1. Formalizing arguments
Philosophy 4340, Epistemology

2. What is formalizing an argument?
Taking this: “Blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah … (for twenty pages)”

3. What is formalizing an argument?
And turning it into this:
Credit is a surreptitious good of belief.
If something is a surreptitious good of belief, then one cannot be (consciously) motivated by pursuit of that good to believe something.
Thus, one cannot be (consciously) motivated by pursuit of credit to believe something.
If one cannot be motivated to do Z by pursuit of X, then X does not give reasons to Z.
Thus, credit does not give reasons to believe.
If credit does not give reasons to believe, then (if the credit theory of knowledge is true, knowledge is not the aim of belief).
If the credit theory of knowledge is true, then knowledge is the aim of belief.
Thus, the credit theory of knowledge is false.

4. What is formalizing an argument?
More carefully, formalizing an argument is representing an argument so that it is clear that the argument is valid.
This is formalizing because what you produce will be valid in virtue of the form of the argument.
Purely in virtue of it’s structural properties.
Not the meaning of terms.

5. What is validity?
Take a second to ask yourself this question: What does it mean to say that an argument is valid?
An argument is valid iff:
(necessarily) If all of the premises are true, then the conclusion is true.

6. What is formal validity?
A valid argument:
2+2=5
Every entirely green thing is entirely red
Thus, humans have free will.

7. What is formal validity?
A valid argument:
Every unicorn has a horn.
Animals with pointy attachments are dangerous.
Thus, every unicorn is dangerous.

8. What is formal validity?
A formally valid argument:
If p is true, then q is true.
It is the case that p is true.
Thus, it is the case that q is true.
(alternately):
P -> Q P
Thus, Q

9. Why analyze arguments?
Our goal is to learn things that we did not previously know.
We analyze author’s arguments to learn from them.
An author may prove something that we previously disbelieved; they may also give an argument that we tend to accept, but which really is no good.

10. Why make arguments valid?
Invalid deductive arguments aren’t worth paying much attention to.
Making an argument valid calls our attention to what must be accepted to make the argument work.

11. Why formally valid? Validity is necessary but boring.
Casual arguments conceal subtle errors.

12. What are our tools? Propositions: things with truth values
So, no questions, fragments, or imperatives.
Operators and connectives:
And, or, if… then, iff, not
(alternately) &, ^, ->, <->, ~
Numbers
To indicate: this is a distinct step in the argument.
“Thus,” “So,” “therefore,” etc
To signal “This follows from what comes before it”

13. Don’t re-invent the wheel
If p then q P
Thus, q
P is true about Fred.
Thus, q is true about Fred.

14. Don’t re-invent the wheel
If P then Q ~Q
Thus, ~P
Q is false about Susie.
Thus, P is false about Susie.

15. Don’t re-invent the wheel
If A then B.
If B then C.
Thus, If A then C.
X or Y ~X
Thus Y
X -> Z
Y ->Z
Thus, Z

16. Don’t re-invent the wheel
Rather than reductio:
A->B
B->~A
Thus, ~A
X->Y
X->~Y
Thus, X-> Y&~Y
Thus, ~X

17. Continue to not re-invent the wheel
A->B
B->C
Thus, A->C
C->D
Thus, A->D ~D
Thus, ~A

18. Getting arguments from text
Steps 1 & 2:
Figure out the main conclusion of the paper.
(brainstorm) List the key points the author seems to think establish the main conclusion.

19. Getting arguments from text
Steps 1 & 2 (for example):
Conclusion: The credit theory of knowledge is false.
Why? It thinks knowledge is the aim of belief.
But we can’t be motivated to believe by credit.
So we couldn’t be motivated by knowledge.

20. Getting arguments from text
Step 3: Construct the core argument. Start with the conclusion: “Thus, the credit theory of knowledge is false.”

21. Constructing the core argument
If p then q
A->B P
X or Y
B->~A
Thus, q ~X
Thus, ~A
Thus Y
If P then Q
X->Y ~Q
X->~Y
Thus, ~P
X -> Z
Thus, X-> Y&~Y
Y ->Z
Thus, ~X
If A then B.
Thus, Z
If B then C.
Thus, If A then C.

22. Constructing the core argument
If P then Q
A->B P
X or Y
B->~A
Thus, Q ~X
Thus, ~A
Thus Y
X->Y ~Q
X->~Y
Thus, ~P
X -> Z
Thus, X-> Y&~Y
Y ->Z
Thus, ~X
If A then B.
Thus, Z
If B then C.
Thus, If A then C.

23. If P then Q ~Q
Thus, ~P
A->B
B->~A
Thus, ~A
X->Y
X->~Y
Thus, X-> Y&~Y
Thus, ~X
Conclusion: The credit theory of knowledge is false. Why? If it is true, then knowledge is the aim of belief.

