The Problem of The Problem of InductionInduction

Aristotle’s InductionsAristotle’s Inductions

Aristotle’s structure of knowledge Aristotle’s structure of knowledge consisted of explanations such as:consisted of explanations such as:

Statue is BronzeStatue is BronzeBronze is BrownBronze is BrownStatue is BrownStatue is Brown

Eventually fundamental truths need to Eventually fundamental truths need to be known through sensation or be known through sensation or inductioninduction

Aristotle’s InductionsAristotle’s Inductions

‘‘Induction proceeds through an Induction proceeds through an enumeration of particular cases’:enumeration of particular cases’:

Bronze thing 1 is brownBronze thing 1 is brownBronze thing 2 is brownBronze thing 2 is brown

……Bronze is BrownBronze is Brown

Recall: in a good induction, if the premises Recall: in a good induction, if the premises are true they make the conclusion are true they make the conclusion probably probably truetrue

Inductions and ScienceInductions and Science

Modern science also uses inductions Modern science also uses inductions to discover regularities in natureto discover regularities in nature Sometimes these are formalised as Sometimes these are formalised as

Laws of NatureLaws of Nature Boyle’s LawBoyle’s Law

p1V1 = p2V2

Inductions and ScienceInductions and Science

Modern science uses these laws in a Modern science uses these laws in a similar way to Aristotlesimilar way to Aristotle

p1= 10kPa

V1 = 1l

V2 = ½l

p1V1 = p2V2

----------------P2 = 20kPa

Hume’s ProblemHume’s Problem

What faith can we have in ‘laws’ What faith can we have in ‘laws’ derived by induction?derived by induction?

Hume says: not much.Hume says: not much. There are only two known ways to There are only two known ways to

justify induction, and neither of them justify induction, and neither of them will workwill work Induction!Induction! DeductionDeduction

Hume’s ProblemHume’s Problem

Induction: We should trust induction Induction: We should trust induction because it’s worked in the pastbecause it’s worked in the past

Induction was successful in case 1Induction was successful in case 2…Induction is a generally successful method

But this depends upon trusting But this depends upon trusting induction!induction!

Hume’s ProblemHume’s Problem

Deduction: We can demonstrate Deduction: We can demonstrate deductively that induction worksdeductively that induction works Suppose that were true, then there’s Suppose that were true, then there’s

some sound argument that goessome sound argument that goes

Premiss 1Premiss 2…Induction works

Hume’s ProblemHume’s Problem

Deduction: We can demonstrate Deduction: We can demonstrate deductively that induction worksdeductively that induction works Then when we have a normal inductive Then when we have a normal inductive

argument we can slip in the conclusion of argument we can slip in the conclusion of that argumentthat argument

Bronze thing 1 is brownBronze thing 2 is brownInduction worksBronze is brown

But it just isn’t logically true that bronze is brown

Hume’s ProblemHume’s Problem

Probability: Restate principle of Probability: Restate principle of induction as a probabilistic rule.induction as a probabilistic rule.

Bronze thing 1 is brownBronze thing 2 is brown…Bronze thing n is brownBronze is probably brown

But this still isn’t good enoughBut this still isn’t good enough What if we now find What if we now find n+1n+1 green bronze green bronze

things?things?

Popper’s SolutionPopper’s Solution

Reject the idea of induction being Reject the idea of induction being fundamental to successful sciencefundamental to successful science We think science is successful because We think science is successful because

induction generates true laws from induction generates true laws from observationsobservations

If induction doesn’t work, science doesn’t If induction doesn’t work, science doesn’t workwork

But science But science does does workwork

So induction So induction must must workwork

Popper’s SolutionPopper’s Solution

We’ve already seen how science We’ve already seen how science worksworks Elenchus (Aristotle, from Socrates)Elenchus (Aristotle, from Socrates) Modus TollensModus Tollens Hypothetico-Deductive MethodHypothetico-Deductive Method

Hypothesis 1: There were land bridgesConsequence: If there were land bridges there would be traces of themObservation: There are no traces of themConclusion: There were no land bridges Hypothesis 2: …

Popper’s SolutionPopper’s Solution

Science doesn’t work by generating Science doesn’t work by generating reliably true theories by inductionreliably true theories by induction

Science works by eliminating Science works by eliminating demonstrably false theories by demonstrably false theories by deductiondeduction

This is the This is the Falsificationist Falsificationist view of view of ScienceScience

Popper’s SolutionPopper’s Solution

If we can’t observationally disprove X, If we can’t observationally disprove X, does that prove X?does that prove X? If Socrates couldn’t disprove Euthyphro’s If Socrates couldn’t disprove Euthyphro’s

claim about piety, would that show E was claim about piety, would that show E was right?right?

No, the definition is still provisionalNo, the definition is still provisional When observations are consistent with a When observations are consistent with a

theory, and don’t disprove ittheory, and don’t disprove it They are said to They are said to confirmconfirm it. it. They can’t prove it.They can’t prove it.

Popper’s SolutionPopper’s Solution

What would it look like to What would it look like to observationally ‘prove’ a theory?observationally ‘prove’ a theory?

If the theory T is true then we should observe X

We do observe XTheory T is true

This is the fallacy of affirming the This is the fallacy of affirming the consequentconsequent

Popper’s SolutionPopper’s Solution

What would it look like to What would it look like to observationally ‘prove’ a theory?observationally ‘prove’ a theory?

If my battery is flat then my car won’t start

My car won’t start My battery is flat

This is the fallacy of affirming the This is the fallacy of affirming the consequentconsequent

Popper’s SolutionPopper’s Solution

Theories are always ‘provisional’Theories are always ‘provisional’ Better or worse confirmedBetter or worse confirmed

Science isn’t a structure of Science isn’t a structure of necessary truthsnecessary truths It’s a system of hypotheses, constantly It’s a system of hypotheses, constantly

being improvedbeing improved

Objections to Popper’s Objections to Popper’s SolutionSolution

Popper’s view explains the processPopper’s view explains the process

Ptolemy Ptolemy Copernicus Copernicus Kepler Kepler

But, surely, we really do know things But, surely, we really do know things about the world, and these things are about the world, and these things are known by inductionknown by inductionWhat happens if I drop this pen?What happens if I drop this pen?

It fallsIt falls I turn into a duckI turn into a duck

Goodman’s New ProblemGoodman’s New Problem

Induction works on properties like ‘brown’Induction works on properties like ‘brown’

Bronze thing number 1 is brownBronze thing number 2 is brown…Bronze thing number n is brown----------------------------------------Bronze is brown

Goodman’s New ProblemGoodman’s New Problem

We can define a property ‘brue’ as:We can define a property ‘brue’ as: Something is ‘brue’ if it is first observed before

[tomorrow’s date] and is brown, or is not first examined before [tomorrow’s date] and is blue.

Bronze thing number 1 is brue (it was seen before tomorrow and was brown)

Bronze thing number 2 is brue (ditto)

…Bronze thing number n is brue (ditto)

----------------------------------------

Bronze is brue

Goodman’s New ProblemGoodman’s New Problem

Something wrong hereSomething wrong here Two different conclusions from two good Two different conclusions from two good

inductions on exactly the same observationsinductions on exactly the same observations The problem seems to be that ‘brue’ isn’t the The problem seems to be that ‘brue’ isn’t the

right sort of property (it’s not ‘projectible’)right sort of property (it’s not ‘projectible’) What makes a predicate projectible?What makes a predicate projectible?

If it’s the sort of predicate we’re accustomed to If it’s the sort of predicate we’re accustomed to using in inductionsusing in inductions

Not a very informative answerNot a very informative answer