Variability in fMRI: An Examination of Intersession Differences
Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day...
-
Upload
kristopher-harrington -
Category
Documents
-
view
214 -
download
1
Transcript of Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day...
![Page 1: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/1.jpg)
Elementary Logic
PHIL 105-302Intersession 2013
MTWHF 10:00 – 12:00ASA0118C
Steven A. MillerDay 4
![Page 2: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/2.jpg)
Formalizing review
Symbolization chart:
It is not the case = ~And = &Or = v
If … then = → If and only if = ↔ Therefore = ∴
![Page 3: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/3.jpg)
Logical semantics
Our interpretations are concerned with statements’ truth and falsity.
Principle of bivalence: Every statement is either true or false (and not both).
![Page 4: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/4.jpg)
Logical semantics
Negation semantics
“The Cubs are the best team” is true, then … what’s false?
“It is not the case that the Cubs are the best team.”
![Page 5: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/5.jpg)
Logical semantics
Negation semantics
Likewise, if:“The Cubs are the best team”
is false, then … what’s true?“It is not the case that the Cubs are
the best team.”
![Page 6: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/6.jpg)
Logical semantics
Negation semantics (truth table)
P ~PT FF T
![Page 7: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/7.jpg)
Logical semantics
Conjunction semantics
“My name is Steven and my name is Miller.” is true when
“My name is Steven Miller.”
![Page 8: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/8.jpg)
Logical semantics
Conjunction semantics
“My name is Steven and my name is Miller.” is false when
“My name is not Steven or Miller, or both.”
![Page 9: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/9.jpg)
Logical semantics
Conjunction semantics (truth table)
P Q P & QT T TT F FF T FF F F
![Page 10: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/10.jpg)
Logical semantics
Disjunction semantics
“My name is Steven or my name is Miller.” is true when
“My name is Steven or Miller, or both.”
![Page 11: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/11.jpg)
Logical semantics
Disjunction semantics
“…or both”:
“Soup or salad?”
![Page 12: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/12.jpg)
Logical semantics
Disjunction semantics
Inclusive disjunction:this, or that, or both
Exclusive disjunction:this, or that, but not both
![Page 13: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/13.jpg)
Logical semantics
Disjunction semantics
For our purposes, unless stated otherwise, all disjunctions are inclusive:
“or” means:this, or that, or both
![Page 14: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/14.jpg)
Logical semantics
Disjunction semantics (truth table)
P Q P v QT T TT F TF T TF F F
![Page 15: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/15.jpg)
Logical semantics
Disjunction semantics
Exclusive disjunction symbolization:
(P v Q) & ~(P & Q)
![Page 16: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/16.jpg)
Logical semantics
Exclusive disjunction semantics (truth table)
P Q (P v Q) & ~ (P & Q)T T T TT F T FF T T FF F F F
![Page 17: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/17.jpg)
Logical semantics
Exclusive disjunction semantics (truth table)
P Q (P v Q) & ~ (P & Q)T T T F TT F T T FF T T T FF F F T F
![Page 18: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/18.jpg)
Logical semantics
Exclusive disjunction semantics (truth table)
P Q (P v Q) & ~ (P & Q)T T T F F TT F T T T FF T T T T FF F F F T F
![Page 19: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/19.jpg)
Logical semantics
Exclusive disjunction semantics (truth table)
P Q (P v Q) & ~ (P & Q)T T T F F TT F T T T FF T T T T FF F F F T F
![Page 20: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/20.jpg)
Logical semantics
Material conditional semantics
Follows the rules of deductive validity (in fact, every argument is an if-then statement).Is false only when antecedent (premises) is true and consequent (conclusion) is false.
![Page 21: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/21.jpg)
Logical semantics
Material conditional semantics
This can be counter-intuitive, see:
If there are fewer than three people in the room, then Paris is the capital of Egypt.
![Page 22: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/22.jpg)
Logical semantics
Material conditional semantics
If there are fewer than three people in the room, then Paris is the capital of Egypt.
Antecedent = falseConsequent = false
![Page 23: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/23.jpg)
Logical semantics
Material conditional semantics (truth table)
P Q P → QT T TT F FF T TF F T
![Page 24: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/24.jpg)
Logical semantics
Biconditional semantics
Biconditional is conjunction of two material conditionals with the antecedent and consequent reversed:
P ↔ Q = (P → Q) & (Q → P)
![Page 25: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/25.jpg)
Logical semantics
Biconditional semantics (truth table)
P Q (P → Q) & (Q → P)T T T TT F F TF T T FF F T T
![Page 26: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/26.jpg)
Logical semantics
Biconditional semantics (truth table)
P Q (P → Q) & (Q → P)T T T T TT F F F TF T T F FF F T T T
![Page 27: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/27.jpg)
Logical semantics
Biconditional semantics (truth table)
P Q (P ↔ Q)T T TT F FF T FF F T
![Page 28: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/28.jpg)
Seventh Inning Stretch
(“…Buy Me Some Peanuts …”)
![Page 29: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/29.jpg)
Logical semantics
Combining truth tables
Always work from the operator that affects the least of the formula to that which affects the most of it.
