fast
Contributor
Lol.... There is an underlying theme at play and it has to do with collective exhaustivity. ...
I think together we've succeeded in that effort. I concede ...
P2' and P2" arecontradictorycontrary to each other. Or else I just do not get it.
ETA- Either that or an elephant is a type of giraffe in which case C' is false, as well as C"'.
ETA - I hope I'm using the word concede correctly.
I want to say something that might help illuminate matters. What may appear as a tangent on my part with arguing that the sentences aren’t contradictory isn’t as much of a tangent as one may realize.
There are a couple overarching rules to be mindful of when categorizing things, and it pertains to mutual exclusitivity and collective exhaustivity. Let’s say I wanted to track the hair color of everyone entering a building. I might make a form that reads: a) blonde, b) brunette, and c) redhead. As each person enters, I would observe the hair color and simply record the observation, but in the end, it’s very important that there’s a match between the number of observations made and the number of checks made in the boxes.
The categories should be mutually exclusive, meaning the categories I write down should accommodate the observations such that each person belongs in one and only one box. That would of worked in the 1950’s when whoever came in the building would be observed as either being one and never more than one. Today in San Francisco, a person might be part blonde and part brunette. That might require being more specific with the form: a) originally blonde, b) originally brunette, etc. the point is still that the categories should be such that for each person, there should be only one box that is applicable to them. At any rate, that has to do with mutual exclusivity.
However, it’s the other rule of categorizing that I would like to focus on: collective exhaustivity. If a person came in and was bald and was born with a defect such that she has no hair, there would be no category written on my paper to cover the instance. What people ordinarily do (and we see it all the time) is that they will tag on another catch-all category, often dubbed as “other.” For instance, if we were to write down the following categories:
A) completely blonde
B) completely brunette
C) completely red head
That would not be collectively exhaustive, but if we added
D) other
Then, no matter who came in, there would be a box for the person entering the building no matter what.
Second example: whoever enters the building is either
A) shorter than four feet tall
Or
B) taller than four feet tall
That would work out great except for the rare times someone enters and happens to be exactly four feet tall.
The problem is that the list isn’t collectively exhaustive, and what needs to be done is that the list needs to be remedied such that no matter who enters, there’s a category for them to belong to.
A versus not A is collectively exhaustive
A, B, and neither A nor B is collectively exhaustive.
A, B, C and everyone else is collectively exhaustive
Valid and not valid is exhaustive, but valid and invalid is not. This speaks to form, so it’s mighty important. If the argument is valid, then it’s a deductive argument such that the conclusion can be trusted IF the premises are true.
If it’s false that an argument is valid, and if that’s all I know, I cannot discern whether the argument is deductive or not; as far as I know, it could be an extremely strong inductive argument that would be foolish to immediately dismiss. An argument that is not valid might be deductive, or it might be nondeductive; if an argument is invalid, then I know immediately that we’re dealing with a deductive argument whose conclusion cannot be guarenteed. Validity allows for trust. Sprinkle a deductive argument that is valid with true premises, and the conclusion is guarenteed. Remember, never does nondeductive arguments give rise to that trust because they never have true guarentee-producing validity.
A contradiction such as I am in SC and I am not in SC guarentees the truth of one because there is collective exhaustivity.
An argument with true premises that has a valid form provides the same guarentee because of the precise definition of validity that allows for there to be collective exhaustivity between valid and invalid when only pertaining to deductive arguments. It’s getting late; I hope I worded that halfway right.