Science is Falsifiable - Lecture Notes

Science is Falsifiable

Previously

• The Problem of Induction: How does science get from observations to scientific laws?

Attempt 1: Logical Positivism

• Early 20th Century.
• Verification Principle:
  • The meaning of a factual statement just is the finite procedure that conclusively determines its truth.
• Logical Positivism is dead.
• The Verification Principle is self-refuting.

Attempt 2: Falsificationism

• Karl Popper (1902-1994)
• Consider two examples of scientific theories:
  • "All human actions are motivated by feelings of inferiority."
  • Einstein’s theory of gravity.

Falsification

• Impossible to establish a scientific law from individual observations, but
• Possible to disprove a scientific law from individual observations.
• E.g. All swans are white

How to be Falsifiable

• It never rains on Wednesdays.
• All substances expand when heated.
• Heavy objects such as a brick when released near the surface of the earth fall straight downwards if not impeded.
• When a ray of light is reflected from a flat mirror, the incoming angle is equal to the outgoing angle.

How to be Unfalsifiable

• Either it is raining or it is not raining.
• All points on a Euclidean circle are equidistant from the centre.
• If you bet on sports, you might get lucky.

The Falsification Criterion

1. Propose scientific laws (for whatever reason you like)
2. Derive predictions (deductively).
3. Perform experiments.
4. Either the theory:
   • Is falsified (deductively, by modus tollens). We discard it.
   • Isn't falsified. Then we try again with more and different experiments.

The Falsification Criterion (Popper's View)

• Popper isn’t just saying:
  • that falsification is good criteria, or
  • the best criteria we have, or even
  • an essential criteria.
• He’s saying it’s the only criteria.
• Popper: "there is no such thing as induction".

Degrees of Falsification

• Some claims are more falsifiable than others. Consider:
  • A. No elephants have gills.
  • B. No mammals have gills.
• Popper: “[we prefer] a bold conjecture, even (and especially) if it soon turns out to be false, to any recital of a sequence of irrelevant truisms.”

Where do Scientific Laws Come From?

• Richard Feynman explains the process of forming new scientific laws:
  1. Guess a new law.
  2. Compute the consequences of the guess.
  3. Compare the computation results to nature.
  4. If it disagrees with experiment, it’s wrong.
• Feynman emphasizes that guessing is a valid part of science.

Avoiding Ad Hocness

• Example of testing a psychic:
  • Scientist: If the psychic guesses wrong 20 times in a row, the ‘you can speak to the dead’ hypothesis is falsified.
  • Psychic: Dead people don’t like to talk on Mondays (ad hoc modification to avoid falsification).

Bold and Cautious Claims

• Significant advances in science:
  • Successful predictions of bold conjectures.
  • Falsification of cautious conjectures.
• Little is learnt from:
  • Falsification of a bold conjecture.
  • Successful predictions of a cautious conjecture.

The Truth in Falsificationism

• Confirmation bias: Scientists should actively try to prove their ideas wrong.

Falsificationism Problem 1: Uranus and Newton's Theory

• 1687: Newton's theory of gravity.
• 1781: Uranus is discovered.
• Mid-1800's: Uranus isn't where it's predicted to be. Is Newton falsified?

Falsificationism Problem 1: Newtonian Prediction

• How to make a Newtonian prediction:
  • A. Newton’s laws of motion, including his law of gravity.
  • B. The mass, and initial position and velocity of Uranus.
  • C. The mass, and initial position and velocity of the other large bodies in the Solar System: Sun, Mercury, Venus, Earth, Mars, Jupiter, and Saturn.

Falsificationism Problem 1: Duhem/Quine Thesis

• Which assumption has been falsified?
• We can't tell.
• Duhem/Quine thesis: it is difficult to conclusively falsify a realistic scientific theory, because they are complex. There are often many assumptions, and we often can’t tell which one is wrong.

Falsificationism Problem 1: Neptune and General Relativity

• 1687: Newton's theory of gravity
• 1781: Uranus is discovered
• Mid-1800's: Uranus isn't where it's predicted to be.
• 1846: Neptune discovered
• Late-1800's: Mercury isn't where it's predicted to be.
• 1913: General Relativity (Einstein)

Falsificationism Problem 2: Probability

• Data: 50 heads in a row
• Hypothesis: this is a fair coin.
• Problem: the hypothesis is not falsified by the data. What now?

Falsificationism Problem 3

• Falsificationism: never conclude that a scientific theory is true or even probably true.
• A scientific theory is either falsified, or not yet falsified. That's it.
• We know more about the natural world now than we did 50 years ago, and much more than we did 500 years ago.

Inference to the Best Explanation

• We should infer that the hypothesis which provides the best explanation of the evidence is probably true.
• Explanatory virtues: there are certain qualities that, when a scientific theory has them, it is more likely to be correct.

