Applying Deductively Strong, Inductively Strong, and Weak Argument Distinctions to Real World Arguments

Now that we’ve learned the basics of logical form and strong and weak arguments, we can apply this formal approach to arguments as we often encounter them in the real world.  Our goal in this chapter is to take reasoning in arguments as it often occurs when we are talking informally, writing casually, or being imprecise, and reconstruct the argument according to the stricter, formal rules of argument that we have been learning all semester.  This process is a way of clarifying vague concepts, getting clear on the background information that we are relying on, making implicit assumptions explicit, and presenting the argument is the best, strongest form that we can.  

Through reasoning, you will recall from the first chapter, we are trying to develop a more accurate picture of the world that will facilitate our achieving our goals.  There is an important philosophical foundation here that connects the moral right to free speech to reasoning through arguments.  

Free speech and argument: Famously, John Stuart Mill, the 19th century philosopher, gave this defense of free speech, and argument that has become a cornerstone of modern political democracies.  Being able to speak your ideas freely is crucial as an of ideas between rational agents.  It’s an error correction method.  We need the free and open exchange of ideas to learn and discover the truth.  Individuals are fallible, and no authority can reliably determine the truth.  An open expression model that fosters civil disagreement does the best job at finding the truth.  We need ideas to conflict.  

Furthermore, in order to be a free, autonomous moral agent, I must discover, form, and express my own judgments.  Exposure to diverse ideas, and powerful arguments for opposing views, helps me develop my own ideas, my rational autonomy, my intellect, and my moral character.  Moral agents need to speak and listen.  

Democracies function best when citizens can freely and openly deliberate, disagree, and exchange ideas through constructive argument.  Speech, and thoughtful arguments for new ideas, even ones that seem outrageous or offensive, are necessary to prevalent tyranny and autocracy.  

The goal of arguments is not to win debates, it’s not to score embarrassing points on our opponents.  When you disagree with someone or when they have a different view of the world, that’s an opportunity for both of you to learn, to improve, to get a broader understanding.  Importantly, when I’m wrong, and we are all wrong often, encountering someone who disagrees with us with a strong argument for their conclusion is a chance for me to change my mind.  A reasonable person always proportions their belief to the quality and quantity of the evidence.  Changing my mind in the light of new evidence is a hallmark of rationality–the opposite is dogmatism.  I learn, grow, and develop a better picture of the world by changing my mind.  

Charity is the central epistemic virtue that drives this phase of the rational belief process.  My goal when I encounter an argument is to be charitable.  

To be charitable in reconstructing an argument means making it as strong as possible.  And strong has a technical account for us: arguments, we have seen, can be deductively strong or inductively strong.  So the goal in reconstructions is to make the argument deductively or inductively strong, if possible.  

Then and only then, after it has been charitably reconstructed as strong as possible, do we start the critical evaluation process.

The big picture: what we’re going to do: 

First, we’re going to apply what we’ve learned, first, about valid, cogent, and ill-formed arguments.  Then we will apply what we’ve learned about deductively strong arguments, inductively strong arguments, and weak arguments.  We are going to take people’s reasoning for conclusions as we find it in prose, conversation, debate, and other expressions, and we are reconstructing those arguments in the strongest and most charitable form we can in order to:

1. Understand their arguments

2. Consider the best reasons on both sides of an argument

3. Reflect on which positions are the most reasonable

4. Figure out what the truth is or which arguments are most reasonable and accept their conclusions.     

Our reconstruction method will ultimately allow us to be able to critically evaluate those arguments to be able to decide whether to accept their reasoning and conclusions if they are deductively strong or inductively strong.  A rational person, recall, proportions their beliefs to the quality and quantity of their evidence, and changes their mind in the light of new evidence.  Or, if the argument is weak, then we will critically evaluate it and point out where the logical structure is ill-formed or the premises aren’t reasonable.

