FalsifiabilityFalsifiability

Friedrich von Langenfeld, a Friedrich von Langenfeld, a Jesuit priest, wrote the Jesuit priest, wrote the Cautio Cautio CriminalisCriminalis (1631). In it he (1631). In it he mocked witch trials:  mocked witch trials: 

On being accused, a woman On being accused, a woman might run or stay; if she ran, might run or stay; if she ran, that proved her guilt; if she that proved her guilt; if she stayed, the devil had kept her stayed, the devil had kept her so she could not get away.so she could not get away.

If the witch had led an bad If the witch had led an bad life, she was guilty.life, she was guilty.

If she had led a good life, she If she had led a good life, she was guilty, for witches always was guilty, for witches always try to appear virtuous. try to appear virtuous.

Once in prison: if she was Once in prison: if she was afraid, this proved her guilt.afraid, this proved her guilt.

If she was not afraid, this If she was not afraid, this proved her guilt, for witches proved her guilt, for witches have magic powers.have magic powers.

Witchcraft: An unfalsifiable Witchcraft: An unfalsifiable beliefbelief

Langenfeld acted as confessor to many Langenfeld acted as confessor to many witches; he was in a position to observe witches; he was in a position to observe allall outcomes. He knew that no matter outcomes. He knew that no matter whatwhat the the accused witch said or did, it would count accused witch said or did, it would count against her.  against her. 

The charge of being a witch was The charge of being a witch was unfalsifiableunfalsifiable: no evidence could show you : no evidence could show you were not a witch, that is, no evidence could were not a witch, that is, no evidence could falsify it. falsify it.

(This is why scientists predict (This is why scientists predict before before experiment.)experiment.)

Falsifiability: Karl Popper Popper (1902-1994)

argued that, to be scientific, “it must be possible for an empirical scientific system to be refuted by experience.”

Evidence does not prove a hypothesis is true, but can show it is false.

Falsifiability is not verification

Consider “All ravens are black”. One could never prove (verify) that

claim, no matter how many ravens one finds. (cf. Hume)

But it takes only one non-black raven to disprove or falsify it.

This asymmetry underlies Popper’s argument for the primacy of falsification over verification.

Falsification: Falsification: Modus Modus TollensTollens

If P then QIf P then Q Q is false.Q is false. Therefore, P is false.Therefore, P is false.

This is a logically valid argument This is a logically valid argument pattern. pattern.

Falsification: Falsification: Modus Modus TollensTollens

Suppose a theory implies “this sample Suppose a theory implies “this sample of metal will expand when heated.”of metal will expand when heated.”

So: “If this theory is true, then this So: “If this theory is true, then this metal will expand under heat.”metal will expand under heat.”

The sample is heated but does not The sample is heated but does not expand.expand.

Therefore, the theory is false.Therefore, the theory is false.

(Popper thinks this shows that science (Popper thinks this shows that science doesn’t rely on induction.)doesn’t rely on induction.)

Popper and DemarcationPopper and Demarcation

Strict empiricists distinguish science Strict empiricists distinguish science from non-science by saying science must from non-science by saying science must be based on experience.be based on experience.

Popper demarcates science from non-Popper demarcates science from non-science by saying science is science by saying science is falsifiablefalsifiable by by experience.experience.

A statement is A statement is falsifiablefalsifiable if it rules out if it rules out some observable state of affairs or event. some observable state of affairs or event. It does not allow all possibilities, like It does not allow all possibilities, like witch trials.witch trials.

Falsifiable claimsFalsifiable claims

G = Mm/dG = Mm/d22 is falsifiable: the law could have is falsifiable: the law could have been been G = Mm/dG = Mm/d1.31.3 or any other value. or any other value.

““All metals expand when heated” is falsifiable: All metals expand when heated” is falsifiable: the next bit of copper heated might not the next bit of copper heated might not expand.expand.

““Humans evolved from primates” is falsifiable: Humans evolved from primates” is falsifiable: we could find human fossils older than any we could find human fossils older than any other primates’, or our DNA could crucially other primates’, or our DNA could crucially differ from primate DNA. differ from primate DNA.

““The planets orbit in ellipses” is falsifiable: The planets orbit in ellipses” is falsifiable: they could have been circles or squares.they could have been circles or squares.

Unfalsifiable claimsUnfalsifiable claims

““The gravitational force is some The gravitational force is some function of some variables.”function of some variables.”

““For every house, there is a buyer.”For every house, there is a buyer.” ““Everything happens for a reason.”Everything happens for a reason.” ““Your dreams are actually about sexual Your dreams are actually about sexual

desire for your father.”desire for your father.” ““Communism will eventually overthrow Communism will eventually overthrow

capitalism.”capitalism.” ““Your love life will take a turn for the Your love life will take a turn for the

better.”better.”

