Based on the passage, it can be concluded that the author and Broyles-González hold essentially the same attitude toward

Amani on October 12, 2019

Example 4 conclusion explanation for quantifiers

/Users/amanistrickland/Desktop/Screen Shot 2019-10-12 at 3.46.03 PM.png Currently going over the practicing rules for quantifiers. I understand the exception in the previous example. Therefore, a valid deduction can be found. However, the instructor was not entirely clear with how they concluded Y-Some-Z. Can you explain please?

2 Replies

Amani on October 12, 2019

Sorry, it reads.

P: X-Most-Y

C: Y-Some-Z

I am confused as to how the conclusion was achieved. However, I understand the rules and the exception.

Skylar on October 12, 2019

@AmaniElisa Happy to help! I'm unable to see your attached screenshot and I do not see the correlation between your question and Example #4 from the video lesson, so I will use your stated premises/conclusion as the question. Please let me know if this is not what you are looking for.

P: X-most-Y
P: X-most-Z
C: Y-some-Z

We know that, in order to make a valid deduction, we need to have an S->N statement and a quantifier that shares the Sufficient condition. However, we also know that there is one exception to this requirement- A valid deduction can be drawn from two most statements that have the left side in common. The resulting conclusion will be: (right side #1) - some - (right side #2) or, because some statements are reversible, (right side #2) - some - (right side #1). The given premises fit the requirements for this exception, so we can make a deduction.

If we take a step back and think about the premises, we see that at least 50.1% of X's are Y's, and at least 50.1% of X's are Z's. Since over half of X's fall into these categories, this means that there will be at least some overlap between Y's and Z's. In other words, at least some Y's will be Z's.

Ultimately though, this question is testing your knowledge of the exception to the rule. Familiarize yourself with this rule, and if you forget it, take a moment to breakdown what the premises are ultimately saying.

Does this make sense? Please let us know if you have any additional questions.