Standard Form Argument Reconstruction Study Guide

Overview of Standard Form

• Definition: An argument is in standard form when its premises and conclusion have been listed, labeled (as premises or conclusion), and numbered, with the final conclusion stated last.

• Purpose of Standard Form:

  • Enables clear understanding and accurate evaluation of argument components.

  • Represents the clearest and strongest presentation of an argument that conforms directly to the author's intent.

• Figure displaying the core procedure:

• The Six Sequential Steps:

  

  1. Identify premises, sub-conclusions, and conclusions.

  2. Provide justifications for each line in the argument.

  3. Eliminate unnecessary words, phrases, and sentences.

  4. Re-write statements in straightforward logical form.

  5. Eliminate stylistic variations that express the same concept.

  6. Make explicit any implicit premises.

Core Principles: Fairness and Charity

• Reconstructing arguments in standard form is guided by two foundational principles:

  • Principle of Fairness: Dictates rewriting the argument in keeping with the author's intent. Requires a good-faith effort to fully understand the view being represented.

  • Function: Helps avoid merely verbal disputes. Merely verbal disputes arise when parties misunderstand a key concept or issue, leading them to appear to disagree when they are actually "talking past each other" due to a lack of effort to comprehend the opposing view.

  • Principle of Charity: Dictates reconstructing the argument in its strongest possible rendition.

  • Function: Serves as the direct antithesis of the straw man fallacy.

Step 1: Identifying Premises, Sub-Conclusions, and Conclusions

• Compound Arguments and Sub-Conclusions:

  • Compound arguments contain smaller embedded arguments within them.

  • Sub-conclusions are the conclusions of these smaller arguments and serve as premises for the final conclusion.

  • Because sub-conclusions are frequently introduced by conclusion indicators, the presence of a conclusion indicator does not guarantee that the statement is the final conclusion.

• Strategies for Disambiguating Sub-Conclusions from Final Conclusions:

  • There is no formal rule or structural order that decides which statement is the final conclusion.

  • Clue 1 (Direction of Support): Evaluate which statement supports the other. Identify the direction in which the logical inference flows.

  • Clue 2 (Comprehensive Indicator Terms): Final conclusions often feature comprehensive indicators such as "all things considered," "given all the evidence," and "as a result of all these factors," which are broader and more inclusive than simple indicators like "so" or "therefore."

• Case Study 1: Driving in Alaska

  • Original Passage text:     > "Driving in Alaska is ridiculously dangerous. Consider the conditions drivers face. Ice and snow cover the roads through much of the year. Wildlife wanders out into the street. Tourists and RV’s clog the roads in the summer, often to look at the wildlife that is also on the street. So, the state of Alaska absolutely must pass laws to protect innocent drivers. While we can’t outlaw moose, tourists, or bad weather, the state of Alaska can outlaw driving while talking on cell phones. And we’ve all seen those morons motoring along, dialing, chatting, and not paying any attention to the road. Since this is a factor that we can control and one that impacts the safety of our roads, it follows that the Alaska legislature should ban cell phone use while driving."

  • Analysis of Conclusions:

  • Intermediate Sub-conclusion: "The state of Alaska must pass laws to protect innocent drivers."

  • Final Conclusion: "The Alaska legislature should ban cell phone use while driving."

  • Standard Form Reconstruction:

  • 1. Weather conditions, wildlife, tourist traffic, and cell phone use contribute to dangerous driving conditions in Alaska. (Pr.)

  • 2. So, the state government must pass laws to increase traffic safety. (1)

  • 3. The state government has no control over weather conditions, wildlife, or tourists. (Pr.)

  • 4. The government can control cell phone use. (Pr)

  • So, 5. The state government must pass laws to ban cell phone use by drivers. (2-4)

• Case Study 2: Pebble Mine Development

  • Original Passage text:     > "I bet there is a lot you don’t know about mining companies. Did you know that mining companies create pools filled with cyanide? They do. The cyanide helps draw impurities off gold and other metals. It is called the cyanide leach method. And sure, the companies always promise to clean up after the mine closes. But they have another dirty trick they play so they won't have to. Mining companies create subsidiaries—smaller companies to run the mines. These companies go bankrupt and cannot pay the cost of cleanup or bear any legal responsibility for the left over cyanide. So, mining companies have a pretty bad history of making good on their promises. Now, we hear loads of promises from the people who want to develop the Pebble Mine. Should we really risk the greatest wild salmon run and the livelihoods of thousands of people on promises from proven liars? All things considered, Alaskans need to oppose the development at Pebble Mine."

  • Analysis of Conclusions:

  • Sub-conclusion: "Mining companies have a pretty bad history of making good on their promises."

  • Final Conclusion: "Alaskans need to oppose the development at Pebble Mine."

