The problem of induction
We cannot appeal to some sort of necessity in causal explanation. We cannot say "future causes and effects will be like past ones because they MUST be like them" because we have no basis for this claim.
Acc to Hume, we get our idea of A CAUSING B through having always observed event A being followed by event B ( a 'constant conjunction') and thus coming to expect B whenever A occurs. But we have no grounds for asserting any necessity about the connection as 1) it is not a truth of logic (a relation of ideas) 2) it is not sth we observe (a matter of fact). all we OBSERVE is one event and then a second event. we don't observe the necessity. If we repeat the same action, there will certainly be a certain regularity (constant conjunction) but not a necessity. we do not see the necessary connection.
According to Hume
All statements can be classified :
Induction and Science
Hooke's Law: the extension of an elastic object is directly proportional to the force applied to it. imagine the relevant experiment. we draw a line from observed data and we draw conclusion about unobserved data (between the measures) what is the relation of the readings to the general law?
We cannot say "we doing so because it has always worked in the past"
because that would be an inductive inference
Relations of ideas
e.g. deductive (logical) proofs, truths of arithmetic, tautologies these statements are made true or false by the meanings of the words involved, such as "all triangles have three sides" If true, they are BOUND to be true - triangles MUST have three sides. If false, they are bound to be false - triangles cannot have four sides.
Karl Popper, Conjectures and Refutations
if we understand science correctly, scientists are not really trying to prove the generalisations that we call laws of nature to be true, so induction is not relevant to their methods. They are actually trying to falsify them, and seeking well-tested but so far unfalsified generalisations. But does this really avoid induction? Does it provide a good method for science ?
induction goes beyond what we've observed
nothing justifies induction
Matters of fact
statements about observable objects and events in the world. These statements are made true or false by how the world actually is, such as "there is a computer in the room". Even if they are true, they are NOT BOUND to be true- there might not have been a computer in the room. Equally, if false, they are not bound to be false - there might have been a computer in the room.
Induction
the drawing of a conclusion (an 'inductive inference') about unobserved cases based on what has been observed. Conclusions about the future based on the past.
clarification
the problem is not that we might be wrong using induction and so it would be a problem problem = what justifies us in doing so ?
Inductive inferences are not provable a priori
they are not relations of ideas
The problem of induction
we expect the future to be in many ways like the past AND we think we are JUSTIFIED in expecting so BUT, Hume asked, what exactly is the justification for doing this kind of inference ?