A Primer on Arguments

Fundamentals of Philosophical Reasoning and Argumentation

Philosophical practice involves the use of reason and arguments to defend or challenge specific answers (theses) to philosophical questions.
The fundamental tool in this process is the argument, which necessitates a clear definition for academic inquiry.

Defining the Argument

Technical Definition: An argument is an attempt at a transition in thought from premises to a conclusion.
Expression: Arguments are expressed via a set of statements, which may be either verbal or written.
Structure: * Premises: Statements designated as the starting point; they provide the reasons to endorse the conclusion. * Conclusion: The single statement designated as the destination or the claim being supported.
Metaphorical Relationship: The premises are the "starting point," and the conclusion is the "destination."

Distinctions and Misconceptions of 'Argument'

Common Use vs. Academic Use: In this course, the term is specifically not used to refer to: * Quarrels or verbal fights. * Formal mathematical functions, such as $f(x) = y$ (where $x$ is the argument of function $f$ ). * Mere differences of opinion. * Isolated claims without supporting reasons.
Act vs. Object Distinction: * Object Sense: A set of propositions consisting of a conclusion and premises. * Act Sense: The series of acts involved in giving reasons to support a specific claim.

Identifying Arguments in Text

Indicator Words: Certain phrases often signal the presence of an argument, though they are not foolproof guarantees. * Premise Indicators: "Since." * Conclusion Indicators: "So," "therefore," "it follows that."
Complexity: Arguments can exist without indicator words, and indicator words can appear in passages that are not arguments.
Key Identification Questions: * Is the author offering reasons to support a specific conclusion? * Is the author making claims that, if true, would make another claim likely or plausible?

Criteria for Argument Evaluation

The Goal: A good argument is "rationally persuasive," meaning it provides sound reasons to believe the conclusion is true. This differs from the persuasive tactics of advertisers or politicians, which may rely on tricks rather than good reasons.
Standard Form: To evaluate an argument, it must first be interpreted into standard form (see the section on "Standard Form" below).
Primary Evaluating Criteria: 1. Factual Strength: Pertains to the truth or acceptability of the premises. 2. Logical Strength: Pertains to the relationship between the premises and the conclusion.

Factual Strength

Definition: An argument is factually strong if all its premises are true or, at minimum, plausible and acceptable.
Factually Weak Arguments: Arguments containing one or more false or implausible premises.
Examples for Evaluation: * "Edmonton is in Treaty Six Territory" (Factually strong/true). * "If the Liberal Party of Canada won a majority, then a majority of people voted for them" (Factually weak; a majority of seats does not necessarily mean a majority of the popular vote). * "The square of the hypotenuse is equal to the sum of the squares of the opposing sides" (Factually strong; Pythagoras' Theorem). * "Pluto is a planet" (Currently factually weak/false under modern astronomical definitions).

Logical Strength and Validity

Definition: An argument is logically strong if, IF its premises were true (factually strong), THEN its conclusion would be at least very likely to be true.
Independence of Strength: Logical strength is independent of factual strength. An argument can be logically strong even if its premises are completely ridiculous or false.
The "IF" Condition: Validity depends on the hypothetical truth of the premises. If those premises were true, would the conclusion follow?
Comparative Examples: * Argument A (Logically Strong/Valid but Factually Weak): 1. All Cobras can dance. 2. All dancing things have feet. 3. So, all cobras have feet. * Analysis: Though cobras cannot dance and reptiles do not have feet, the logic holds: if they could dance and all dancers had feet, cobras would have feet. * Argument B (Logically Weak): 1. Students must study to pass the exam. 2. Kendra studied for the exam. 3. So, Kendra will pass the exam. * Analysis: Even if both premises are true, the conclusion is not "very likely." Studying is necessary but not sufficient; factors like how much she studied or what topics were covered remain unknown.

Successful vs. Unsuccessful Arguments

Success: An argument is successful only if it is both factually strong and logically strong.
Failure: An argument fails if it lacks either factual or logical strength.
Example Case (Cujo): 1. All cats are reptiles. 2. Cujo is a cat. 3. Therefore, Cujo is a reptile. * Evaluation: This argument is logically strong (valid) but unsuccessful because it is factually weak (Premise 1 is false; Premise 2 is false as Cujo is a dog from Stephen King's novel).

Types of Argument Standards

Arguments are categorized based on the standard of logical support they aim to provide: Deductive or Ampliative.

Deductive Arguments and Validity

Deductive Validity: This is a technical term defined of the highest standard. An argument is valid if and only if the truth of the premises absolutely guarantees the truth of the conclusion.
Certainty: It is literally impossible for the premises to be true and the conclusion false. A valid argument takes "no risks."

Ampliative (Non-Deductive) Arguments

These arguments provide support that makes a conclusion likely but not certain.

