1 Splinter’s Logic Lesson: Arguments, Premises, and Conclusions

A Little More Logical | Brendan Shea, Ph.D.

In this opening chapter, we dive into the foundational concepts of logic and argumentation through the engaging lens of Splinter teaching the Teenage Mutant Ninja Turtles. By exploring what qualifies as a logical argument, the different types of reasoning, and common pitfalls to avoid, readers will gain a solid grounding in the principles of clear thinking and rational discourse. The chapter draws on relatable examples from the world of the Turtles while also making connections to real-life applications in fields like journalism, science, and ethics. In studying the anatomy and varieties of arguments, we take the first steps in honing our analytical abilities – skills as essential for navigating the sewers of public discourse as they are for battling the fallacies that threaten truth and reason.

Learning Outcomes: By the end of this chapter, you will be able to:

Identify the key components of an argument, including premises, conclusions, and inferential links.

Distinguish between arguments and non-arguments such as reports, illustrations, and statements of belief.

Recognize and apply the three main types of logical reasoning: informal, formal deductive, and inductive probabilistic logic.

Put arguments into standard form and interpret them charitably using the Principle of Charity.

Analyze real-world arguments by identifying common flaws such as hasty generalizations, circular reasoning, and appeals to ignorance.

Keywords: Logic, Argument, Statement/Proposition, Premise, Conclusion, Inferential link, Conclusion indicator words, Premise indicator words, Standard form, Principle of Charity, Formal deductive logic, Inductive probabilistic logic, Informal logic, Statement of belief, Report, Illustration, Conditional statement, Sufficient condition, Necessary condition, Explanation, Explanans, Explanandum, Socratic method

Splinter’s Logic Lesson

In the sewers of New York, where the city’s grime meets the turtles’ grit, Splinter stands before his four students: Leonardo, Donatello, Raphael, and Michaelangelo. The air is tinged with the smell of pizza and the whiff of youthful skepticism. “Gather around,” says Splinter, his voice calm but carrying the weight of unspoken wisdom. “Today, we delve into a different kind of training.” April, notebook in hand, leans against a wall of damp bricks, her eyes alight with the promise of a story only she could tell. “Logic,” Splinter announces, “will be our weapon and shield today.” And so, in a corner of the world where mutants and ninjas coexist, a new lesson unfolds—one that promises to be as enlightening as it is unconventional.

What is Logic? Why Should I Study It?

Splinter, leaning on his staff, surveys his pupils and asks, “Which skills are most essential for a ninja?”

Leonardo, the leader, is quick to respond: “Tactics and discipline are crucial. They allow us to make effective plans and execute them flawlessly.”

Donatello, ever the intellectual, counters, “While tactics are important, knowledge and technological innovation give us the edge. We can outsmart our enemies.”

Raphael, the muscle of the group, scoffs. “Tactics and tech are fine, but what you really need is raw strength and speed. That’s how you win fights.”

Michaelangelo, never one to miss an opportunity for levity, chimes in: “You guys are overthinking it. Pizza and fun keep us going!”

Splinter nods, absorbing their words. “You’ve each presented an Argument, a reasoning structure aimed at establishing a truth. An argument is composed of Premises and a Conclusion. The premises are the reasons you give, and the conclusion is what you’re trying to prove.”

He turns to Leonardo. “Your premise is that tactics and discipline enable effective planning. Your conclusion is that they are the most important skills for a ninja. That’s an argument.”

Splinter then addresses the group. “But how do we know which argument is best? That’s where Logic comes in. Logic is the systematic study of arguments, the processes that allow us to draw conclusions based on premises.”

Splinter elaborates on the importance of studying logic: “It’s not just about winning debates or choosing pizza toppings. Logic equips you with the skills to evaluate the quality of arguments, yours and others’. It helps you make better decisions, whether in battle or in life.”

Donatello interjects, “So, logic is like the operating system for thinking?”

“Exactly,” Splinter replies. “And just like an operating system, it can be upgraded and refined. There are different types of logic—informal, formal, inductive—and we’ll explore those next.”

April, scribbling furiously in her notebook, realizes that this lesson is not just about abstract reasoning. It’s a foundational skill, as practical and essential as any weapon in the turtles’ arsenal.

What is an Argument?

Splinter picks up a slice of pizza, its cheese stretching in a satisfying arc. “Before we dissect the anatomy of an argument, let’s first understand its basic unit: the Statement. A statement is a sentence that can be either true or false. For example, ‘The pizza is hot’ is a statement because it can be verified as true or false. On the other hand, ‘Is the pizza hot?’ is not a statement; it’s a question and cannot be true or false.”

Examples of statements include:

• Leonardo leads: A declarative sentence asserting the leadership role of Leonardo.
• If Michelangelo is eating pizza, then he is happy: A conditional statement linking Michelangelo’s happiness to his consumption of pizza.
• Donatello believes that technology can solve any problem: A statement about belief, asserting Donatello’s faith in technology.
• Splinter is originally from Japan: A statement with an unknown truth value, concerning Splinter’s origins.
• April O’Neil is either a reporter or a spy for Shredder: A disjunctive statement outlining two possible roles for April O’Neil.

Examples of non-statements include:

• Cowabunga, dudes!: An exclamatory sentence expressing excitement, not subject to truth evaluation.
• What is the secret of the ooze?: A question probing the mystery behind the ooze, not a claim of truth or falsity.
• Tell Shredder to stop!: An imperative sentence directed at halting Shredder’s actions, not a statement.
• Splinter’s wisdom: A noun phrase describing a quality of Splinter, but not making a claim.

Donatello, always keen on definitions, nods. “So, in programming terms, a statement is like a Boolean variable—it can only hold a true or false value.”

“Exactly,” Splinter affirms. “Now, an Argument is a structured set of statements. It consists of Premises and a Conclusion. The premises are the foundational claims, the reasons you offer for a particular belief. The conclusion is the belief itself, the point you’re trying to establish.”