~[(P & ~Q) v (Z ↔ Q)]
![Page 30: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/30.jpg)
Logical semantics
Combining truth tables
P Q ~~ (P & Q)T T TT F FF T FF F F
![Page 31: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/31.jpg)
Logical semantics
Combining truth tables
P Q ~~ (P & Q)T T F TT F T FF T T FF F T F
![Page 32: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/32.jpg)
Logical semantics
Combining truth tables
P Q ~~ (P & Q)T T T F TT F F T FF T F T FF F F T F
![Page 33: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/33.jpg)
Logical semantics
Combining truth tables
P Q ~~ (P & Q)T T T F TT F F T FF T F T FF F F T F
![Page 34: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/34.jpg)
![Page 35: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/35.jpg)
Logical semantics
Combining truth tables
P Q (~P & Q) → ~ (Q v P)T T T T T TT F T F F TF T F T T FF F F F F F
![Page 36: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/36.jpg)
Logical semantics
Combining truth tables
P Q (~P & Q) → ~ (Q v P)T T F T T T TT F F T F F TF T T F T T FF F T F F F F
![Page 37: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/37.jpg)
Logical semantics
Combining truth tables
P Q (~P & Q) → ~ (Q v P)T T F T F T T TT F F T F F F TF T T F T T T FF F T F F F F F
![Page 38: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/38.jpg)
Logical semantics
Combining truth tables
P Q (~P & Q) → ~ (Q v P)T T F T F T T T TT F F T F F F T TF T T F T T T T FF F T F F F F F F
![Page 39: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/39.jpg)
Logical semantics
Combining truth tables
P Q (~P & Q) → ~ (Q v P)T T F T F T F T T TT F F T F F F F T TF T T F T T F T T FF F T F F F T F F F
![Page 40: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/40.jpg)
Logical semantics
Combining truth tables
P Q (~P & Q) → ~ (Q v P)T T F T F T T F T T TT F F T F F T F F T TF T T F T T F F T T FF F T F F F T T F F F
![Page 41: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/41.jpg)
Logical semantics
Combining truth tables
P Q (~P & Q) → ~ (Q v P)T T F T F T T F T T TT F F T F F T F F T TF T T F T T F F T T FF F T F F F T T F F F
![Page 42: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/42.jpg)
![Page 43: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/43.jpg)
Three kinds of formulas
Tautologies – true in all cases
P P v ~PT T FF F T
![Page 44: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/44.jpg)
Three kinds of formulas
Tautologies – true in all cases
P P v ~PT T T FF F T T
![Page 45: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/45.jpg)
Three kinds of formulas
Tautologies – true in all cases
P P v ~PT T T FF F T T
![Page 46: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/46.jpg)
Three kinds of formulas
Contradictory (or truth-functionally inconsistent) – false in all casesP P & ~PT T FF F T
![Page 47: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/47.jpg)
Three kinds of formulas
Contradictory (or truth-functionally inconsistent) – false in all casesP P & ~PT T F FF F F T
![Page 48: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/48.jpg)
Three kinds of formulas
Contradictory (or truth-functionally inconsistent) – false in all casesP P & ~PT T F FF F F T
![Page 49: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/49.jpg)
Three kinds of formulas
Contingent – can be both true and false
Z R Z & R T T T T F F F T F F F F
![Page 50: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/50.jpg)
![Page 51: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/51.jpg)
Putting it all together
Either Peter or Saul went to the bar.Peter did not go.Therefore, Saul went.
1) P v S2) ~P3) ∴ S
![Page 52: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/52.jpg)
Putting it all together
1) P v S2) ~P3) ∴ S
What’s this argument’s form?Disjunctive syllogism.
![Page 53: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/53.jpg)
Putting it all together
1) P v S2) ~P3) ∴ S
[(P v S) & ~P] → S
![Page 54: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/54.jpg)
Putting it all together
P S [(P v S) & ~P] → ST T T T T T
T F T F T F F T F T F T F F F F F F
![Page 55: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/55.jpg)
Putting it all together
P S [(P v S) & ~P] → ST T T T F T T
T F T F F T F F T F T T F T F F F F T F F
![Page 56: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/56.jpg)
Putting it all together
P S [(P v S) & ~P] → ST T T T T F T T
T F T T F F T F F T F T T T F T F F F F F T F F
![Page 57: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/57.jpg)
Putting it all together
P S [(P v S) & ~P] → ST T T T T F F T T
T F T T F F F T F F T F T T T T F T F F F F F F T F F
![Page 58: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/58.jpg)
Putting it all together
P S [(P v S) & ~P] → ST T T T T F F T T T
T F T T F F F T T F F T F T T T T F T T F F F F F F T F T F
This argument is valid; there is no line where the premises are all true and the conclusion is false.
![Page 59: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/59.jpg)
Putting it all together
A truth table that has no lines where the premises are all true and the conclusion false presents a valid argument.
A truth table that has at least one line where the premises are all true and the conclusion false presents an invalid argument.
![Page 60: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/60.jpg)
Things we’re skipping
- Truth / refutation trees, S. pp. 68-77
- identical in purpose to tables- more efficient- but no time = no need
![Page 61: Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 4.](https://reader030.fdocuments.in/reader030/viewer/2022032705/56649dda5503460f94ad00e1/html5/thumbnails/61.jpg)