Logical Reasoning

PT148 · S3 · Q26 The older a country is

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The older a country is, the more likely it is to be ruled by a monarch.

Conclusion (Thus)

If a country is new, it is probably not ruled by a monarch.

Evidence (since)

Most countries are not ruled by monarchs.

The older a country is, the more likely it is to be ruled by a monarch.

Evaluate

Since we're seeing conditional logic (if), quantifiers (most), a volume dial (the more x, the more y), and repeating ideas (new/old, ruled by monarch), it seems like we should turn this argument into abstract algebra.

We have two premises:

P1: Most countries are not Most C's are ~M ruled by monarchs

P2: The older a country, The more O, the more likely it's the more likely M ruled by a monarch

C: If a country is new, If ~O, it's probably not ruled then prob ~M by a monarch

This argument's logic is pretty sound. Say there are 100 countries. We know at most 49 of them are ruled by monarchs.

From that claim, we could say , but we wouldn't be able to say

Why? Because the new countries might be atypical. It might be that all the new countries are ruled by monarchs, but only 30% of countries are new. If all the other countries are not ruled by monarchs, then it would be true that "most countries are not ruled by monarchs", but it wouldn't be true that .

But, the other premise removes this possibility. It's impossible for the new ones to be the ones ruled by monarchs and the older ones to be the ones not ruled by monarchs when we add the premise that .

Goal

Knowing the logical validity can sometimes help, but it's mainly important that we see the structure. If it truly stays to form, we have some signature ingredients to look for:

a "most" premise Most A's are not B

a "volume dial" premise the more X, more likely B

a "conditional" conclusion if A has less X, then probably not B.

How do they relate to each other?

The 2nd half of the "volume dial" should sound like the opposite of the 2nd half of the conclusion (more likely to be ruled by monarch vs. probably not ruled by a monarch).

The 2nd half of the "most" should sound like the 2nd half of the conclusion (not ruled by monarchs vs. probably not ruled by monarchs)

26.

The pattern of reasoning in the argument above is most similar to that in which one of the following arguments?

  1. Most novels are not made

    Bad Conclusion Match

    This does have all three types of claims we wanted: - a "most" premise - a "volume dial" premise - a "conditional" conclusion Does the 2nd half of the "volume dial" sound like the opposite of the 2nd half of the conclusion (more likely to be ruled by monarch vs. probably not ruled by a monarch)? Nope, the 2nd half of the volume dial is "more likely made into movie" and the 2nd half of the conclusion is "probably not based on novel". That's enough of a mismatch to move on. But it's also true that the 2nd half of the "most" fails to match the 2nd half of the conclusion (not ruled by monarchs vs. probably not ruled by monarchs) The 2nd half of the most is "not made into movie" and the 2nd half of the conclusion is "not based on a novel".

    12% picked this

  2. Most novels are not made

    Bad Evidence / Conclusion Match

    This does have all three types of claims we wanted: - a "most" premise - a "volume dial" premise - a "conditional" conclusion Does the 2nd half of the "volume dial" sound like the opposite of the 2nd half of the conclusion? Nope, the 2nd half of the volume dial is "more likely based on a novel" and the 2nd half of the conclusion is "probably be made into movie". That's enough of a mismatch to move on. But it's also true that the 2nd half of the "most" fails to match the 2nd half of the conclusion. The 2nd half of the most is "not made into movie" and the 2nd half of the conclusion is "probably will be made into a movie".

    7% picked this

  3. Most novels are not made

    Bad Evidence / Conclusion Match

    This was the inventory of the three types of claims we wanted: - a "most" premise - a "volume dial" premise - a "conditional" conclusion This answer choice has these claims: - a "most" premise - a "conditional" premise - a "volume dial" premise

    9% picked this

  4. Correct

    Most novels are not made

    Why this is right

    This does have all three types of claims we wanted: - a "most" premise - a "volume dial" premise - a "conditional" conclusion Does the 2nd half of the "volume dial" sound like the opposite of the 2nd half of the conclusion? Yes, the 2nd half of the volume dial is "more likely made into movie" and the 2nd half of the conclusion is "probably not be made into movie". Does the 2nd half of the "most" match the 2nd half of the conclusion? The 2nd half of the most is "not made into movie" and the 2nd half of the conclusion is "not be made into movie".

    Skill tested: Parallel · how this choice captures the argument's function is the move to repeat next time.

    66% picked this

  5. Most novels are not made

    Bad Conclusion Match

    This does have all three types of claims we wanted: - a "most" premise - a "volume dial" premise - a "conditional" conclusion Does the 2nd half of the "volume dial" sound like the opposite of the 2nd half of the conclusion? Kind of. The 2nd half of the volume dial is "less likely made into movie" and the 2nd half of the conclusion is "probably will be made into movie". Does the 2nd half of the "most" match the 2nd half of the conclusion? No. The 2nd half of the most is "not made into movie" and the 2nd half of the conclusion is "probably will be made into a movie".

    5% picked this

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