#22 - Only a minority of those who engage in political action do so out of a sense

[spikesjb]

Can you disregard the above? I no longer agree with it.

Instead, I wrote out why the the stimulus is flawed and why Answer A has a parallel flaw, both logically and in the english language. Can you tell me what you think of the below:

From an english language standpoint, here is why the stimulus is flawed and why Answer A has a parallel flaw:

The stimulus says that, of all the people who engage in political action (EPA), a minority (less than 50%) do so out of a sense of social justice (SSJ). It then, inappropriately, concludes that some people (at least one, possibly all) who have a sense of social justice (SSJ) do not engage in political action (EPA). But what if it is true that everyone with a sense of social justice engages in political action? If enough people engage in political action (for various reasons), isn’t it possible that all the people who have a sense of social justice (assuming all people who have a sense of social justice engage in political action) could still make up a minority (less than 50%) of the total people who engage in political action? Of course this is possible, which is why we cannot arrive at the conclusion in the stimulus: if all the people who have a sense of social justice engage in political action, than this number of people (let’s call it x), could still be a minority of the people who engage in political action (which we can call y). X can still be less than 50% of the people who engage in Y, making X a minority, which means that we cannot conclude that some people with a sense of social justice do not engage in political action: what if they all engage in political action, but this number of people is still less than 50% of all the people who engage in political action.

So, we are looking for an answer choice that makes an assumption about a subset of people based on a claim that, of those that pursue a certain action, only some of them come from this subset of people.

Answer A) does this.

A is: Most scholars are not motivated by a desire to win prestigious academic prizes. Thus, some of those who want to win prestigious academic prizes are not scholars.

The first sentence from A can be translated to: of all the people who are scholars, most (greater than 50%) of them are not motivated by a desire to win prestigious academic prizes. The second sentence then says that among all of those who want to win prestigious academic prizes, some of them are not scholars. However, what if all the people who want to win academic prizes are scholars, but it just so happens that these scholars who are motivated to win academic prizes are a minority group within the total set of all scholars? So, this flaw parallels the one in the stimulus, because it fails to rule out the contradictory possibility that a minority subset (the number of scholars who are motivated by winning prestigious academic prizes) could still be the entirety of people who pursue a certain action (those that are motivated by prestigious academic prizes).

From a logical standpoint, here is why the stimulus is flawed and why Answer A has a parallel flaw:

The reason why the stimulus is flawed is that it is an incorrect reversal of a SOME conditional statement.

A SOME → B can be reversed to make B SOME → A.

The issue with the stimulus is that it does this:

It starts with A SOME → B, but then makes the mistake of saying B SOME → -A.

That's an incorrect reversal of a some statement. It reverses A and B, but negates the necessary clause.

Answer A does the same thing.

It says: most scholars are not motivated by the desire to win prestigious academic prizes. You cannot reverse this statement, but you can rewrite it as: some scholars are motivated by the desire to win prestigious academic prizes, or S SOME → MDW (motivated by desire to win).

This could be reversed as: MDW SOME → S.

But, the second sentence of answer A, which is the conclusion, says that some of those who want to win prestigious academic prizes are not scholars, or MDW SOME → -S.

This is an incorrect reversal of a some statement, because it reverses MDW and S, but negates the necessary clause.

[Robert Carroll]

spike,

Everything up to "From a logical standpoint" is perfect (and, as an aside, that's almost the title of a book by WVO Quine...).

Beyond that point, I have a few quibbles, but largely you're on the right track! I just want to be precise so that you can be precise when it makes a difference, although here, your analysis is good to prove answer choice (A).

First, "some" statements aren't conditionals. We diagram them with a double-sided arrow because there are perfectly reversible statements, and conditionals aren't. A conditional is a specific kind of statement, and "some" statements aren't the same. So I'd avoid that wording.

"Some" statements can be reversed, as you point out. But only reversed - if we change them by negating on one or both sides, we've making a mistake. You're right about that!

Because "some" statements aren't conditionals, there is no "necessary" clause to them at all. They have no order, so no order is privileged as the correct one, nor is either necessary because of the other, unlike in a conditional.

It says: most scholars are not motivated by the desire to win prestigious academic prizes. You cannot reverse this statement, but you can rewrite it as: some scholars are motivated by the desire to win prestigious academic prizes, or S SOME → MDW (motivated by desire to win).

When you say "you can rewrite it as", that's not correct. A "some" statement is not equivalent to a "most" statement. I'll use examples to illustrate.

