Logical Workspace

  • Real-life arguments are often enthymemes, partly stated arguments with unstated premises or conclusion to be inferred from the context.
  • Take the real-life John Oliver argument:
    • John Oliver is not eligible to be president because only natural-born U.S. citizens are eligible.
  • The premise that John Oliver isn’t a natural-born U.S. citizen is implicit, left to the reader to fill in.
  • Real-life arguments are often embedded in prose.
  • Consider the NY Times argument against capital punishment above:
    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.
  • Here’s how the argument appeared (in part) in the real-life editorial.
    • 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.
    • 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.
    • 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?
    • 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 put forth in the final paragraph.
    • First, premise 2:
      • “Death is the only final and irreversible criminal punishment.”
    • Second, premise 3:
      • “… humans and their governments are fallible and corruptible.”
    • Third, premise 1:
      • “Prudent humility dictates that fallible people refrain from inflicting irreversible punishments.”
    • Finally, the conclusion is implicit.
  • Two common kinds of evidential arguments:
    1. Reliable-Process Arguments
    2. Abductive Arguments
1. Reliable Process Arguments
  • A reliable-process argument is an argument whose conclusion is (purportedly) made probable by a reliable process.
  • Example
    • There’s somebody at the door — I hear the doorbell 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.
2. 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.
  • 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.
  • Two common kinds of normative arguments:
    1. Deontic Arguments
    2. Consequence Arguments
1. Deontic (or Deontological) Arguments
  • A deontic argument is an argument that a particular action should (or shouldn’t) be done based on a principle.
  • 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.
2. Consequence (or Consequentialist) Arguments
  • A consequence argument is an argument that a particular action should (or shouldn’t) be done based on the probability and desirability (or undesirability) of its possible consequences.
  • 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.
  • Analogical arguments may be evidential or deductive.
1. Analogical Evidential Arguments
  • 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.
2. Analogical Deductive Arguments
  • 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.
  • Addendum Arguments and Evidence
  • Arguments and evidence are distinct but related.
  • Evidence is a fact that supports or casts doubt on a proposition (or, alternatively, makes the proposition more or less probable.
  • An argument is a instance of reasoning, from premises to a conclusion.
  • Evidence may be premise of an argument.
    • A premise of an argument for a conclusion may be evidence for the conclusion
  • blind taste test — yes
  • Sometimes evidence is a truncated argument.
  • Argument spells out why the evidence makes the conclusion probable.
  • Evidence and arguments — during a trial evidence is presented but at the end of the trail closing arguments are presented (criminal and civil?)
  • Addendum Mere Statements vs Arguments
  • Compare the statements:
    1. John Oliver is not eligible to be president.
    2. John Oliver is not eligible to be president because only natural-born U.S. citizens are eligible.
  • Propositions
  • The first makes the claim that John Oliver isn’t eligible to be president.
  • The second puts forth 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.
  • Some statements express arguments
  • Others don’t, e.g. hypotheses, theses, facts
  • A thesis is a proposition supported by an argument
  • A thesis is a statement that does not express an argument.
    • mere statement
  • Conclusions of example arguments are theses.
  • https://www.ahdictionary.com/word/search.html?q=thesis
    • A proposition that is maintained by argument.
  • Five examples
  • A deductive argument is an argument whose conclusion (purportedly) follows necessarily from its premises.
  • An evidential argument is an argument whose premises are evidence (purportedly) making its conclusion probable.
    • Reliable-Process Argument: conclusion is made probable by a reliable process.
    • Abductive Argument: conclusion is made probable by explaining and/or predicting the evidence.
  • A normative argument is an argument whose premises are (purportedly) reasons why a particular action should (or shouldn’t) be done.
    • Deontic Argument: particular action should (or shouldn’t) be done based on a principle.
    • Consequence Argument: particular action should (or shouldn’t) be done based on the probability and desirability (or undesirability) of its possible consequences.
  • An analogical argument is an argument that, because things are alike in certain respects, they are therefore (purportedly) alike in a further respect.
    • Analogical Evidential Argument: premises make the conclusion probable.
    • Analogical Deductive Argument: conclusion follows necessary from premises.