Splinter sets the pizza slice down and continues, “But remember, an argument isn’t just a random collection of statements. There must be an Inferential Link, a logical thread that ties the premises to the conclusion.”

He turns to Raphael. “For instance, you argued that strength and speed are essential because they help win fights. Your premises and conclusion are connected. You’re saying that if A (strength and speed) leads to B (winning fights), then A is essential for a ninja.”

Raphael smirks, clearly pleased with the validation.

“But what about collections of statements that aren’t arguments?” Leonardo asks, always eager to explore the boundaries of a concept.

Splinter smiles. “Ah, good question. Consider these two sets of statements:

‘It’s raining outside. Therefore, the ground will be wet.’

‘It’s raining outside. I enjoy eating pizza.’

The first set forms an argument because the premise (‘It’s raining outside’) logically supports the conclusion (‘the ground will be wet’). The second set, however, doesn’t form an argument. While both sentences are statements, there’s no inferential link between them. The fact that it’s raining has no logical bearing on one’s enjoyment of pizza.”

April, her pen flying across her notebook, realizes the depth of what Splinter is teaching. An argument is not a mere collection of statements or an emotional outburst; it’s a carefully constructed edifice of reasoning. Each statement serves a purpose, and the inferential links between them are the mortar that holds the structure together. In a world as chaotic and unpredictable as the one they navigate daily, the ability to construct and evaluate arguments is not just an intellectual exercise—it’s a survival skill.

Sample Problem: Is it a Statement?

Determine whether the following sentences are statements.

Sentence	Is it a statement? (Or “Does it express a proposition?”)
Leonardo is the leader of the Teenage Mutant Ninja Turtles.	Yes. Simple declarative sentences are statements. This is a claim about the world that might be true (Leonardo really is the leader), or it might be false (if, in an alternate storyline, he is not). Either way, though, it’s a statement.
When will the Teenage Mutant Ninja Turtles defeat Shredder?	No. Questions are not statements since they can’t be true or false.
Michelangelo, stop eating so much pizza.	No. Commands (like questions) are not statements since they cannot be true or false.
If you watch a Teenage Mutant Ninja Turtles episode, you should watch “The Invasion.”	Yes. If-then statements (conditional statements) are still statements.
I don’t like the new Teenage Mutant Ninja Turtles series.	Yes. This sometimes confuses people, but claims about how you feel, or what you think/believe/like, ARE statements. They can be true (if you are being honest) or false (you are lying).
Raphael is hot-headed and often acts impulsively; however, if he’s the leader, then he acts more cautiously.	Yes. This (complex) sentence is a statement. It also contains subparts that are statements. In general, if A and B are statements, then so are sentences like “A and B”, “A or B”, and “A but B.”
Donatello is a tech genius.	Yes, this is a statement. It might just be your “opinion” (and you might be wrong about it), but this doesn’t change the fact that it is a claim about how the world is.
Cowabunga!	No.
Leonardo believes that Splinter is the wisest being in New York.	Yes. Claims about what people “believe” or “think” are still statements. After all, you might be wrong about them.
The Teenage Mutant Ninja Turtles live in a secret laboratory.	Yes. Even if this statement might not align with the canonical location of their home (which is usually depicted as a sewer), it is still a statement because it makes a claim about the world that can be true or false.

Types of Logic

Splinter, sensing that the turtles are grasping the foundational elements, decides it’s time to introduce the various styles of logical reasoning. “Just as there are different forms of martial arts, there are different types of logic. Each has its own strengths and weaknesses, its own rules and applications.”

He starts with the first. “Informal Logic is akin to street fighting. It’s the logic we use in everyday conversations and decisions. It’s practical and flexible but lacks the strict rules you’d find in more formal systems. You might use informal logic when deciding which route to take when patrolling the city. It’s quick, it’s dirty, and it gets the job done most of the time.”

Michaelangelo nods. “So, it’s like choosing to eat pepperoni pizza because it’s awesome, without needing a detailed analysis?”

“Exactly,” Splinter confirms.

He moves on to the second type. “Formal-Deductive Logic is like classical martial arts. It’s structured, rigorous, and operates under a strict set of rules. In formal logic, an argument’s form is scrutinized to ensure its validity. It’s the type of logic you’d find in mathematical proofs or scientific theories.”

Donatello’s eyes light up. “Ah, so it’s like coding! Every syntax has to be correct, or the whole program fails.”

“Correct,” Splinter says. “And finally, we have Inductive-Probabilistic Logic. This is the logic of likelihood and experience. It’s the ninja’s intuition. You use inductive logic when you make predictions based on past experiences, like anticipating an enemy’s move.”

Raphael grins. “So, it’s like knowing that a certain type of enemy is likely to attack in a specific way because that’s what they’ve done before?”

“Exactly,” Splinter replies. “Each type of logic has its place, just as each fighting style has its optimal application. Knowing when to use which type of logic is a skill that comes with practice and experience.”

April pauses her note-taking, struck by the realization that logic is not a monolithic entity but a spectrum of methodologies, each with its own domain of applicability. She understands that mastering these types is essential for making sound decisions, whether in the heat of battle or the calm of reflection.

