Arguments

An argument is a set of propositions, one of which (the conclusion) is purportedly supported by the others (the premises)

Outline

  1. Definition
  2. Six Arguments
  3. Argument Reconstruction
  4. Nature of Support, Kinds of Arguments
  5. Evaluating Arguments
  6. Addendum

Definition

  • An argument is a set of propositions, one of which (the conclusion) is purportedly supported by the others (the premises).
  • “Support” is used in the sense in which facts and evidence support claims and hypotheses.
  • “Propositions” are the bearers of (i) truth and falsity, (ii) the metaphysical modalities (e.g. necessary, contingent, impossible), and (iii) the epistemic probabilities (e.g. certain, likely, doubtful).
  • “Purportedly” allows for bad arguments.

Six Arguments, Reconstructed in Premise-Conclusion Form

  • The core of the Declaration of Independence is the argument:
    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.
    2. The British government of the colonies has violated those rights.
    3. Therefore the American people have a right to alter or abolish the British government of the colonies.
  • Before he flew a kite in a thunderstorm, Benjamin Franklin set forth an argument that lightning was electrical in nature.
    1. Lightning and sparks are alike in the following respects:
      • 1. Giving light, 2. Color of the light, 3. Crooked direction, 4. Swift motion, 5. Being conducted by metals, 6. Crack or noise in exploding, 7. Subsisting in water or ice, 8. Rending bodies it passes through,  9. Destroying animals, 10. Melting metals, 11. Firing inflammable substances, 12. Sulphureous smell
    2. A spark is electrical in nature.
    3. Therefore, lightning is likely electrical in nature.
      • “Let the experiment be made.”
  • The New York Times presented this argument against capital punishment:
    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.
  • Despite the Fifth Amendment’s prohibition against double jeopardy, the Supreme Court effectively ruled that a person can be prosecuted for the same act by state and federal governments.
    1. It’s possible for an act to be an offense against both state and federal law.
    2. Offenses that violate laws of different sovereigns are different offenses.
      • Per the ruling.
    3. State and federal governments are different sovereigns.
    4. Therefore, it’s possible for an act to be an offense against state law and a different offense against federal law.
    5. A government may prosecute a person for an offense against its law.
    6. Therefore, it’s possible for a person to be prosecuted for the same act by state and federal governments.
      • Without being prosecuted for the same offense.
  • The Britannica is an authoritative source.
    1. In its article on Matt Damon the Britannica says that Damon left Harvard 12 credits short of graduation.
    2. The Britannica is a reliable source of information.
    3. Therefore, Matt Damon left Harvard 12 credits short of graduation.
  • Edwin Hubble inferred that the universe is more than just the Milky Way from his observation of a star in the Andromeda Nebula.
    1. The universe is either a myriad of galaxies (including the Milky Way) or the Milky Way Galaxy alone.
    2. If the universe is the Milky Way Galaxy alone, the Andromeda Nebula would be no further from Earth than the stars in the Milky Way.
    3. The Andromeda Nebula is much further from Earth than the stars in the Milky Way.
    4. Therefore, the universe is a myriad of galaxies.

Argument Reconstruction
Real-life Arguments and Arguments in Premise-conclusion Form

  • Compare the statements:
    • John Oliver is 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 puts forth an argument for that claim:
    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 are the premises of the argument.
  • Statement 3 is the conclusion.
  • The argument so stated is in premise-conclusion (or canonical) form.
  • The five examples of arguments above are in premise-conclusion form.
    • Nowhere in the Declaration of Independence, for example, will you find the words:
      • 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.
      • The British government of the colonies has violated those rights.
      • Therefore the American people have a right to alter or abolish the British government of the colonies.
    • Rather, the argument in premise-conclusion was “reconstructed” from the text of the Declaration.
  • Argument Reconstruction is the process of restating a real-life (naturally-occurring) argument so its premises, conclusion, and reasoning are clear.

View page on Argument Reconstruction

Nature of Support, Kinds of Arguments

  • Premises support conclusions in three basic ways and a fourth way that crosscuts them:
    • Necessarily
    • Probabilistically
    • As a reason for an action
    • By analogy.
  • There are accordingly four kinds of argument:
    • Deductive Argument
    • Inductive Argument
    • Normative Argument
    • Analogical Argument.

Deductive Arguments

  • A deductive argument is an argument whose conclusion (purportedly) follows necessarily from its premises.
    • The conclusion of a valid deductive argument is a logical consequence of its premises.
  • That John Oliver is ineligible to be president follows from the facts that (i) John Oliver is not a natural-born U.S. citizen and that (ii) only natural-born U.S. citizens are eligible to be president.

