1. Today’s Outline Hume’s Problem of Induction Two Kinds of Skepticism
Three Distinctions
Deduction vs. Induction
Relations of Ideas vs. Matters of Fact
A Priori Knowledge vs. A Posteriori Knowledge
The Problem of Induction
The Principle of the Uniformity of Nature
The Argument
Hume’s Anti-Rationalism
Some Replies to Hume’s Argument
Analytic Inductionism
Induction Justifies Induction
Evidential Relativism

2. David Hume (1711-1776) British philosopher and historian
Considered the greatest philosopher to write in the English language
Greatest Philosophical Work: A Treatise of Human Nature (1739)
(this was began when he was 23 years old)
Famous doctrines: empiricism, skepticism.
Immanuel Kant said Hume “awoke me from my dogmatic slumber.”

4. III. Hume’s Problem of Induction

5. A. Two Kinds of Skepticism
Skepticism about knowledge
Perhaps after reading Descartes we conclude we can’t be absolutely certain about the external world.
Perhaps we can live with this.
Skepticism about justification
Hume is here to tell us we have no reason whatsoever to believe certain things we thought obvious.
This would be hard to live with.

6. B. Three Distinctions Deduction vs. Induction
Relations of Ideas vs. Matters of Fact
A Priori Knowledge vs. A Posteriori Knowledge

7. 1. Deduction vs. Induction
“All reasonings may be divided into two kinds, namely demonstrative reasoning, or that concerning relations of ideas, and moral reasoning, or that concerning matter of fact and existence”
- from Hume’s Enquiry (1777)

8. 1. Deduction vs. Induction
In deductive reasoning (or for deductive arguments), it is supposed to be that:
the premises logically entail the conclusion
the truth of the premises guarantees the truth of the conclusion
it is impossible for the premises to be true and the conclusion to be false.

9. 1. Deduction vs. Induction
EXAMPLES of deductive arguments:
EXAMPLE 1:
1. All men are mortal.
2. Socrates is a man
3. Therefore, Socrates is mortal.

10. 1. Deduction vs. Induction
EXAMPLES of deductive arguments:
EXAMPLE 2:

11. 1. Deduction vs. Induction
EXAMPLES of deductive arguments:
EXAMPLE 2:
1. If it’s raining, then the streets are wet.
2. It’s raining.
3. Therefore, the streets are wet.

12. 1. Deduction vs. Induction
EXAMPLES of deductive arguments:
EXAMPLE 3:

13. 1. Deduction vs. Induction
EXAMPLES of deductive arguments:
EXAMPLE 3:
1. All cats are toaster ovens.
2. All toaster ovens can fly.
3. Therefore, all cats can fly.

14. 1. Deduction vs. Induction
In inductive reasoning (or for inductive arguments), it is supposed to be that:
the premises support (without logically entailing) the conclusion
the truth of the premises makes likely the truth of the conclusion
it is improbable for the premises to be true and the conclusion to be false

15. 1. Deduction vs. Induction
EXAMPLES of inductive arguments:

16. 1. Deduction vs. Induction
EXAMPLES of inductive arguments:
EXAMPLE 1:
1. Every emerald that has ever been observed is green.
2. Therefore, all emeralds are green.

17. 1. Deduction vs. Induction
EXAMPLES of inductive arguments:
EXAMPLE 2:

18. 1. Deduction vs. Induction
EXAMPLES of inductive arguments:
EXAMPLE 2:
1. The sun has risen every day in the past.
2. Therefore, the sun will rise tomorrow.

19. 1. Deduction vs. Induction
EXAMPLES of inductive arguments:
EXAMPLE 3:

20. 1. Deduction vs. Induction
EXAMPLES of inductive arguments:
EXAMPLE 3:
1. Every time I have eaten bread in the past it has nourished me.
2. Therefore, the next time I eat bread it will nourish me.

21. The target of Hume’s Problem of Induction is just this sort of inductive reasoning.
Although such reasoning seems totally legitimate and rational and justified, Hume aims to show that it is in fact totally unjustified.
In other words, Hume aims to show that the premises of such arguments provide no reason at all to think that the conclusion is true.

22. B. Three Distinctions  Deduction vs. Induction
Relations of Ideas vs. Matters of Fact
A Priori Knowledge vs. A Posteriori Knowledge

23. 2. Relations of Ideas vs. Matters of Fact
“All the objects of human reason or enquiry may naturally be divided into two kinds, to wit, Relations of Ideas, and Matters of Fact.”

24. 2. Relations of Ideas vs. Matters of Fact
“Propositions of this kind are discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe.”

25. 2. Relations of Ideas vs. Matters of Fact
DEFINITION: relations of ideas are statements that are true simply in virtue of the concepts contained in them, and not in virtue of the way the world is.
They are “true by definition.”
They usually seem to be fairly trivial truths.

26. 2. Relations of Ideas vs. Matters of Fact
EXAMPLES:
‘All triangles have three sides.’
“Three times five is equal to half of thirty.”
‘If Bob is a bachelor, then Bob is unmarried.’
‘Either it’s raining or it’s not raining.’
Relations of ideas are also called analytic truths.