Unfalsifiable claimsUnfalsifiable claims

Take the example: ‘Your dream is Take the example: ‘Your dream is about sexual desire for your father.’about sexual desire for your father.’ If this claim is rejected, the If this claim is rejected, the

psychoanalyst says the true desire psychoanalyst says the true desire is just being denied.is just being denied.

Or: ‘Your love life will get better.’Or: ‘Your love life will get better.’ If you have just broken up with If you have just broken up with

someone: “Well, that will be for the someone: “Well, that will be for the better!”better!”

Popper’s ‘Bullshit Popper’s ‘Bullshit Detector’Detector’

If someone claims to have a If someone claims to have a theory about the world, ask that theory about the world, ask that person: under what circumstances person: under what circumstances would you give it up?would you give it up?

If the answer is “never”, then it’s If the answer is “never”, then it’s unfalsifiable bullshit! Like the witch unfalsifiable bullshit! Like the witch trials, the theory could be twisted to trials, the theory could be twisted to fit any evidence and still claim to be fit any evidence and still claim to be ‘true’.‘true’.

PredictionsPredictions

So the more falsifiable a theory is – So the more falsifiable a theory is – the more it rules out – the better it is. the more it rules out – the better it is. E.g.:E.g.:

Einstein’s theory of relativity Einstein’s theory of relativity predicted a precise bending of predicted a precise bending of light around the sun.light around the sun.

Evolution predicted an inheritable Evolution predicted an inheritable but changeable basis for traits (i.e., but changeable basis for traits (i.e., genes).genes).

Popper’s Scientific Popper’s Scientific MethodMethod

Popper’s model of science:Popper’s model of science: Make bold explanatory conjectures.Make bold explanatory conjectures. Deduce unexpected (but Deduce unexpected (but falsifiablefalsifiable) )

predictions from them.predictions from them. Try to falsify your conjectures by Try to falsify your conjectures by

testing your predictions.testing your predictions. Reject what is falsified; work with Reject what is falsified; work with

what survives.what survives.

Popper’s view of sciencePopper’s view of science Science, then, is Science, then, is notnot certain knowledge. It certain knowledge. It

is is notnot Nature’s Laws, nor empirical ‘Facts’. Nature’s Laws, nor empirical ‘Facts’. ““We must not look upon science as a ‘body We must not look upon science as a ‘body

of knowledge’, but rather as a of knowledge’, but rather as a system of system of hypotheses hypotheses which in principle cannot be which in principle cannot be justified, but justified, but withwith which we work as long as which we work as long as they stand up to teststhey stand up to tests, and of which we are , and of which we are never justified in saying that we know they never justified in saying that we know they are ‘true’ or ‘more or less certain’ or even are ‘true’ or ‘more or less certain’ or even ‘probable’.” (‘probable’.” (Logic of Scientific DiscoveryLogic of Scientific Discovery))

Simple observations?Simple observations?

Do you believe it because Do you believe it because you see it? you see it?

Or see it because you Or see it because you believe it?believe it? One common-sense view of science One common-sense view of science

(traceable back to Francis Bacon (traceable back to Francis Bacon (1561-1626)) is that science is based (1561-1626)) is that science is based on facts: on undeniable, publicly on facts: on undeniable, publicly verifiable, objective observations.verifiable, objective observations.

However…However…

A problem for ‘facts’A problem for ‘facts’

What we see depends on the context in What we see depends on the context in which it appears, or on what we already which it appears, or on what we already believe (the background, our prior believe (the background, our prior beliefs, our theories).beliefs, our theories).

Consider the claim ‘the earth does not Consider the claim ‘the earth does not move.’ 500 years ago, almost everyone move.’ 500 years ago, almost everyone would agree that this claim was an would agree that this claim was an obvious ‘fact’ that we could just obvious ‘fact’ that we could just seesee was was true. To reject it, we need theories such true. To reject it, we need theories such as inertia to revise our ‘observation.’as inertia to revise our ‘observation.’

Facts depend on theoriesFacts depend on theories

So we can’t simply appeal to ‘facts’ as the So we can’t simply appeal to ‘facts’ as the basis for science or common sense. basis for science or common sense.

What I see partly depends on my beliefs, What I see partly depends on my beliefs, beliefs assumed in the words I use to express beliefs assumed in the words I use to express what I see, and what parts I choose to pay what I see, and what parts I choose to pay attention to.attention to.

We have to be on guard against the We have to be on guard against the possibility that supposedly simple possibility that supposedly simple observations of ‘fact’ are observations of ‘fact’ are theory-ladentheory-laden: they : they wouldn’t be “seen” if not for prior beliefs.wouldn’t be “seen” if not for prior beliefs.

