Arguments

An argument is a piece of reasoning, from premises to a conclusion

Table of Contents

  1. Arguments
  2. The Basics
    1. Argument Reconstruction
    2. Claims and Opinions vs Arguments
    3. Kinds of Arguments
    4. Argument Evaluation
    5. Ubiquity of Arguments
  3. Examples of Arguments
    1. John Oliver Argument
    2. Black Swans
    3. Editorial on Capital Punishment
    4. Declaration of Independence
  4. Kinds of Arguments
    1. Deductive Arguments
    2. Probability Arguments
      1. Reliable Process (or Reliabilist) Arguments
      2. Abductive Arguments (Inference to the Best Explanation)
    3. Normative Arguments
      1. Deontic (or Deontological) Arguments
      2. Consequence (or Consequentialist) Arguments
    4. Analogical Arguments
      1. Analogical Probability Arguments
      2. Analogical Deductive Arguments
    5. Summary of Kinds of Arguments
  5. Analysis of Arguments
    1. Formulating Arguments
    2. Evaluating Arguments
  6. Most Important Things about Arguments
  7. Addenda
    1. Awareness of Arguments
    2. Myth that Facts Speak for Themselves
    3. Ubiquity of Arguments
    4. Exercises: Do these arguments establish their conclusions?
    5. Defeasible Arguments and ‘Other Things Being Equal’
    6. Supplementary Topics
    7. Epistemic Pitfalls
    8. Formal Systems
    9. Obsolete Classification of Arguments

Arguments

An argument is a piece of reasoning, from premises to a conclusion.

The Basics

Argument Reconstruction

  • Argument Reconstruction is the process of restating a naturally-occurring (or real-life) argument so its premises, conclusion, and reasoning are clear.
  • Real-life Argument:
    • John Oliver is not eligible to be president because only natural-born U.S. citizens are eligible.
  • Reconstruction:
    • Only natural-born U.S. citizens are eligible to be president.
    • John Oliver isn’t a natural-born U.S. citizen.
    • Therefore, he’s not eligible to be president.
  • Real-life arguments are often enthymemes, partly stated arguments with unstated premises or conclusion inferred from the context.
  • View Argument Reconstruction

Claims and Opinions vs Arguments

  • Compare the statements:
    • John Oliver’s not eligible to be president.
    • John Oliver is not eligible to be president because only natural-born U.S. citizens are eligible.
  • The first makes the claim that John Oliver isn’t eligible to be president.
  • The second expresses an argument for that claim.
    • Only natural-born U.S. citizens are eligible to be president.
    • John Oliver isn’t a natural-born U.S. citizen.
    • Therefore, he’s not eligible to be president.
  • Dialectic Note:
    • When a dubious claim is made you can request an argument, since the speaker has the burden of proof. You can ask, for example:
      • How do you know that?
      • Why do you think that’s true?
      • What’s the evidence?
      • What’s your proof?
      • Can you back up your claim?
      • What are your reasons for believing that?
    • View Dialectic

Kinds of Arguments

There are four basic kinds of arguments:

  • A deductive argument is an argument from premises to a logical consequence.
    • John Oliver is not eligible to be president because he’s not a natural-born U.S. citizen (and only natural-born U.S. citizens are eligible).
  • A probability argument is an argument from evidence to a probable hypothesis.
    • Reliable Process (or Reliabilist) Argument
      • The suspect’s fingers were in contact with the murder weapon because the suspect’s fingerprints match those on the murder weapon (and a fingerprint match is reliable evidence that the fingerprints belong to the same person).
    • Abductive Argument (Inference to the Best Explanation)
      • Thomas Jefferson likely fathered some of Sally Hemings’ children because that’s the best explanation of her children’s physical appearance and a one-in-thousand Y-chromosome match between a male descendant of Jefferson’s paternal uncle and a male descendant of one of Hemings’ sons.
  • A normative argument is an argument from reasons to a course of action.
    • Deontic (or Deontological) Argument
      • You shouldn’t shoplift because stealing is wrong (and shoplifting is stealing).
    • Consequence (or Consequentialist) Argument
      • You shouldn’t shoplift because you might get caught (and getting caught is bad).
  • An analogical argument is an inference from known similarities to a further similarity
    • Analogical Deductive Argument
      • Cheating is morally wrong because there’s no morally relevant difference between cheating and surreptitiously changing your grade on the instructor’s spreadsheet (and the latter is morally wrong).
    • Analogical Probability Argument
      • Your house will likely sell for about $250,000 because it’s very similar to three recently-sold houses nearby that sold for about that amount.
  • The Oliver argument is a deductive argument, since the conclusion follows necessarily from the premises.