Procedure for reconstructing arguments:

A.  Be charitable.

B.  Find the conclusion. 

C.  Find the explicit premises. 

D.  Add implicit premises or conclusions to make it strictly valid or cogent, consistent with the author’s intentions.  

E. Make charitable revisions in language to make the argument valid or cogent if possible, and as strong as possible. 

F.  Make the language between premises and the conclusion match.  If the argument has this form, for instance, "1.  If P then Q. 2. P. 3. Therefore, Q" then make P in 1. and 2. match exactly.

G.  Put argument into standard form.  Number each premise, separate the premises from the conclusion with a line.  

H.  Add justifications after every line:  [EP] explicit premise, [IP] implicit premise, [1,2, MT] follows from 1, 2, and Modus Tollens.  Our Justification Rules:  Valid and Cogent Argument Patterns  We are using MP, MT, HS, DS, UA, UN, and IS

I.  Make sub-arguments explicit.  If the larger argument is longer than 3 total lines, and has more than one inference, then make those sub-arguments explicit, separating their premises and their conclusion with a line. 

Let’s discuss each of these steps.  

A. Be charitable:  Steel manning and charity.  

Our goal, as we saw above is to reconstruct arguments we encounter in their strongest, most charitable version.  That matters and is important because it will it avoids wasting time on caricatures or trivial objections.

It improves your own grasp of the issue, since you’re forced to engage with the most compelling case.

It builds credibility: if you can rebut the strongest version, your critique carries more weight.

It makes for more productive debates, because the other side feels heard rather than distorted.

Straw man fallacy:  A classically defined fallacy in reasoning is the straw man fallacy.  This is the mistake of portraying an opponents argument in a bad light, with weakness amplifies, or misconstruing it purposefully to make it look bad.  For example, 

Smith says, "I think we should redirect some of the budget from the military into public healthcare and education."

Jones replies, "So, what you're saying is you want to leave our country completely defenseless and vulnerable to invasion because you don't care about our national security?"

We will strive to steel man arguments.  When I steel man someone’s argument I reconstruct it in such a charitable and strong way, such that the author of that argument would readily agree to how I’ve portrayed it.  In fact, we can go even further; our goal should be give a reconstruction of their argument that they would view as even better than the argument they presented.  

Then and only then, after we have steel manned the argument, do we move on to critical evaluation.  

B.  Finding Conclusions

The first step when we encounter reasoning from any source is, ironically, the reverse of what we’ve been doing so far.  We should listen to read the reasoning in its entirety, without jumping to objections or quibbles about details midway, and we should figure out the conclusion.  The first questions we should be asking are: What is the main point, the takeaway, the final result that the author wants us to believe?  

The conclusion of an argumentative piece of writing (or speech) is the claim that the author intends for you to accept on the basis of the reasoning that has been given. It is the central point, or the proposition that all of the other claims support. It is the overall thesis that the author hopes to convince you to believe. There may be many claims that the author wants you to accept, and there may be subordinate arguments with sub conclusions, but the main conclusion, for our purposes, is the final, overall, most important claim that the other assertions ultimately support. If the piece is written and argued well, the central thesis will be obvious from indicators that make it explicit, from the structure of the reasoning, or it will be implicit in the writing. It may help to ask, “which of the claims being argued for is the broadest in scope or the most general?” That will often reveal the central thesis.

Finding the conclusion in a piece of argumentative writing is where we start in our efforts to understand and then reconstruct the argument. How do we determine what the conclusion is? Generally, there are three ways:  1) look for explicit conclusion indicators.  2) look at the logical structure of the reasoning, and 3) look for implicit conclusions.  

Explicit conclusion indicators:  There are a number of explicit terms that authors will use to signify the thesis they are arguing for. Some of these terms can be obvious, such as: "therefore," "in conclusion," "it follows that," "we should draw the conclusion that," X "implies" Y, or X "because," Y, "so," or "clearly..." and so on.

“Therefore, abortion in cases of rape or incest should be allowed by law.”

“We should draw the conclusion that the defendant is innocent.”

