Critical Thinking: Relevance Relevance-Related Logical Fallacies, and Sufficiency

Last week we revisited premise acceptability and looked at rules of thumb for acceptance, rejection, or “questionable” status.   This week we’re going to continue our happy reinvestigation of foundational principles by reexamining premise relevance and sufficiency.  Recall from previous discussions that relevance and sufficiency are measures of logical force; that is, the degree to which a conclusion follows from premises.  In other words, premises have strong logical force if they force us to accept the conclusion (and the opposite is true of weak premises).  Also, lets remind ourselves that when we evaluate logical force (relevance and sufficiency) we assume the premises to be true–regardless of if they are or not

One more time with the definitions to be clear:  Premise acceptability is our assessment of the truth value or reasonableness of a premise.  Logical force (made up of relevance and sufficiency) is a measure of how strongly the premises (either individually or in conjunction) force us to accept a conclusion. 

A deductive argument’s premises are all relevant and sufficient.  An inductive argument has premises that are relevant but not 100% sufficient.

Note:  The book uses the term “inductive validity” to indicate an inductive argument that has strong logical force. For this course (and everyone else in the philosophy department) doesn’t use this term because it causes confusion with actual validity.  

In logic, the only arguments that are valid are deductive. So, in line with the UNLV philosophy department and conventional formal definitions, we will reserve the term “valid” for deductive arguments only.  

If in your evaluation of an argument you come across an inductive argument that is has very strong logical force, say it has “strong logical force” but do not say it is valid.

Premise Relevance
When we first encountered premise relevance, we understood it as something like whether the premises and the conclusion are talking about the same thing.  This is a good starting point, but we’re going to modify this approach because sometimes a premise can be about the same topic as the conclusion but fail to be relevant.  

Premise relevance increases or decreases the likelihood that a conclusion is true.  For example, suppose I want to prove that (MC) a certain animal ‘x’ is a duck.  I give the following premises 

P1.  The animal waddles.
P2.  The animal quacks.
P3.  The animal has a stomach.
P4.  The animal has a reality TV show and is a primate. 

Notice that P1 increases the likelihood that (MC) the animal is a duck.  Same goes for P2.  P3 is neutral.  And P4 actually decreases the likelihood of the conclusion being true.   It increases the probability of another conclusion: that the animal is a cast member of Duck Dynasty.  Premises that swing the probability against the main conclusion can be used as premises in a counter-argument. 

A note on extended arguments:  The argument we just looked at is a simple argument because no premise requires further support.  In the case of extended arguments some premises require further support.  In these cases, the sub-premises will be relevant to the sub-conclusion they support but not directly relevant to the main conclusion.  In your evaluation you should indicate this. 

Summary and Key Points:  
(1) When we evaluate for premise relevance we are looking at whether the information in a premise increases or decreases the likelihood of a conclusion being true. 
(2)  When we evaluate for relevance we assume the premises are all true–even if they aren’t. 
(3)  When we evaluate for relevance we evaluate each premise individually.  It’s possible that some premises will be relevant while others might not be.

Informal Logical Fallacies Associated with Relevance (i.e. Failures of Relevance)

Ad hominem (against the person): When a claim is rejected or judged to be false based on an alleged character flaw of the person making the claim. A second form occurs whenever someone’s statement or reasoning is attacked by way of a stereotype, such as a racial, sexual, or religious stereotype. A third form involves the use of circumstances of a person’s life to reject his claims. Exception: denying someone’s claim by calling them a liar and they have a reputation for being one. 

Why should I believe what he says about our economy? He’s not even a citizen! 

You can’t accept her advice. She is so old she has no idea what goes on in today’s world. 