Table: The Many Types of Logic

Logic Type	Description	Example
Informal Logic
Analogy	Arguing based on similarity or comparison between two things	If Michelangelo enjoys skateboarding, and Raphael is similar to Michelangelo, then Raphael probably enjoys skateboarding too.
Generalization	Drawing a general conclusion from specific instances	Donatello is intelligent, Leonardo is intelligent, Michelangelo is intelligent, and Raphael is intelligent. Therefore, all teenage mutant turtles are intelligent.
Formal-Deductive Logic
Propositional Logic	Reasoning with propositions and logical connectives (e.g., and, or, if-then)	IF the turtles train hard, THEN they will become stronger. The turtles train hard. Therefore, they will become stronger.
Categorical Logic	Reasoning with categorical propositions (e.g., all, some, no)	ALL mutants have special abilities. SOME turtles are mutants. Therefore, SOME turtles have special abilities.
Predicate Logic	Reasoning with predicates and quantifiers (e.g., for all, there exists)	For all x, if x is a teenage mutant turtle, then x fights crime. Donatello is a teenage mutant turtle. Therefore, Donatello fights crime.
Modal Logic	Reasoning with modalities (e.g., necessity, possibility)	It is possible that the turtles will defeat the Shredder. It is necessary for the turtles to work together to defeat the Shredder.
Deontic Logic	Reasoning with obligations, permissions, and prohibitions	The turtles are obligated to protect the city. The turtles are permitted to use their weapons to fight crime. The turtles are prohibited from revealing their identities.
Inductive-Probabilistic Logic
Bayesian Reasoning	Updating the probability of a hypothesis based on new evidence	The probability of Splinter being a great sensei is high. After observing his training methods, the probability of him being a great sensei increases further.
Null Hypothesis Testing	Determining whether to reject or fail to reject a null hypothesis based on evidence	Null hypothesis: The turtles’ training has no effect on their fighting skills. Alternative hypothesis: The turtles’ training improves their fighting skills. If evidence suggests a significant improvement, reject the null hypothesis.

Arguments are Everywhere!

Splinter, feeling the intellectual energy in the room, decides it’s time to ground the theory in the practical. “Arguments are not just the stuff of ancient philosophy or legal battles; they’re the bread and butter of our daily lives.”

April, notebook at the ready, steps in. “I’ve been documenting our adventures and daily decisions, and it’s clear that we’re constantly engaged in argumentation, often without even realizing it.”

Splinter nods and turns to Donatello. “When you’re programming, you’re essentially engaged in Formal-Deductive Logic. Each line of code is like a premise, and the program’s output is the conclusion. If your code is logically sound, the program will run successfully.”

Donatello’s eyes light up. “Exactly! In programming, we use conditional statements to create logical flows based on the truth of some premise. For instance, in Python, we might write:

enemy_detected = True

if enemy_detected:

    engage_stealth_mode()

else:

    continue_patrol()

Here, the enemy_detected = True serves as a premise, leading to conclusions that dictate the program’s actions.”

Splinter then turns to April. “Your journalistic work often involves Inductive-Probabilistic Logic. When you’re investigating a story, you gather data, look for patterns, and then make a probabilistic conclusion, much like the scientific method or statistical analysis.”

April nods. “Absolutely. When I’m investigating, I collect evidence, analyze it statistically to see if there’s a significant trend, and then draw a conclusion. It’s not 100% certain, but it’s based on a high likelihood.”

Finally, Splinter looks at Michaelangelo. “And let’s not forget your passionate debates about pizza toppings, which are prime examples of Informal Logic. You’ll argue that pepperoni is superior to mushrooms based on its flavor, texture, and how it complements other toppings. While your argument might not be as structured as Donatello’s code or April’s data analysis, it’s still a form of logical reasoning.”

Michaelangelo grins. “Well, when it comes to pizza, you’ve got to consider all the angles, dude!”

Splinter concludes, “So you see, whether we’re coding, investigating, or even just choosing a pizza, we’re employing different types of logic. Recognizing the arguments that underlie our decisions helps us understand our choices better and navigate the complexities of life more effectively.”

April puts her pen down, realizing that the art of argumentation is not confined to textbooks or debate halls. It’s a living, breathing practice that they all engage in, each in their own unique way, every single day.

Finding the Conclusion of an Argument

Splinter, sensing that the group is ready for more advanced techniques, introduces the concept of Indicator Words. “In the heat of a debate or while analyzing a complex situation, it can be challenging to identify the premises and the conclusion. Indicator words serve as signposts that help us navigate the structure of an argument.”

He turns to Leonardo. “Think of these words as tactical cues in a battle plan. They help you quickly decipher the core of an enemy’s strategy.”

Leonardo nods, seeing the immediate utility of such a tool in his role as the team’s strategist.

Splinter continues, “There are two main types of indicator words: Conclusion Indicator Words and Premise Indicator Words. Conclusion indicators signal that what follows is the point of the argument. Premise indicators, on the other hand, signal that what follows is a supporting statement.”

He then presents a table to illustrate:

Type	Indicator Words	Example Sentence
Conclusion Indicator	Therefore	It’s raining, therefore the ground will be wet.
	Hence	She is late, hence we should start without her.
	Thus	He is a skilled fighter, thus he won the match.
	So	You forgot your weapon, so you must go back.
Premise Indicator	Since	Since it’s raining, we should stay indoors.
	Because	We lost because we were outnumbered.
	Given that	Given that he’s skilled, he should lead the team.
	Assuming	Assuming she’s right, we should follow her plan.

Splinter elaborates, “For example, in the sentence ‘It’s raining, therefore the ground will be wet,’ the word ‘therefore’ indicates that ‘the ground will be wet’ is the conclusion drawn from the premise ‘It’s raining.'”

April finds this particularly useful for her journalistic work, where dissecting arguments quickly can be crucial. “This is a great tool for critical reading. It helps to quickly identify the core claims and supporting evidence in a piece of writing.”

Splinter nods. “Exactly, April. And these indicator words are not just useful for dissecting others’ arguments. They can also help us construct our own arguments more clearly, making it easier for others to understand our reasoning.”

By the end of this section, each member of the group, from the tactical Leonardo to the investigative April, sees the value in these linguistic signposts. They understand that these simple words can be powerful tools in both constructing and deconstructing arguments, in battle as in life.

