# PHLA The Problem of Induction

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2 Knowledge versus mere justified belief Knowledge implies truth Justified belief does not imply truth Knowledge implies the impossibility of error Justified belief does not imply impossibility of error Justified belief comes in grades of more or less You are more justified in believing you will lose the 649 lottery than in believing this coin will come up heads We often express this gradation in terms of probability The concept of evidence can be expressed in terms of probability too P is evidence in favour of Q = P raises the probability of Q Learning you rolled an even number is (some) evidence in favour of you having rolled a six

3 Ordinary skepticism attacks knowledge Claims that we have no (or almost no) knowledge Does not deny that some beliefs are more reasonable than others... Does not deny that some beliefs are evidence for others (e.g. raises their probability) Justified belief skepticism attacks rationality Claims that we have no reason to think that any belief is either more or less probable than any other Denies we have any good reason to think that any belief is evidence in favour of (or against) any other possible belief (A priori beliefs/probabilities may be an exception)

4 Review: what is induction A method of amplifying or adding knowledge (or at least adding to our stock of beliefs) Unlike in a valid deductive argument, the conclusion of an inductive argument is not guaranteed to be true, even if the premises are true example: (1) Most dogs are pets (2) Fido is a dog (3) therefore, Fido is a pet Recall what makes a good inductive argument good sample size good sample distribution (sample must be representative of total) These requirements assume there are better or worse evidential relations

5 Two (closely related) forms of induction (1) Generalization (GEN) example: All observed mammals have hair; therefore all mammals have hair. (2) Prediction (PRED) example: All observed reptiles are cold blooded; therefore the next reptile to be observed will be cold blooded. Obviously (GEN) and (PRED) are not deductively valid argument forms. But it seems intuitively obvious that the premises give us a good reason to believe the conclusion Hume argues that this intuition is unsupportable and wrong

6 Hume s version Hume believed that all inductive arguments involved one crucial assumption: the Principle of the Uniformity of Nature (PUN). PUN = nature will continue to behave in the future as it has in the past / nature will generally be similar to the way it is around here David Hume ( )

7 How does PUN fit into inductive arguments? Instead of All thus far observed mammals have hair, so the next mammal we meet will have hair We have All thus far observed mammals have hair and PUN, so the next mammal we meet will have hair Does PUN turn an inductive argument into a deductive argument? Perhaps it is meant to. But what kind of proposition is PUN? A priori (can be deductively proven)? A posteriori (can only be inductively proven)?

8 Is PUN a priori? Can we give a deductive proof of PUN? Is it possible that nature should not be uniform? It seems possible Therefore, PUN is not a priori Therefore, PUN is a posteriori So it must be proven either by observation or induction We cannot observe PUN (because it is about the future) So we must give an inductive argument for PUN Whatever this argument might look like it will be an inductive argument. Therefore, the argument will contain an assumption The assumption according to Hume will be PUN This is circular reasoning and cannot show PUN

9 Example argument: In the past, PUN has always been true Therefore (inductively) PUN is true Hume notes that this argument depends on the assumption that nature will continue to obey PUN So the argument ought to be: In the past, PUN has always been true PUN Therefore, PUN is true This argument fails because it blatantly assumes what it wants to prove!

10 Hume s attitude towards induction Hume thought we should reason inductively even though we have no rational reason to do so He thought we (and many other animals) are naturally structured to believe in and use induction Example: Pavlov s dogs Hume sometimes called this habit He also noticed instincts which are built in by nature and carry information about how organisms expect the world to work Hume wondered how instincts arose and came somewhat close to a concept of evolution But rationality cannot support the beliefs expressed in instinct or by the habit of inductive inference

11 But is PUN needed for inductive arguments or the attack on induction? What, exactly, is the content of PUN? Is nature always uniform? Do the seasons of the year show uniformity or diversity? Is the death of animals a feature of natural uniformity or a sudden dis-uniformity in an animal s life It seems impossible to state PUN in any non-trivial way But PUN is not needed to create the problem of induction