Evidential Virtues

• EV1. Evidential accuracy: your theory accounts for or fits the data well.
• EV2. Causal adequacy: your theory posits causes that account for the effects we see in the data.
• EV3. Explanatory scope: your theory applies to a wide range of scenarios.
  • Keas, M.N, "Systematizing the theoretical virtues". Synthese volume 195, pages 2761–2793 (2018)

Internal Virtues

• EV4. Internal consistency: your theory does not contradict itself.
• EV5. Internal coherence: your theory’s various parts fit together neatly and naturally, with no internal tension or ad hoc assumptions.
• EV6. Universal coherence: your theory sits well with other warranted principles.

Aesthetic Virtues

• EV7. Beauty: your theory strikes scientists as beautiful.
• EV8. Simplicity: your theory explains the same facts with fewer basic assumptions.
• EV9. Unification: your theory explains more kinds of facts than rivals, relative to its starting assumptions.

Predictive Virtues

• EV10. Durability: your theory has survived testing by new experiments and new data.
• EV11. Fruitfulness: your theory has pointed to new discoveries, such as successful novel prediction and unification.
• EV12. Applicability: your theory has led to the development of new technology.

Repeated List of Virtues

• EV1. Evidential accuracy
• EV2. Causal adequacy
• EV3. Explanatory scope
• EV4. Internal consistency
• EV5. Internal coherence
• EV6. Universal coherence
• EV7. Beauty
• EV8. Simplicity
• EV9. Unification
• EV10. Durability
• EV11. Fruitfulness
• EV12. Applicability

Induction Makes a Comeback

• "The probability of rain tomorrow is 80%."
  • a. I counted the possibilities; 80% are rainy.
  • b. I time-travelled to all possible tomorrows; 80% are rainy.
  • c. On days like today in the past, 80% had rainy tomorrows.
  • d. Given what we know of how the weather works and our measurements, we're 80% sure it will rain tomorrow.
• $Probability = \frac{favourable}{possible}$

Induction Makes a Comeback

• Probability is degree of plausibility or degree of support.
• “Given our experimental data, matter is probably made of atoms”.
  • a. 80% of matter is made of atoms
  • b. Matter is made of atoms on Tuesdays
  • c. We’ve travelled to many parallel universes, and in 80% of them matter is made of atoms.
  • d. What we know (data) strongly supports (or makes very plausible) the conclusion that matter is made of atoms.

Cox's Theorem

• Why think degrees of support obey the mathematical rules of probability?
• Cox’s Theorem.

Bayesianism

• Bayesianism: degrees of plausibility obey the rules of probability, and provide the mathematical basis for inductive reasoning.
• Reverend Thomas Bayes (1701-1761)
• 19,000 physics/astronomy papers have the word “Bayesian” in the title of the paper
• The probabilities can be expressed with the following formulas:
  • $p(AB|C) = p(A|BC) p(B|C) = p(B|AC) p(A|C)$
  • $p(A + B|C) = p(A|C) + p(B|C) − p(AB|C)$
  • $p(\overline{A}|C) = 1 − p(A|C)$
  • $p(A|BC) = \frac{p(B|AC) p(A|C)}{p(B|C)}$

Summary

• How does science get from observations to scientific laws?
  • Falsificationism: we falsify ideas with experiments, and try to test as-yet unfalsified ideas.
  • Inference to the Best Explanation: Find the hypothesis that best explains the evidence.
  • Bayesianism: degrees of plausibility/support obey the rules of probability, and provide the mathematical basis for inductive reasoning.

Science Is…

• Empirical
• Non-Linear
• Inductive
• Falsifiable

Informal Fallacies

• Formal Fallacy: when an argument is not deductively valid.
• Informal Fallacy: one of the premises is false, or the induction is weak.

Informal Fallacies: Argument from Authority and Silence

• Argument from authority: experts can be wrong. Not necessarily fallacious – some authorities are more reliable than others.
• Argument from silence: arguing from a lack of evidence. Not always fallacious, but it can be difficult to establish that absence of evidence shows evidence of absence.

Informal Fallacies: Ad Hominem

• Ad hominem: attacking a person on irrelevant grounds, instead of their argument.
• Genetic fallacy: identifying the causes of someone’s belief doesn’t invalidate the reasons for that belief.
• Tu quoque, or “whataboutism”: the fact that someone doesn’t live up to their own principles doesn’t make those principles false.
• Subject/motive shift, or Bulverism: instead of evaluating an idea, we speculate about the motives of adherents to the idea. Whatever people’s motives, they may have good reasons for their beliefs as well.

