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Tweedledum:%20

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Socrates is a man. Socrates is mortal. This argument is truth-preserving. ... Socrates could be the name of any living thing. Logic and humor ... – PowerPoint PPT presentation

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Title: Tweedledum:%20


1
  • Tweedledum I know what youre thinking, but it
    isnt so. No how.
  • Tweedledee Contrariwise, if it was so, it might
    be and if it were so, it would be but as it
    isnt, it aint. Thats logic.

2
PHIL 120 Introduction to Logic
  • Professor
  • Lynn Hankinson-Nelson
  • lynnhank_at_u.washington.edu
  • 206.543.5094
  • Instructors
  • Lars Enden
  • Cheryl Fitzgerald
  • Mitch Kaufman
  • Joe Ricci

3
PHIL 120 Introduction to Logic
  • Course website
  • http//faculty.washington.edu/lynnhank/PHIL120.htm
    l
  • Syllabus and course requirements
  • Power point lectures
  • Sample tests
  • Office hours and locations e-mail addresses.
  • Announcements
  • Course Text
  • The Logic Book, 5th edition. McGraw Hill.
  • A solutions manual is available online.

4
PHIL 120 Requirements
  1. Attendance and participation in lectures and
    discussion sections, including assigned homework
    and pop quizzes (20)
  2. 5 tests (16 each)
  3. You may take 1 test over to raise the grade
  4. Practice, practice, practice logic is not a
    spectator sport!
  5. Ask questions!

5
Logic
  • The study of reasoning
  • The drawing of inferences what follows from what
    and what doesnt follow
  • We can talk in terms of ideas, beliefs, and
    the like, but its more concrete to talk about
    sentences those entities that we use to
    express ideas, beliefs, and claims.
  • One focus arguments
  • A set of at least two sentences, one of which is
    the conclusion and the other or others is/are
    reasons (premises) that support it.

6
Good arguments vs. bad arguments
  • All men are mortal.
  • Socrates is a man.
  • __________________
  • Socrates is mortal.
  • This argument is truth-preserving. It is
    deductively valid.
  • If it is true that all men are mortal, and true
    that Socrates is a man, then it must be true that
    Socrates is mortal.
  • All men are mortal.
  • Socrates is mortal.
  • ____________________
  • Socrates is a man.
  • This argument is not truth preserving. It is
    deductively invalid.
  • Even if the premises are true, they do not
    guarantee the truth of the conclusion.
  • Socrates could be the name of any living thing.

7
Logic and humor
8
Good arguments vs. bad arguments
  • If you studied a lot, you did well in the logic
    course.
  • You studied a lot.
  • _________________________
  • You did well in the logic course.
  • This argument is truth-preserving. It is
    deductively valid.
  • It is not possible for the premises to be true
    and the conclusion false.
  • If you studied a lot, you did well in the logic
    course.
  • You did well in the logic course.
  • ____________________
  • You studied a lot.
  • This argument is not truth preserving. It is
    deductively invalid.
  • It is possible for the premises to be true and
    the conclusion false.

9
The language SL
  • A symbolic language used to illustrate the
    logical structure of sentences, of sets of
    sentences, of arguments, and of other
    relationships between sentences
  • In sentential logic, the most basic unit is the
    simple declarative sentence.
  • Simple no logical connectives
  • Declarative either true or false
  • We assume bivalence

10
The language SL
  • The vocabulary of SL
  • Roman capital letters, A through Z, with or
    without subscripts (e.g., S and S3) used to
    symbolize simple, declarative sentences
  • 5 (sentential) connectives
  • (tilde)
  • (ampersand)
  • v (wedge)
  • ? (horseshoe)
  • ? (triple bar)
  • The first is a unary connective.
  • The rest are binary connectives.
  • Punctuation ( ) and

11
The language SL
  • Every sentence of SL is either simple/atomic or
    compound/molecular.
  • Simple/atomic sentences have no connectives.
  • Compound/molecular sentences have at least one
    connective.
  • Meta variables
  • Object language and meta language
  • P, Q, R, and S are meta variables used to talk
    about sentences of SL.

12
The recursive definition of SL
  1. Every sentence letter is a sentence.
  2. If P is a sentence of SL, P is a sentence of SL.
  3. If P and Q are sentences, then (P Q) is a
    sentence.
  4. If P and Q are sentences, then (P v Q) is a
    sentence.
  5. If P and Q are sentences, then (P ? Q) is a
    sentence.
  6. If P and Q are sentences, then (P ? Q) is a
    sentence.
  7. Nothing else is a sentence.