View Kinds of Arguments

Argument Evaluation

Argument evaluation is the process of determining how strongly, if at all, the argument supports its conclusion.

  • An argument establishes its conclusion if:
    • its premises are true
    • its reasoning is sound.
  • Such is the case with the Oliver Argument
    • The premises are true
      • Only natural-born U.S. citizens are eligible to be president, per the Constitution.
      • John Oliver was not born an American citizen but was naturalized in 2019.
    • The reasoning is correct, having the valid deductive form:
      • Only A’s are B’s
      • x is not a A
      • Therefore x is not an B.
    • Any argument having this form is valid, for example:
      • Only members are allowed.
      • Harry is not a member.
      • Therefore, he’s not allowed.

Ubiquity of Arguments

  • People infer things. They investigate matters and draw conclusions. They deliberate and make decisions. They give reasons for their opinions. They justify their decisions. They establish claims. They refute claims. They explain why things are true. They persuade people. They engage in argumentation.
  • All these activities involve arguments.

Examples of Arguments

John Oliver Argument

  • Conversation between Lucas and Mia:
    • Lucas: I really like John Oliver. I wish he would run for president.
    • Mia: There’s a problem with that. He’s not eligible.
    • Lucas: Sure he is. He’s an American citizen.
    • Mia: Yes he’s an American citizen, but he’s not eligible to be president because only natural-born U.S. citizens are eligible.
  • Mia justifies her claim that Oliver is not eligible by putting forth the argument:
    1. Only natural-born U.S. citizens are eligible to be president.
    2. John Oliver isn’t a natural-born U.S. citizen.
    3. Therefore, he’s not eligible to be president.
  • Statements 1 and 2, the premisses of the argument, are set forth to establish the truth of statement 3, the conclusion.
  • The second premise, unstated in the conversation, is inferred from the context, since it’s needed to draw the conclusion. Mia’s statement of the argument is an enthymeme, a partly stated argument.
  • Mia could have put forth the same argument by stating premise 2 rather than premise 1:
    • Lucas: Sure he is. He’s an American citizen.
    • Mia: Yes he’s an American citizen, but he’s not eligible to be president because he’s not a natural-born U.S. citizen.
  • The first premise would have then been inferred from the context.
  • Mia could also have put forth the argument by stating both premises:
    • Mia: Yes he’s an American citizen, but he’s not eligible to be president because he’s not a natural-born U.S. citizen and only natural-born U.S. citizens are eligible.
  • But this is verbal overkill, violating Strunk and White’s admonition to “omit needless words.” You don’t say what the reader knows or can infer.

Black Swans

  • Conversation between Shane and Quinn:
    • Shane: Did you know there are black swans?
    • Quinn: No I didn’t. Have you ever seen any?
    • Shane: No, never.
    • Quinn: Then how do you know they exist?
    • Shane: I read it in the Britannica.
  • Shane justifies his belief that there are black swans by putting forth the argument:
    1. The Britannica says there are black swans.
    2. The Britannica is a reliable source of information.
    3. Therefore, there are black swans.
  • The second premise, unstated in the conversation, is inferred from the context, since it’s needed to draw the conclusion. Like Mia’s argument, Shane’s statement of the argument is an enthymeme.
  • The argument is a probability argument, from evidence (that the Britannica says there are black swans) to a highly likely conclusion (that there are indeed black swans).
  • The argument is not a deductive argument because a reliable source of information, no matter how strong, can be mistaken. Reliability is not infallibility.

Editorial on Capital Punishment

The New York Times published the following editorial on capital punishment in 1989:

  • “How many James Richardsons does it take to change an attitude? It is a deadly serious question.
  • James Richardson, a Florida migrant worker, was sentenced to death in 1968 after being convicted of poisoning his seven children. But he was saved from execution by the Supreme Court’s 1972 decision striking down state capital punishment laws.
  • This week he went free after a judge ruled his conviction tainted by prosecutorial misconduct and perjured testimony. It now appears that someone else killed the Richardson children.
  • Mr. Richardson was the second man in two months to win freedom after it became clear that he was wrongly convicted of a capital crime. Randall Dale Adams, who once came within a week of execution for the murder of a Dallas police officer, was released in March from a Texas prison. Misconduct by a prosecutor and perjured testimony also tainted Mr. Adams’s trial.
  • According to Michael Radelet, a University of Florida specialist on capital punishment, there have been 30 cases since 1972 in which someone was convicted and sentenced to death, only to be freed later after the state admitted a mistake.
  • The question is real and urgent: How many James Richardsons or Randall Adamses does it take to change a nation’s attitude about capital punishment? No one has yet demonstrated any clear deterrent value for the death penalty. Its only real function is to satisfy a primitive sense of retribution. But is that sort of satisfaction worth the life of 30 innocent people? Or even one?
  • Death is the only final and irreversible criminal punishment. As the Richardson and Adams cases vividly show, humans and their governments are fallible and corruptible. Prudent humility dictates that fallible people refrain from inflicting irreversible punishments.”

