we get:

Fathers < some > Adults

Rearranging the terms we get:

Adults < some > Fathers (crossed out) Wants children eat candy before bedtime

The correct inference should be:

Adults < some > (crossed out) Wants children eat candy before bedtime

In plain English, this means that some adults do not want children to eat candy before bedtime.

However, the actual conclusion states that some people who do want children to eat candy before bedtime are not adults (i.e. children), which would be diagrammed:

Wants children eat candy before bedtime < some > (crossed out) Adults

(Note that it's important to diagram "children" as "not adults" to correctly match up the terms/logic with the stimulus).

Answer A does not contain this flaw and is in fact a valid argument using the "some train."

Using

Native Australia < some > Marsupials (crossed out) Lays Eggs

We can infer:

Native Australia < some > (crossed out) Lays Eggs

which is what the conclusion of Answer A correctly states.

[bonbon94]

I think I am stuggling with diagraming the premise/answers to these types of questions. I am confused why the answer is B and not D.

How does diagramming change when most and some are apart of the same premises. Is there a trick to making the diagraming aspect easier? I thought I understand the argument, but I keep getting questions wrong when I diagram them out and I think its in part because the arrows still confuse me when using most/some. How could I better diagram these types of questions.

[Jeff Wren]

Hi bonbon,

First, as I mentioned in my post above (Post #21), if you are not familiar with formal logic, you should study those concepts before reading the explanations here because they won't necessarily make sense until you are familiar with those concepts. I recommend reading and thoroughly studying chapter 13 of "The Logical Reasoning Bible."

As for the stimulus, sentences can contain more than one formal logic statement. You simply diagram out each one. For example, the statement "Some people like ice cream and some people like pizza" would be diagrammed as two some statements. Since each statement contains the term "people" you could link these together in one diagram, such as:

LIC < some > People < some > LP

In the stimulus, the second sentence contains a premise and a conclusion, so it is very important that you separate these out when diagramming so that you can correctly follow the logic of the argument. The first half of the sentence is a premise (the word "since" is a premise indicator), and the second half of the sentence is the conclusion.

As for Answer D, the simplest explanation is that Answer D does not commit the flaw that occurs in the stimulus. In fact, Answer D is a valid argument. It correctly uses the "Most Train" to link "instant film" to "not as sharp as the best black-and-white film." Since "most" implies "some"(as discussed in "The Logic Ladder" section of chapter 13), it is valid to conclude that some instant film is not as sharp as the best black-and-white film.

As for how to diagram better, the first step is studying the rules of formal logic and making sure that you understand how to correctly diagram each type of formal logic statement and when you can and cannot make inferences by combining these statements. After memorizing these rules/steps, then it is simply a matter of practice. Formal logic, like conditional reasoning, can be difficult for many students at first, but it does get easier with proper studying/practice.