24. If P then Q ~Q
Thus, ~P
A->B
B->~A
Thus, ~A
X->Y
X->~Y
Thus, X-> Y&~Y
Thus, ~X
If CTK is true, then knowledge is the aim of belief. Knowledge is not the aim of belief.
Thus, CTK is false.

25. If P then Q ~Q
Thus, ~P
A->B
B->~A
Thus, ~A
X->Y
X->~Y
Thus, X-> Y&~Y
Thus, ~X
If CTK is true, then knowledge is the aim of belief. If knowledge is the aim of belief, then CTK is false.
Thus, CTK is false.

26. If P then Q ~Q
Thus, ~P
A->B
B->~A
Thus, ~A
X->Y
X->~Y
Thus, X-> Y&~Y
Thus, ~X
If CTK is true, then knowledge is the aim of belief. If CTK is true, then knowledge is not the aim of belief. Thus, if CTK is true, knowledge is and is not the aim of belief.
Thus, CTK is false.

27. If CTK is true, then knowledge is the aim of belief.
If CTK is true, then knowledge is not the aim of belief.
Thus, if CTK is true, knowledge is and is not the aim of belief.
Thus, CTK is false.

28. Thus, if CTK is true, then knowledge is not the aim of belief.
If CTK is true, then knowledge is the aim of belief.
Thus, if CTK is true, knowledge is and is not the aim of belief.
Thus, CTK is false.

29. “Thus, if CTK is true, then knowledge is not the aim of belief.”
If P then Q
A->B P
X or Y
B->~A
Thus, Q ~X
Thus, ~A
Thus Y
X->Y ~Q
X->~Y
Thus, ~P
X -> Z
Thus, X-> Y&~Y
Y ->Z
Thus, ~X
If A then B.
Thus, Z
If B then C.
Thus, If A then C.

30. If A then B.
If B then C.
Thus, if A then C.
If CTK is true, then …
If …, then knowledge is not the aim of belief.
Thus, if CTK is true, knowledge is not the aim of belief.

31. Brainstorming from steps 1 & 2:
Conclusion: The credit theory of knowledge is false.
Why? It thinks knowledge is the aim of belief.
But we can’t be motivated to believe by credit.
So we couldn’t be motivated by knowledge.

32. If A then B.
If B then C.
Thus, if A then C.
If CTK is true, then we can’t be motivated by knowledge.
If we can’t be motivated by knowledge, then knowledge is not the aim of belief.
Thus, if CTK is true, knowledge is not the aim of belief.

33. If CTK is true, then we can’t be motivated by knowledge.
If we can’t be motivated by knowledge, then knowledge is not the aim of belief.
Thus, if CTK is true, then knowledge is not the aim of belief.
If CTK is true, then knowledge is the aim of belief.
Thus, if CTK is true, knowledge is and is not the aim of belief.
Thus, CTK is false.

34. Thus, if CTK is true, then we can’t be motivated by knowledge.
If we can’t be motivated by knowledge, then knowledge is not the aim of belief.
Thus, if CTK is true, then knowledge is not the aim of belief.
If CTK is true, then knowledge is the aim of belief.
Thus, if CTK is true, knowledge is and is not the aim of belief.
Thus, CTK is false.

35. “Thus, if CTK is true, then we can’t be motivated by knowledge.”
If P then Q
A->B P
X or Y
B->~A
Thus, Q ~X
Thus, ~A
Thus Y
X->Y ~Q
X->~Y
Thus, ~P
X -> Z
Thus, X-> Y&~Y
Y ->Z
Thus, ~X
If A then B.
Thus, Z
If B then C.
Thus, If A then C.

36. If …, then we can’t be motivated by knowledge.
If A then B.
If B then C.
Thus, if A then C.
If CTK is true, then …
If …, then we can’t be motivated by knowledge.
Thus, if CTK is true, then we can’t be motivated by knowledge.

37. Brainstorming from steps 1 & 2:
Conclusion: The credit theory of knowledge is false.
Why? It thinks knowledge is the aim of belief.
But we can’t be motivated to believe by credit.
So we couldn’t be motivated by knowledge.

38. If A then B. If B then C. Thus, if A then C.
If CTK is true, then motivation by knowledge is motivation by credit.
If motivation by knowledge is motivation by credit. , then we can’t be motivated by knowledge.
Thus, if CTK is true, then we can’t be motivated by knowledge.

39. If CTK is true, then motivation by knowledge is motivation by credit.
If motivation by knowledge is motivation by credit, then we can’t be motivated by knowledge.
Thus, if CTK is true, then we can’t be motivated by knowledge.
If we can’t be motivated by knowledge, then knowledge is not the aim of belief.
Thus, if CTK is true, then knowledge is not the aim of belief.
If CTK is true, then knowledge is the aim of belief.
Thus, if CTK is true, knowledge is and is not the aim of belief.
Thus, CTK is false.