Abduction (Inference to the Best Explanation): Inferring a proposition is true because it provides the best explanation for observed phenomena. * Examples: Black holes, Mendel’s discovery of genes, medical diagnostics. * Logical Strength: Determined by whether the conclusion is the best possible explanation among alternatives.
Induction: Taking a description of a sample and extending it to items outside that sample. * Example: "55% of Saskatchewan residents voted Conservative; therefore, 55% of the Canadian population will vote Conservative." * Evaluation Factors: Sample size and representativeness. A large, representative sample leads to a logically strong induction.

Cogency and Premise Standards

Cogent Argument: A technical term for a non-deductive argument that is (i) logically strong, (ii) has acceptable premises, and (iii) has relevant premises.
Acceptability: Premises are acceptable if they are reasonable to believe, even if their exact truth-value is unknown. This includes: * Claims supported by a cogent sub-argument. * Common sense or widely known facts. * "A priori" truths. * Credible testimony.
Unacceptability: Claims are unacceptable if they are easily refuted, "a priori" false, or come from incredible testimony.
Relevance: * Positive Relevance: Truth of $P$ provides evidence that $Q$ is true (e.g., "It is below zero" is relevant to "It is snowing"). * Negative Relevance: Truth of $P$ provides evidence that $Q$ is false (e.g., "It is above 30 degrees" is negatively relevant to "It is snowing"). * Irrelevance: $P$ provides no evidence for or against $Q$ (e.g., "Donald Trump has funny hair" is irrelevant to his qualifications for presidency).

Standard Form and Argument Reconstruction

Formatting Rules: * Labels all premises clearly. * Separate lines for each premise and the conclusion. * Numbered lines for reference. * Each line must be a single declarative statement. * Indicate parenthetically which premises support which conclusion.

Example: The Monty Python Witch Logic

Wood burns. (Observation)
Witches burn. (Observation)
Thus, witches burn because they are made out of wood. (From 1 and 2)
Wood floats in water. (Observation)
Ducks float in water. (Observation)
So, if S weighs the same as a duck, then S is made of wood. (From 4 and 5)
So, if S is made of wood, then S is a witch. (From 1–3)
Rita weighs the same as a duck.
Therefore, Rita is a witch. (From 7 and 8)

Argument Schemas (Skeletons)

Using these forms guarantees a valid deductive argument if substitution is done properly. Capital letters ( $P$ , $Q$ , $R$ ) represent arbitrary declarative sentences.

Form 1: Modus Ponens 1. If $P$ , then $Q$ . 2. $P$ 3. Therefore, $Q$ .
Form 2: Modus Tollens 1. If $P$ , then $Q$ . 2. Not- $Q$ . 3. Therefore, not- $P$ .
Form 3: Disjunctive Syllogism 1. Either $P$ or $Q$ . 2. Not- $P$ . 3. Therefore, $Q$ .
Form 4: Constructive Dilemma (Proof by Cases) 1. Either $P$ or $Q$ . 2. If $P$ , then $R$ . 3. If $Q$ , then $R$ . 4. Therefore, $R$ .
Form 5: Reductio ad Absurdum 1. If $P$ , then ( $Q$ and not- $Q$ ). 2. Therefore, not- $P$ .

Complex Reconstruction: The Traditional Ontological Argument (TOA)

This argument demonstrates how multiple forms (Modus Ponens, Disjunctive Syllogism, etc.) can be nested. It includes intermediary conclusions (claims that serve as both a premise and a conclusion).

Part 1: 1. Suppose you can conceive of the best possible being (greatest-than-which-cannot-be-conceived). (Assumption) 2. Either the being exists or it does not. (Logic premise) 3. If it does not exist, then it is not the best possible being. (Premise) 4. So, the being you conceive of exists. (From 2 and 3; Disjunctive Syllogism) 5. So, if you can conceive of it, then it exists. (From 1–4)
Part 2: 6. You can conceive of the best possible being. (Premise) 7. So, the best possible being exists. (From 5 and 6; Modus Ponens) 8. God = the best possible being. (Definition) 9. Therefore, God exists. (From 7 and 8)

Constructing an Argumentative Essay

Goal: To evaluate whether a specific argument (e.g., Anselm's TOA) is cogent.
Thesis Example: "Anselm's ontological argument is not cogent because it is factually weak."
Five-Paragraph Structure: 1. Introduction: State the thesis. Present your own argument for why the target argument fails in standard form. Explicitly identify the valid form you are using for your own argument. 2. Explanation: Provide an accurate, clear explanation of the target argument (e.g., Anselm’s TOA) in standard form. 3. The Case: Argue that a specific premise of the target argument is false or not rationally acceptable (proving factual weakness). 4. Objection and Reply: Consider the best possible objection to your position and provide a reply. 5. Conclusion: Summarize how you have shown the argument to be non-cogent.

Cultural Relativism vs. Universal Wrongs

In critiquing arguments like the Monty Python witch trial, one might encounter objections based on community standards (e.g., the community believes the premises are relevant).
Counter-Response: If a community's understanding leads to harmful actions (arbitrary burning of people, racism, slavery, the Holocaust, colonialism), cultural relativism does not justify those actions. One should critique the underlying principles if they are immoral or destructive of life and relationships.