“The defendant is innocent because he was not present at the scene of the crime.”

“The absence of the compound in the chemical assay implies that Smith did not take steroids.”

 With terms like "hence," or "thus," the conclusion comes after.  With terms like "because," and “since,” notice that the conclusion will come first and the reasons will come after: “The defendant is innocent because he was not present at the scene of the crime. " The defendant is innocent," is the conclusion, and "He was not present at the scene of the crime." 

Consider this example of a famous and historic argument:  

“It doesn’t make sense that there is a God.  If a loving, all-powerful, all knowing God exists, then there wouldn’t be pointless suffering.”

The conclusion, the belief that this author is advocating that we accept is “There is no God.”  How do we know?  First, the author says it in so many words in the first sentence.  The second sentence is a conditional, an If…then premise.  Conditionals can be the conclusion in an argument.  But a conditional doesn’t by itself show that some result is actual.  A conditional says that IF p THEN q.  This author is arguing that some state of affairs is actually true, not merely that some antecedent is conditionally connected to a conditional.  And if we construe the second sentence as the conclusion, this argument becomes very hard to understand or reconstruct charitably.  Learn to trust your innate or intuitive ability to get the overall gist of a passage; what is the big point they are making, the main point?  What is the one belief or claim that the author wants you to walk away from this argument believing? 

Revising the language of the conclusion:  We might be tempted in this example to take, “It doesn’t make sense that there is a God.” as the conclusion.  In general, we should strive to be concise, direct, and clear in our reconstructions.  If it’s wordy, trim it down.  Get to the point, use active voice; fewer words are better if they can serve the purpose.  “There is no God,” is straight to the point, and clear.  And the author’s intention is for this to be an argument about whether there’s a God, not about what does or doesn’t make sense.  

What are the other ways to find a conclusion? We can also look at the logical structure of the reasoning. We have been studying formalized arguments that have valid or cogent structures. If a passage contains claims that can be represented at “If P then Q,” and “Q,” and “P,” for instance, the obvious conclusion that could follow from what the author has said is “Q” from the premises “If P then Q,” and “P.” If we interpret the conclusion as “P,” in this case, we would be attributing an invalid, and poor argument to the author. If the author makes that sort of egregious logical mistake, and it is clear that she does in the passage, then that is her mistake and you must take her at her word. (Your first criticism of the reconstructed argument should be that it is invalid, so the conclusion does not follow from the premises even if they were true.) But if the author is being careful, and we are being charitable, attribute a valid argument to them if it is consistent with what is in the passage, all other things being equal. That is, get a sense of what the logical structure of the argument is, and that can help you identify the conclusion, if other methods fail.

Elaine isn't home. She went to class, and if she is in class, then she is not home.

The most natural way to reconstruct this argument that makes it valid is:

1. If Elaine is in class, then she is not home.

2. Elaine is in class. VALID

______________________

3. Therefore, Elaine is not home.

No other arrangement of the sentences makes it valid or cogent:

1. Elaine is not home.

2. Elaine is in class.              ILL-FORMED

______________________

3. Therefore, if Elaine is in class, then she is not home.

1. If Elaine is in class, then she is not home.

2. Elaine is not home.             ILL-FORMED

______________________

3. Therefore, Elaine is in class.

In general, we want to reconstruct an author's reasoning as charitably and as strong as we can. So we should make it valid or cogent, if one of those argument patterns conforms with the author's writing. Sometimes an author makes an error in reasoning and employs ill-formed reasoning. In those cases, we can still determine what their conclusion is, but it may not be possible to charitably reconstruct their argument in a way that makes it valid or cogent without seriously changing their intent or reasoning. See the lectures on reconstructing arguments for more details.  So our second rule for finding the conclusion is, look at the logical structure of the reasoning to see what is logically implied by a valid or cogent reconstruction.

