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Thinking Philosophically (Part 2): The Basics of Logic

Thinking Philosophically (Part 2): The Basics of Logic

In part 1, I covered the essential mindset for thinking and arguing philosophically — and hopefully, by extension, more effectively and productively. But although charity, fallibility, and truth-seeking are necessary, they are usually not sufficient. One also needs the correct technique for understanding, accepting, rejecting, or creating arguments.

Logic is the study and application of reason, specifically the rules which govern kinds of inferences to be valid or invalid.

There are three kinds of inferences:

  1. Deduction: Deductive inferences are conclusions which necessarily follow from the premises. If the premises are true, then the conclusion must be true. Deductions are the strongest kind of logical argument.
    Example: Premise (1): All men are mortal
                     Premise (2): Socrates is a man
    Conclusion: Socrates is mortal
  2. Induction: Inductive inferences are conclusions which probably follow from the premises. If the premises are true, then they serve as strong evidence for the truth of the conclusion, although they do not establish the conclusion with certainty.
    Example: Premise (1): The store closes at 9 PM
                     Premise (2): The store locks its doors when it closes
    Premise (3): It is currently 9:10 PM
    Conclusion: The doors of the store are locked
  3. Abduction: Abductive inferences are conclusions which seem to best explain a set of premises. If the premises are true, then the conclusion is plausible, but not established with certainty.
    Example: Premise (1): The store closes at 9 PM
                     Premise (2): The store locks its doors when it closes
    Premise (3): The doors of the store are locked
    Conclusion: It is currently after 9 PM

Because the emotive, associative, and prejudicial views we may have regarding particular premises or conclusions have no bearing on whether an argument is logically valid or invalid, philosophers will often replace the premises and conclusions with letters, not unlike algebra.

Example: If Aunt Gertrude went to Grandma’s Thanksgiving party, then you know Uncle Frank would have gone too. But Ben says Frank’s still at the clubhouse, so Aunt Gertrude must not have gone to Grandma’s.

This can be converted into the following syllogism, or a formal logical argument deducing a conclusion from two or more premises:

Modified example: If (p), then (q); not (q), therefore not (p)
Formal: P ⇒ Q; ~Q ⇒ ~P

Often times, simple letter formulations are easier to determine as valid or invalid, not only because they are clearer, but because they are not burdened with our own biases in the way that other statements might be. In this way, arguments can be understood structurally, and evaluated based upon the validity of that underlying structure.

Consider the above example. The argument that Gertrude didn’t go to Grandma’s is not valid because of our knowledge of our extended family (although that may help us establish dependable premises), but because of the sound underlying structure. By contrast, look at the following unsound argument:

Example: If Aunt Gertrude went to Grandma’s Thanksgiving party, then you know Uncle Frank would have gone too. Ben says Frank arrived at Grandma’s about an hour ago, so Aunt Gertrude must have gone to Grandma’s.

This can be re-written into the following syllogism:

Modified example: If (p), then (q); (q), therefore (p)
Formal: P ⇒ Q; Q ⇒ P

Think about this for a moment. It was never established that Aunt Gertrude would go to the party if Uncle Frank went; it was only assumed that Uncle Frank would go if Aunt Gertrude went. It is entirely possible that Uncle Frank could have gone of his own volition, and Aunt Gertrude stayed home to watch television or comfort the cat. While the fact that Uncle Frank attended Grandma’s party might be evidence of Aunt Gertrude’s probable presence, it is not deductive proof. The argument, stated as a deduction, is unsound.

To make make this more clear, consider the exact same fallacious argument, but with altered objects:

If it is raining, then there are clouds in the sky.
There are clouds in the sky.
Therefore, it is raining.

Obviously, anyone familiar with an overcast day can see the problem. Rain does not cause clouds. But the formulation of this argument, if converted into the language of formal logic, reads exactly the same as the second story of Uncle Frank and Aunt Gertrude:

If (p), then (q); (q), therefore (p)

This faulty argument is a logical fallacy, an argument that is structurally invalid. Logical fallacies often have names, to assist in spotting them. For instance, the fallacious argument we discussed regarding Uncle Frank’s attendance and the presence of clouds is known as “affirming the consequent,” for which Wikipedia provides an additional example:

If an animal is a dog, then it has four legs.
My cat has four legs.
Therefore, my cat is a dog.

These are all easy enough to see when the conclusion is obviously wrong. Clearly, it can be cloudy and not rainy, and clearly, a cat is not a dog. But the usefulness of understanding valid and invalid logical arguments comes into its own when the conclusion is not so obvious, as in the case of Frank and Gertrude.

