PHLA10H3 Lecture Notes - Lecture 8: Logical Truth, Phantom Limb, Fallacy
The Problem of Induction
Knowledge vs. mere justified belief: knowledge implies truth, justified belief does not.
Knowledge implies to impossibility of error, justified belief does not.
Two forms of induction:
Generalization: all observed mammals have hair, so all mammals do.
Prediction: All observed reptiles are cold-blooded, therefore the next reptile to be
observed will be cold-blooded.
!-How many mammals/reptiles have you observed? What if it’s 1-2? Problems!
!-these are not deductively valid obviously
David Hume believed in the Principle of the Uniformity of Nature (PUN).
!-nature will continue to behave in the future as it has in the past; or nature will
generally be similar to the way it is around here.
How does PUN fit into inductive arguments? Instead of “all thus mammals observed
have hair, so the next mammal will have hair” we have “all thus mammals observed
have hair and PUN, so the next mammal will have hair”.
PUN is a posteriori, so it must be proven either by observation or induction.
Example argument, fails because it assumes what it wants to prove:
!-In the past, PUN has always been true. PUN. Therefore, PUN is true.
Hume thought that we should reason inductively even though we have no rational
reason to do so. When you have a pet and put it’s food dish in the same place all the
time, it goes to that place. These habits have worked. You can’t know it’ll be like that
tomorrow, it’s a habit.
Animal faith: You have faith about the future, you don’t have reason though.
Is nature always ‘uniform’? Do the seasons show uniformity or diversity? Will it be warm
tomorrow because it’s July? It seems impossible to state PUN in a non-trivial way.
Induction and reliability: Reliable method of inference: usually leads to truth (let’s say
that)!
-”usually” can be thought of as a scale from not very reliable to highly reliable. Example:
prediction of solar eclipses (highly reliable) and the prediction of weather (not very)
-This scale can be expressed in terms of probability
How do we know that induction is reliable? Can you prove it deductively? Is it somehow
guaranteed that it’ll work? No. So you inductively prove it. But then we’re back in a
circle.
Document Summary
Knowledge vs. mere justi ed belief: knowledge implies truth, justi ed belief does not. Knowledge implies to impossibility of error, justi ed belief does not. Generalization: all observed mammals have hair, so all mammals do. Prediction: all observed reptiles are cold-blooded, therefore the next reptile to be observed will be cold-blooded. David hume believed in the principle of the uniformity of nature (pun). generally be similar to the way it is around here. Nature will continue to behave in the future as it has in the past; or nature will. Instead of all thus mammals observed have hair, so the next mammal will have hair we have all thus mammals observed have hair and pun, so the next mammal will have hair . Pun is a posteriori, so it must be proven either by observation or induction. Example argument, fails because it assumes what it wants to prove: In the past, pun has always been true.
