1/12: PHIL 105 - Types of Arguments & Validity
Class Overview and Structure
Diagramming arguments will only take two days due to its complexity and will be less of a focus in the logic course.
Instructor Availability
Office Hours:
Mondays and Wednesdays from 11:30 AM to 1 PM
Open to meetings via Zoom or other timings by email.
Homework:
First homework posted on Canvas, due Sunday by 11:59 PM
Slides and notes will be posted within an hour after class, with reminders to email if not received.
Review of Previous Week's Concepts
Topics discussed included arguments and declarative assessments.
Key points raised by students:
The difference between rhetorical questions and imperatives in arguments.
Understanding arguments vs. explanations:
Arguments aim to persuade and convince.
Explanations aim to clarify.
Important Properties of Arguments
Four properties essential to understanding arguments:
Inductive and Deductive Arguments
Two families of arguments.
Validity and Invalidity (within deductive arguments)
Most significant distinction.
Definition of Deductive Arguments:
Aim for certainty.
Conclusion must necessarily follow the premises.
Impossibility of premises being true while the conclusion is false.
Example:
"Felix is a student" implies someone is a student; both cannot be false.
Characteristics of Deductive Arguments
Deductive argument validity:
If premises are true, conclusion must definitely be true.
Can be valid or invalid, with validity tied to the structure of the argument, not its truthfulness.
Variable substitution (e.g., mammals, reptiles, etc.) maintains validity.
Inductive Arguments:
Conclusions are probable rather than certain.
Strength is measured by likelihood.
Example: Observing the sun rising led to the conclusion it will rise tomorrow.
Distinction Between Types of Arguments
Deductive arguments assume certainty while inductive arguments allow for likelihood.
Validity and invalidity not related to the truth of premises:
Validity described as:
An argument is valid when true premises cannot lead to a false conclusion.
Invalidity:
Occurs when even valid arguments lead to false conclusions.
Soundness of Arguments
An argument is defined as sound when:
It is valid.
All premises are true.
Valid arguments can have:
False premises and false conclusions.
Validity pertains solely to the structure, independent of truthfulness of claims.
Examples of Valid and Invalid Arguments
Discussion of hypothetical arguments:
If the sky is blue, God exists; sky is blue; therefore, God exists.
The validity of these arguments is assessed by whether you can imagine true premises leading to a false conclusion.
Modus Ponens:
Known valid structure where if P, then Q, followed by affirming P leads to concluding Q.
Example given: If P (sky is blue), then Q (God exists), affirming P leads to concluding Q must hold true.
Modus Tollens:
An invalid form, affirming the consequent.
Learning through Practice
Validity checks through class engagement.
Examples from the textbook showing:
Valid arguments with all propositions true.
Invalid arguments displaying misleading relationships between premises and conclusions.
Homework will help reinforce these concepts.
Preparation for Chapter Two
Focus on analyzing arguments and techniques for diagramming.
Keys to understanding arguments:
Paraphrasing to clarify language and intentions.
Diagramming to display logical structure effectively.
Techniques for Argument Analysis and Diagramming
Importance of clarity:
Use explicit nouns for pronouns.
Rearrange sentences for maximum inference visibility.
Keep propositions distinct and avoid ambiguity.
Examples of Paraphrasing Arguments
Example from a notable figure highlighting the permanence of mathematical ideas versus language.
Recognition of sources and barriers to clarity in argumentation.
Summary of class discussion with conclusions resting on recognized premises.
Closing Remarks
Future focus on correlation between argument structures, their validity, and how to communicate effectively within arguments.