Putting an Argument in Standard Form

Splinter, sensing the group’s readiness for a more advanced lesson, introduces the concept of Standard Form. “While it’s crucial to understand the individual elements of an argument, it’s equally important to know how to assemble these parts into a coherent structure. That’s where Standard Form comes into play.”

He outlines the guidelines: “In Standard Form, each Statement is written on its own line. The Premises are listed above the Conclusion, and all extraneous words are removed for clarity. Additionally, any Implicit Content—unstated assumptions or premises—should be explicitly included.”

To illustrate, Splinter first presents the arguments in their original, “paragraph form”:

• “Given that Shredder is the most dangerous villain we currently face, it stands to reason that we should confront him first.”
• “I’ve made mistakes by acting on impulse, but I’ve also missed out on opportunities by not acting quickly. So, I guess I need to find a balance between being impulsive and cautious.”
• “I really like sweet and savory flavors. Pineapple is sweet, and ham is savory. So, a pizza with both pineapple and ham would probably be really tasty.”

He then shows how these arguments can be transformed into Standard Form:

Example 1: Choosing a Villain to Fight

• Shredder is the most dangerous villain we face.
• The most dangerous villain should be confronted first.
• Therefore, Shredder should be confronted first.

Example 2: Raphael’s Internal Debate on Impulsivity

• Acting on impulse has led to mistakes in the past.
• Not acting quickly has also led to missed opportunities.
• Therefore, a balance between impulsivity and caution is needed.

Example 3: Michaelangelo’s Pizza Choice

• I enjoy both sweet and savory flavors.
• Pineapple is sweet, and ham is savory.
• Pineapple and ham together would satisfy my flavor preferences.
• Therefore, a pineapple and ham pizza would be enjoyable.

Donatello finds the method akin to debugging code. “It’s like isolating the logic errors in a program. You have to see the messy code first to appreciate the elegance of the refined version.”

April sees its applicability in journalism. “This could help me structure my articles. By converting the messy thoughts into standard form, I can ensure that my argument is both coherent and compelling.”

The Importance of Being Charitable

Splinter, having guided his pupils through the intricacies of putting an argument in standard form, decided it was time to delve deeper into the art of rational discourse. “The next step in understanding arguments,” Splinter began, “is learning to apply the Principle of Charity. This principle is about interpreting others’ arguments in the most rational and strongest form possible. It’s about assuming the best in what others say before we critique it.”

He explained further, “This doesn’t mean we blindly accept every argument, but rather that we approach them in a fair and empathetic manner. We reconstruct them to their strongest version, giving the benefit of the doubt to the speaker. It’s a practice that not only fosters understanding but also tempers our emotional responses with reason.”

Splinter then encouraged his students to provide examples to illustrate charitable and uncharitable interpretations of arguments.

Raphael, with his typically direct approach, jumped in first. “So, if someone says, ‘I think practicing meditation can improve martial arts skills,’ an uncharitable interpretation would be, ‘Oh, so sitting quietly is going to make me a better fighter? Doubt it!'”

“Exactly, Raphael. That interpretation dismisses the argument without considering its potential merits.”

Michelangelo, always eager to add a lighter touch, offered, “But charitably, we could interpret it like this: ‘They might be suggesting that meditation improves focus and mental clarity, which are important for martial arts.'”

Donatello, thoughtful as ever, integrated both examples. “So, the key is to avoid jumping to conclusions or mocking the argument, but instead, trying to see the underlying rationale, even if we eventually disagree with it.”

April, relating it to her profession, added, “In journalism, this means I shouldn’t twist someone’s words to make a more sensational story. Instead, I should present their argument in the strongest way, whether I’m supporting or critiquing it.”

Splinter nodded in agreement. “Precisely. This approach not only makes us fairer in our judgments but also helps us become well-integrated individuals. As Aristotle taught with his doctrine of the mean, our goal is not to be devoid of emotions but to let our emotions and reason work together harmoniously. The Principle of Charity helps us ‘train’ our emotional responses to be more aligned with reason. We aim not to become emotionless but to respond appropriately, with both emotion and logic in balance.”

Splinter nods, pleased with their insights. “Correct. The process of translating an argument into standard form, and doing so charitably, is akin to refining raw ore into a valuable metal. It allows you to see the structure clearly, identify any flaws, and make necessary adjustments.”

Graphic: Putting An Argument in Standard Form

Discussion Questions: Logic and Arguments

• Reflect on Splinter’s initial explanation of logic. How does his definition align with or differ from your understanding of logic? Discuss the relevance of logic in the context of the Teenage Mutant Ninja Turtles’ world and our own.
• Analyze the arguments presented by Leonardo, Donatello, Raphael, and Michelangelo regarding the most essential skills for a ninja. Which argument do you find most compelling, and why? How do these arguments illustrate the structure of premises leading to a conclusion?
• Consider the examples of statements and non-statements provided by Splinter. Discuss why it’s important to differentiate between statements and non-statements in logical reasoning. Can you provide additional examples of each from other contexts?
• Splinter introduces three types of logic: Informal, Formal-Deductive, and Inductive-Probabilistic. Discuss each type with examples from your own experiences or other fictional contexts. How do these types of logic manifest in different areas of life and decision-making?
• Discuss the importance of putting arguments into standard form. Take an argument from a current debate or a fictional scenario and convert it into standard form. How does this process clarify the argument?
• Reflect on the importance of following the Principle of Charity in interpreting the arguments of others. Have you had experiences where other people didn’t interpret your arguments charitably? Where you yourself failed to be charitable?

Splinter’s Lesson, Part 2: Arguments and Non-Arguments

Splinter decides to delve deeper into the nuances of reasoning. “We’ve explored the anatomy of arguments, but it’s crucial to recognize what doesn’t qualify as an argument. Misidentifying these can lead to logical errors.”

Statements of Belief

Splinter begins with a familiar topic. “Let’s consider Statements of Belief. Michaelangelo, when you proclaim, ‘I believe pineapple belongs on pizza,’ you’re expressing a personal preference, not offering premises and a conclusion.”

