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

[bricbas]

Hey, I understand why there is a flaw in this question but I'm having trouble reiterating the flaw back to myself. Is there a formal name for this kind of flaw or is it rare. The first time through I tried diagramming it like this.

Social Justice --some--> politically active

therefore,

Social justice --some--> not politically active

Upon reviewing it I was surprised there was a flaw because It seemed that it was sound but I realized that it wasn't taking into account the fact that everyone who has a sense of social justice is politically active but that's not what I diagrammed. I must have messed up something. should it be the other way around?

Politically active --some--> Social Justice

Therefore,

Politically active --some--> not social justice

If this is the case I think it would be some sort of mistaken negation... I'm not sure help me out. What is the best way to approach this question. And what is the formal name for this sort of logical fallacy?

[Adam Tyson]

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!

[biskam]

I'm struggling to understand the following part: 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.

If there are less than half of people who have a sense of social justice, what's the impact?

Tried to write it out to understand but I still don't (I fail at the end):
1st statement is that most who engage in political action do not do so out of a sense of social justice. 2nd statement is that some who have a sense of social justice do not engage in political action. This is a flaw because you can't work backwards from a most statement, there's no contrapositive. The population of the first statement is 51%. those who do engage out of a sense of social justice is 49%. but do we know anything about the population of people overall who have a sense of social justice? No. the author assumes that population is at least 50%, meaning there's at least one person who has a sense of social justice that does not engage in political action. But what if there isn't? What if the population of people overall who has a sense of social justice is 49% or 20%? Then the argument fails. then...

Can someone please help me to make the connection?

[nicholaspavic]

Tried to write it out to understand but I still don't (I fail at the end):
1st statement is that most who engage in political action do not do so out of a sense of social justice. 2nd statement is that some who have a sense of social justice do not engage in political action. This is a flaw because you can't work backwards from a most statement, there's no contrapositive. The population of the first statement is 51%. those who do engage out of a sense of social justice is 49%. but do we know anything about the population of people overall who have a sense of social justice? No. the author assumes that population is at least 50%, meaning there's at least one person who has a sense of social justice that does not engage in political action. But what if there isn't? What if the population of people overall who has a sense of social justice is 49% or 20%? Then the argument fails. then...

Can someone please help me to make the connection?

Hi Biskam,
Just a reminder for you and others that we have a virtual module and analysis on formal logic in the Lesson 8 Lesson and Homework Supplements in the Online Student Center. And you are correct that "most" statements do not readily convert to conditional logic.

Here, Adam was using those numbers to illustrate the point that when we talk about a "minority," we may have 49% who are concerned with social justice and 51% who may not care about social justice. The author's second statement is assuming that there is at least 50% who are concerned with social justice because of his "some" statement in the second sentence. It appears that you understand that some may be only 1 person in certain circumstances. But where is that 1 coming from? And is the author justified in making that assumption? Without a statement that "most" or a "majority" of people are concerned with social justice, this turns into a numbers and percentages flaw. We don't know if a majority of people are concerned with social justice, so we cannot say if there are actually some (i.e. at least 1) who is worried about social justice but NOT taking political action. Thus Answer (A) mimics the flaw and is the correct choice.

Thanks for the great question and I hope this helps!

[lilmissunshine]

Hello,

I'm having trouble understanding the "49", "51" part... But (A) makes sense to me, since the diagrams of (A) are most similar to those of the stimulus.

Stimulus: Political Action NOT Social Justice
Social Justice NOT Political Action

(A): Scholar NOT Motivated by prize
Motivated by prize NOT Scholars

However, my original diagram for the stimulus was:
Political Action (minority) Social Justice
Social Justice NOT Political Action

So I wanted to ask why we had to change the "minority" diagram into "most". It'd very helpful if you could explain that for me! Thanks a lot!

[Alex Bodaken]

lilmissunshine,

Thanks for the question! Let me see if I can help.

First of all, I don't read what Adam says above as needing to change the "minority" into "most" - he diagrams it the way it makes the most (no pun intended!) sense to him, but that doesn't mean that everyone needs to diagram it that way. If your diagram, using the exact language from the stimulus and answer choices, makes more sense to you, you should use that and not think twice about it (and on a side note, your diagramming makes sense to me as well).