27. 2. Relations of Ideas vs. Matters of Fact
DEFINITION: matters of fact are statements that are not relations of ideas.
So when they are true, they are true not in virtue of the concepts contained in them but in virtue of the way the world is.
They are NOT true by definition.
They tend to be substantive rather than trivial.

28. 2. Relations of Ideas vs. Matters of Fact
EXAMPLES:
‘The earth is round.’
“The sun will rise tomorrow.”
‘All bachelors have messy apartments.’
‘Either it’s raining or it’s snowing.’
Matters of fact are also called synthetic truths.
Hume says, “The contrary of every matter of fact is still possible.”

29. B. Three Distinctions   Deduction vs. Induction
Relations of Ideas vs. Matters of Fact
A Priori Knowledge vs. A Posteriori Knowledge 

30. 3. A Priori Knowledge vs. A Posteriori Knowledge

31. 3. A Priori Knowledge vs. A Posteriori Knowledge
DEFINITION of a priori knowledge:
S knows (or is justified in believing) p a priori if and only if S knows (or is justified in believing) p independent of experience.
That is: if and only if S’s reason for believing p makes no mention of any sensory experience.
‘a priori’ is Latin for ‘from what is before’

32. 3. A Priori Knowledge vs. A Posteriori Knowledge
EXAMPLES of things that can be known a priori:
‘All triangles have three sides.’
‘The internal angles of any triangle total 180º.’
‘If Bob is a bachelor, then Bob is unmarried.’
‘Either it’s raining or it’s not raining.’
RECALL: the Ontological Argument was an a priori argument for the existence of God. If it is sound, then ‘God exists’ is knowable a priori.

33. 3. A Priori Knowledge vs. A Posteriori Knowledge
TWO MORE THINGS about a priori knowledge:
When we say you can know a priori that ‘All triangles have three sides’, we are NOT saying you would know this even if you never had any experiences. We are saying the justification for believing the proposition need not involve any evidence from experience.
Things that one can know a priori may also be knowable a posteriori. (E.g., I know a posteriori that Fermat’s Last Theorem is true, even though it is knowable a priori.)
When we say you can know a priori that ‘All triangles have three sides’, we are NOT saying you would know this even if you never had any experiences. We are saying the justification for believing the proposition need not involve any evidence from experience.
Things that one can know a priori may also knowable a posteriori. (E.g., I know a posteriori that Fermat’s Last Theorem is true, even though it is knowable a priori.)

34. 3. A Priori Knowledge vs. A Posteriori Knowledge
DEFINITION of a posteriori knowledge:
S knows (or is justified in believing) p a posteriori if and only if S knows (or is justified in believing) p through experience.
That is: if and only if S’s reason for believing p involves some sensory experience(s).
‘a posteriori’ is Latin for ‘from what comes after’

35. B. Three Distinctions    Deduction vs. Induction
Relations of Ideas vs. Matters of Fact
A Priori Knowledge vs. A Posteriori Knowledge  

36. QUESTION: Are there any interesting connections between the relation of ideas / matter of fact distinction and the a priori / a posteriori distinction?
SOME HUMEAN ANSWERS:
We can have a priori knowledge of a proposition only if it is a relation of ideas.
Matters of fact can be known only a posteriori.

37. C. The Problem of Induction
The “Problem of Induction” is an argument (a deductive argument) for the following conclusion:
The premises of an inductive argument never provide any reason to think that the conclusion is true.

38. Inductive Arguments:
1. Every emerald that has ever been observed is green.
2. Therefore, all emeralds are green.
1. Pressing the brake pedal has always stopped my car.
2. Therefore, pressing the brake pedal will stop my car in the future.
1. Breathing has never killed me.
2. Therefore, my next breath won’t kill me.

39. So if Hume is right, then the next time you want to stop your car, it would be no more rational to press the brake pedal than to snap your fingers!

40. 1. The Principle of the Uniformity of Nature
“all inferences from experience [about what will happen in the future] suppose, as their foundation, that the future will resemble the past … . If there be any suspicion, that the course of nature may change, and that the past may be no rule for the future, all experience becomes useless, and can give rise to no inference or conclusion.”
PUN: The future, by and large, will resemble the past.

41. 2. The Argument FIRST PART:
If there is any reason to believe PUN, then our justification for PUN is either a priori or a posteriori.
Our justification for PUN is not a priori.
Our justification is not a posteriori.
Therefore, there is no reason to believe PUN.

42. 2. The Argument SECOND PART: There is no reason to believe PUN.
If there is no reason to believe PUN, then the premises of an inductive argument never provide any reason to think that the conclusion is true.
Therefore, the premises of an inductive argument never provide any reason to think that the conclusion is true.

43. induction is totally unjustified.
In other words:
induction is totally unjustified.

44. You thus have no more reason to believe
‘The next time I press the brake pedal in my car, my car will stop.’
than you do this:
‘The next time I press the brake pedal in my car, my car will blow up.’
You have absolutely no reason to think your next breath won’t kill you.

45. D. Hume’s Anti-Rationalism
“Even after we have experience of the operations of cause and effect, our conclusions from that experience are not founded on reasoning, or any process of the understanding.”
“Men are not impelled by any reasoning or process of the understanding, but rather from Custom or Habit. ... Custom, then, is the great guide of human life.”

46. E. Some Replies to Hume’s Argument
Analytic Inductionism
Induction Justifies Induction
Evidential Relativism