the problem of induction. aristotle’s inductions aristotle’s structure of knowledge consisted of...
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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