lecture 7/9/01

Critical Reasoning

Intro to Arguments (proofs, derivations)

• When we create an argument, we offer a set of reasons or evidence in support of a conclusion.


• Criticial reasoning is the process by which we diagnose arguments.


• Why arguments?
  • Inquiry: To assess which are the better views
  • Jusification: To defend views
  • For this class: To resolve ethical dilemmas and formulate public policy

What is an argument?

Argument

a sequence of statements aimed at demonstrating the truth of a statement.

Statement (Proposition, Claim)

a sentence that is either true or false, but not both.

• Types of Statements in arguments
  • Premises
    • Principles
    • Observations
    • Assumptions
  • Conclusion
    • Inference (the
  • Support
  
  
• Truth-bearing
  • Can be factual (empirical, descriptive
  • Can be normative (prescriptive)
  • Not Commands
  • Not Questions
  • Not Exclamations
  
  
• Deductive vs. Inductive Arguments

	Deductive	Inductive
Truth Preserving?	Yes	No
Ampliative?	No	Yes
Monotonic?	Yes	No
All-or-nothing?	Yes	No

• Deductive Validity & Soundness

Validity

an argument is valid when the the truth of the premises necessitates the truth of the conclusion.



Soundness

an argument is sound when (i) it is valid and (ii) the premises are true.

• Peter Suber, "Truth and Validity"

More on Statements

• Simple vs. Complex
• Logical particles
• and
• or
• not
• if...then
• Specific
• Qualified
  
• Generalizations
• Universal
• Existential
• Conditionals
• Indicative
(note: every argument can be expressed as a complex conditional)
• Subjunctive (counterfactual, "what if...")
  
• Comparative
• Fact and Opinion
• Descriptive (Factual, Empirical, Verifiable, "is")
• Normative (Prescriptive, Advocatory, "ought")

Valid Deductive Rules of Inference

• Modus Ponens
• Modus Tollens
• Hypothetical Syllogism
• Disjunctive Syllogism
• Dilemma
• Reductio ad absurdum (e.g., Vindication of the Rights of Brutes)

Other Argument forms

• Argument from Authority (useful only for empirical claims)
• Argument from Analogy (e.g., the Design Argument)
• Induction
  • "Argument by Example"
  • Inductive strength
  • Causality
    • direct cause
    • indirect cause
    • causal independence

The Clinical Attitude (adapted from Peter Suber)

1. The clinical attitude is the willingness to look for truth regardless of its consequences for our interests.
2. Be willing to recognize strength in arguments whose conclusions you reject and weakness in arguments whose conclusions you accept.
3. To examine the validity or soundness of an argument is to attempt to discover the truth.
4. Whether you agree or disagree with the conclusion is unnecessary and irrelevant to this task.
5. Be willing to change your mind in the face of good reasons.

Spotting Arguments

• Argument
  • conclusions, major claims
  • relevant statements
  • conclusion indicators: "therefore," "thus," "so," and "hence"
  • premise indicators: because," "since," and "for"
  • rhetorical questions
• These types of statments (or statment combinations) are not arguments:
  • Certain types of explanations
  • Conditional statements
  • Reports
  • Illustrations
• Power Of Logic Web Tutor
• Exercises

Explication (adapted from Peter Suber)

Explication

to restate an argument in a clear and orderly list of (numbered) propositions.

• Why do this?
  • To help decide whether an argument is valid and sound.
  • To be in a better position to assess an argument's strengths and weaknesses. (This is much easier to do with an explicated arguments than with arguments in their natural habitats.)
  • By itself, an explication doesn't assess but clarify.
  
  
• How do you do this? (Carefully.)
  1. disentangle it from other arguments for other conclusions
  2. omit what is irrelevant
  3. restate it in your own words
  4. clarify the language
  5. decide which propositions are premises for the given conclusion
  6. supply missing or implicit premises (identify them)
  7. state each premise as a single proposition
  8. cite the text by page number for each proposition
  9. put the propositions in logical order (premises first, conclusion last)
  10. number each proposition.

Example: Bentham

Fallacies

• Hasty Generalization [Generalizing from incomplete information] (Weston, 72)
• Overlooking alternatives (72); one-sidedness
• ad hominem (73)
• Argument from Ignorance (74)
• affirming the consequent (74)
• Denying the Antecedent (75)
• begging the question (75)
• False Dilemma(76)
• False Analogy
• Slippery Slope

for more info, see

• The logical Fallacies
• Mission: Critical
• A List Of Fallacious Arguments