  • Standard Form Reconstruction:

  • 1. Mining companies use chemicals that are harmful to people and the environment. (pr)

  • 2. Mining companies acknowledge their obligation to clean up harmful chemicals. (pr)

  • 3. Mining companies often avoid the requirement to clean up after the mine has closed. (pr)

  • So, 4. Mining companies cannot be trusted to clean up harmful chemicals. (1-3)

  • 5. Harmful chemicals at Pebble mine would threaten one of the world’s largest runs of wild salmon, along with the jobs and lifestyles that depend on that salmon run. (pr)

  • So, 6. It is not in Alaska’s interest to permit Pebble mine to be developed. (4-5)

• Flexibility in Reconstruction:

  • Multiple valid ways exist to reconstruct an argument in standard form.

  • While wording and structure may vary, all reconstructions must prioritize maximum clarity and logical strength.

Step 2: Providing Justification for Each Line

• Role of Annotations:

  • Essential for compound arguments to track which premises justify which conclusion.

  • Assists in following the complete chain of reasoning and distinguishes claims supported by arguments from unbacked assumptions.

• Annotation Rules:

  • Premises and primary assumptions are annotated at the end of the line with (pr) or (Pr).

  • Sub-conclusions and conclusions are annotated with the specific line numbers of the premises supporting them in parentheses, such as (1-3) or (2-4).

Step 3: Eliminating Unnecessary Words, Phrases, and Sentences

• Procedure for Content Reduction:

  • Examine every word, phrase, and sentence in the original argument.

  • Ask whether removing the element weakens the logical force of the argument. If it does not, remove it.

• Types of Irrelevant Language:

  • Extraneous words: Adverbs and intensifiers like "ridiculously."

  • Unnecessary sentences: Conversational prompts (e.g., "Consider the conditions drivers face") or insults/anecdotes (e.g., "And we've all seen those morons motoring along…").

  • Non-essential clauses: Clauses containing irrelevant details (e.g., "often to look at the wildlife that is also on the street").

• Treatment of Adverbs and Rhetorical Intensifiers:

  • Adverbs and intensifiers are logically irrelevant.

  • Claims formatted with phrases like "obviously true" or "indisputably proven" must have those phrases removed and be subjected to extra scrutiny.

  • Speakers often substitute adverbs for substantive arguments to mask weak reasoning.

  • Claims are virtually never true "simply as a matter of logic."

Step 4: Re-Writing Statements in Straightforward Logical Form

• The Six Statement Categories:

  • Atomic Statements:

  • Simple statements containing no other statements or logical operators as parts (e.g., "the dog is brown", "the fence is red").

  • Obscured by Hedges: Phrases intended to make a claim appear weaker or less intrusive (e.g., "Although people may disagree, I believe that…", "While some people may ridicule this position, it seems to me that…"). Hedges add no logical value.

  • Obscured by Intensifiers: Phrases asserting absolute truth or unassailability (e.g., "It is absolutely true that…", "No one can deny the truth that…").

  • Negations:

  • The denial of a statement. For any atomic statement $P$, its negation is $\text{not-}P$.

  • Formulations in English: "The door is not red", "It is not the case that the door is red", "The assertion 'The door is red' is false."

  • Canonical English Form: "It is not the case that $P$". This isolates the negation operator from the proposition being denied.

  • Philosophical Significance: Phrasing "God does not exist" as "It is not the case that God exists" clarifies that the proposition "God exists" is false, avoiding the metaphysical puzzle of predicating non-existence of an entity.

  • Complex Negations: Negations can negate compound statements (e.g., "It isn't true that either you are a Republican or you aren't a real American", "It's not the case that if you pass the final you will pass the class and graduate on time").

  • Conjunctions:

  • The combination of two statements into an assertion that both are true simultaneously. Canonical connector: "and".

  • Truth Condition: True only when both conjoined statements are true; false if either statement is false.

  • English Phrasing Variations:

    • "George W. Bush is an idiot and Barack Obama is intelligent."

    • "Although George W. Bush is an idiot, Barack Obama is intelligent."

    • "While George W. Bush is an idiot, Barack Obama is intelligent."

    • "George W. Bush is an idiot, but Barack Obama is intelligent."

    • "George W. Bush is an idiot, however, Barack Obama is intelligent."

    • "Despite the fact that George W. Bush is an idiot, Barack Obama is intelligent."

  • Commutative Property: Order does not matter ($P \text{ and } Q$ is logically identical to $Q \text{ and } P$).

  • Disjunctions:

  • Joins two statements together, asserting that at least one is true. Canonical connector: "or".

  • Truth Condition: True when at least one (or both) disjoined statements are true.

  • False Dichotomy Note: A false dichotomy can still be a true disjunction.

  • English Phrasing Variations:

    • "Either the Yankees will win another World Series or Cashman screwed up."

    • "Unless Cashman screwed up the Yankees will win another World Series."

