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Summary Notes

These are summary notes so that you can really listen in class and not spend the entire time copying notes. These notes will not substitute for reading the chapters in the text, nor can they replace the text as there are many subtleties we will discuss in class that are also presented in the text. Use these as a supplement.

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Section 1.1| Section 1.2 | Section 1.3 | Section 1.4 | Section 1.5

Smartboard notes


1.1 Arguments, Premises and Conclusions

Concepts:

These are terms you should be able to define and recognize after covering Section 1.1.

  1. definition of logic
  2. definition of an argument
    You will be responsible for memorizing this definition (word for word) on the first quiz and midterm. It is the only instance when I will ask you to memorize material in this fashion.
  3. statement
  4. truth values: statements are either true or false
  5. premise & conclusions indicators
  6. Know the difference between "For this reason" and "for the reason that."
  7. Not all arguments have premise and conclusion indicators.When you are faced with such an argument attempt to find the "topic sentence" or main point of the argument. Good bets for its location are the first or last sentence of the argument.
  8. inference
  9. proposition

Premise Indicators

Conclusion Indicators

  • since
  • as indicated by
  • because
  • for
  • in that
  • may be inferred from
  • as
  • given that
  • seeing that
  • for the reason that
  • inasmuch as
  • owing to
  • therefore
  • wherefore
  • accordingly
  • we may conclude
  • entails that
  • hence
  • thus
  • consequently
  • we may infer that
  • whence
  • so
  • it follows that
  • implies that
  • as a result

 

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1.2 Recognizing Arguments

Concepts:

These are terms you should be able to define and recognize after covering Section 1.1.

Breakdown:

Passages lacking an inferential claim:

  1. Warnings: often end in an exclamation point.
  2. Pieces of Advice
  3. Statements of Opinion: these must always be supported by evidence to be considered arguments in the strict logical sense.
  4. Loosely Associated Statements: these are statements in which the premise will not bear any common-sense or logical relation to the conclusion.
  5. Report: absent here is the claim that the statements support or imply anything; report passages should read like a chronicle of events without the interjection of opinion.
  6. Expository passage: just as it sounds, this is merely an explanation.
  1. Illustration: statement and examples that further clarify the category being discussed. For our class, think of an illustration as a set of instructions, a how-to procedure.
  2. Explanations:
    Two Parts:
    1. Explanans: "statement or group of statements that purports to do the explaining" reasons.
    2. Explanandum: "statement that describes the event of phenomenon to be explained"

    Note: the method for distinguishing arguments from explanations; there must be an element of persuasion present to classify a passage in the argument category. If a passage presents generally known facts, then it is an explanation.

     

  3. Conditional Statements:
    • These are "if … then" statements.
    • Review the definition of antecedent & consequent.
    • One conditional statement does not an argument make.
    • Note the rules for recognizing conditional statements as arguments.

Summary:

  1. Look for indicator words (Section 1.1), and
  2. an inferential relationship between statements.
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1.3 Deduction and Induction

Inductive Argument: conclusion follows probably from the premises (51% or better)

Indicator words: improbable, plausible, implausible, likely, unlikely, reasonable

Types of Inductive Arguments:

  1. predictions
  2. arguments from analogy
  3. inductive generalizations
  4. arguments from authority
  5. arguments based on signs
  6. causal inferences

Deductive Argument: conclusion follows necessarily from the premises (100%) certainty

Indicator words: certainly, absolutely, definitely

See examples

Types of Deductive Arguments:

  1. arguments based on mathematics
  2. arguments from definition
  3. categorical syllogisms
  4. hypothetical syllogisms
  5. disjunctive syllogisms

Language Patterns for syllogisms & examples:

Categorical Syllogisms:

Hypothetical Syllogisms:

Disjunctive Syllogisms:

An Either _______ or ________.  statement paired with two other statements in  which one alternative is eliminated and we are left with the remaining alternative.

The pattern:

Factors that help us decide between deductive and inductive arguments:

  • The presence of indicator words.
  • The "actual strength of the inferential ink between premises and conclusions."
  • Instances in which the conclusion does not follow from the premises either necessarily or probably.
  • The easiest way to learn to distinguish deductive from inductive arguments is to learn to recognize the deductive argument forms on sight. If your argument does not follow the form [i.e., language pattern] of a deductive argument, then it is necessarily inductive by the process of elimination.

Some cautions/notes from reading:

  1. Geometric arguments are always deductive
  2. Scientific arguments can be either inductive or deductive.
  3. The common definition for distinguishing between deductive and inductive arguments (general/particular) does not hold.

 

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1.4 Validity, Truth, Soundness & Cogency

Valid Deductive Arguments

Inductive Arguments

decision tree inductive/deductive

 

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1.5 Argument Forms: Proving Invalidity

Numbers in parenthesis refer to page numbers in the text.

This week we are looking at the validity/invalidity of deductive arguments. "The validity of an argument has nothing to do with its specific subject matter. ...Its validity rests purely upon the arrangement of the letters within the statements and it has nothing to do with what the letters might stand for."

The process of "uniformly substituting terms or statements in place of the letters in an argument form is called a substitution instance of that form."

 

Valid Form: Categorical Syllogism
Invalid Form: Categorical Syllogism

All A are B.

All B are C.

All A are C.

All A are B.

All C are B.

All A are C.

 

Counterexample Method:

STEP-BY-STEP METHOD FOR  PROVING AN ARGUMENT INVALID BY THE METHOD OF COUNTEREXAMPLE:

  1. Locate the conclusion of the argument.
  2. Symbolize the given argument using statement letters in place of phrases. This reveals the argument's form.
  3. Consistently substitute the generic terms: cats, dogs, mammals, fish and animals to generate an argument with true premises and a false conclusion.
  4. It is helpful to begin your term substitutions with the conclusion by choosing two terms that make it false.
  5. Next, work through the premises selecting a third term that makes the premises true.
  6. If you are presented with a hypothetical syllogism, try using the suggested substitutions in Section 1.5: e.g., Abraham Lincoln, suicide and dead. The goal is to use terms that have a necessary connection (e.g., rain-wet, snow-cold, suicide-dead).
  7. If the conclusion is a conditional statement, join a true antecedent with a false consequent.

Things to remember when working on substitution:

 

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Smartboard Notes from Chapter 1 Lectures:

 

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