The only thing I would add is that, if you have time, to be able to work out why the flaw is a flaw can be helpful. That is to say, taking the time to do the conceptual thinking that Adam does in his answer can be helpful. I get that the "49" vs. "51" issue is challenging...but in truth, the numbers are irrelevant. There could be 1, 2, or 49 people out of 100 who engage in political action out of a sense of social justice, but the relevant flaw is that this fact alone says nothing about whether there are others who don't engage in political action who have social justice - that is the only thing that would prove the conclusion. Understanding that can make it a bit easier to attack and find the parallel flaw if the diagramming is difficult (although in this case you nailed the diagramming).

Hope that helps!
Alex

[lilmissunshine]

Thank you very much Alex! Sometimes I prefer to draw a different kind of diagrams and it makes more sense to me, as it explains the numbers more visually. Would you recommend this method (see the attached)?

[Adam Tyson]

What you've drawn is what's known as a Venn Diagram, lilmiss, and we tend not to use those in our explanations because they often lead to bad inferences. Here, for example, your diagram suggests that there is only a small overlap in the two groups. But what if there is a complete overlap? What if the circle that indicates "sense of social justice" was entirely inside the circle that represents "political action"? As long as the social justice circle represents less than half of the political action circle, that would be consistent with the stimulus (a minority of PA are SJ), but would be inconsistent with the author's conclusion (there need not be even one SJ outside the PA circle). The flaw is assuming that the SJ group has some portion that is outside the PA group! Where is the evidence for that?

If Venn diagrams help you, go ahead and use them, but always bear in mind that the circles can intersect, or not, in many different ways. Maybe there is some overlap, maybe none, maybe completely. Be sure that you follow the evidence in the stimulus and that you don't make any unwarranted assumptions of your own!

[lilmissunshine]

Hi Adam,

Thank you for your explanation. But that's exactly why I used dashed lines instead of solid lines for Social Justice, because there might not be any Social Justice outside Political Action. I should've explained it earlier. Sorry!

[spikesjb]

I got this question wrong initially, but upon review, I'm fairly confident I understand the flaw in the stimulus, and why answer A has a parallel flaw.

For me, the flaw with the conclusion of the stimulus argument is that it commits a mistaken reversal of the first sentence, which is the premise of the conclusion.

The premise of the conclusion is a statement about people who pursue political action: some people who pursue political action do so out of a sense of social justice, or, PPA SOME --> SSJ (Pursue Political Action SOME --> Out of a Sense of Social Justice).

The second sentence, which we know is the conclusion, and must be derived from the first sentence because it is the only premise, commits a mistaken reversal by making a statement about people with a sense of social justice (SSJ), where SSJ is the sufficient clause: SSJ SOME--> -PPA (Some people with a sense of justice (SSJ) do not pursue political action (-PPA).

As a result, we have a mistaken reversal in the conclusion of the stimulus: SSJ is a necessary clause in premise 1, but then becomes a sufficient clause in the conclusion. Therefore, we need an answer choice that has a mistaken reversal, preferably in a similar format as the stimulus.

Answer A satisfies this.

In answer A, premise 1 (which is the first sentence), makes a statement about scholars: that most scholars are not motived by a desire to win prestigious academic prizes, or, S (Scholars) MOST --> -MDWP ( not Motivated by Desire to Win Prize).

The second sentence, which is the conclusion, and must flow from the first sentence of answer A since it is the only premise, then makes a statement about people who are motivated by a desire to win academic prizes: MDWP SOME --> -S (some who are motivated to win prizes are not scholars). However, this is a mistaken reversal, because the first sentence of Answer A, which is the sole premise, makes a conditional statement where S (scholars) is the sufficient clause. The conclusion of A then makes a statement where S is the necessary clause, and MDWP (the necessary clause of premise 1) becomes a sufficient condition in the conclusion, which is impossible, because this is a mistaken reversal: we cannot use the necessary clause from a conditional statement as the sufficient clause of another statement (unless there is some third clause that allow us to do this, which is NOT the case here).

Would you agree with my line of reasoning?