The argument is set forth in the final paragraph.

  • Argument reconstructed:
    1. Fallible governments should refrain from inflicting irreversible punishments
    2. Capital punishment is irreversible.
    3. Governments are fallible.
    4. Therefore, governments should refrain from inflicting capital punishment.
  • Like the earlier arguments, the Times’ argument is an enthymeme. But in this case it’s the conclusion that’s unstated rather than a premise.
  • The argument is deductive.
  • Dialectic Note:
    • If a proponent of capital punishment disputes the conclusion, they must reject one of the premises or show that the conclusion doesn’t follow from the premises.
    • View Dialectic

Declaration of Independence

  • The Declaration of Independence has three sections:
    • Preamble
    • Grievances
    • Resolution

Image Source: Britannica

  • From the Preamble
    • “When, in the course of human events, it becomes necessary for one people to dissolve the political bands which have connected them with another, and to assume, among the powers of the earth, the separate and equal station to which the laws of nature and of nature’s God entitle them, a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation.“
    • “We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable rights, that among these are life, liberty, and the pursuit of happiness. That, to secure these rights, governments are instituted among men, deriving their just powers from the consent of the governed. That, whenever any form of government becomes destructive of these ends, it is the right of the people to alter or to abolish it, and to institute new government, laying its foundation on such principles, and organizing its powers in such form, as to them shall seem most likely to effect their safety and happiness.”
  • In the first paragraph Jefferson says that the colonies are obligated to publicly explain their argument for declaring independence.
    • “a decent respect to the opinions of mankind requires…“
  • The Declaration’s argument is set forth in the second paragraph:
    1. The people have the right to alter or abolish a government if it violates basic human rights such as the rights to life, liberty and the pursuit of happiness.
      • “all men are created equal, that they are endowed…“
      • “whenever any form of government becomes destructive of these ends…“
    2. The British government of the colonies has violated those rights.
      • Per the Grievance Section
    3. Therefore the American people have a right to alter or abolish the British government of the colonies.
  • The second premise is supported by the very long argument of the Grievance Section:

A leader of the Enlightenment in America, it’s not surprising that Jefferson thought in terms of arguments.

Kinds of Arguments

  • A deductive argument is an argument from premises to a logical consequence.
    • John Oliver is not eligible to be president because he’s not a natural-born U.S. citizen (and only natural-born U.S. citizens are eligible).
  • A probability argument is an argument from evidence to a probable hypothesis.
    • Reliable Process (or Reliabilist) Argument
      • The suspect’s fingers were in contact with the murder weapon because the suspect’s fingerprints match those on the murder weapon (and a fingerprint match is reliable evidence that the fingerprints belong to the same person).
    • Abductive Argument (Inference to the Best Explanation)
      • Thomas Jefferson likely fathered some of Sally Hemings’ children because that’s the best explanation of her children’s physical appearance and a one-in-thousand Y-chromosome match between a male descendant of Jefferson’s paternal uncle and a male descendant of one of Hemings’ sons.
  • A normative argument is an argument from reasons to a course of action.
    • Deontic (or Deontological) Argument
      • You shouldn’t shoplift because stealing is wrong (and shoplifting is stealing).
    • Consequence (or Consequentialist) Argument
      • You shouldn’t shoplift because you might get caught (and getting caught is bad).
  • An analogical argument is an inference from known similarities to a further similarity
    • Analogical Deductive Argument
      • Cheating is morally wrong because there’s no morally relevant difference between cheating and surreptitiously changing your grade on the instructor’s spreadsheet (and the latter is morally wrong).
    • Analogical Probability Argument
      • Your house will likely sell for about $250,000 because it’s very similar to three recently-sold houses nearby that sold for about that amount.

Deductive Arguments

  • A deductive argument is an argument from premises to a logical consequence, i.e., an argument whose conclusion (purportedly) follows necessarily from its premises.
    • Purportedly allows for bad deductive arguments.
    • An argument is valid if its conclusion follows necessarily from its premises.
  • Example
    • Only natural-born U.S. citizens are eligible to be president.
    • John Oliver isn’t a natural-born U.S. citizen.
    • Therefore, he’s not eligible to be president.