Our third rule for finding the conclusion is: Look for an implicit conclusion. In some cases, a premise or the conclusion are clearly implied by what the author says and by the logical structure of the passage. That is, a premise isn't stated explicitly, but it is clearly needed to make the argument valid or cogent, and the author has taken it for granted that the reader will see the implication. In these cases, take what has been explicitly written and try to put into either a valid or cogent argument form, and see if there is a missing premise that, if added, would make the argument valid of cogent, and the author appears to have assumed it. Implicit conclusions work the same way. 

If you are in Calculus, then you must have passed Algebra 2. And Jacob didn't pass Algebra 2.

Here a conclusion is implied that isn't stated explicitly, but given the logical structure and what we know about Modus Tollens, we can infer:

1. If you are in Calculus, then you must have passed Algebra 2. (EP)

2. Jacob didn't pass Algebra 2. (EP)

________________________

3. Therefore, Jacob isn't in Calculus. (1, 2, MT)

Attempting to reconstruct the argument in any other order, without the implied conclusion produces an ill-formed argument that misses the point:

1. If you are in Calculus, then you must have passed Algebra 2. (EP)

_______________

2. Therefore, Jacob didn't pass Algebra 2. ILL-FORMED

Or,

1. Jacob didn't pass Algebra 2.

_______________

2. Therefore, If you are in Calculus, then you must have passed Algebra 2. ILL-FORMED

So our three guidelines for finding conclusions are:

Look for explicit conclusion indicators.

Look at the logical structure of the reasoning to see what is logically implied by a valid or cogent reconstruction.

Look for an implicit conclusion.

C.  Finding Explicit Premises

Explicit premises are premise that the author writes out or speaks that is used as evidence or a reason in the argument.  Implicit premises are reasons that the author does not write out or speak, but they rely on the audience to understand as a premise in the argument, and it is part of a valid or cogent reconstruction of the argument.  In this example: 

It doesn’t make sense that there is a God.  If a loving, all-powerful, all knowing God exists, then there wouldn’t be pointless suffering.

If a loving, all-powerful, all-knowing God exists, then there wouldn’t be pointless suffering,” is the explicit premise.  Besides the conclusion, it is the only sentence that the author has explicitly stated.  Not every sentence that an author expresses in an informal argument will make it into our revised reconstruction; there are often words, or claims that we don’t need for the formal reconstruction, or passages that don’t add substantially to the final argument.  But in this case, the second sentence, the If–then reasoning is clearly explicit and necessary.  

When a premises is explicit, we will add a justification after it as (EP)  See below for details about justifications.  

D.  Finding Implicit Premises

Sometimes premises are not explicitly stated, but the author relies on them to support the conclusion.  A charitable reconstruction will add implicit premises that are consistent with the author’s intentions and that make the argument stronger.  When we try to put this argument into standard form, something becomes clear:  

1.  If a loving, all-powerful, all-knowing God exists, then there wouldn’t be pointless suffering.  (EP)

_________________________________

2. Therefore, there is no God.

This draft of the argument is not valid, but clearly the author is implicitly relying on us to see a premise that completes the inference.  Also notice that all of our logical inference rules require at least two premises.  Premise 1 by itself is not a reason to believe the conclusion, even if it is true.  What is needed to make this argument valid?  And what is the author implicitly relying on to drive the logic of the argument?  The author has an implicit premise, a reason that is not stated outright in the original passage, but it is clearly assumed that the reader will understand it and agree with it.  When we add the implicit premise, “There is pointless suffering,” this argument comports with the author’s intentions, it’s improved, and it is closer to being valid:  

1. If a loving, all-powerful, all-knowing God exists, then there wouldn’t be pointless suffering. (EP)

2.  There is pointless suffering. (IP)

_________________________________

       3.  Therefore, there is no God.  (1,2, MT)

We will add (IP) after the premise for a justification when there’s an implicit premise.  