Michaelangelo elaborates, “Yeah, it’s like saying I prefer nunchucks over katanas. I’m not arguing that nunchucks are objectively better; it’s just what suits my fighting style.”

Splinter adds, “In the realm of public discourse, especially in polarized topics like politics or ethics, distinguishing between a statement of belief and an argument is vital for constructive dialogue.”

Illustrations

“Next, we have Illustrations,” Splinter continues. “Raphael, you once likened fighting Shredder to a game of chess, emphasizing the need for strategic thinking. While vivid, this isn’t an argument.”

Raphael expounds, “Right, I’m not saying that fighting and chess are the same thing. I’m using the chess analogy to make the complexities of combat more relatable.”

Splinter notes, “In academic philosophy, illustrations are often employed to elucidate abstract concepts like existentialism or the nature of time. However, they are not substitutes for rigorous argumentation.”

Conditional Statements

Splinter then addresses Donatello. “You frequently use Conditional Statements in your tech endeavors. For example, ‘If we implement this encryption, then our communications will be secure.’ This is a hypothetical scenario, not an argument.”

Donatello explains, “Exactly, it’s a conditional relationship. If the condition is met—implementing the encryption—then the result follows. But I’m not arguing that we should implement this specific encryption; that would require additional premises.”

Splinter observes, “In scientific research, conditional statements often form the basis for hypotheses that will be rigorously tested. They set the parameters but don’t argue for a specific outcome.” Some other examples include:

• If Leonardo meditates, then he achieves inner peace: A straightforward conditional, positing that Leonardo’s meditation leads to a state of inner tranquility.
• Donatello solves complex problems if he has access to his lab: An inverted conditional, suggesting that the availability of his lab is a sufficient condition for Donatello to tackle intricate issues.
• Michelangelo enjoys a battle only if pizza is promised afterward: Employing the “only if” construction, this statement restricts the conditions under which Michelangelo finds joy in combat to the promise of pizza.
• Splinter teaches life lessons, provided that his students are attentive: Utilizing the “provided that” form, this statement sets forth the condition under which Splinter imparts wisdom.
• Raphael will spar with Leonardo unless he is injured: The “unless” form introduces an exception to the general rule, indicating that injury is the only condition that prevents Raphael from sparring with Leonardo.

Reports

Finally, Splinter turns to April. “Your journalistic work often consists of Reports, such as ‘The Foot Clan attacked three locations last night.’ These provide factual accounts but don’t argue for or against a particular interpretation.”

April concurs, “That’s correct. A report aims to inform, not persuade. My role is to present the facts as clearly as possible, allowing the public to form their own opinions.”

Splinter concludes, “In both journalism and scholarly research, the ability to differentiate between reports and arguments is essential for maintaining objectivity and intellectual integrity.”

Splinter gazes at his students, each engrossed in thought. “The mastery of logic isn’t just about constructing and deconstructing arguments. It’s also about discerning when an argument is not present, thereby avoiding the pitfalls of flawed reasoning. This skill is invaluable, whether you’re deciphering an ancient text or navigating the labyrinthine corridors of social media discourse.”

Explanations vs. Arguments

Splinter, sensing the maturation of his students’ intellectual faculties, decides it’s time to explore another subtle yet crucial aspect of reasoning: the difference between Explanations and Arguments. “Understanding this distinction,” he begins, “is essential for both the philosopher and the warrior.”

“Let’s start with Explanations,” Splinter says. “When we offer an explanation, we’re not trying to prove that something is the case; rather, we’re trying to shed light on why or how it is the case. For example, if I say, ‘The Foot Clan is attacking more frequently because Shredder has acquired a new weapon,’ I’m not arguing that the Foot Clan is attacking; I’m assuming that’s a given. What I’m doing is providing an explanans, or reason, for this known explanandum, or fact.”

Donatello chimes in, “So, in scientific terms, an explanation would be like saying, ‘Water boils at 100 degrees Celsius at sea level due to atmospheric pressure.’ The boiling point is the explanandum, and the atmospheric pressure is the explanans.”

“Exactly,” Splinter nods. “In scientific research, explanations are crucial for understanding phenomena, but they don’t serve to establish the phenomena themselves.”

“Now, let’s contrast this with Arguments,” Splinter continues. “In an argument, we present premises with the aim of establishing a conclusion. For instance, if I say, ‘If Shredder has a new weapon, then the Foot Clan will attack more frequently. Shredder has a new weapon. Therefore, the Foot Clan will attack more frequently,’ I’m making an argument. The conclusion, that the Foot Clan will attack more frequently, is what I’m trying to establish.”

Raphael adds, “So, in an argument, the conclusion isn’t assumed to be true; it’s what you’re trying to prove with your premises.”

“Correct,” Splinter affirms. “In legal settings, for example, arguments are used to establish guilt or innocence, not to explain why a defendant is guilty or innocent.”

Argument from Explanation

Splinter then elucidates how explanations and arguments can be linked. “Sometimes, we encounter what’s known as an Argument from Explanation. In this case, the best explanation for a given fact is used as a premise to argue for a conclusion. For example, ‘The best explanation for the Foot Clan’s increased attacks is that Shredder has a new weapon. Therefore, it’s likely that Shredder has a new weapon.'”

April reflects, “So, in journalism, an argument from explanation could be used to justify further investigation into a story. If increased pollution levels are best explained by illegal dumping, then that warrants an investigation into potential culprits.”

“Indeed,” Splinter concludes. “Arguments from explanation are often used in detective work, scientific theories, and investigative journalism. They bridge the gap between explaining known facts and establishing new ones.”

Splinter looks at his students, their faces a blend of contemplation and enlightenment. “The line between explanation and argument can be subtle but is fundamental. Mastering this distinction equips you with the analytical tools to navigate not just the physical battles we face but also the intellectual challenges posed by a complex world.”