Why would you listen to him? He’s too young to have any wisdom about life. 
Type 3: Of course Senator X thinks my administration’s tax proposals are bad for the country. After all, his political party lost the last election, and everyone knows that losers are jealous. 
You don’t want cars to get better gas milage because you are a self-centered rich bastard who isn’t affected by gas prices. All you care about it how big your engine is. 
Of course you think that people should take drugs. You work for a pharmaceutical company and you make more money if more people take drugs. 
Notice in all cases, the issue is not being addressed by bringing up reasons for or against the position, rather it is the person or their circumstances that is being criticized. 
Poisoning the Well: Pre-emptive ad hominem to discredit the opponent before they make their point. 

Eg.  “Only an ignoramus would disagree with fluoridating water.” 
Tu Quoque: Another variety of ad hominem fallacy in which one person attempts to avoid the issue at hand by claiming the other person is a hypocrite. 

You’re always telling us to do our homework and study but you never did your homework when you were an undergrad. 
Many Arab countries put house their prisoners in inhumane conditions. Who are they to lecture us about our prison practices? 
Argumentum Ad Populum/Bandwagon Effect: 
Ad Populum: Appeal to the people
This fallacy is committed when the arguer appeals to popular opinion to support their claim.
Eg. (Historically) Everybody agrees that group x shouldn’t have equal rights, therefore they shouldn’t have them.
Eg. Most people agree that vitamin C cures the common cold.  Therefore, you should take it.
Eg. Most people agree that Hondas are better than Fords. 

Bandwagon Effect (variation of argument from popularity)

Often used in advertising through images of beautiful/happy people using a product…”you can be like us too!”

Appeal to Emotions: When the arguer tries to elicit feelings of pity, outrage, compassion, pride, nationalism, etc…instead of providing reasons for or against a position.

The new PowerTangerine computer gives you the power you need. If you buy one, people will envy your power. They will look up to you and wish they were just like you. You will know the true joy of power. TangerinePower.

The new UltraSkinny diet will make you feel great. No longer be troubled by your weight. Enjoy the admiring stares of the opposite sex. Revel in your new freedom from fat. You will know true happiness if you try our diet!

Charities use this a lot in their advertising.

Give Bob a lighter sentence because he’s an orphan that grew up in hardship.  Have a heart!
Debatable cases: when human emotions are an important factor in the issue. 

Appeal to Force:  When the arguer essentially presents a threat of force instead of a reason for accepting a position.

If you don’t get rid of your chemical weapons we will bomb you.

Missing the point (non-sequitur): Generic catch all for arguments where the conclusion doesn’t follow from the premises and the premises seem to suggest a different conclusion should be drawn.

Professor Brown is a really hard grader. Not only does he force you to attend class, participate in discussion, and do homework. He actually expects us to think about the material outside of class. So, you can believe that his class teaches students nothing about real life.

Ami likes cheese, ice cream, and yogurt.  He should eat more vegetables.
Appeal to (Unqualified) Authority (Arugmentum Ad Verecundiam—Arg. from reverence or respect):

Celebrity endorsements: Jenny McCarthy on vaccines, Oprah on psychology and medicine. 
Sufficiency is the measure of whether there is enough evidence to guarantee the truth of the conclusion (or at least make it very likely).  When an argument’s premises are all relevant and 100% sufficient, the argument is deductive.  When an argument’s premises are relevant but do not 100% guarantee the conclusion, the argument is inductive (and invalid).  Being able to make this distinction is one reason why evaluating sufficiency is important. 

A few more comments:  in an argument it’s possible (but very rare) for a single premise to be sufficient to guarantee the conclusion.  Eg:
P1.  Bob and Joe are humans
C.   Bob is a human.

Or an argument may require several premises working together to be sufficient for the conclusion: 

P1.  If the Canucks win the Stanley Cup, I will be happy.
P2.  The Canucks won the Stanley Cup.
C.    I am happy.

