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
- Asserting the Consequent
- Given a conditional, concluding its converse.
- If P, then 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.”
- 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.”
- 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!!
- 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)
- 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.”
- 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