Case Study: Society’s Poor Treatment of the Turtles as Examples of Bad Arguments

Splinter decides to conclude by tackling the issue of flawed reasoning. “We’ve discussed good arguments at length, but it’s equally vital to recognize bad arguments, especially when they have real-world implications for us and others.”

He grows solemn. “Society often marginalizes us based on poor arguments. Let’s dissect these arguments in Standard Form and identify their flaws, while also drawing parallels to societal issues.”

Example 1: “Hasty Generalization”

Splinter recalls a time when the Turtles had a brief skirmish with a rival gang of sewer-dwelling mutants who were causing havoc. The next day, the news headlines read, “Mutant Sewer Dwellers Clash: Are All Sewer Mutants a Threat?” The story frustrates him, as it takes one isolated incident and generalizes it to include the Turtles, who have been protectors of the city.

Standard Form:

• A small group of mutants living in the sewers caused trouble.
• Therefore, all mutants living in the sewers, including the Turtles, are dangerous or evil.

Flaws:

• Premise 1 is true for a specific group but is used to make a broad conclusion about all mutants living in sewers, including the Turtles. This is a Hasty Generalization.
• Weak Inferential Link: The premise about a small group doesn’t provide a strong enough basis to conclude that all sewer-dwelling mutants are dangerous or evil.

Example 2: Begging the Question/Circular Argument

Splinter thinks back to a city council meeting he had secretly observed. The council was discussing the “shadowy figures” seen around the city and concluded that they must be up to no good because they operate in secrecy. The irony is not lost on Splinter; they were debating the Turtles’ actions in the very room the Turtles had saved from a bomb threat a week earlier.

Standard Form:

• The Turtles hide in the shadows.
• Things that hide in the shadows are up to no good.
• Therefore, the Turtles are up to no good.

Flaws:

• Premise 2 begs the question; it assumes what it’s trying to prove.
• Weak Inferential Link: The argument is circular, making the conclusion unsupported.

Example 3: Appeal to Ignorance

Splinter remembers a time when April tried to publish an article about the Turtles’ positive impact on the city. Her editor refused, stating that there was no concrete evidence to prove that these “vigilantes” were actually beneficial. Splinter finds this reasoning flawed, as the absence of evidence is not evidence of absence.

Standard Form:

• There is no concrete evidence proving the Turtles are good.
• If there’s no evidence proving something is good, then it must be bad.
• Therefore, the Turtles are bad.

Flaws:

• Premise 2 is an appeal to ignorance, mistaking the absence of evidence for evidence of absence.
• Weak Inferential Link: The lack of evidence doesn’t logically lead to the conclusion.

Each of these stories serves as a poignant reminder that flawed reasoning can have real-world consequences, affecting not just the Turtles but society at large.

Minds that Mattered: Socrates

Socrates (c. 470-399 BCE) was an ancient Greek philosopher who is widely considered one of the founders of Western philosophy. Born in Athens, he spent most of his life engaging in philosophical discussions with his fellow citizens. Socrates is best known for his method of inquiry, known as the Socratic method, which involves asking a series of questions to stimulate critical thinking and expose the underlying assumptions and beliefs of the interlocutor. This method is based on the idea that true knowledge comes from within and that the role of the philosopher is to help others discover this knowledge for themselves. It emphasizes the importance of clear and precise definitions, and the use of counterexamples to refute faulty arguments.

Socrates’ philosophy centered on the concept of virtue, which he believed was the highest good and the key to happiness. He argued that virtue is knowledge and that ignorance, or the lack of knowledge, is the root of all evil. (In fact, he thought that no one would WILINGLY do evil things. They just did them because they didn’t’ know better!). Socrates also believed in the importance of self-knowledge and the need to question one’s own beliefs and assumptions.

Despite his popularity among his students and followers, Socrates was not without his critics. He was accused of corrupting the youth of Athens and of questioning the gods. In 399 BCE, he was put on trial and sentenced to death by drinking hemlock, a poisonous plant.

Key Ideas

At least as he is portrayed In Plato’s dialogues. Socrates demonstrates his commitment to the pursuit of truth and virtue through the use of the Socratic method, the embodiment of Socratic virtues, and the use of counterexamples to challenge faulty arguments.

The Socratic method is a way of teaching by asking questions that encourage critical thinking and self-reflection. In the dialogue “Euthyphro,” Socrates demonstrates this method by engaging in a conversation with a young man named Euthyphro, who believes he knows what piety (being faithful and respectful to gods) means. Euthyphro wants to put his father on trial for murder, claiming that it is the pious thing to do. Socrates, however, asks Euthyphro a series of probing questions to help him examine his beliefs more closely. One of the most famous questions Socrates asks is known as the “Euthyphro Dilemma“: “Is an action good because it is loved by the gods [or God[, or is it loved by the gods [or God[ because it is good?” This question, known as the “Euthyphro Dilemma,” is difficult for theists to answer because it requires them to consider the relationship between the gods and morality. If they say that an action is good because it is loved by the gods, it suggests that morality is arbitrary and subject to the whims of the gods. In other words, if the gods decided to love murder, then murder would be considered good. On the other hand, if they say that the gods love an action because it is good, it implies that there is a standard of goodness independent of the gods, which raises questions about the nature and authority of the gods. This dilemma challenges the idea that morality is simply a matter of obedience to divine commands and encourages deeper reflection on the nature of goodness and its relationship to the divine.

In the dialogue “Crito,” Socrates exemplifies several important virtues, particularly justice and integrity. Despite facing execution, Socrates refuses to escape from prison when his wealthy friend Crito offers to help him. Socrates argues that it would be unjust to violate the laws of Athens, even if those laws have been applied unfairly in his case. He maintains that it is better to suffer injustice than to commit it. To illustrate his point, Socrates presents a thought experiment in which the laws of Athens appear as a person and engage in a conversation with him. The personified laws explain to Socrates what he owes them and why it would be wrong for him to break these laws, even if he believes he has been wrongly convicted. This dialogue is a famous early example of the principles of civil disobedience, which involves voluntarily accepting a punishment, even when one believes it is unjust, as a form of protest against unjust laws or policies.