13
What the recursive definition of SL does
  • It tells us what will count as a sentence of SL
  • It also tells us what will not.
  • For example, these are not sentences of SL
  • A
  • clause 3 is a binary connective
  • B C ?
  • SL does not include ?
  • must be used before a sentence (clause 2)
  • and must connect 2 sentences (clause 3)

14
What the recursive definition of SL does
  • It tells us what will count as a sentence of SL
  • These are sentences of SL
  • A B (clause 3)
  • (B B) B (clause 3)
  • B (clause 2)
  • A v B (clause 4)
  • A ? B (clause 5)
  • A ? B (clause 6)

15
Using SL to symbolize sentences
  • Roman capital letters A through Z (with or
    without subscripts) to symbolize simple
    declarative sentences
  • Mary went to the store (we could symbolize as
    M).
  • John went to the store (we could symbolize as
    J).
  • These are NOT simple declarative sentences
  • Either Mary went to the store or John did.
  • Mary did not (or didnt) go to the store.

16
Using SL to symbolize sentences
  • Mary did not (or didnt) go to the store
  • The logic of this sentence is
  • It is not the case that Mary went to the store
  • symbolizes it is not the case that
  • So, using M for Mary went to the store, we use
    M to symbolize It is not the case that Mary
    went to the store
  • Sentences whose main connective is the tilde are
    called negations.

17
The characteristic truth table for the
P P
T F
F T
18
Using SL to symbolize sentences
  • Mary and John went to the store
  • This is a compound/molecular sentence to be
    translated as
  • Mary went to the store and John went to the
    store
  • We can use M to symbolize Mary went to the
    store, and J to symbolize John went to the
    store
  • We use the for and
  • So we have
  • M J

19
The characteristic truth table for the
P Q P Q
T T T
T F F
F T F
F F F
20
Using SL to symbolize sentences
  • Sentences whose main connective is the are
    called conjunctions and each of the sentences
    connected by the is called a conjunct. We can
    refer to them as the right or the left conjunct.
  • We use as a connective in all cases in which
    the compound sentence is only true if both of its
    component sentences are true.
  • This is the case for
  • Mary went to the store but John did too
  • the logical structure of which is
  • Mary went to the store and John went to the
    store

21
Using SL to symbolize sentences
  • Mary went to the store but John did not
  • Is paraphrased as
  • Mary went to the store and it is not the case
    that John went to the store
  • M can symbolize Mary went to the store
  • And is used for but. So far we have
  • M
  • J can symbolize it is not the case that John
    went to the store
  • So we have
  • M J

22
Using SL to symbolize sentences
  • Either Mary went to the store or John did
  • Is translated as
  • Either Mary went to the store or John went to
    the store
  • We use the v to symbolize either/or
  • If we use M to symbolize Mary went to the store
    and J to symbolize John went to the store we
    symbolize the whole sentence as
  • M v J

23
The characteristic truth table for v
P Q P v Q
T T T
T F T
F T T
F F F
24
Using SL to symbolize sentences
  • Because either/or and the v assume the
    inclusive sense of or (at least one is true),
    we will need to do more if we believe a sentence
    makes use of the exclusive sense of or (at most
    one of the two) and should be symbolized to
    reflect this.
  • On a restaurant menu, for example, the phrase
    either soup or salad is included reflects the
    exclusive sense of or.
  • Context may tell us that a claim comes to Either
    Mary went to the store or John did, but not both

25
Using SL to symbolize sentences
  • If Mary went to the store, John did
  • If Mary went to the store, then John went to the
    store
  • M Mary went to the store
  • J John went to the store
  • We use ? to symbolize if, then
  • So we have
  • M ? J

26
The characteristic truth table for the ?
P Q P ? Q
T T T
T F F
F T T
F F T
27
Using SL to symbolize sentences
  • The reasoning behind the ?
  • Consider the following claim
  • If the operation is a success, the patient
    survives.
  • The condition, the operation is a success, is a
    sufficient but not a necessary condition for the
    patients survival.
  • The docs decided not to operate and the patient
    survived they discovered they were wrong about
    the need for an operation
  • If the claim was Only if the operation is a
    success, the patient survives, then the
    operations success would require the patients
    survival for the claim to be true but that is
    not what If by itself entails.

28
Using SL to symbolize sentences
  • Mary went to the store if and only if John did
  • Mary went to the store if and only if John went
    to the store
  • We use ? for if and only if
  • So we have
  • M ? J
  • P if and only if Q is equivalent to
  • (If P then Q) and (If Q then P)

29
The characteristic truth table for the ?
P Q P ? Q
T T T
T F F
F T F
F F T
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