Some people take the time to memorize logical fallacies, which of course can be useful in identifying bad arguments and false or improbable conclusions. But among the fallacies to be aware of is the argument from fallacy, or the “fallacy fallacy.” Just because a premise is false does not automatically mean that the conclusion is also false. Consider:

All horses are white.
Blueskin was a horse.
Therefore, Blueskin was white.

The first premise is observably false (George Washington’s other horse, Nelson, was a chestnut brown). But the conclusion — that Blueskin is white — is actually still true. So while knowing logical fallacies can be helpful, using logical fallacies to beat others over the head with can often miss the point, which is to arrive at true conclusions, not to “win.”

It is unreasonable to expect ordinary people to become formal logicians in their own time. The time and intelligence required is simply beyond most. But it is not unreasonable for ordinary people to aspire to the following basic standards of basic logic:

  • Understand the difference between deduction, induction, and abduction
  • Be able to see the underlying structure of an argument, and gauge its validity based upon that structure, rather than emotive reactions to conclusions
  • Have a working knowledge of some of the more common logical fallacies, including:
    • Straw-man fallacy: An oversimplified or misrepresented restatement of an adversary’s position.
      A: I think we should delay the project for a month.
      B: You think we should delay the project indefinitely?
    • No True Scotsman fallacy: Changing a generalization to exclude a counter-example.
      A: No Scotsman eats porridge for breakfast
      B: My father is Scottish and eats porridge for breakfast
      A: Your father isn’t a True Scotsman!
    • Appeal to Authority fallacy: Accepting or rejecting an argument on the basis of an authority figure.
      A: For these reasons, I think that evolution is actually compatible with Christianity.
      B: Well Richard Dawkins is an evolutionary biologist and he thinks that’s preposterous.
    • Hasty Generalization fallacy: Drawing conclusions from insufficient evidence.
      Sarah was late to the meeting yesterday, so she’s clearly an unconscientious person.
    • Ad Hominem fallacy: Arguing that a certain conclusion is false or irrelevant by attacking the person who is making the argument.
      A: I think we should vote for Senator Smith because his tax policy is best for this state
      B: Senator Smith cheated on his wife, he couldn’t possibly be best for this state.
    • Correlation/Causation fallacy: Arguing that two variables are causally related because of a perceived correlation.
      It’s rained every day that Aunt Jodie has taken her umbrella to work with her…
    • Red Herring fallacy: A irrelevant assertion meant to distract from the argument in question.
      A: I think that the proposed gun control is unlikely to achieve the desired effects because of the logistical challenges.
      B: You would say that; you’re a member of the NRA, and the NRA gives millions of dollars to conservative groups that oppose gun control.

If that last example felt touchy to you, and if you felt yourself thinking, “but wait, the NRA does give millions to conservative groups that oppose gun control; isn’t that valid?” then try going through the steps above. Broken down, we have the following:

A: Opposes X
B: If C pays money to D to oppose X, then C is wrong
C pays money to D to oppose X
Therefore C is wrong
    Therefore X is good
A is a member of C
Therefore A is wrong to oppose X

The problem that becomes apparent, upon viewing this more objectively, is that something is not wrong simply because someone gets paid to do it. Fixing a broken bone is not rendered suspicious because the doctor gets paid for performing his service, or for the fact that the patient or the patient’s family pays. Money is simply irrelevant to the question of X, whether X be a doctor’s services, or a proposed bill, against — or for — gun control.

It is, in fact, precisely on these more touchy political subjects that philosophy and logic becomes the most invaluable to productive debate. We don’t need formal logic to know that an overcast day doesn’t necessarily mean rain, because it isn’t an emotionally charged subject. But when the conversation shifts from the weather to religion, abortion, weapons, Trump, Hillary, foreign policy, immigration, or other more contentious issues, it becomes very easy to forget how to argue properly, and to fall into the sophistry and fallacious talking points of the pundits and politicians we so often see. While this can often help to dominate conversations and humiliate adversaries, it does not help in the pursuit of truth, or in the pursuit of meaningful and positive conversations with others.

Because we are usually not rewarded for “winning” debates against our friends and family, and because our relationships are repetitive in nature (unlike with strangers), it is better to strive towards truth than victory. The result will be more productive and enjoyable debates, and in the long run, will leave you with the stronger position anyhow, and holding the stronger position increases your odds of “winning” should you one day find yourself in a truly adversarial debate.

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