View full page on Deductive Arguments

Probability Arguments

  • A probability argument is an argument from evidence to a probable hypothesis, i.e., an argument whose premises (purportedly) make the conclusion probable
    • Purportedly allows for bad probability arguments.
  • Types of probability arguments:
    • Reliable-Process Arguments
    • Abductive Arguments
Reliable Process (or Reliabilist) Arguments
  • A reliable-process argument is an argument whose conclusion is (purportedly) made probable by a reliable process.
  • Basic Form
    1. E, the evidence, is true
    2. E-ness is reliable evidence of H-ness
      • Because of a reliable process
    3. So H is true
  • Example
    • There’s somebody at the door — I hear the doorbell is ringing.
      1. The doorbell is ringing.
      2. A doorbell ringing is reliable evidence that someone’s at the door.
      3. So someone’s at the door.
Abductive Arguments (Inference to the Best Explanation)
  • An abductive argument is an argument whose conclusion is (purportedly) made probable by explaining and/or predicting the evidence
  • Basic Form
    1. E, the evidence, is true
    2. Hypothesis H explains and/or predicts E better than competing hypotheses.
    3. Therefore H is more likely than the competing hypotheses
  • Example
    • In December 2008 Bernie Madoff confessed to running a $50 billion Ponzi scheme, the largest in history.  But for the previous ten years Harry Markopolos, a Boston accountant, tried unsuccessfully to persuade the Securities and Exchange Commission that Madoff Investment Securities was running a scam.  Here’s his argument:
      1. Bernie Madoff’s fund Fairfield Sentry had only 7 losing months out of 174; its largest monthly loss was only 0.55%; and its longest losing streak was one month every few years.
      2. The hypothesis that Madoff is running a scam explains and predicts Fairfield Sentry‘s performance far better than the hypothesis Madoff is an honest investor.
      3. Therefore it’s much more likely that Madoff is running a scam than he’s an honest investor.

View full page on Probability Arguments

Normative Arguments

  • A normative argument is an argument from reasons to a course of action.
  • Types of normative arguments:
    • Deontic Arguments
    • Consequence Arguments
Deontic (or Deontological) Arguments
  • A deontic argument is an argument from a principle to a course of action
  • Basic Form
    1. Principle
    2. Facts
    3. Therefore, course of action
  • Example:
    • You should take your little brother to the zoo because promises should be kept.
      1. Promises should be kept.
      2. You promised to take your little brother to the zoo.
      3. So you should take your brother to the zoo.
Consequence (or Consequentialist) Arguments
  • A consequence argument is an argument from possible consequences to a course of action.
  • Basic Form
    1. Probability, improbability, or possibility of the consequences of a course of action.
    2. Value of the consequences of the course of action.
    3. Therefore, course of action
  • Example
    • You shouldn’t shoplift because you might get caught.
      1. If you shoplift you might get caught.
      2. Getting caught would be bad.
      3. Therefore, you shouldn’t shoplift.

View full page on Normative Arguments

Analogical Arguments

  • An analogical argument is an inference from known similarities to a further similarity
  • Analogical arguments are either probability or deductive arguments.
Analogical Probability Arguments
  • Form
    • A and B are alike in respects X, Y, Z
    • X, Y, and Z are relevant to whether a thing is W.
    • A is W
    • Therefore B is likely W
  • Example
    • A small model water turbine has been successfully tested under the same conditions under which full-size turbines are expected to operate. 
    • Except for size, the model turbine is just like the full-size turbines. 
    • Therefore, in all probability, the full-size turbines will operate without a problem.
Analogical Deductive Arguments
  • Form
    • A and B are alike in all respects relevant to whether a thing is W.
    • A is W
    • Therefore B is W
  • Example:
    • There’s no morally relevant difference between cheating and surreptitiously changing your grade on the instructor’s spreadsheet.
    • Changing your grade on the instructor’s spreadsheet is morally wrong.
    • Therefore, cheating is morally wrong.

