logic: contraries

two propositions are said to be contrary if the cannot both be true. that is the truth of one entails the falsity of the other.

they can both be false

All poets are dreamers (A)
No poets are dreamers(E)

A&E propositions having the same subject and predicate terms are contraries.

propositions that are neither necessarily true nor necessarily false are said to be contigent.

for example the following propositions:

all squares are rectangles
no squares are circles

each represents a mathematical truth and therefore cannot have a contrary.

logic: class and complements

a class is a collection of all objects having a certain common attribute that we may refer to as a "class-defining characteristic."

complement is the class of all things not belonging to the original class.

logic: contrapositives

contraposition can be reduced to obversion and conversion. to form the contrapositive of a given proposition, we place its subject term with the complement of its predicate term and we replace its predicate term with the complement of its subject term.

from text:

1. contraposition is a valid form of immediate inference when applied to A propositions and to O propositions.
2. for I propositions the contrapositive is not generally valid
3. for E propositions, not valid
   

i need to flesh out 2 and 3 more, but for now i am tired.

so, the complement of P is not P.

state the contrapositives and indicate which are equivalent to the original

1. all journalists are pessimists
2. some soldiers are not officers
3. all scholars are nondegenrates
4. all things weighing more than fitty pounds are objects not more than four feet high.
5. some non-citizens are not nonresidents
   

so, to state the contrapositve:

subject term with the complement of its predicate term and we replace its predicate term with the complement of its subject term.

hm, that seems like swap and negate:

1. all non-pessimists are non-journalists
2. some non-officers are non-soldiers
3. all degenerates are non-scholars
4. all non-objects ... are not things weighing more ...
5. some residents are citizens
   

logic: contraditories

two propositions are contradictory if one is the denial or the negation fo the other. they cannot both be true and they cannot both be false.

i think it means if one is true the other can not possibly be true. so, if all cars are dogs. the contradictory of that would be some cars are not dogs.

• must differ from one another in quantity
• must differ from one another in quality

from the text

all judges are lawyers (A proposition)
some judges are not lawyers? (O proposition)

no politicians are idealists (E)
some politicians are idealists (I)

of the pair, exactly one is true and exactly one is false. they cannot both be true and cannot both be false.

A&O propositions are contradictories
E&I propositions are contradictories

logic: obverse propositions

here, i shall borrow a bit of text directly from my favorite source of wikipedia. in obversion subject is the same as the original subject, but the predicate is the contradictory of the original predicate. perhaps i should go ahead and add contradictory here.


from the text we have:

some college athletes are professionals. the obverse of that would be some college athletes are not professionals. oops. i want to say non-professionals, because my modifier needs to apply directly to the predicate.

ah, the obverse also changes quality, so that would be some college athletes are not non-professionals.

wikipedia let me down there -- well, only because i didn't finish reading the entry.

so, to sum up, the quality of the original changes and the contradictory of the predicate is used.

first we will have the original, then i will type up the obverse

1. some college athletes are professionals
2. no organic compounds are metals
3. some clergy are not abstainers
4. no geniuses are conformists
5. all objects suitable for boat anchors are objects weighing at least fifteen pounds

the obverse of each of those .. need to change the quality and the contradictory of the predicate:

1. some college athletes are nonprofessionals
2. no organic compounds are nonmetals
3. some clergy are not non-abstainers
4. no geniuses are conformists
5. all objects suitable for boat anchors are nonobjects weighing at least fifteen pounds.

will check answers later

logic: converse propositions

ok, so in the converse of a proposition the subject and predicate are essentially reversed. a very simple example would be. dogs are cats. the converse of that would be that cats are dogs. or so i think ...

in conditional form, something like this ... comes to mind:

if it is raining, i am wet. the converse of that would be: if i am wet, it is raining.

here's one from the text:

some european cars are overpriced and underpowered vehicles.

the converse of that should be:

some overpriced and underpowered vehicles are european cars.

in this case, what i also notice is that the quality and quantity have remained constant.

conversion is an inference that proceeds by interchanging the subject and the predicate terms of a categorical proposition. not all conversions are valid.

conversion is perfectly valid for all E propositions and all I propositions.


Answers ... didn't want to write in the book:

1. E proposition -- no reckless drivers ... are people who are considerate of others... (Equivalent)
   
2. A proposition all commissioned officers in the navy are graduates of west point (Nonequivalent)
3. O proposition some overprices and underpowered vehicles are european cars (equivalent)
4. E proposition no warm blooded animals are reptiles (Equivalent)
   
5. I proposition some elderly persons ... are professional wrestlers ... (Equivalent)