  • Commutative Property: Order does not matter ($P \text{ or } Q$ is logically identical to $Q \text{ or } P$).

  • Conditional Statements (Hypothetical / If-Then Statements):

  • Connects an antecedent to a consequent. Canonical form: $\text{If } p\text{, then } q$.

  • Equivalent Expressions for $\text{If } p\text{, then } q$:

    • "If there is a God, then I am going to pay for my sins."

    • "There is a God only if I pay for my sins."

    • "There is a God is a sufficient condition for my paying for my sins."

    • "Paying for my sins is a necessary condition for there to be a God."

    • "Given that there is a God, I am going to pay for my sins."

    • "Since there is a God, I am going to pay for my sins."

    • "When there is a God, I am going to pay for my sins."

    • "Whenever there is a God, I am going to pay for my sins."

    • "Paying for my sins depends on there being a God."

    • "God's existence entails that I am going to pay for my sins."

  • Categorical Expressions of Conditionals:

    • "All cats are animals."

    • "Only animals are cats."

  • NON-COMMUTATIVE PROPERTY: Order cannot be reversed. Reversing the statements fundamentally alters the meaning:

    • Example 1: "If Thomas Jefferson was in a fatal car accident, then he died."

    • Example 2: "If Thomas Jefferson died, then he was in a fatal car accident."

  • Bi-Conditional Statements:

  • Asserts that two statements always share the same truth value (both true or both false).

  • Canonical Connector: "if and only if".

  • Equivalent Phrasing Variations:

    • "Someone is human if and only if she is a rational animal."

    • "Someone is human just in case she is a rational animal."

    • "All and only humans are rational animals."

    • "If someone is human then she is a rational animal and if she is a rational animal, then she is human."

    • "Being human is necessary and sufficient for being a rational animal."

• Summary of Canonical Expressions (where $P$ and $Q$ represent statements):

  • Atomic / Negation: $P$, $\text{not-}P$

  • Conjunction: $P \text{ and } Q$

  • Disjunction: $P \text{ or } Q$

  • Conditional: $\text{If } P\text{, then } Q$

  • Bi-conditional: $P \text{ if and only if } Q$

Step 5: Eliminating Stylistic Variants of the Same Claim

• Identifying and Removing Redundancy:

  • Speakers and writers express the same premise in multiple rhetorical ways to reinforce points.

  • Eliminating stylistic variants reveals the underlying simplicity of the argument's core substance.

• Redundancy in Advertising and Politics:

  • Television advertisements frequently rely on heavy repetition based on the strategic assumption that average consumers require hearing a message $4$ times within $30$ seconds to retain it.

  • Millions of dollars are spent developing these ad frameworks.

  • Typical Advertisement Example: "The Toyota Treehugger is the most fuel efficient car in its class. With the Treehugger you get more miles per gallon than with competitors models. This means less gas in your tank and more money in your pocket."

  • Ads function as arguments supporting the final conclusion that consumers should purchase product $x$

  • Applying uniform language in Step 4 makes redundant premises immediately obvious and easy to eliminate.

Step 6: Making Explicit Any Implicit Premises

• Definition and Function of Implicit Premises (Enthymemes):

  • Key components left unstated in an argument.

  • Omitting common-sense or obvious premises is often done for brevity.

  • Omitting controversial premises allows authors to avoid scrutiny on assumptions doing heavy logical lifting.

  • Example: "Pat is a mother. So, Pat is a woman." (Implicit premise: "All mothers are women.")

• Indicators of Implicit Premises:

  • Abstract Concepts:

  • Arguments depending on unstated assumptions about concepts like goodness, beauty, truth, power, freedom, or oppression.

  • Example Argument: "Feminists complain that women are oppressed. But women have long had the right to vote. Politicians go to great lengths to win female voters' favor. With all of the protections in the workplace against harassment and sexism, women have as much opportunity as men. Clearly, the feminists misrepresent women's situation in our day and age."

  • Implicit Assumption: Assumes oppression is strictly defined as institutional or legal denial of rights. Feminists may define oppression differently, such as social or cultural forces resulting in lower socio-economic status.

  • Culturally Relative Concepts:

  • Concepts whose meanings vary across cultures and contexts, such as "normal."

  • Historical/Cultural Variations in Normal Attire: $2022$ in Alaska vs. $1922$ in Saudi Arabia vs. $17\text{th}$ century Italy.

  • Descriptive vs. Evaluative Definitions of "Normal":

    • Descriptive Category: Refers to what is typical or average (e.g., left-handedness is descriptively abnormal because only $10\%$ of the population is left-handed).

    • Evaluative Category: Refers to what is natural or proper (left-handedness is normal because nothing is wrong with it).

  • Exceptionality: Being abnormal is not inherently negative (e.g., Einstein's abnormal intelligence, skills of Olympic athletes).