View full page on Analogical Arguments

Summary of Kinds of Arguments

  • Deductive Argument: from premises to a logical consequence
  • Probability Argument: from evidence to a probable hypothesis.
    • Reliable-Process Argument: conclusion made probable by a reliable process.
      • E, the evidence, is true
      • E-ness is reliable evidence of H-ness
        • Because of a reliable process
      • So H is true
    • Abductive Argument: conclusion made probable by explaining and/or predicting the evidence
      • E, the evidence, is true
      • Hypothesis H explains and/or predicts E better than competing hypotheses.
      • Therefore H is more likely than the competing hypotheses
  • Normative Argument: from reasons to a course of action
    • Deontic Argument: from a principle to a course of action
      • Principle
      • Facts
      • Therefore, course of action
    • Consequence Argument: from possible consequences to a course of action
      • Probability, improbability, or possibility of the consequences of a course of action.
      • Value of the consequences of the course of action.
      • Therefore, course of action
  • Analogical Argument: from known similarities to a further similarity.
    • Analogical Probability Argument
      • A and B are alike in respects X, Y, Z
      • X, Y, and Z are relevant to whether a thing is W.
      • A is W
      • Therefore B is likely W
    • Analogical Deductive Argument
      • A and B are alike in all respects relevant to whether a thing is W.
      • A is W
      • Therefore B is W

View Obsolete Classification of Arguments

Analysis of Arguments

Argument analysis is the two-step process of formulating and evaluating an argument.

Formulating Arguments

  • Formulating or reconstructing an argument is the process of stating an argument so its premises, conclusion, and reasoning are clear.
  • For example, the sentence “John Oliver is not eligible to be president because he’s not a natural-born U.S. citizen” expresses an argument more clearly and completely stated as:
    • Only natural-born U.S. citizens are eligible to be president.
    • John Oliver is not a natural-born U.S. citizen.
    • Therefore, he’s not eligible to be president
  • The unstated first premise is made explicit.
  • The logical form of the reasoning is clear:
    • Only Ns are Es.
    • x is not an N
    • So, x is not an E.

View Argument Reconstruction

Evaluating Arguments

  • Argument evaluation is the process of determining how strongly, if at all, the argument supports its conclusion.
  • This means:
    • Determining whether the premises are true.
    • Determining whether the argument’s reasoning is sound.
  • The evaluation of arguments has become very sophisticated since 1900, with an emphasis on clarity and precision, a better understanding of language, and the development of formal logic, probability theory, and decision theory.

Most Important Things about Arguments

Addenda

Awareness of Arguments

  • Though everyone uses arguments, awareness of arguments varies greatly.
  • Philosophers, judges, lawyers, mathematicians, and scientists are especially aware of arguments.
    • Philosophers’ modus operandi is the analysis of arguments.
    • Judges set forth arguments in judicial opinions. 
    • Lawyers present arguments in lawsuits, briefs, and arguments at trial
    • Mathematicians construct proofs — very, very long arguments.
    • Scientific theories are supported or refuted by their predictions.
  • Thinkers during the Enlightenment were keenly aware of arguments. It’s not surprising that the Declaration of Independence is framed as one long argument, having been written by one of the leaders of the Enlightenment in America.

Myth that Facts Speak for Themselves

A misconception is that arguments don’t matter because facts speak for themselves.

  • Sometimes facts indeed speak.  But when they do, they speak, not for themselves, but as premises of an argument.  For example, Mia can put forward the argument that John Oliver can’t be president by stating two facts:
    • Only natural-born U.S. citizens are eligible to be president.
    • John Oliver isn’t a natural-born U.S. citizen.
  • The obvious inference is that John Oliver isn’t eligible to be president.
  • But merely listing sundry facts too often results in either a bad argument or puzzlement about what the point is.
  • Example:
    • Here are the facts: When Biden was inaugurated on January 20, 2021 inflation was increasing at the rate of 1.7%.  In June 2022 that figure was 9%.
  • What conclusion is supposed to be drawn?  That inflation has increased?  That Biden’s policies are responsible for the increase?.  If the latter, the argument is fallacious, an instance of Post Hoc Ergo Propter Hoc.
  • The takeaway:
    • When facts speak they do so, not for themselves, but as premises of an argument. When someone merely lists facts, the question should be:
      • And what conclusion should we draw from these facts of yours?

Ubiquity of Arguments

  • People infer things. They investigate matters and draw conclusions. They deliberate and make decisions. They give reasons for their opinions. They justify their decisions. They establish claims. They refute claims. They explain why things are true. They persuade people. They engage in argumentation.
  • All these activities involve arguments.

Inferring Things

  • A person infers there are black swans after reading in the Britannica that there are black swans in Australia.
  • Argument
    • The Britannica says there are black swans.
    • The Britannica is a reliable source of information.
    • Therefore, there are black swans.

