method Induction
The of inductive reasoning Hume 2 types of reasoning 1. Reasoning about `relations of ideas' This reasoning is about deductive subjects such as logical truths and mathematics which can be justified a priori Deductive logic licenses conclusions that follow necessarily from premises, for example if the premises `All men are mortal' and `Socrates is a man' are true then the conclusion that `Socrates is mortal' logically follows 2. Reasoning is about `matters of fact', empirical truths from which we inductively construct propositions beyond our past and present experience, ie about our future experience. For example: P: The sun has risen every day in our experience Q: There is no evidence to suggest that this will not continue to be the case R: Therefore the sun will rise tomorrow Our expectations about such matters of fact are formed in the relation of cause and effect It is our sense about this relation that tells us that it is an intelligible proposition that the sun will rise The problem of induction Hume argues that it is just as possible to conceive contrary propositions: "That the sun will not rise to morrow is no less intelligible a proposition, and implies no more contradiction, than the affirmation, that it will rise. We should in vain, therefore, attempt to demonstrate its falsehood. Were it demonstratively false, it would imply contradiction, and could be distinctly conceived by the mind." How do we know that the future will resemble the past? This reasoning has to be either a priori or a posteriori Hume argues that it cannot be a priori if we were to see the sun rising for the first time we would never discover from the object alone what produced it and what its effect was Knowledge of such causal relations must come through experience of the relations between objects therefore our reasoning must be a posteriori
When we project findings about these relations into the future, we must use an intermediate premise: `the uniformity of nature' This premise must in turn be justified
Responses to the problem of induction The New Riddle of Induction Hume: "From causes which seem similar we expect similar effects." Induction cannot be proved deductively as in a deductive argument the conclusion is entailed by the premises, but for induction the conclusion is some future event Induction can be proved false the chicken thinks that the human will always bring it grain until it is slaughtered To justify induction inductively, because it has worked in the past, we have to presuppose it is valid Hume: "It is impossible, therefore, that any arguments from experience can prove this resemblance of the past to the future; since all these arguments are founded on the supposition of that resemblance." Hume: "All inferences from experience, therefore, are effects of custom, not of reasoning." Popper science does not rely on induction but assumes everything as a hypothesis until it has been disproved However, this gives us little ground to make claims about the future Ways of justifying induction: 1. Deductively 2. Inductively 3. Argue that it makes no sense to attempt to justify induction 4. Conceded that induction cannot be validated but argue that it can be vindicated 1. Find a hidden premise when then entails the conclusion or introduce an element of probability a) For such a premise to legitimise induction deductively it could never be the case that the premise true and the conclusion false. However, the premise itself cannot be justified and cannot be proven to be true.
b) Russell: "The most we can hope is that the oftener things are found together, the more probable it becomes that they will be found together another time, and that, if they have been found together often enough, the probability will amount almost to certainty." Bonjour approach By prefixing the conclusion with a level of probability does it not mean that should the content of the conclusion turn out to be false the conclusion as a whole is false Eg P. This dice has rolled a `6' on 16 out of 20 rolls C. There is an 80% chance that the dice will roll a `6' However, this fails to actually justify induction 16/20 rolls of a 6 does not entail an 80% probability of the next role being a 6 unless we use induction to say that the probability will continue to be the same in the future As Hume argues, the term `probable' is just a way of saying `I think' and so we are back to square one 2. The difficulty is to avoid circularity This can be done by introducing levels of justification such as a) Level one consists in arguments about things eg the sun b) Level two consists in arguments about arguments c) Level three consists in arguments about arguments in level 2 The rules of level one are induction, and they are justified by induction on level two, which concerns not objects but theories about objects, and so is sufficiently distinct This counters Hume's contention, but is still unsatisfactory leads to problem of infinite regress This argument is a system of induction and not a proof of it The same style of argument could be used to justify another method, such as `counterinduction' or `wishful thinking' 3. Analytic response that induction is rationality, so asking is induction rational is equivalent to asking `is the law legal' Strawson: "If someone asked what grounds there were for supposing that deductive reasoning was valid...we should have to answer that his question was without sense, for to say that an argument... was valid or invalid would imply that it was deductive" Goodman Paradoxical result Blackburn response to grue paradox grue differentiates between examined and unexamined emeralds, so that to project grueness is to differentiate between some emeralds and others Expecting differences is "exactly what the justification of induction tries to show to be unreasonable" Goodman's problem is why do we project properties like green which don't posit a difference between emeralds and not project ones like grue which do
Ie why do we expect regularity which is just Hume's problem Response projecting greenness does posit a difference between examined and unexamined emeralds Introducing `bleen' means that there is a differe...