Notice in this argument that P1 and P2 on their own don’t do much to guarantee the truth of the conclusion, but working together, the conclusion is guaranteed;  i.e., together they are sufficient.  When you make an analysis of sufficiency, you should point out whether it is a cluster of premises that are sufficient for the conclusion or whether it is a single premise.  However, at this point in the course, you can probably bet that you won’t be seeing too many single premise arguments and if you do, it means there’s a hidden second premise…

Evaluations of sufficiency will take into account all the premises for the argument.  In some arguments single premises will be sufficient for the conclusion whereas in other arguments, sufficiency will be achieved through several premises working together.  In your analysis you don’t need to say of each premise why it on its own isn’t sufficient.  But when premises are obviously meant to work together, you should evaluate their sufficiency collectively

Some Heuristics
Because it’s not always straight forward to determine whether a premise or set of premises are sufficient, here are a couple of general rules we can apply in our analysis:

1.  How strongly worded or broad is the conclusion? 
One thing we might look at is how strongly stated or broad the conclusion is.  Suppose someone wants to conclude that “all men are evil.”  This is a very strong/broad claim.  The arguer will have to provide enough evidence to show that every man on earth is “evil” (lets ignore the vagueness problem for now).  That’s going to require quite a bit of compelling empirical evidence.  

Now suppose this person argues for their conclusion based on personal experience.  “All my boyfriends were mean to me” or something like that.  This is insufficient evidence to support the broad and strongly worded claim that all men are evil for several obvious reasons, one of which is that the arguer hasn’t encountered all men (we can make that reasonable assumption, anyway). 

To simplify this rule we can interpret it this way:  universal claims in the conclusion should set off alarm bells in your head, as should strong (emotional) language.  Also, the strength of evidence should be in proportion to the strength of the claim being made.  We can call this the proportionality principle.  Or to quote Carl Sagan paraphrasing Hume:  extra-ordinary claims require extra-ordinary evidence

Heuristic:  Words like “all”,”every”, “most”, “none”, “never” should set off alarm bells when evaluating sufficiency. 

2.  Don’t Jump to Conclusions
 This rule is closely related to the previous one.  It’s basically a close relative of the proportionality rule (strongly worded/broad claims require a lot of evidence).  If you have a small sample of evidence pointing to a particular conclusion, don’t prematurely jump to that conclusion.  Recognize that results from a small sample size can easily be over-turned by a large sample.   In other words, when stating a conclusion based on initial evidence, temper the language of the conclusion.   

For example, you grew up in a forest and want to argue that all birds can fly.  Your evidence for your claim is that every bird you’ve ever seen can fly.  Of course you haven’t yet seen the humble chicken or majestic turkey or know of their existence.  But as an intelligent forest-dweller you know that the world extends beyond the forest so you should opt for a more reasonable claim in proportion to your evidence: “every bird in the forest can fly.”  Or you might qualify your claim and make a weaker universal claim:  “It’s likely that every bird can fly.”

Using qualifying language is the mark of a careful thinker.  Even more so when it is used to bring a conclusion in line with the amount of current available evidence.

Heuristic:  Words like “up to x%” “some” “a few” should set off sufficiency alarm bells.

3.  Ensure The Arguer Isn’t Engaging in Distortion or Omission
If an argument only presents positive evidence/reasons and doesn’t at least acknowledge (reasonable) competing evidence/reasons, then we have reason to be skeptical of the sufficiency of the premises.  

Suppose a boy wants to argue that “all girls are mean” because all the girls in his class tease him.  His evidence is that each girl in his class teased him at some point.  However, he’s missing the following evidence:  his teacher, mother, and sister are all girls and they are nice to him.  Also, sometimes little Susie shares her lunch every week with the boy, even though she teased him only once.  As we investigate, we find that sometimes girls are nice to the little boy.  Not only that, but sometimes girls that the little boy never met in his life are always nice and never tease any of their classmates in other schools and classrooms.  All this evidence is missing and undercuts the strength of the conclusion.  

So, if we were evaluating the little boy’s argument for sufficiency we’d say there is insufficient evidence for his conclusion because he hasn’t considered contravening evidence. 

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