Logical Failures

Date:2013-03-16
Speaker:Luke Sneeringer

Why this talk?

  • Identifying logical steps in your thinking.
  • All programmers are professional logicians.
  • Logical mistakes are easy to make; easier than you may think.

A Question

  • Linda is 3 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.
  • Which is more likely?
    • She’s a bank teller. (Yes. 90% of people choose this)
    • Shes a bank teller in a womans rights movement. (No. 10%)
  • NO conjunction can be more probably than any of its conjuncts.
    • It’s more likely that she’s a bank teller than that she is both.

Just Enough Logic

  • Logical languages look a lot like programming
    • Booleans: True vs. False
    • Operators: not, and, or, xor, if, iff (if-and-only-if)

Validity

  • A set of statements if any of its values are true: NO
  • A statement is valid if all permises are true and conclusions are also true
  • Validity does not entail truth
    • Invalid conclusions may be true
  • Necessary & Sufficient conditions
    • Necessary: if any condition not met: can’t be true
    • Sufficient: the oppositeo
  • Epistemology: The study of how we know what we know.
    • True belief + faulty reasoning is still true

Fallacies

  1. Asserting the Consequent
    • Given a conditional, concluding its converse.
    • If P, then Q
      • Assume P, Conclude Q
    • Inverse (modus tollens)
    • Converse isn’t true
    • Example: “If it’s raining, then the (uncovered) grass will be wet.”
      • Valid: ‘“Grass not wet, therefore not raining.”
      • Invalid: “Grass wee, therefore raining”
      • Invalid: “Grass dry, not raining.”
  2. Questionable Cause
    • A group of fallacies centered on misidentifying caues
    • P occured, therefore Q happened.
    • “We never had a problem with the air conditioner until you moved into the house.”
    • Sequence is necessary but insufficient condition for causality.
    • “The code hasn’t changed, therefore it can’t be the cause.”
  3. Hasty Generalization
    • Reaching a conclusion w/ insufficient evidence
    • “3 is prime, 5 is prime, 7 is prime, therefore all odd numbers are prime.”
    • NM has towns named “Pie Town” and “Truth or Consequences”, therefore all cities in NM have awesome names.
    • “It works on my machine, therefore not a code problem.”
    • User inputs that break because we didn’t expect that input type.
    • NoSQL for every solution!!
  4. False Compromise
    • Assuming that a compromise between two statements is correct.
    • If John wants to build a bridge across a 10-mile river, and I don’t.
      • You don’t build have the bridge.
    • Incrementalism (let’s do some of all the things we want)
  5. Regression Fallacy
    • Misattribution of causality.
    • When a statistically extreme circumstance occurs, it is usually followed by a return to normal circumstances.
    • Misinterpreting this return to normalcy as being the result of a response.
    • “Traffic cameras stop accidents.”
      • Often installed after a seris of traffic fatalities
    • “Observe high cpu, ctake action, CPU goes down.”
  6. Argument From Fallacy
    • Concluding that because an argument is invalid, its conclusion must be false.
    • Invalid args may nonetheless have true conclusions.
    • Take what you learn, expand it, and learn to spot poor reasoning.
    • Don’t throw out the conlsusion, correct the reasoning