Phil 140 - Module 5 / 6

Syllogisms

a deductive argument with exactly two premises and one conclusion

Categorial Syllogisms

both premises and the conclusion of the argument are categorial propositions - three statements

the premises and the conclusions contain exactly 3 different terms between them

each term appears twice in different propositions

Major term 

the term that occurs as the predicate of the conclusion and in one of the premises

• term at end of the conclusion 

Major premise 

the premise in which the major term occurs - should be listed first 

• same end term as the conclusion 

Minor term

the term that occurs as the subject of the conclusion and in one of the premises

• first term in the conclusion

Minor premise

the premise in which the minor term occurs

• should be listed second

• has the same term as the subject in conclusion

Middle term 

the term that occurs in both premises but does nor occur anywhere in the conclusion

the term that cancels out

the third term that is not included in the conclusion 

Standard-Form

major premise listed first

minor premise listed second

conclusion listed last

• both premises and the conclusion are standard form categorial propositions

• the two occurrences of each term are the same

• each term has the same meaning in each of its occurrences

Mood

the letter names of the constituent propositions of a categorial syllogism in the following order : major premise, minor premise, conclusion

• give each statement their letter proposition - A,E,I,O

• the order of letters gives the mood

Figure - 4 options 

1. the middle term occupies the subject position in the major premise and the predicate position in the minor plane 

• middle term first, then middle term second 

2. middle term occupies the predicate position in both premises 

• middle term last in both statements 

3. the middle term occupies the subject position in both premises 

• middle term first in both statements 

4. the middle term occupies the predicate position in the major premise and the subject position in the minor premise 

• middle term last, then middle term first 

Validity

based on the mood and figure

certain moods with certain figures are not valid

based on chart

Venn Diagrams - Step One : set up

produce a diagram consisting of three interlocking circles

• lower left - minor term (S)

• lower right - major term (P)

• upper middle - middle term (M)

each section is numbered

I have no idea if I have to remember it, they numbered weird

Venn Diagrams - Characteristic Diagrams 

if shaded it means its empty - not it, none of it 

just two circles, S and P

• A prop - All S are P - S is shaded

• E prop - No S are P - middle shaded

• I prop - Some S are P - an x in the middle

• O prop - Some S are not P - an x in S

Venn Diagrams - when doing 

• label properly 

• break down into statements 

• split into premises - do each separately 

Premise 1 - find the two classes it follows and use the characteristic diagrams, ignore other circles

Premise 2 - do the same as 1

do not diagram the conclusion

I and O premises

if one premise requires shading and the other requires an x, do the shading first

• can’t put an x in an area that is shaded, it’s “empty”

if an x can go into two separate regions, place it on the line between those regions

Interpreting Venn Diagrams

a diagram shows an argument to be valid if and only if the diagram for the premises makes the conclusion true

true conclusions

• A-prop : regions 2 and 5 shaded

• E-prop : regions 3 and 6 shaded

• I-prop : an x in region 3 or 6

• O-prop : an x in region 2 or 5

Reducing Number of Terms - Counting and Abbreviations

• can be up to 6 different terms but all come in sets of 2

• abbreviations make it easier to see the transformations

  • will have letters and non-letters

  • the pairs are complements of each other

ex) Some donkeys are not well-tempered beasts

No ill-tempered beasts are literate readers

Some illiterate readers are non-donkeys

• Pairs : donkeys - D; non-donkeys - non-D

• well-tempered beasts - W; ill-tempered beasts - non-W

• literate readers - L; illiterate readers - non-L

Some D are not W

No non-W are L

Some non-W are non-D

Reducing Terms 

reduce the number of terms to three terms by manipulating the statements with converse, obverse, and contrapositive

• recall the equivalence chart

• all obverse is equivalent

• Converse - not equal with A and O

• Contra - not equal with E and I

• operations - more than one series of operations can be used to produce an equivalent categorial syllogism; can use converse and then obverse to the same statement

• terms - there is no requirement that the three terms you end up with are non or not

• make sure that the operations used to yield statements that are equivalent to the original statements

Chpt 6 - Casual Reasoning

used to identify the causes behind a phenomenon

kind of inductive reasoning, the probability of the conclusion

Causation

a relation between events or facts that hold when an earlier fact or event makes a later fact or event happen

one event makes/causes another event to happen

Necessary Conditions 

condition A is necessary for condition B if A is required for B / B cannot be present or occur without the presence or occurrence of A

in order for it to be, it HAS to be this 

ex) being a mammal is a necessary condition for being a dog 

Sufficient Conditions

condition A is sufficient for condition B is A is good enough for B / the presence or occurrence of A ensures the presence or occurrence of B

its good enough for it to be this

ex) being a dog is sufficient for being a mammal

Necessary Cause

A is a necessary cause of B if the occurrence of A is required to bringing about B

ex) the presence of oxygen is a necessary cause of a fire

Sufficient Cause 

A is a sufficient cause of B is the occurrence of A is by itself good enough to bring about B 

ex) striking a match in the presence of fuel and oxygen is a sufficient cause of a fire

Necessary and Sufficient Cause

A is a necessary and sufficient cause of B if A is both requires for the occurrence of B and A is by itself good enough to cause B

ex) ignition (by some means or other) in the presence of fuel and oxygen is a necessary and sufficient cause of a fire

Mill’s Methods - 3

1. Method of Agreement

2. Method of Difference

3. Joint Method of Agreement and Difference

all are charts indicating if an occurrence is caused or not and by which factor

Method of Agreement 

consists of a systematic effort to find a single factor that is common to multiple occurrences of a phenomenon to identify that factor as a necessary cause of the phenomenon

find the common factor that would lead to the conclusion, factor that is common in all instances

an entire row will be yes or no 

Method of Difference

consists of systematic effort to identify a single factor that is present in an occurrence in which a phenomenon is present and absent from an occurrence in which the phenomenon is absent and identify that factor as a sufficient cause of the phenomenon

what is the difference in the instances, what was good enough to cause it

only two cases

Joint Method of Agreement and Difference

consists of a systematic effort to identify a single condition that is present whenever a phenomenon is present and absent whenever a phenomenon is absent and identify that factor as a necessary and sufficient cause of the phenomenon

looking for something requires and something that is good enough

the factor will be identical to the conclusion row