12 Induction and reliability We want our inductive knowledge to be secure Let s say that a reliable method of inference is one that usually leads to the truth usually can be thought of as a scale, from the not very reliable to the highly reliable examples: prediction of solar eclipses (highly reliable) to weather prediction (not highly rel.) This scale can be expressed in terms of probability The probability of an eclipse given what we know about Sun, Earth and Moon is virtually 1 The probability of rain next week given our current knowledge is slightly more than ½ Sober s version of the problem of induction How do we know that induction in general is a reliable way to get knowledge?

13 Sober s new version of the problem of induction How do we know that induction in general is a reliable way to get knowledge? Now we replay Hume s point Either we can deductively prove that induction is a reliable way to get knowledge, or We have to inductively prove it is reliable There is no way to prove deductively that induction is reliable (because we can consistently imagine induction failing) But to prove that induction is reliable inductively is to argue in a circle PUN plays no part in this argument

14 Sober s version of the problem of induction Think about what this means We have zero reason to think that induction is reliable This implies that we have no reason to believe what is inductively reasonable versus the opposite Example: we have zero reason to believe that the Sun will rise tomorrow it is exactly as reasonable to believe it will not rise as that it will?! How can that be right? Can we save induction?

15 Strawson s attempt to save induction Maybe it is an analytic truth that induction is a rational way to amplify knowledge (Recall what an analytic truth is) Strawson seems to be claiming that the idea that induction is a good way to reason is part of the concept of rationality Suppose that is true Would this prove that induction is reliable? It would seem not Sir Peter Strawson ( )

16 Black s attempt to save induction Recall the argument in favour of induction: Induction has been successful in the past, so it will be successful in the future Is the argument in favour of induction really circular? Note the difference between a premise of an argument and a rule of inference Black argues that an argument is circular just in case the conclusion appears (maybe only implicitly) among the premises On that understanding, the inductive argument in favour of induction is not circular it just uses the inductive rule of inference Max Black ( )

17 Black s attempt to save induction Is Black s notion of circularity right? Or is there something wrong with an argument that defends a form of argument which you can accept only if you already accept that form of argument? We could also ask Black: even if we could give this inductive proof of induction, would that show that induction is reliable? No, because counter-induction (CI) is equally supported by a counter-inductive argument CI = if X has happened in the past, expect not-x example: gambler s fallacy The CI argument in favour of CI CI has failed in the past, so expect it to succeed in the future This is a good CI argument!

18 Sober s Trip Beyond Foundationalism Note how Sober divides knowledge claims into 3 levels Indubitable beliefs (a priori / introspectible) Present and past observations Predictions and generalizations Descartes had problems getting from 1 to 2 Hume adds problems getting from 2 to 3 Sober thinks there is no way to Move deductively from a level to a higher level Even use lower level stuff as evidence as higher level That is, IF one is restricted to the lower level This is because something is evidence only relative to additional background beliefs Example: phantom limb pain...

19 The relativity of evidence Suppose we have this evidence: we have examined 10,000 emeralds and they are all green Is this evidence for: all emeralds are green Not if we also believe X: There are many emeralds and they are 99% green OR all emeralds are green but there are very few emeralds in the world Notice that X is not a level 2 statement Sober s thesis: no strictly level n statements justify any level n+1 statements Why? Because of the relativity of evidence What if we had no level n+1 beliefs? Then we could say nothing about level n+1 based only on level n evidence (except for trivial or a priori truths) Is that true?

20 Anti-foundationalism about justification Is rational justification strictly about inter-level justification? If so, Sober thinks it s impossible to achieve Or is there a sense of rational justification that takes into account our current epistemic position? That is, could we say something like Given our current epistemic situation (what we believe now) evidence E would justify belief P This assumes an idea of shared epistemic situation Neurath s Boat

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