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 an evidential argument, whose premises (that the Britannica says there are black swans) make the conclusion (that there are indeed black swans) probable.
  • 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.
  • 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?
  • 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 against capital punishment 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 page on Dialectic

Declaration of Independence

  • The core of the Declaration of Independence is the following 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.
  • The first premise appears in two sentences of the preamble. The second premise is supported by the long list of so-called grievances that follows. Statement #3 is the obvious conclusion to be drawn.
  • For details. view A Logical Analysis of the Declaration of Independence
  • 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 sound, having the valid form of inference:
      • Only A’s are B’s
      • x is not a A
      • Therefore x is not an B.
  • 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.
  • 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

  • Defeasible arguments can be reformulated using the phrase “other things being equal” (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.
  • Defeasible arguments can be reformulated using the phrase “other things being equal” (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.
  • Argument:
    • John Oliver isn’t eligible to be president because he isn’t a natural-born U.S. citizen.
  • Argument Reconstructed:
    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.
  • The argument is a valid deductive argument since the conclusion, that Oliver’s not eligible to be president, follows necessarily from the premises:
    • Only natural-born U.S. citizens are eligible to be president.
    • John Oliver isn’t a natural-born U.S. citizen.
  • Or, equivalently, the premises can’t be true and the conclusion false:
    • Only natural-born U.S. citizens are eligible to be president.
    • John Oliver isn’t a natural-born U.S. citizen
    • Yet, he’s still eligible to be president.
  • A deductive argument is valid if its conclusion follows necessarily from its premises, no matter the truth of the premises.
    • That is, the premises can’t be true and the conclusion false.
  • The John Oliver argument is valid because the following can’t all be true:
    1. Only natural-born U.S. citizens are eligible to be president
    2. John Oliver isn’t a natural-born U.S. citizen
    3. Yet John Oliver is eligible to be president.
  • The Damon argument is likewise valid, for the same reason:
    1. Only natural-born U.S. citizens are eligible to be president
    2. Matt Damon isn’t a natural-born U.S. citizen
    3. Yet Damon is eligible to be president.
  • Indeed, any argument of this form is valid:
    • Only Ns are Es
    • Object O is not an N.
    • So, object O is not an E.
  • For example:
    • Only beings with brains are conscious.
    • The spider running across the floor lacks a brain.
    • So, the spider isn’t conscious.
  • Compare:
    • John Oliver 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.
    • Matt Damon Argument
      1. Only natural-born U.S. citizens are eligible to be president.
      2. Matt Damon isn’t a natural-born U.S. citizen.
      3. Therefore he’s not eligible to be president.
  • The Oliver Argument establishes that John Oliver is not eligible to be president. But the Damon argument fails to prove the Matt Damon isn’t eligible, since the second premise is false.
  • Aristotle’s insight was that, even so, the arguments have the same valid logical form:
    • Only Ns are Es
    • Object O is not an N.
    • So, object O is not an E.
  1. Formulate the argument so its premises, conclusion, and logic are clear
    • Example:
      • John Oliver isn’t eligible to be president because he’s not a natural-born U.S. citizen.
        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.
    • View Argument Reconstruction
  2. Determine whether premises are beyond a reasonable doubt.
  3. Determine whether the argument is valid
    1. View Validity
    2. View Ways of Proving Validity
    3. View Ways of Proving Invalidity
    4. View Deductive Fallacies
  • Example 1
    • Argument
      1. If Newton’s Theory of Gravitation were true, Mercury’s orbit would precess 5,557 seconds of arc per century.
      2. Mercury’s orbit does not precess 5,557 seconds of arc per century.
      3. Therefore, Newton’s Theory of Gravitation is false.
    • Analysis
      • Premises are beyond a reasonable doubt.
      • Argument is valid.
      • Therefore the argument establishes its conclusion.
  • Example 2
    • Argument
      1. Consciousness requires a functioning brain.
      2. A person’s brain ceases to function when they die.
      3. Therefore, a person ceases to be conscious when they die.
    • Analysis
      • First premise is disputed. Second premise is true.
      • Argument is valid
      • So, the argument does not establish conclusion
  • Example 3
    • Argument
      1. Had Saddam Hussein been responsible for the 9/11 attacks, the U.S. invasion of Iraq would have been morally justified.
      2. But Hussein was not responsible for the 9/11 attacks.
      3. Therefore, the U.S. invasion of Iraq was not justified.
    • Analysis
      • First premise seems true. Second premise is true.
      • Argument is invalid
      • Therefore, the argument does not establish its conclusion.