Throughout Plato’s dialogues, Socrates often uses counterexamples to challenge definitions proposed by the people he engages in conversation. A counterexample is a scenario or case that fits the given definition but leads to an obviously false or absurd conclusion, thus demonstrating that the definition is flawed or incomplete. Here are three examples of counterexamples:

• If someone defines courage as “never retreating in battle,” we might give a counterexample of a soldier who stays and fights against overwhelming odds, leading to the unnecessary deaths of himself and his comrades. This counterexample shows that courage does not always mean never retreating and that sometimes strategic retreat can be the wisest course of action.
• If someone defines justice as “giving people what they are owed,” Socrates might present a counterexample of a friend who has loaned you their sword (or gun) and later, while undergoing a mental breakdown, asks for it back (while refusing to tell you why). It wouldn’t be a “just” thing (for the friend or the world) to give them back their weapon in this case.
• If someone defines friendship as “always agreeing with and supporting one’s friends,” we might offer a counterexample of a friend who tells a hard truth to another friend, even if it causes temporary distress, because they believe it will ultimately help the friend grow and improve. This counterexample shows that true friendship sometimes involves challenging one another and that always agreeing is not necessarily a sign of a strong friendship.

By using counterexamples, Socrates encourages his conversation partners to refine their definitions and to think about these issues in more depth.

Influence

Socrates’ influence has been profound and enduring, shaping the course of Western philosophy and serving as a model of reason, critical thinking, and moral integrity for countless thinkers and activists.

Socrates’ most direct and immediate influence can be seen in the works of his student Plato. Plato’s dialogues, which feature Socrates as the central character, have preserved his ideas and methods for posterity. Plato’s own philosophical system, known as Platonism, was heavily influenced by Socratic thought and has had a lasting impact on Western philosophy. Plato’s Academy, founded in Athens, became a center of learning and philosophical inquiry, and his ideas about the nature of reality, knowledge, and the ideal state have continued to shape philosophical discourse for centuries.

Perhaps one of the most striking examples of Socrates’ influence in the modern era can be seen in the life and work of Martin Luther King Jr. King, who studied philosophy and theology, was deeply influenced by Socratic ideas about the importance of moral courage and the power of nonviolent resistance. In his famous “Letter from a Birmingham Jail,” King invoked Socrates as a model of civil disobedience, writing: “Just as Socrates felt that it was necessary to create a tension in the mind so that individuals could rise from the bondage of myths and half-truths to the unfettered realm of creative analysis and objective appraisal, so must we see the need for nonviolent gadflies to create the kind of tension in society that will help men rise from the dark depths of prejudice and racism to the majestic heights of understanding and brotherhood.”

Discussion Questions: Splinter and Socrates

• How do statements of belief influence public discourse, particularly in polarized topics? Can they be misleading if not properly identified? Discuss the implications of conflating personal beliefs with logical arguments in ethical debates or political discussions.
• Illustrations, like Raphael’s chess analogy, are common in philosophical texts. How do they enhance or potentially obscure philosophical arguments? Consider Plato’s allegory of the cave as an example. Does it serve as an argument, an illustration, or both?
• Explore the use of conditional statements in formulating scientific hypotheses. How do they differ from arguments in scientific reasoning? Discuss examples where conditional statements have been pivotal in scientific breakthroughs.
• Examine the role of reports in journalism and scholarly research. How does the distinction between reporting facts and arguing for interpretations impact the integrity of information dissemination?
• Using the examples of the Turtles or from real life, discuss how identifying flawed arguments (like hasty generalization or begging the question) is crucial in social and political discourse. How can these skills be applied to contemporary societal issues?
• Reflect on Socrates’ contributions to logic and ethics. How does the Socratic Method foster critical thinking and ethical reasoning? Discuss the relevance of Socrates’ ideas in modern philosophical and ethical debates.

Sample Problem: Is it an Argument?

Identify the following as arguments or non-arguments and explain your answer.

Passage	Is it an argument?
Have you ever read Plato?	No! This isn’t even a statement.
I’d recommend reading Plato’s Apology. You should stay away from the Laws, though.	No. The first statement appears to be a piece of advice, while the second looks like a warning. The person still hasn’t tried to give you any reasons, though.
If Socrates taught Plato, then Plato was influenced by Socrates.	No. This is a conditional statement (and it’s almost certainly true, but I haven’t given you any reasons to think this). The claim is that Socrates teaching Plato was sufficient for influencing him. Another way of saying the same thing: Socrates’ influence on Plato was a necessary consequence of his teaching.
Plato is one of the most influential philosophers of all time. After all, his work inspired everyone from Christian and Islamic theologians to the founders of democracy to the early scientist.	Yes. This is an argument—it’s trying to provide reasons for believing a claim about Plato.
I believe that Aristotle is actually a more rigorous thinker than Plato. However, I think Zeno is more innovative than either of them.	Again, we’re back to non-arguments here (this looks like a simple statement of belief, not backed up by any premises/evidence).
The unexamined life is not worth living. So, many seemingly successful people are currently leading lives that are not worth living.	Yes, this is an argument (based on a famous claim by Socrates and one which may have led to him being executed).
Plato wrote the Apology partially because he wanted to record Socrates’ speech, but also because he wanted to advance his own philosophical views.	While this contains the word “because,” it is NOT an argument. Instead, it is a causal explanation (“this happened because that happened.”). It might be true, and it might be false, but we don’t have any evidence either way right now.
In most areas of life outside of politics, we trust knowledgeable experts more than ignorant laypeople. For example, when I’m sick, I go to the doctor. When I need my car fixed, I go to the mechanic. By analogy, we can conclude that the government should be run by experts, not ignorant lay people (as in a democracy).	Yes, this is a (somewhat complex) argument. The examples are used to clarify a premise (about how we usually trust experts more than laypeople). This premise is then used to argue for a (pretty controversial) conclusion: democracy is an inferior form of government.
Plato believed that every idea and object we had corresponded to something called a Form that existed outside the physical world. For example, he thought there was a Form of “Bed,” a Form of “Cat”, a Form of “Three” and a Form of “Good.”	No, this isn’t an argument. Instead, it simply illustrates what Plato means by “Form.” We might extend this into an expository passage explaining Plato’s ideas.
Plato thought people in power shouldn’t have their “own” money, spouses, or even children. He thought this because he saw how these things could lead people to become corrupt and behave immorally.	No. This is a report about an argument Plato made, but it is not itself an argument because no effort is made to convince you that Plato is right/wrong.
Plato’s arguments against democracy inspired many dictators over the past 2,500 years. Because of this, his books should be banned.	Yes, this is an argument. If you wanted to critique this argument, you’d probably want to spell it out at greater length. So, for example, what implicit premises might you want to include if you expressed it in standard form?