Investigating Matters and Drawing Conclusions

  • Special Counsel Robert Mueller investigated Russian interference in the 2016 presidential election.  In the process he found evidence of ten alleged instances of obstruction of justice by Donald Trump.  One of these is that he directed Don McGahn to tell the Acting Attorney General to remove the Special Counsel.
  • Mueller’s argument that Trump obstructed justice from the Mueller Report:
    • A person obstructs justice if he/she does something with the specific intent to influence, obstruct, or impede a judicial proceeding.
    • On June 17, 2017 Trump directed Don McGahn to inform the acting Attorney General that the Special Counsel had conflicts of interest and must be removed.
    • Trump’s intent in directing McGahn was to influence, obstruct, or impede Mueller’s investigation.
    • Therefore, Trump obstructed justice

Deliberating and Deciding Things

  • In Dobbs v. Jackson Women’s Health Organization the Supreme Court held that there is no constitutional right to abortion and thus overturned Roe and Casey
  • Argument there is no constitutional right to abortion.
    • There is a constitutional right to abortion only if at least one of the following conditions is true:
      • the Constitution explicitly states that there is a right to abortion.
      • the right can be inferred from certain constitutional provisions, e.g. the Due Process Clause of the Fourteenth Amendment.
      • the right is included in a broader constitutional right, e.g. the right to privacy.
    • None of these conditions is satisfied.
    • Therefore, there is no constitutional right to abortion
  • Argument that Roe v. Wade should be overturned.
    • A Supreme Court decision that’s wrongly decided should be overturned.
    • Roe and Casey were wrongly decided.
    • Therefore they should be overturned,

Justifying a Decision

  • The Bush administration justified its invasion of Iraq on the grounds that Iraq’s WMD’s posed a threat to the United State.
  • Argument
    • The US had clear and convincing evidence that Iraq possessed chemical and biological WMDs that might be used against it.
    • A country is justified in launching a war against another country if it has clear and convincing evidence that the other country possesses WMDs that might be used against it.
    • Therefore the US was justified in launching war against Iraq

Giving Reasons for an Opinion

  • The last paragraph of a New York Times editorial.
    • “Death is the only final and irreversible criminal punishment. As the Richardson and Adams cases vividly show, humans and their governments are fallible and corruptible. Prudent humility dictates that fallible people refrain from inflicting irreversible punishments.”
  • Argument
    • Fallible governments should refrain from inflicting irreversible punishments
    • Capital punishment is irreversible.
    • Governments are fallible.
    • Therefore, governments should refrain from inflicting capital punishment.

Establishing that something is true

  • Conversation between Lucas and Mia:
    • Lucas: Did you know that John Oliver is eligible to be president, since he’s an American citizen?
    • Mia: As a matter of fact he’s not eligible. He’s not a natural-born U.S. citizen
  • Mia’s Argument
    • Only natural-born U.S. citizens are eligible to be president.
    • John Oliver isn’t a natural-born U.S. citizen.
    • Therefore, he’s not eligible to be president.

Explaining why something is true

  • Second conversation between Lucas and Mia:
    • Lucas: I understand John Oliver is not eligible to be president. Do you know why?
    • Mia: Yes. Only natural-born U.S. citizens are eligible to be president.
  • In this case the premises of the argument explain the conclusion.
    • That John Oliver isn’t a natural-born U.S. citizen and that only natural-born U.S. citizens are eligible to be president are why he’s not eligible to be president.
      • They explain his ineligibility.
      • They are the reason he’s ineligible.
      • He’s not eligible because he’s not a natural-born U.S. citizen and only natural-born U.S. citizens are eligible.
  • View Logical Equivalences among Why, Because, Reason, Therefore, Explain

Exercises: Do these arguments establish their conclusions?

Establish means to prove or make acceptable beyond a reasonable doubt
(Merriam-Webster Unabridged).