Let's say I claim the following: "Most books on my shelf were published in Indianapolis." That entails that at least some of the books on my shelf were published in Indianapolis. It does not entail that some of the books on my shelf were not published in Indianapolis, though. If I have 20 books on my shelf, all of which were published in Indianapolis, it's still true to say that "most books on my shelf were published in Indianapolis." We at PowerScore usually recite the mantra "most can include all" at this point. Even that first entailment, while true, doesn't mean equivalence - the "most" entails the "some", but not vice versa, so they aren't equivalent expressions. As I said, the second attempted entailment isn't true at all.

I think you wanted to make answer choice (A) similar to what you thought the stimulus said. Answer choice (A) takes the the elements of the "most" statement, negates each one, and makes that into a "some" statement. The stimulus does the same. Remember, the first sentence is saying "most who engage in political action do not do so out of a sense of social justice", or:

engage in political action sense of social justice

The conclusion:

sense of social justice engage in political action

Both were negated, not just one clause. I think you forgot that "only a minority of A is B" means "Most A are not-B". The original statement in the first sentence isn't directly the "most" statement; I have to convert it, and in doing so, make the right-hand clause negative. So the conclusion doesn't just add a negative to one clause - it negates both.

Robert Carroll

[spikesjb]

Hi Robert,

Thank you for this--this clears a lot up, especially the bit about how a some statement isn't actually a conditional.

Also-->huge fan of Quine here, from the time I spent in college as a philosophy major. Thanks for pointing out that easter egg!

Spikes

[nivernova]

Hey there bricbas, thanks for the question! I might actually attack this question with "most" rather than some, and a negation. I think your second set of diagrams is closer to what the argument said than the first go around, so great job working through that!

Here's how I might approach this from a diagrammatic standpoint:

Premise: PA (political action) --Most--> SJ (Social Justice) (in other words, among those that engage in political action, most do not do it for social justice)

Conclusion: SJ --some--> PA

This almost looks like a contrapositive, but it isn't, thanks to the some/most issue.

Throw some numbers at it to help illustrate the problem.

People who engage in political action: 100

People who do so out of a sense of social justice: 49 (a minority, although a large one)

Now, how many people have a sense a social justice? Does this stimulus give us any way to determine that, once we have gotten here? It assumes (without justification) that there must be at least one more - a 50th social justice warrior out there - who does not engage in political action. What if that is not true? What if the total number of people who have a sense of social justice is 49, and all of them engage in political action? They are still outnumbered, a minority, within that group of 100 politically active folks, but they are all in there. The other 51 have other reasons for being there, that's all.

Answer A does the same thing, and you can apply the same numbers:

# of scholars: 100

# who are motivated by prizes: 49

How many people have such motivation? The author assumes at least a 50th prize seeker out there, a non-scholar who wants prizes. What if there's just those 49?

Now, I'll confess that I don't typically approach these types of questions with diagrams. My approach, when I see "some" or "most" or "not all", is usually to throw numbers at the categories to see what sticks and what doesn't, like I did here. I usually keep them simple - 100, 10, etc. While I do love conditional diagrams, I have never gotten fully comfortable with using them for formal logic, although I know they can be a fantastic tool if you do get used to using them. We have some modules on how to do that, including a chapter in the Logical Reasoning Bible, that could help you with that better than I could.

See if my "throwing numbers" approach works for you as a supplement to using diagrams. I hope it helps!

Why can't the premise in the stimulus be reduced to "social justice --M-> NOT engage"?

The word "only" means necessity, so I don't get your formula

Please help!!!

[Luke Haqq]

Hi nivernova!

You ask,

Why can't the premise in the stimulus be reduced to "social justice --M-> NOT engage"?

In the conditional reasoning you provide, the diagram looks like what would be the contrapositive of the way Adam diagrammed the premise (it looks like a contrapositive because yours flips the variables around and negates both). However, that process for finding the contrapositive is reliable when we just have an arrow ( ), but not when the conditional reasoning includes quantifying language like "most" ( ) or "some" ( ).

The premise in the stimulus is: "Only a minority of those who engage in political action do so out of a sense of social justice." Since the language lets us conceptualize this in terms of minority/majority and understand what one implies about the other, another way of saying that premise is: Most of those who engage in political action do so for reasons other than social justice. That most do so for reasons other than social justice is the flip side of only a minority engaging in political action for the reason of social justice. That would be diagrammed as:

Engage ~social justice

In other words, if we have people engaging in political action, then it's the case that most do so for reasons other than social justice. This is the same way that Adam diagrams the premise in the quoted explanation. I've used "Engage" for the variable to stick with the variables used in your question. This is equivalent to "PA" his diagrams, both being shorthand for "engage in political action."