This is Introductory Logic PHI 120 Get a syllabus online, if you don't already have one 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 – Exercise 1.3: 1-25

MW 10:00 am - 10:50 amCB M 3:00 pm - 3:50 pm 002 M 9:00 am - 9:50 am 003 M 11:00 am - 11:50 am 004 M 12:00 pm - 12:50 pm 005 M 1:00 pm - 1:50 pm 006 M 2:00 pm - 2:50 pm 007 F 9:00 am - 9:50 am 008 F 10:00 am - 10:50 am 009 F 11:00 am - 11:50 am MW 1:00 pm - 1:50 pm BioSci 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 Conclusion might be true might be false Inference stronger weaker 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 Q Since not P Q follows Either P or Q Since not P Q follows Either P or Q Not Q So 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., Barbara All 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 Not a Valid Argument errors in reasoning other than false premises.

Valid Argument  Valid Form Invalid Argument  Invalid Form Form of Barbara All A are B All B are C All A are C Form of Barbara All A are B All B are C All A are C Form of Modus Ponens (->E) If A, then B A B Form of Modus Ponens (->E) If A, then B A B Form of Undistributed Middle All A are B All C are B All C are A Form of Undistributed Middle All A are B All C are B All C are A Form of Denying the Antecedent If A, then B not A not B Form of Denying the Antecedent If A, then B not 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 statements

TRUTH Good 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 Study This Concept At Home Validity versus Soundness Validity versus 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. 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 – Exercise 1.3: 1-25