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Inductive Arguments

  • An inductive argument is an argument whose premises (purportedly) make its conclusion probable to a certain degree (e.g. very likely or beyond a reasonable doubt).
    • The premises of good inductive argument are evidence that its conclusion is true.
  • Thus, the facts that (i) the Britannica says Matt Damon left Harvard 12 credits short of graduation and that (ii) the Britannica is a reliable source of information make it reasonable to believe that Matt Damon left Harvard 12 credits short of graduation.

View page on Inductive Arguments

Normative Arguments

  • A normative argument is an argument that prescribes a course of action based on reasons.
  • Thus, for the New York Times, governments shouldn’t execute people because (i) governments are fallible and (ii) fallible governments shouldn’t impose irreversible punishments.

View page on Normative Arguments

Analogical Arguments

  • An analogical argument is an argument that things are alike in a given respect because they are alike in others respects.
  • Thus, according to Benjamin Franklin (before people knew what lightning was), there was good reason to think that lightning was an electrical discharge on the grounds that, except for size, lightning was a lot like an electrical spark.

View page on Analogical Arguments

Evaluating Arguments

  • Evaluating an argument means determining the extent that the premises support the conclusion.
    • Three steps:
      • Reconstruct the argument
      • Assuming the premises true, determine the extent of the support of the conclusion by the premises
      • Determine the truth of the premises.
  • The second step depends on the kind of argument. For example:
    • For a deductive argument, determining the extent of support means determining whether the argument is valid.
    • For a statistical argument, determining the extent of support involves seeing whether the data is cherry-picked, apples are compared to oranges, and the wrong baseline is used.
    • For an analogical argument, determining the extent of support involves determining whether the analogs are truly analogous and whether there are relevant dissimilarities.

Addendum

  1. Argument Pages
  2. Pitfalls of Reasoning
  3. Awareness of Arguments
  4. Facts don’t speak for themselves
  5. When it’s not clear what a person’s argument is
  6. Ubiquity of Arguments
  7. Obsolete Classification of Arguments
  8. Exercises: Do these arguments establish their conclusions?

Argument Pages

Pitfalls of Reasoning

Awareness of Arguments

  • Though everyone uses arguments, awareness of arguments varies.
  • Philosophers, judges, lawyers, mathematicians, and scientists are especially aware of arguments.
    • Philosophers investigate issues by means of rational argument.
    • Judges set forth arguments in judicial opinions. 
    • Lawyers present arguments in lawsuits, briefs, and opening and closing arguments at trial.
    • Mathematicians construct proofs — very, very long arguments.
    • Scientific theories are supported or refuted by predictions derived from their postulates.
  • 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.

Facts don’t speak for themselves

  • Facts sometimes speak.  But when they do, they speak, not for themselves, but as premises of an argument.  For example, the argument that John Oliver can’t be president (above) can be put forth 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 can result 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?

When it’s not clear what a person’s argument is

  • Sometimes in a discussion it’s not clear what a person’s argument is.  Clarence Thomas has an interesting method for eliciting arguments.
  • The Supreme Court was hearing oral arguments in the case of CFPB v. Community Financial Services.
  • Noel Francisco, arguing for the plaintiffs, maintained that how the CFPB is funded violates the Appropriations Clause of the Constitution.
  • The justices had a hard time understanding his argument.
  • Justice Sonia Sotomayor said, “I’m trying to understand your argument, and I’m at a total loss.”
  • Finally, Clarence Thomas asked Francisco to “complete this sentence: Funding of the CFPB violates the Appropriations Clause because …?”
  • Francisco replied “Because Congress has not determined the amount that this agency should be spending.”

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

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.
  • Deductive inference is today understood to be an inference from premises to a conclusion that follows necessarily, not an inference from universal to particular.
  • Analogical inference is not merely an inference from particular to particular. There have to be resemblances among the particulars.
  • In an older but still used sense of the word, “induction” means inference from the particular to the general. But in philosophy and logic today an inductive inference is an inference from premises to a probable conclusion.

Exercises: Do these arguments establish their conclusions?

  • 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.
  • 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.
  • 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

  • A defeasible argument is an argument whose premises (purportedly) support its conclusion other things being equal (and which support can therefore be “defeated” by additional information).
  • An example is the Black Swan argument above:
    • It’s reasonable to believe there are black swans because the Britannica is reliable. But reliability is not infallibility. The argument would be nullified if, for example, it were discovered that black swans are not really swans but a different species.

View page on Defeasible Arguments