Here’s another example:  “The defendant is innocent because he was not present at the scene of the crime.”  If we attempt to put this argument into our standard form for reconstructed arguments as is, it would look like this:

1. The defendant was not present at the scene of the crime. (EP)

______________________________________

2. Therefore, the defendant is innocent.

This argument is not valid.  This time there is an implied conditional premise that the author is relying on, and if we add it, the argument becomes valid:  

1. The defendant was not present at the scene of the crime. (EP)

2. If the defendant was not present at the scene of the crime, then the defendant is innocent. (IP)

______________________________________

2. Therefore, the defendant is innocent. (1,2, MP)

We should add implicit premises where it is clear that the author intended the premise to be part of the reasoning, the addition makes the argument stronger, and it is a charitable revision.  When a premise is implicit, we will add (IP) after it as the justification.  See below for more details about justifications.  

E. Make charitable revisions in language 

When we reason informally, particularly when we talk, we change terms, leave out points, use pronouns, change language, and add points or language that aren’t necessary.  Our goal in a strong reconstruction is to make the reasoning as clear and specific as possible, to eliminate equivocations in language, and to remove as many ambiguities as we can.  The final reconstructed argument should favor clarity and disambiguation over style, and it should eliminate language or even whole sentences if they are not a necessary part of a valid or cogent reconstruction.

So in our reconstructions, we will get rid of extra claims, stylistic expressions, unnecessary information.  And we will make the premises clear, direct, and to the point.  In the case above, “There is no God.” is better than, “It doesn’t make sense that there is a God.”  “It stands to reason that Smith must be sick with Covid,” should simply be, “Smith has Covid.”  

In a case like this, we may have to make some substantial revisions in the language to get the argument to fit into one of our patterns:

I believe in astrology.  It works.  A lot of the time, I read my forecast and it is accurate. 

This author appears to mean that since his forecasts are accurate “a lot of the time,” then it must be accurate.  So we can adjust the language and restate the argument as conditional, modus ponens, reasoning.  

1. If a lot of the time, I read my forecast and it is accurate, then astrology works. (IP)

2. A lot of the time, I read my forecast and it is accurate.  (EP)

____________________________________________

3.  Therefore, astrology works.  (1, 2, MP)

F. Make the language between premises and the conclusion match.  

As we revise drafts of a reconstructed argument, the logical structure should become clearer.  In this case, it appears that the author is employing a modus tollens style logical inference.  We will see more complicated arguments with more logical inferences.  And we will be looking to apply our list of basic inference rules here: Valid and Cogent Argument Patterns to our reconstructions.  Our next step will be to make charitable revisions in the language between premises and conclusions to make the argument stronger, if possible.  Return to this example we’ve been reconstructing:

“It doesn’t make sense that there is a God.  If a loving, all-powerful, all knowing God exists, then there wouldn’t be pointless suffering.”

This might appear to be a good good reconstruction, but notice that in the version of this argument that we are now considering, there is shift in the language from premise 1 to the conclusion:  

1. If a loving, all-powerful, all-knowing God exists, then there wouldn’t be pointless suffering.  (EP)

2. There is pointless suffering. (IP)

_________________________________

      3.  Therefore, there is no God.  (1, 2, MT)

The God that premises 1 describes is not the same as the God in the conclusion.  Premise 1 is about a loving, all powerful, all knowing God, but the conclusion doesn’t make mention of those specific properties.  That is, the conclusion cannot strictly follow logically from the premise because they are not about the same thing.  We can make this revision, that is surely consistent with the author’s intention, to make the argument better.  

1. If a loving, all-powerful, all-knowing God exists, then there wouldn’t be pointless suffering.  (EP)

2. There is pointless suffering. (IP)

_________________________________

       3.  Therefore, there is no loving, all-powerful, all-knowing God.  (1, 2, MT)

G. Put argument into standard form.  As we have seen in arguments in the previous chapters, our goal is to have a strong argument that is in standard form.  Standard form helps us clarify and separate the premises so we know each individual claim that is being made in support of the conclusion, and it helps to make the logical structure (or lack thereof) clear.  It also makes the conclusion precise, and it separate sub-conclusions and puts them and sub-arguments into relationship with the rest of the argument.  When we put it in Standard Form, number each premise, separate the premises from the conclusion with a line.  Arguments can have more than three lines, unlike the simple examples we’ve been considering.  And arguments can have sub-conclusions and sub-inferences.  These should be separated from the premises with a line inside the larger reconstruction too.  Make all of the implicit reasoning explicit in your reconstructions.  

