Validity Flashcards
If the premises are true, then the conclusion must be true
If the premises are true, then the conclusion must be true
Truth
sentences
valid
arguments
Valid argument 1: affirming the sufficient
a > b a \_\_\_\_\_\_\_\_ b if affirm the sufficient condition, then you conclude the necessary condition.
Valid argument 2: negating the necessary
a > b
/b
______
/a
Valid argument 3:
a > b > c
_______
a > c
a > b
b > c
_____
a > c
Some
Many = Some
at least one
ranges from 1 to 100
a b
a some b
these don’t have contrapositives
All
speaks of a point = 100
Most
more than half
means half plus 1 = 51 and upper bound is 100
a most b
- doesn’t have a contrapositive
Few
= some are
= most are not
All implies Most implies Some
0_________50________100
Some (at least 1_________
but it goes up to “all”)
Few(some are and most are not)
+1 Most_____
All
The existential quantifier is a fancy name to express the relationship of intersections. The three logical indicators here are “some” which means at least 1 up to all; “most” which means half plus 1 up to all; and “few” which usually means some are and most are not.
The existential quantifier is a fancy name to express the relationship of intersections. The three logical indicators here are “some” which means at least 1 up to all; “most” which means half plus 1 up to all; and “few” which usually means some are and most are not.
The SOME group
some, many, several, at least one, lots, not none
The Most group
most, a majority, more than half
Few
Few
These have no contrapositives
No contrapositives
Negations
Negations
Negate SOME statements
some = none
Negate ALL
all = some not
The easiest way to get the contradiction of any sentence is to tag the clause “It’s not the case that…” in front of the sentence.
“It’s not the case that…”
A is not sufficient for B and B is not necessary for A
A is not sufficient for B and B is not necessary for A
You can formulate the contradiction (i.e., the negations) by saying “Some [of the sufficient] is not [the necessary].” Or, if grammatically it doesn’t make sense to use “some,” you can fall back on the more general rule of “One can be [the sufficient] and not be [the necessary].” For example, “If the President endorses this bill, then it will pass.” Here, it clearly doesn’t make sense to use “some.” So, we fall back on the more general rule and say “The President can endorse the bill and it could not pass.”
You can formulate the contradiction (i.e., the negations) by saying “Some [of the sufficient] is not [the necessary].” Or, if grammatically it doesn’t make sense to use “some,” you can fall back on the more general rule of “One can be [the sufficient] and not be [the necessary].” For example, “If the President endorses this bill, then it will pass.” Here, it clearly doesn’t make sense to use “some.” So, we fall back on the more general rule and say “The President can endorse the bill and it could not pass.”
All negates - some not
ALL negates - some not
Some negate - none
Some negate - none
To negate slap in front of the sentence - It’s not the care that ….
To negate slap in front of the sentence - It’s not the care that ….
Valid argument 4:
A some > B >(all) C
__________
A some C
Valid argument 5:
A most > B >(all) C
____________
A most C
Valid Argument 6:
A > (all) B > (all) C
_____________
A some C
Valid Argument 7:
A > B
A some C
______
B some C
Valid Argument 8:
A > B
B most C
______
A some C
