The Problem of Induction Aristotles Inductions n Aristotles

The Problem of Induction

Aristotle’s Inductions n Aristotle’s structure of knowledge consisted of explanations such as: Statue is Bronze is Brown Statue is Brown n Eventually fundamental truths need to be known through sensation or induction

Aristotle’s Inductions n ‘Induction proceeds through an enumeration of particular cases’: Bronze thing 1 is brown Bronze thing 2 is brown … Bronze is Brown n Recall: in a good induction, if the premises are true they make the conclusion probably true

Inductions and Science n Modern science also uses inductions to discover regularities in nature Sometimes these are formalised as Laws of Nature n Boyle’s Law n p 1 V 1 = p 2 V 2

Inductions and Science n Modern science uses these laws in a similar way to Aristotle p 1= 10 k. Pa V 1 = 1 l V 2 = ½l p 1 V 1 = p 2 V 2 --------P 2 = 20 k. Pa

Hume’s Problem What faith can we have in ‘laws’ derived by induction? n Hume says: not much. n n There are only two known ways to justify induction, and neither of them will work n Induction! n Deduction

Hume’s Problem n Induction: We should trust induction because it’s worked in the past Induction was successful in case 1 Induction was successful in case 2 … Induction is a generally successful method n But this depends upon trusting induction!

Hume’s Problem n Deduction: We can demonstrate deductively that induction works n Suppose that were true, then there’s some sound argument that goes Premiss 1 Premiss 2 … Induction works

Hume’s Problem n Deduction: We can demonstrate deductively that induction works n Then we have a normal inductive argument we can slip in the conclusion of that argument Bronze thing 1 is brown Bronze thing 2 is brown Induction works Bronze is brown n But it just isn’t logically true that bronze is brown

Hume’s Problem n Probability: Restate principle of induction as a probabilistic rule. Bronze thing 1 is brown Bronze thing 2 is brown … Bronze thing n is brown Bronze is probably brown n But this still isn’t good enough n What if we now find n+1 green bronze things?

Popper’s Solution n Reject the idea of induction being fundamental to successful science n We think science is successful because induction generates true laws from observations If induction doesn’t work, science doesn’t work But science does work So induction must work

Popper’s Solution n We’ve already seen how science works Elenchus (Aristotle, from Socrates) n Modus Tollens n Hypothetico-Deductive Method n Hypothesis 1: Consequence: There were land bridges If there were land bridges there would be traces of Observation: Conclusion: Hypothesis 2: There are no traces of them There were no land bridges … them

Popper’s Solution Science doesn’t work by generating reliably true theories by induction n Science works by eliminating demonstrably false theories by deduction n This is the Falsificationist view of Science n

Popper’s Solution n If we can’t observationally disprove X, does that prove X? If Socrates couldn’t disprove Euthyphro’s claim about piety, would that show E was right? n No, the definition is still provisional n n When observations are consistent with a theory, and don’t disprove it They are said to confirm it. n They can’t prove it. n

Popper’s Solution n What would it look like to observationally ‘prove’ a theory? If theory T is true then we should observe X We do observe X Theory T is true n This is the fallacy of affirming the consequent

Popper’s Solution n What would it look like to observationally ‘prove’ a theory? If my battery is flat then my car won’t start My battery is flat n This is the fallacy of affirming the consequent

Popper’s Solution n Theories are always ‘provisional’ n n Better or worse confirmed Science isn’t a structure of necessary truths n It’s a system of hypotheses, constantly being improved

Objections to Popper’s Solution n Popper’s view explains the process Ptolemy ® Copernicus ® Kepler ®. . . n But, surely, we really do know things about the world, and these things are known by induction n What happens if I drop this pen? n It falls n I turn into a duck

Goodman’s New Problem n Induction works on properties like ‘brown’ Bronze thing number 1 is brown Bronze thing number 2 is brown … Bronze thing number n is brown --------------------Bronze is brown

Goodman’s New Problem n We can define a property ‘brue’ as: n 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 Problem n n Something wrong here Two different conclusions from two good inductions on exactly the same observations The problem seems to be that ‘brue’ isn’t the right sort of property (it’s not ‘projectible’) What makes a predicate projectible? n If it’s the sort of predicate we’re accustomed to using in inductions n Not a very informative answer