Informal Fallacies: Bad Statistics

• Biased sample: drawing a conclusion about a population from a sample that is not representative of the population.
• Correlation is not causation: if A and B are correlated, there are three possibilities: A causes B, or B causes A, or some third thing C is the cause of both A and B. It is fallacious to fail to consider all these possibilities.
• Fallacy of the single cause: reasoning as if there is only one cause of a particular effect. There could be multiple causes, or contributing factors.
• Hasty generalisation: drawing a general conclusion from too few examples.

Informal Fallacies: Equivocation and Straw-Man

• Equivocation: a crucial term has distinct meanings in different parts of the argument.
• Straw-man fallacy: misrepresenting an idea so that it can be more easily refuted.

Informal Fallacies: False Analogy, Dichotomy, and Slippery Slope

• False analogy: just because A is similar to B in some respects, doesn’t mean that A will be similar to B in all respects.
• False dichotomy: presenting only two options, when there are actually more.
• Slippery slope: action X will (or could) result in consequence Y, and we don’t want Y. Not always a fallacy, for example: “X will create a legal precedent for Y.” But it can require speculation about the future.

Informal Fallacies - Reminder

• Remember: these fallacies are accusations. Saying the name of the fallacy doesn’t magically make the accusation true.

Argument from Authority

1. If most scientists believe something, then it is probably true.
2. Most scientists believe that climate change is happening.
3. Therefore, it is probably true that climate change is happening.

Argument from Authority - Carl Sagan Quote

• Carl Sagan: One of the great commandments of science is, "Mistrust arguments from authority." … Too many such arguments have proved too painfully wrong. Authorities must prove their contentions like everybody else."

Argument from Authority - Considerations

• If most experts believe X, then
  1. The experts have been convinced of X by good evidence,
  2. The experts have been misled by incomplete or faulty evidence,
  3. The experts have been misled by fraudulent evidence,
  4. The experts have been misled by theoretical prejudice: they overlooked important evidence against X because they didn’t know how to fit it into a theory in which X is false,
  5. The experts who disagree with X have been silenced, creating a false consensus,
  6. The experts have been affected by social or personal factors, which have produced an unconscious bias in favour of X, or
  7. There is a conspiracy: the scientists consciously know that that X is false, but lie about X for some reason.

Whataboutism

• Instead of answering an accusation, you respond with a counter-accusation.
• Example:
  • “Your room is messy.” “My brother’s room is worse!”

Bulverism

1. People who believe X do so only for psychological motive Y, not for any good reason.
2. Believing something without good reason is irrational.
3. Therefore, people who believe X are irrational.

Bulverism - Example

1. Capitalists only think that capitalism is a good idea because they want to control society.
2. Believing something without good reason is irrational.
3. Therefore, capitalists are irrational.

Bulverism - Example

1. Communists only think that communism is a good idea because they want to control society.
2. Believing something without good reason is irrational.
3. Therefore, communists are irrational.

Correlation is not Causation

• Ice Cream Sales vs. Sunglasses Sold - both increase but are not necessarily causal.

Correlation is not Causation

• Example of swimming pool drownings correlating with films Nicolas Cage appeared in to demonstrate lack of causation.

Equivocation

• By sneakily changing the definition of a word, you can make an argument Self-Sealing: substantive, but impossible to refute.
• Example:
  • Person A: "No Scotsman puts sugar on his porridge."
  • Person B: "But my uncle Angus is a Scotsman and he puts sugar on his porridge."
  • Person A: "Ah, yes, but no true Scotsman puts sugar on his porridge."

Lecture Checkpoint

• In vUWS, under “Module 06”, find the link for “Science is Falsifiable: In-Lecture Quiz”. There are 8 arguments to comment on.
• Please discuss these with those around you. But make sure you answer for yourself.

Question 1

• I used to work with a UNSW student. So I can say from experience: all of those UNSW students are really socially inept.

Question 2

• The professor says that the students who cheat on exams should not automatically be expelled from school. He is clearly wrong because it is ridiculous to insist that students should never be punished for cheating.

Question 3

• Random drug testing in schools is very effective in reducing drug use because the regular use of the testing makes drug use less likely.

Question 4

• The study found that 80 percent of patients who took the drug daily had no recurrence of breast cancer. But that study does not mean anything. After all, the study was funded in part by the company that makes the drug.

Question 5

• Of course this program will work. It aims to improve the lives of children, so anyone who opposes the program must hate children.

Question 6

• We asked 100 people in Casula Mall where they prefer to shop, and 95 of them said they love shopping in Casula Mall. So, 95% of people would love shopping at Casula Mall.

Question 7

• Humans and robots both can move about, solve mathematical equations, and win chess games. Humans have intelligence. So robots have intelligence.

Question 8

• In all known writings of Greek historians of the fifth century BC, there is no reference to the city or people of Rome. Therefore, probably, Rome did not exist in the fifth century BC.