Popper on knowledgePopper on knowledge

For Popper, humans have biological For Popper, humans have biological and social tendencies, and we and social tendencies, and we interpret the world through those interpret the world through those theories.theories.

But our theories may be wrong.But our theories may be wrong. We should let our theories die in our We should let our theories die in our

stead. (Contrast the frog, which has stead. (Contrast the frog, which has a built-in theory that it cannot a built-in theory that it cannot doubt.)doubt.)

Popper on knowledgePopper on knowledge Our individual certainty or doubt is not the Our individual certainty or doubt is not the

best guide to truth. (Notice how different best guide to truth. (Notice how different Popper is from Descartes or Hume.)Popper is from Descartes or Hume.)

We can’t ground-clear. We don’t start with We can’t ground-clear. We don’t start with ‘facts’ or uninterpreted experiences. ‘facts’ or uninterpreted experiences. We We alwaysalways start from theories start from theories. .

We only test one theory at a time, while We only test one theory at a time, while taking others for granted, at least for the taking others for granted, at least for the moment. moment.

But no worthwhile theory is immune from But no worthwhile theory is immune from criticism. Knowledge is criticism. Knowledge is falliblefallible. .

Popper on knowledgePopper on knowledge

Do you claim to know somethingDo you claim to know something? ? Then make a claim that could be proved Then make a claim that could be proved

wrong, and wrong, and test ittest it. And be ready to . And be ready to change your mind.change your mind.

That’s all knowledge is: accepting a claim That’s all knowledge is: accepting a claim based on good reasons. You’re betting based on good reasons. You’re betting on it. But: we could be wrong. The only on it. But: we could be wrong. The only confidence we can have in beliefs is that confidence we can have in beliefs is that they are falsifiable, and that they they are falsifiable, and that they withstand our best tests.withstand our best tests.

Criticisms of PopperCriticisms of Popper

Popper does not allow any Popper does not allow any positive knowledge, only positive knowledge, only theories that haven’t been theories that haven’t been falsified. So he is really a falsified. So he is really a skeptic.skeptic.

We can’t definitively falsify We can’t definitively falsify theories: you can always shift theories: you can always shift the blame onto another theory.the blame onto another theory.

Shifting the blame onto another theory

Our hypothesis: the hare is faster than the Our hypothesis: the hare is faster than the tortoise.  tortoise. 

So we predict: the hare will outrace the tortoise.  So we predict: the hare will outrace the tortoise.  We then observe: We then observe: the tortoise winsthe tortoise wins.  .  The hypothesis that the hare is faster than the The hypothesis that the hare is faster than the

tortoise is tortoise is NOTNOT thereby falsified because we could thereby falsified because we could say say anotheranother hypothesis was falsified instead.  For hypothesis was falsified instead.  For example:  example:  The hare did not stop in the middle of the race for a nap. The hare did not stop in the middle of the race for a nap. The hare did not get run over while crossing the road.The hare did not get run over while crossing the road. The hare did not get entangled in a philosophical The hare did not get entangled in a philosophical

discussion about the rationality of scientific methods discussion about the rationality of scientific methods with his friend gopher before crossing the finish line.with his friend gopher before crossing the finish line.

A real example of shifting the blame

A neutron can decay into a proton and electron A neutron can decay into a proton and electron (beta decay).(beta decay).

In the 1920s physicists found the combined In the 1920s physicists found the combined energies of the proton and electron were less than energies of the proton and electron were less than the original neutron’s. This seems to falsify the the original neutron’s. This seems to falsify the principle of conservation of energy.principle of conservation of energy.

Pauli suggested another particle is emitted: Pauli suggested another particle is emitted: invisible, tiny, and electrically neutral. Fermi invisible, tiny, and electrically neutral. Fermi called it the “neutrino”.called it the “neutrino”.

At the time, there was no way to detect neutrinos, At the time, there was no way to detect neutrinos, so Popper would have said “falsified.”so Popper would have said “falsified.”

But neutrinos But neutrinos werewere detected in 1956. Conservation detected in 1956. Conservation of energy is correct. (Or so it seems!)of energy is correct. (Or so it seems!)

Can we ever falsify?

If a prediction of a theory is found to be If a prediction of a theory is found to be false, and we can’t think of a revised false, and we can’t think of a revised hypothesis that leads to new testable hypothesis that leads to new testable predictions, then Popper says we must predictions, then Popper says we must conclude that the theory is false.conclude that the theory is false.

But it could be that the theory is true and the But it could be that the theory is true and the other hypothesesother hypotheses are responsible for the are responsible for the failed prediction, and those others can’t be failed prediction, and those others can’t be tested tested yetyet..

So can we ever conclusively disprove a So can we ever conclusively disprove a theory? And why believe current theories?theory? And why believe current theories?