Glossary of Important Terms

Term	Definition
Argument	A set of statements or propositions, made up of premises and a conclusion, where the premises are presented to provide support or evidence for the truth of the conclusion.
Civil disobedience	A form of political protest involving the deliberate violation of unjust laws or decrees, often accompanied by the willing acceptance of legal punishment, as advocated by Socrates in the “Crito.”
Conclusion	The statement in an argument that the premises are intended to support or prove.
Conclusion Indicator Words	Words or phrases used to signal that a conclusion is being stated, such as “therefore,” “thus,” “hence,” “consequently,” and “as a result.”
Conditional Statement	A statement in the form “If P, then Q,” where P is the antecedent and Q is the consequent.
Counterexamples	Instances or cases presented in philosophical argumentation to refute universal claims or general principles by demonstrating their inapplicability or inconsistency in specific contexts.
Euthyphro Dilemma	A logical problem posed by Socrates concerning the relationship between piety and divine approval, which questions whether an action is good because it is approved by the gods or approved by the gods because it is good.
Examined life	A philosophical ideal championed by Socrates, which holds that the pursuit of wisdom and virtue through critical self-reflection and dialogue is essential to human flourishing and the attainment of the good life.
Explanandum	The statement or phenomenon that is being explained in an explanation. It is the subject or event that the explanans seeks to clarify or account for.
Explanans	The set of statements in an explanation that provides the reasoning or basis for understanding the explanandum. It is the part of the explanation that does the explaining.
Explanation	A set of statements that clarifies, elucidates, or accounts for a fact or event, often answering why or how something is the case. It differs from an argument in that it aims to provide understanding rather than to prove a conclusion.
Formal (Deductive) Logic	A type of logic where the focus is on the form of the argument. It involves the use of strict principles and rules to determine the validity of arguments. It is used in mathematics, computer science, and philosophy.
Illustration (non-argument)	A description or example given to make something clear or to explain it, without intending to argue for or against any particular point. It is used to elucidate a concept or idea but does not in itself constitute an argument.
Inductive (Probabilistic) Logic	A form of reasoning where conclusions are drawn from observations or experiences and are presented with a degree of probability, rather than certainty. It is often used in scientific reasoning and in everyday life.
Inferential Link	The logical connection between the premises and the conclusion in an argument. It is the reasoning process that justifies the transition from the premises to the conclusion, indicating how the conclusion follows from the premises.
Informal Logic	A branch of logic that deals with natural language arguments. It includes the study of fallacies and rhetorical strategies.
Logic	The study of arguments or correct reasoning.
Necessary Condition	A condition that must be present for an event or statement to be true, but on its own may not be sufficient to guarantee it.
Platonism	The philosophical system developed by Plato, which incorporates and expands upon Socratic ideas, particularly in the realms of metaphysics, epistemology, and ethics.
Premise	A statement in an argument that serves as the basis or reason for the conclusion.
Premise Indicator Words	Words or phrases that indicate a statement is a premise, such as “because,” “since,” “for,” “given that,” and “as indicated by.” They are used to introduce the reasons or evidence in an argument.
Principle of Charity	The requirement that we interpret another’s argument in the most rational way possible. We should avoid attributing irrationality, logical fallacies, or falsehoods to it unless absolutely necessary for the argument’s interpretation.
Report (non-argument)	An objective presentation of information or facts, without any argument or inference. These provide data or findings without drawing conclusions or persuading the audience.
Self-knowledge	The philosophical imperative to critically examine one’s own beliefs, values, and assumptions through introspection and dialogue, as exemplified by Socrates’ famous dictum, “Know thyself.”
Socratic Method	A form of cooperative argumentative dialogue between individuals, based on asking and answering questions to stimulate critical thinking and to draw out ideas and underlying presuppositions.
Socratic method	An approach to philosophical inquiry characterized by the use of systematic questioning to elicit definitions, challenge assumptions, and expose contradictions in the interlocutor’s beliefs.
Standard Form	A way of presenting an argument where the premises are listed first, followed by the conclusion, often with clear indicators for each. This format is used to clearly delineate the structure of the argument, making it easier to analyze and evaluate its validity.
Statement (Proposition)	A declarative sentence that is either true or false, but not both. It is an assertion that something is or is not the case and is the basic unit of discourse in logic.
Statement of Belief (non-argument)	A declaration of personal conviction or opinion that does not present reasons or evidence to support it. Unlike an argument, it does not attempt to persuade others through reasoning.
Sufficient Condition	A condition or set of conditions that, if met, guarantees the occurrence or truth of another statement.

References

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