1. Premise 1

2.  Premise 2

……

      N.

     _______________

      N + 1.  Therefore, conclusion  

H. Add justifications after every line: 

Justifications are notations that we will add at the end of every line that indicates where we got it.  It’s a way to cite where the line came from and to cite the logical inference that it is connected to.  We have a list of legal or permissible logical inference rules that we have learned and come to trust for reasoning.  We also understand explicit premises (EP) and implicit premises (IP).  So we will use all of those abbreviations for our justifications. 

(EP) explicit premise

(IP) implicit premise

(1, 2, MT)  means that this line follows from line 1, 2, and Modus Tollens.

(1, 2, UA) means that this line follows from 1, 2, and Universal Syllogism, Affirmative.  

Vaid and Cogent Argument Patterns.  

Every line in the argument should have one of these justifications.  There should be no lines that don’t have some record or information in the justification about where they came from or why they are in the argument.  Conclusions will have numbered premises and the logical inference rule as their justification.  And since we are making all logical inferences explicit, a conclusion will have no more than two premise numbers listed, and then the inference rule.  Our inference rules are all limited to two premises.  Now we can see that we’ve gone from the original text: 

“It doesn’t make sense that there is a God.  If a loving, all-powerful, all knowing God exists, then there wouldn’t be pointless suffering.”  to a completed reconstruction:

1. If a loving, all-powerful, all-knowing God exists, then there wouldn’t be pointless suffering.  (EP)

2. There is pointless suffering. (IP)

_________________________________

       3.  Therefore, there is no loving, all-powerful, all-knowing God. (1,2, MT)

I. Making subarguments explicit

Arguments often involve more than one inference, and often there are subarguments that are part of the larger argument.  Reconstruct those subarguments, separating their premises from their conclusions within the larger argument.  Consider this example.  

Smith has either got Covid or some other respiratory infection.  If he’s got Covid, then he would test positive.  But he hasn’t.  If he’s got a respiratory infection, then he will need antibiotics.  So that’s what we need to prescribe for him.   

1. If Smith’s got Covid, then Smith would test positive.  (EP)

2. Smith did not test positive. (EP)

__________________________________

3. Therefore, Smith doesn’t have Covid. (1, 2, MT)

4. Smith has either got Covid or Smith has some other respiratory infection.  (EP)

___________________________

5. Therefore, Smith has some other respiratory infection. (3, 4, DS)

6.  If Smith has some other respiratory infection, then he will need antibiotics.  

____________________________

7. Therefore, he will need antibiotics.  (5, 6, MP)

Note that the order of premises has been rearranged from the original passage.  And note that two inferences, the modus tollens inference in line 3, and the dysjunctive syllogism inference in line 5, have been brought out and made explicit as subarguments that lead toward the overall conclusion in 7.  Also note the revisions in language that have made it match between conclusions and premises in the reconstruction.  

Here’s another example of a longer argument with subarguments.  Notice that not every sentence in the original makes it into the logical structure of the reconstructed version.  Some editing is often required to formalize in the reconstruction.  

“While it is convenient and inexpensive, fast food meals are consistently loaded with excessive sodium and saturated fats that lead to heart disease. If you want to maintain a healthy body, you have to prioritize whole foods over processed ones.  Eating fast food every day is a mistake for anyone who values their long-term health.”