  • False Statements to FBI (Answer)
    • On July 2, 2016 Hillary Clinton was interviewed for over three hours at the FBI headquarters regarding her private email server.  
    • In a congressional hearing on July 7, 2016 James Comey said that Clinton made six false statements during the interview.
    • According to 18 U.S. Code § 1001:
      • Whoever, in any matter within the jurisdiction of the executive, legislative, or judicial branch of the Government of the United States, knowingly and willfully makes any materially false, fictitious, or fraudulent statement or representation shall be fined under this title or  imprisoned not more than 5 years.
    • Therefore Hillary Clinton violated 18 U.S. Code § 1001. 
  • John Oliver (Answer)
    • John Oliver isn’t eligible to be president because he’s not a natural-born U.S. citizen.
  • Invasion of Iraq was not Justified (Answer)
    • Had Saddam Hussein been responsible for the 9/11 attacks, the U.S. invasion of Iraq would have been morally justified.
    • But Hussein was not responsible for the 9/11 attacks.
    • Therefore, the U.S. invasion of Iraq was not justified.
  • Abortion (Answer)
    • Abortion should be legal because abortions will be performed whether legal or not.
  • Random Drug Test (Answer)
    • You’re given a random drug test that’s 95 percent reliable, meaning 95 percent of drug users test positive and 95 percent of non-drug users test negative.   
    • You test positive.
    • Therefore, there’s a 95 percent probability you’re a drug user.
  • Bible not Word of God (Answer)
    • The Bible says that Jesus of Nazareth was crucified about 9:00 AM the day after Passover (Mark 14:12; 15:25). 
    • The Bible also says that Jesus was crucified about noon the day before Passover (John 19:14).  
    • Both statements can’t be true.  
    • If the Bible is the inerrant word of God, everything the Bible says is true.  
    • Therefore the Bible is not the inerrant word of God.
  • Smoking Pot (Answer)
    • Most heroin addicts first smoked pot.
    • So, if you smoke pot you’re more likely to become addicted to heroin than if you don’t
  • Active and Passive Euthanasia(Answer)
    • There is no morally relevant difference between killing a person and letting them die.
    • It is morally wrong to kill a terminally ill person. 
    • Therefore, it is morally wrong to let a terminally ill person die.
  • Overweight (Answer)
    • Most Americans are overweight.
    • Therefore, most American children are overweight.
  • Kalam Cosmological Argument(Answer)
    • Whatever begins to exist has a cause
    • The universe began to exist.
    • Therefore, the universe has a cause
    • If the universe has a cause, an uncaused, personal creator of the universe exists
    • Therefore, an uncaused, personal creator of the universe exists.
  • Killing in Self-defense(Answer)
    • Killing is wrong.
    • Therefore, killing in self-defense is wrong.
  • Justification for Iraq War (Answer)
    • A country is justified in launching a war against another country if it has clear and convincing evidence that the other country possesses weapons of mass destruction that might be used against it.
    • The US had clear and convincing evidence that Iraq possessed chemical and biological weapons of mass destruction that might be used against it.
    • Therefore the US was justified in launching a war against Iraq.
  • Venus (Answer)
    • The Morning Star is the planet Venus.  The Evening Star is also the planet Venus. So the Morning Star is the Evening Star.
  • General Relativity (Answer)
    • If Einstein’s general theory is true, then clocks at 30,000 feet run faster than clocks at sea level.  Clocks at 30,000 feet do in fact run faster than clocks at sea level.  Therefore, Einstein’s general theory is true.
  • War on Drugs (Answer)
    • If Prohibition had succeeded in the 1920s, the War on Drugs will succeed.  But Prohibition failed.  Therefore, so will the War on Drugs.
  • Hume’s Argument against Miracles (Answer)
    • Testimony establishes a miracle only if the falsehood of the testimony would be more unlikely than the miracle itself.
    • The falsehood of the testimony of a miracle is always more likely than the miracle itself.
    • Therefore testimony never establishes that a miracle has occurred.
  • Capital Punishment (Answer)
    • “Death is the only final and irreversible criminal punishment.  As DNA exonerations vividly show, humans and their governments are fallible and corruptible.  Fallible governments should refrain from inflicting irreversible punishments.” (NY Times)
  • Fetal Homicide (Answer)
    • After her pregnancy ended in the stillbirth of an 8 1/2 month old fetus, Chelsea Becker was charged with murder because toxic levels of methamphetamine were found in the fetus’s system and she admitted using methamphetamines during her pregnancy.  California defines murder as “the unlawful killing of a human being, or a fetus, with malice aforethought.” But the statute does not apply if “the act was solicited, aided, abetted, or consented to by the mother of the fetus.”  As California’s attorney general observed, “a woman necessarily consents to an act that she herself voluntarily undertakes, free of fraud, duress, or mistake.”
  • Most US citizens were not born in the US (Answer)
    • Most US citizens speak English.
    • Most people who speak English were not born in the US.
      • Britannica: As of 2020 there are 1.27 billion English speakers around the world
    • Therefore, most US citizens were not born in the US.
  • Argument that 1 = 0.9999999…(ad infinitum) (Answer)
    1. ⅓ = 0.3333333…(ad infinitum)
      • self-evident
    2. Therefore, 3 x ⅓  = 3 x 0.3333333…
      • multiplying both sides of line #1 by 3
    3. 1 = 3 x ⅓
      • self-evident
    4. 3 x 0.3333333… = 0.9999999…
      • self-evident
    5. Therefore, 1 = 0.9999999…
      • from lines #2, #3, and #4
  • Arguments against Impeachment Article I (Answers)
    • Article I, paraphrased
      • Trump tried to extort Ukraine into announcing investigations into:
        1. the Bidens,
        2. an unsubstantiated theory involving a DNC server
      • by withholding military aid and promising a White House visit.
    • Arguments against Article I from the White House Trial Brief
      • The military aid flowed on September 11, 2019, and a presidential meeting was scheduled for September 1 and then took place on September 25, 2019, all without the Ukrainian government having done anything about investigations. (WH Brief, page 9)
      • Asking another country to examine potential interference in a past U.S. election is always permissible.  (WH Brief, page 81)
      • An impeachable act must violate the law. Trump violated no law. (WH Brief, page 1)
  • Ted Cruz (Answer)
    • Ted Cruz is not eligible to president. Born in Canada, he’s not a natural-born US citizen.
  • Increase in Cases (Answer)
    • Increased testing can’t be the only reason for a surge in new coronavirus infections. If it were, the percentage of positive tests would be dropping or at least remaining the same.
  • Case Fatality Rate (Answer)
    • The US has the lowest case fatality rate in the world. Here’s the proof:
From Our World in Data

