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Introductory Logic

PHI 120

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Presentation: "Good Arguments"Please turn off all cell phones!

Homework for Next Lecture• Allen/Hand,

The Logic Primer(“a text of minimal chattiness”)

– Pay special attention to:• Section 1.1, p. 1-2

– study definitions: argument, validity, soundness

• Section 1.2: p. 3-5 – Study concepts: formal language, vocabulary,

connectives (p. 4-5), metavariable

• Section 1.3: read p. 10-15 – Exercise 1.3: 1-25

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MW 1:00 pm - 1:50 pm BioSci 107

• 010 F 12:00 pm - 12:50 pm• 011 F 1:00 pm - 1:50 pm• 012 F 2:00 pm - 2:50 pm• 013 M 8:00 am - 8:50 am• 014 W 8:00 am - 8:50 am• 015 W 9:00 am - 9:50 am• 016 W 10:00 am - 10:50 am• 017 W 11:00 am - 11:50 am• 018 W 12:00 pm - 12:50 pm

Memorize your section number!

Good Arguments

The Criteria

A Good Argument (p.25)

(A) Given the premises, the conclusion follows with either

deductive validity or inductive strength.

and

(B) The premises are true.”

A Good Argument

(A) Inferential connection– Deductive validity

or– Inductive strength

(B) True premise(s)– Empirical statements

vs.– Non-empirical statements

Either or, but not both

Good Arguments

(A) Inferential Connection ─ the way the conclusion follows from premises ─

Inferential Connection: 2 Kinds

A. Validity: Deductive arguments– Necessary connection between premises and

conclusion • Inferential Connection is one of certainty

B. Strength: Inductive Arguments– Unnecessary or contingent connection

• Inferential connection is one of probability

“the way the conclusion follows”

Inferential Connection: 2 Kinds

A. Validity: Deductive arguments– Necessary connection between premises and

conclusion • Inferential Connection is one of certainty

B. Strength: Inductive Arguments– Unnecessary or contingent connection

• Inferential connection is one of probability

There are 80 women and 20 men in this room. I am going to pick a person at random. So I would likely select a woman.

Inferential Connection

B. Inductive Arguments: conclusion follows with some degree of probability

Three sorts:– Generalizations

– Causal arguments

– Analogies

Inferential Connection

B. Inductive Arguments: conclusion follows with some degree of probability

Three sorts:– Generalizations

– Causal arguments

– Analogies

Conclusion • might be true • might be false

Inference • stronger• weaker

Inferential Connection: 2 Kinds

A. Validity: Deductive arguments– Necessary connection between premises and

conclusion – Conclusion follows with certainty

Either you are a man or a woman. Since you are not a man, it follows that you are a woman.

Either P or QSince not PQ follows

Either P or QNot QSo P

An integer is either even or odd. The integer 2 is not odd. So it is even.

Logical Form

Deductive Arguments

Logical Form

• Valid form, e.g., BarbaraAll A are B All cats are carnivores.All B are C All carnivores are predators.-------------- --------------------------------------All A are C All cats are predators.

• This is a valid argument form.– There is a necessary connection between A and C– Hence, this is a deductively valid argument

Logical Form

• Other valid forms: Modus Ponens (or "->E rule")

If A, then B If a person is a man, then he cannot give birth.A The person is a man. -------------- ----------------------------------------------------------------B Thus he cannot give birth.

The conclusion is necessarily true, given the premises.

Logical Form

• Other valid forms: Modus Tollens

If A, then B If a person is a man, then he cannot give birth.not B This person can give birth, though. -------------- ----------------------------------------------------------------not A Hence she is not a man.

The conclusion is necessarily true, given the premises.

Logical Form

• Other valid forms: Disjunctive Syllogism (or "vE rule")

Either A or B An integer is either even or odd.not A The integer 3 is not even. -------------- --------------------------------------B Therefore the integer 3 is odd.

The conclusion is necessarily true, given the premises.

Logical Form

• Formal Fallacies– No necessary connection between premises and

conclusion

Fallacy of “Undistributed Middle”All A are B All cats are carnivores.All C are B All dogs are carnivores.-------------- --------------------------------------All C are A All dogs are cats.Not a Valid Argument

errors in reasoning other than false premises.

• Valid Argument Valid Form

• Invalid Argument Invalid Form

Form of BarbaraAll A are BAll B are C--------------All A are C

Form of Modus Ponens (->E)If A, then BA--------------B

Form of Undistributed MiddleAll A are BAll C are B--------------All C are A

Form of Denying the AntecedentIf A, then Bnot A--------------not B

Logical Form

Good Arguments

(B) True premise(s)

A Good Argument

• “One in which (A) given the premises, the conclusion follows from them either with deductive validity or inductive strength, and (B) the premises are true.” (p.25)

STOP!

Validity and Strength concern arguments

Truth and Falsity concern statementsTo say an argument is true, makes no sense!

TRUTHGood Arguments

Statements (p.40)

1. empirical statements ─ truth verifiable in principle by experience

• assertions of statistical probability– “45% of Kentuckians over 50 years of age smoke or

ingest tobacco”

• statements of historical fact– “Caesar crossed the Rubicon in 49 B.C.”

• statements of observation– “The far side of the moon never receives direct light

from the sun.”

Statements (p.40)

2. non-empirical statements ─ truth in principle not verifiable by experience

• mathematical formulas– “25 times 5 equals 100”

• Statements of identity– “A rose is a rose.”

• Definitions– “A foot is the measure of twelve inches.”

Sound Deductive Arguments

Study This Concept At Home

Validityversus

Soundness

A Good Argument

• “One in which (A) given the premises, the conclusion follows from them either with deductive validity or inductive strength, and (B) the premises are true.” (p.25)

A good deductive argument is a sound argument.

– question: what kind of statement is this?• Empirical?

or• Non-empirical?

Validity versus Soundness

• Properties of deductive arguments

– Valid Argument: An argument whose conclusion follows necessarily from given premises

– Sound Argument: A valid argument whose premises are all true.

• Validity ≠ soundness

All sound arguments are valid, but not all valid arguments are sound.

Summary• Good arguments have two criteria

1. The manner by which the conclusion follows from given premises

• Deductively valid– Sound Argument = valid + all true premises

• Invalid– Inductively strong– Inductively weak

2. True premise(s)• Empirical vs. non-empirical statements

• Truth vs. Validity/Strength– Arguments are neither true nor false

Homework for Next Lecture• Allen/Hand,

The Logic Primer(“a text of minimal chattiness”)

– Pay special attention to:• Section 1.1, p. 1-2

– study definitions: argument, validity, soundness

• Section 1.2: p. 3-5 – Study concepts: formal language, vocabulary,

connectives (p. 4-5), metavariable

• Section 1.3: read p. 10-15 – Exercise 1.3: 1-25