Foundations Logic Flashcards
1
Q
single arrow
A
- introduced by sufficient and necessary words (i.e. if/then, when all, every, only). Both positive or both negative
Ex: All X are Y (x->y)
Ex: If NOT x then not y (~x-.~y)
2
Q
double arrow
A
- introduced by “if and only if” or “vice versa” or “both ways” (I.e. X ifi and only if Y
- means they happen both or neither
3
Q
double not arrow
A
- introduced by only one negative term or words like “no” and “none” (i.e. NO X are Y)
4
Q
“some”
A
(at least one, possibly all)
(i.e. some X are Y)
- “not all X are Y (not all-some are not)
5
Q
other “some” indicators
A
- some
- at least some
- at least one
- a few
- a number
- several
- part of
- a portion
6
Q
“most”
A
- a majority but possibly all (i.e. most x are y)
7
Q
other “most” indicators
A
- most
- a majority
- more than half
- almost all
- usually
- typically
8
Q
contrapositives for most and some
A
THERE ARE NONE, there is only if/then
9
Q
numeric values for formal logic
A
- all is 100%
- most is 51-100%
- some are not is 0-99%
- most are not is 0-49%
- some is 1-100%
- none is 0%
10
Q
the rules for reversibility
A
- reversible relationships include none, some, and the double arrow
- non-reversible relationships include all and most.
11
Q
be careful with “some are not” reverses
A
(X some ~Y = ~Y some X)
Do NOT move the NOT.
12
Q
inherent v. additive inferences
A
(inherent) if most X are y, then some x are y
(additive) if x-> y & y->z, then x->
13
Q
inherent logic ladder
A
all->most->some
14
Q
note: “if and only if” can be an “all” on the logic ladder
A
15
Q
logic ladder for negatives
A
none->most are not-> some are not
16
Q
rules of logic
A
- start by looking at the ends of the chains
- the vast majority of additive inferences require either an “all” or “none” in the chain
- when looking to make inferences, do NOT with a variable involved in a double negative
- there has to be an arrow leading away from a some to combine (i.e. A some B -> C - A some C) BUT A some B<-C does not equal anything
- most train: same as some but most is not bi-directional and must follow arrow
- an arrow followed by a double not will yield an inference (i.e. A->B</-> C = A</->C)
- use inherent inferences
- Be sure to keep relevant negatives
- two somes won’t yield and neither will some “most” or “vast majority”. But, A(<-most)B(most->)C is A some C. (*2 mosts must lead away from one another)
- Analyze compound statements
- Once an inference is build, you don’t need to build it again