Defeasible Arguments and ‘Other Things Being Equal’

  • The world is complex and reasoning can get complicated. Anything that simplifies matters facilitates reasoning.  A common way of simplifying things is to keep other things equal
  • Consider these arguments
    • A Probability Argument
      • In 1998 CNN reported that the U.S. had used sarin nerve gas in Laos in 1970 as part of Operation Tailwind during the Vietnam War.
      • CNN is a reliable source of news.
      • Therefore, the US used sarin gas in Laos in 1970.
    • A Normative Argument
      • You promised you would take your little brother to the zoo this morning.
      • Promises should be kept.
      • Therefore you should take your little brother to the zoo this morning.
    • An Analogical Argument
      • Three recently purchased houses sold for an average 250K.
      • Your house is like those houses in terms of square footage, number of bedrooms, age, condition, and neighborhood.
      • Therefore your house will sell for about 250K
  • Though the premises support the conclusions in different ways, the arguments have something in common.  They are all defeasible.
  • An argument is defeasible if the support of its conclusion by the premises can be nullified or rebutted by additional facts.
  • Thus the support of the conclusions of the arguments would be “defeated” by the following:
  • The premises of the arguments remain true but no longer support the conclusion. Adding the defeating facts as premises undercuts the premises’ support of the conclusion. For example,
    • In 1998 CNN reported that the U.S. had used sarin nerve gas in Laos in 1970 as part of Operation Tailwind during the Vietnam War.
    • CNN is a reliable source of news.
    • CNN retracted the story.
    • Therefore, the US used sarin gas in Laos in 1970.
  • Defeasible arguments can be reformulated using the phrase “other things being equal” (or ceteris paribus).
  • Here are the reformulations:
    • CNN
      • In 1998 CNN reported that the U.S. had used sarin nerve gas in Laos in 1970 as part of Operation Tailwind during the Vietnam War.
      • It’s reasonable to believe CNN’s news reports, other things being equal.
      • Other things are equal.
      • Therefore, it’s reasonable to believe the US used sarin gas in Laos in 1970.
    • Promise
      • You promised you would take your little brother to the zoo this morning.
      • Promises should be kept, other things being equal
      • Other things are equal.
      • Therefore you should take your little brother to the zoo this morning.
    • CMA
      • Three recently purchased houses sold for an average 250K.
      • Your house is like those houses in terms of square footage, number of bedrooms, age, condition, and neighborhood.
      • Other things are equal.
      • Therefore your house will sell for about 250K
  • Defeating facts render the OTBE premises false.

Supplementary Topics

Epistemic Pitfalls

Formal Systems

Obsolete Classification of Arguments

  • 1911 Encyclopedia Britannica
    1. Analogical Inference, from particular to particular: e.g. border-war between Thebes and Phocis is evil; border-war between Thebes and Athens is similar to that between Thebes and Phocis; therefore, border-war between Thebes and Athens is evil.
    2. Inductive Inference, from particular to universal: e.g. border-war between Thebes and Phocis is evil; all border-war is like that between Thebes and Phocis; therefore, all border-war is evil.
    3. Deductive or Syllogistic Inference, from universal to particular, e.g. all border-war is evil; border-war between Thebes and Athens is border-war; therefore border-war between Thebes and Athens is evil.

View Term ‘Induction’ is Obsolete