The direct method of agreement.

A, D, B, C

2. Describe an eliminating occurrence that would eliminate all the candidates but one.

	Possible conditioning properties	Conditioned property
	A	B	C	D	A	B	C	D	E
Occurrence	P	A	A	P	A	P	P	A	P
Occurrence 1	A	A	A	P	P	P	P	A	A

Eliminate all candidates except A

3. Describe an eliminating occurrence that would eliminate all the candidates.

	Possible conditioning properties	Conditioned property
	A	B	C	D	A	B	C	D	E
Occurrence	P	A	A	P	A	P	P	A	P
Occurrence 1	P	P	A	P	A	A	P	A	A

4. Describe three eliminating occurrences, each of which would eliminate exactly one of the candidates.

	Possible conditioning properties	Conditioned property
	A	B	C	D	A	B	C	D	E
Occurrence	P	A	A	P	A	P	P	A	P
Occurrence 1	P	P	P	A	A	A	A	P	A
Occurrence 2	A	P	P	P	P	A	A	A	A
Occurrence 3	A	P	A	A	P	A	P	P	A

1. Eliminates A

2. Eliminates B

3. Eliminates C

5. What would you conclude if you observed the occurrence that you described in Exercise 2?

The only one sufficient condition for E from candidates A, D, B, C is A

6. What would you conclude if you observed the occurrence you described in Exercise 3?

The only one sufficient condition for E from candidates A, D, B, C is B

7. What would you conclude if you observed the three occurrences you described in Exercise 4?

From each of candidates exactly one of them is eliminated.

8. What would you conclude if you observed all the occurrences that you described in Exercises 2 and 4? There are several correct answers to Exercises 2 and 4. The answer to this question depends on your choice. No sufficient condition for E.

B) Do Exercise 1-5 at pages 93-94 from Skyrms’s textbook “Choice and Chance”, Chapter 5.

Suppose that you have observed the following occurrences:

	Possible conditioning properties	Conditioned property
	A	B	C	D	A	B	C	D	E
Occurrence 1	P	P	A	A	A	A	P	P	P
Occurrence 2	P	A	A	A	A	P	P	P	A
Occurrence 3	A	P	P	P	P	A	A	A	P

1. Suppose you know that one of the possible conditioning properties is a necessary condition for E. Which one is it? What occurrences did you use and which of Mill’s methods did you apply?

B is a necessary condition for E because of the double method of agreement in 1 and 3 oc.

2. Suppose you know that one of the possible conditioning properties which is present in occurrence 1 is a sufficient condition for E. Which one is it? What occurrences did you use and which of Mill’s methods did you apply?

B is a sufficient condition for E in occurrence 1, 2 there is joint method of agreement and difference.

3. Suppose you know that one of the possible conditioning properties is a necessary condition for E and that one of the possible conditioning properties which is present in occurrence 1 is a sufficient condition for E. Do you know whether one possible conditioning property is both a necessary and sufficient condition for E? If so, which one is it and which one of Mill’s methods did you use?

B is a both necessary and sufficient condition for E. The joint method of agreement and difference.

4. Suppose you know that one of the possible conditioning properties is a necessary condition for E. You also know that one of the possible conditioning properties is a sufficient condition for E, but you do not know whether it is a property that is present in occurrence 1. Furthermore, you have observed an additional occurrence:

	A	B	C	D	A	B	C	D	E
Occurrence 4	A	A	P	P	P	P	A	A	A

Do you know whether one possible conditioning property is both a necessary and a sufficient condition for E? If so, which one is it and which one of Mill’s methods did you use?

B is a both necessary and sufficient condition for E. Oc. 1 and 3 eliminate all but B as a necessary condition for E. So it is method of agreement. Oc. 2 and 4 eliminate all but B as a sufficient condition for e. So, we can have an inverse method of agreement and double method of agreement as well.

5. Suppose you had only observed occurrences 1 and 2, but you knew that one of the possible conditioning properties was both a necessary and a sufficient condition for E. Using the two principles of elimination, can you tell which one is it?

B is a both necessary and sufficient condition for E. B is necessary for E because it is not absent when E is present, and B is sufficient for E because it is not present when E is absent.

 

(C)The products of wearing mills can be of low quality (E). It has been supposed that necessary conditions of E can be such factors as low quality of raw materials (A), depreciated machinery (B), low level of workers’ professional skill (C), low motivation of workers as a result of small wages (D), unqualified management (F), corrupt management (G). Construct a table with the results of research which shows that FÚG is a necessary condition for E. What method do you use to eliminate all other possible conditioning properties?

	Possible conditioning properties	Conditioned property
	A	B	C	D	F	G	FvG	E
Occurrence 1	P	A	P	A	A	P	P	P
Occurrence 2	P	A	P	P	A	P	P	A
Occurrence 3	A	P	A	A	P	A	P	P

The direct method of agreement.

(D)Classify each of the following statements as containing an empirical or epistemic (belief-type) probability.

(1)When a flu epidemic strikes, the probability of getting sick for a person who was exposed is between 10% and 15%.

Empirical probability

(2)The probability of preventing the flu by the flu vaccine in a young healthy person is 70 to 90 percent, the probability is only 50 percent in people over 65.

Empirical probability

(3) If there is any probability that God exists, you should believe that he does.

Epistemic probability

(4) According to the weather forecast, the probability that it will snow tomorrow is 80 percent.

Empirical probability

(5) The tales told by Marco Polo when he returned from the Orient were improbable but true.

Epistemic probability

(6) For an American male white-collar worker the probability of surviving his fortieth birthday, given that he has survived his thirty-ninth birthday, is 0.994.

Empirical probability

 

(7) If the probability of getting heads on one toss of a certain coin is one-half, then the probability of getting two heads on two independent tosses of that coin is one-fourth.

Empirical probability

(8) The quantum theory is probably true, in its broad outlines.

Epistemic probability

E) Do Exercise at page 26 from Skyrms’s textbook “Choice and Chance”, Chapter 2, Section 5: Construct two examples in which the epistemic probability of a statement increases or decreases by the addition of new information to a previous stock of knowledge.

1. -Kate works as a pianist in Bolshoi Theater.

- Bolshoi Theater is in Russia.

-Kate plays very well.

-Kate is a diligent.

Epistemic probability of a statement “Kate is a generous” will increase if we add new information:

-Kate works as a pianist in Bolshoi Theater.

- Bolshoi Theater is in Russia.

-Kate plays very well.