Lesson 8: Distribution and Conversion Obversion Contraposition

conversion does work for which forms?

E form and I form statements

Contraposition does not work on the:

E form statement: No S are P (shade middle) No non-P are non-S (meaning you shade outside the circle

ex) no cats are dogs=

E statements distributes the subject and the predicate --we know that cats are not dogs --and we learn dogs are not cats

contraposition doesn't work on:

I and E forms

Contraposition does not work on the:

I form statement some S are P (x goes in the middle) step 1: some P are S step 2: some non-P are non-S (x goes on the outside) does not work on the I form

ex) some students are left handed people=

I statement distributes nothing, its NEITHER --we don't learn more about students or left handed people cause it isn't specific

obversion also works on Form O

O form statement: some S are not P step 1: some S are P step 2: some S are non-P same venn diagram the first statement basically matches statement 2

contraposition also works not the:

O form statment: some S are not P (x on the left circle the S side) step 1: some P are not S step 2: some non-P are not non-S

ex) some people watching this video are not people who like star wars

O statement two groups: people who like star wars and people who don't like star wars --this statement is talking about the people who don't like star wars ---we know that everyone in the world that likes star wars are not in the group of people " some don't like star wars" O form statement distributes the predicate

compliment

add or remove a "-non" ex) trees compliment of that is non-tree non-pineapples/ pineapples houses/ non-houses

contrapose: example

all cats are felines step 1: all felines are cats step 2: all non-felines are non-cats

obversion

changing the quality of a statement, affirmative to negative and vice versa step 1: change the quality step 2: term compliment the predicate (add or remove the non) ex) No S are P (we start with E so we need to change it to A) making it "All S are P" step 2: now add compliment making it "all S are Non-P" only focus on original and step 2

obvert ex)

ex) all dogs are canines step 1: no dogs are canines step 2: no dogs are non-canines

non-P's=

located in space 1 and 4

S and P=

located in space 2

non-S's=

located in space 3 and 4

I form distributes=

neither, it distributes nothing

convert example

no cats are canines step 1: no canines are cats

all S are P

shade left of venn diagram (the left side)

Obvert

step 1: change quality strep 2: term compliment the predicate

contraposition only focus on original statement and step 2 statement

step 1: switch the subject and predicate step 2: term compliment both (add/remove non) ex) all S are P step 1: all P are S step 2: all non-P are non-s

conversion

switch the subject and predicate term in a statement ex given) No S are P so now use conversion making the answer= No P are S look at venn diagram and if the pictures from the statement match the venn diagram then we know it works

So contrapositions works on:

the A and O forms

O form statements distribute the=

the predicate

A form statements distribute=

the subject

E form distributes=

the subject and predicate

when is the truth value known

truth value is unknown when it is done to a statement it doesn't work on ex) conversion doesn't work on A and O forms so we don't know the truth value ex) contraposition doesn't work on E and I so the truth value is unknown ex) obversion works on them all so it works --if no S are P is true, its contraposed form is unknown --if no S are P is false, its contra posed from is unknown (cause it is the E form which doesn't work) --- if some S are P is true, its converted form is unknown --- if all S are P is true, its converted form is unknown

distribution

when i put a term (subject or predicate) into the categorical proposition, some new information is given about eery single member of that term--- we learn something about every member of that category ex) all dogs are canines---- dogs is distributed because canine informs us that is of all dogs --we don't know something knew about canines and that's why it isn't distributed A form statement

what happens with the truth value for the operations?

when it is done to a statement it works on, the truth value always stays the same ex) if all S are P is true, its obverted form is true ex) is all S are P is false, so is is contra posed form ex) if some S are P is false, so is its converted form so the operation works on the statement for the three above so the truth value stays the same true goes to true.....false goes to false

conversion does not work on which form?

A form and O form statements

Contraposition works on the:

A form statement: all S are P so all non-P are non-s

Obversion works on: A, E, I and O

A form: All S are P step 1 makes it: No S are P step 2 compliment predicate makes it: No S are non-P (final answer is always step 2 here) E form statement: No S are P step 1: All S are P step 2: All S are non-P S's occur in space 1 and 2 (need to go away, cause it has a P) in venn diagram I form statement: Some S are P step 1: some S are not P step 2: some S are not non-P some S are P's for the first statement meaning the middle of the venn diagram has an X non-P means S