1. If you want to maintain a healthy body, then you have to prioritize whole foods over processed ones.  (EP)

2. If you have to prioritize whole foods over processed ones, then eating fast food every day is a mistake.  (IP)

3. You want to maintain a healthy body.  (IP)

__________________________________

4. Therefore, you have to prioritize whole foods over processed ones.  (1, 3, MP)

______________________________________

5. Therefore, eating fast food every day is a mistake.  (2, 4, MP)

Summary:  Now we have taken these arguments in their ordinary written form and applied our method for reconstructions to them and we’ve created a clear, concise, charitable formal version of the argument.  And these reconstructed versions will satisfy the steel man test.  The authors could readily agree that this new reconstructed version captures their reasoning and it reflects their intentions in a good light.  Here, again, is the full procedure for taking an informal expression of an argument in a passage and reconstructing it according to our formal method.  

A.  Be charitable.

B.  Find the conclusion. 

C.  Find the explicit premises. 

D.  Add implicit premises or conclusions to make it strictly valid or cogent, consistent with the author’s intentions.  

E. Make charitable revisions in language to make the argument valid or cogent if possible, and as strong as possible. 

F.  Make the language between premises and the conclusion match.  If the argument has this form, for instance, "1.  If P then Q. 2. P. 3. Therefore, Q" then make P in 1. and 2. match exactly.

G.  Put argument into standard form.  Number each premise, separate the premises from the conclusion with a line.  

H.  Add justifications after every line:  [EP] explicit premise, [IP] implicit premise, [1,2, MT] follows from 1, 2, and Modus Tollens.  Our Justification Rules:  Valid and Cogent Argument Patterns  We are using MP, MT, HS, DS, UA, UN, and IS

I.  Make sub-arguments explicit.  If the larger argument is longer than 3 total lines, and has more than one inference, then make those sub-arguments explicit, separating their premises and their conclusion with a line. 

Examples:  here are some more unreconstructed arguments followed by their charitably reconstructed, formal versions:

“Kara's car is illegal to drive at night.  All cars must have fully functioning headlights in order to be legal to drive.”

1. All cars must have fully functioning headlights in order to be legal to drive. (EP)

2. Kara's car does not have fully functioning headlights. (IP)

_____________________________________

3. Therefore, Kara's car is not legal to drive.  (1,2, UN)

“Positive thinking cannot help you win the lottery.  If it could, then lots of people would win." 

1.  If positive thinking could help you win the lottery, then lots of people would win the lottery.  (EP)

2.  Lots of people do not win the lottery.  (IP)

_________________________________

3.  Therefore, positive thinking cannot help you win the lottery. (1,2, MT)

“The starter must be broken.  If the car won't start, then it's either the starter, the alternator, or the battery that's the problem.  It won't start.  And we've ruled out the alternator since we just put a new one in, and it can't be the battery because it's fully charged.”

Notice the editing to make the language match:

1.  If the car won't start, then either the starter is broken, the alternator is broken, or the battery is dead. (EP)      

2.  The car won't start. (EP)

_______________________

3.  Therefore, either the starter is broken, the alternator is broken, or the battery is dead.  (1, 2, MP)

4.  The alternator is not broken.  (IP)     

5.  The battery is not dead.  (IP)     

____________________________________________

6.  Therefore, the starter is broken.  (3, 4, 5, DS)

"If UFOs were abducting human beings from the Earth and doing experiments on them, then there would be a lot of people who claim to have been abducted.  And there are a lot of people who claim to have been abducted.  So it looks like UFOs are abducting humans from the Earth."

1.  If UFOs were abducting human beings from the Earth, then there would be a lot of people who claim to have been abducted. [EP]

2.  There are a lot of people who claim to have been abducted.  [EP]

__________________________

3.  Therefore, UFOs are abducting human beings from the Earth.  [1,2,]

Notice that as stated, and consistent with the author’s expression, this argument is invalid.  The invalid inference is affirming the consequent.

1.  If P then Q.

2. Q

______________

3.  Therefore, P

Fixing the logical error in the reasoning here is beyond what is charitable.  That is, this author has made a logical mistake and it’s their responsibility, not ours, to fix it.  The best we can do for an argument like this is to point out the logical error.