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Philosophy

<OpenstaxParagraph>
	A <OpenstaxTerm>conditional</OpenstaxTerm> is most commonly expressed as an if–then statement, similar to the examples we discussed earlier when considering hypotheses. Additional examples of if–then statements are “If you eat your meat, then you can have some pudding” and “If that animal is a dog, then it is a mammal.” But there are other ways to express conditionals, such as “You can have pudding <OpenstaxEm>only if</OpenstaxEm> you eat your meat” or “<OpenstaxEm>All</OpenstaxEm> dogs are mammals.” While these sentences are different, their logical meaning is the same as their correlative if–then sentences above.
</OpenstaxParagraph>
<OpenstaxParagraph>
	All conditionals include two components—that which follows the “if” and that which follows the “then.” Any conditional can be rephrased in this format. Here is an example:
</OpenstaxParagraph>
<OpenstaxBlockquote>
	 
	<OpenstaxParagraph>
		Statement 1: You must complete 120 credit hours to earn a bachelor’s degree.
	</OpenstaxParagraph> 
	<OpenstaxParagraph>
		Statement 2: If you expect to graduate, then you must complete 120 credit hours.
	</OpenstaxParagraph> 
</OpenstaxBlockquote>
<OpenstaxParagraph>
	Whatever follows “if” is called the <OpenstaxEm>antecedent</OpenstaxEm>; whatever follows “then” is called the <OpenstaxEm>consequent</OpenstaxEm>. <OpenstaxEm>Ante</OpenstaxEm> means “before,” as in the word “antebellum,” which in the United States refers to anything that occurred or was produced <OpenstaxEm>before</OpenstaxEm> the American Civil War. The <OpenstaxEm>ante</OpenstaxEm>cedent is the first part of the conditional, occurring <OpenstaxEm>before</OpenstaxEm> the consequent. A consequent is a result, and in a conditional statement, it is the result of the antecedent (if the antecedent is true).
</OpenstaxParagraph>
<OpenstaxH3>Necessary and Sufficient Conditions</OpenstaxH3>
<OpenstaxParagraph>
	All conditionals express two relations, or <OpenstaxEm>conditions</OpenstaxEm>: those that are necessary and those that are sufficient. A relation is a relationship/property that exists between at least two things. If something is sufficient, it is always sufficient <OpenstaxEm>for something else</OpenstaxEm>. And if something is necessary, it is always necessary <OpenstaxEm>for something else.</OpenstaxEm> In the conditional examples offered above, one part of the relation is required for the other. For example, 120 credit hours are required for graduation, so 120 credit hours is necessary if you expect to graduate. Whatever is the consequent—that is, whatever is in the second place of a conditional—is necessary for that particular antecedent. This is the relation/condition of necessity. Put formally, Y is a <OpenstaxTerm>necessary condition</OpenstaxTerm> for X <OpenstaxEm>if and only if X cannot be true without Y being true</OpenstaxEm>. In other words, X cannot happen or exist without Y. Here are a few more examples:
</OpenstaxParagraph>
<OpenstaxUl>
	<OpenstaxLi>
		Being unmarried is a necessary condition for being a bachelor<OpenstaxEm>.</OpenstaxEm> If you are a bachelor, then you are unmarried.
	</OpenstaxLi>
	<OpenstaxLi>
		Being a mammal is a necessary condition for being a dog. If a creature is a dog, then it is a mammal.
	</OpenstaxLi>
</OpenstaxUl>
<OpenstaxParagraph>
	But notice that the <OpenstaxEm>necessary relation</OpenstaxEm> of a conditional does not automatically occur in the other direction. Just because something is a mammal does not mean that it <OpenstaxEm>must</OpenstaxEm> be a dog. Being a bachelor is not a necessary feature of being unmarried because you can be unmarried and be an unmarried woman. Thus, the relationship between X and Y in the statement “if X, then Y” is not always symmetrical (it does not automatically hold in both directions). Y is always <OpenstaxEm>necessary</OpenstaxEm> for X, but X is <OpenstaxEm>not necessary</OpenstaxEm> for Y. On the other hand, X is always <OpenstaxEm>sufficient</OpenstaxEm> for Y.
</OpenstaxParagraph>
<OpenstaxParagraph>
	Take the example of “If you are a bachelor, then you are unmarried.” If you know that Eric is a bachelor, then you automatically know that Eric is unmarried. As you can see, the antecedent/first part is the sufficient condition, while the consequent/second part of the conditional is the necessary condition. X is a <OpenstaxTerm>sufficient condition</OpenstaxTerm> for Y <OpenstaxEm>if and only if the truth of X guarantees the truth of Y.</OpenstaxEm> Thus, if X is a sufficient condition for Y, then X automatically implies Y. But the reverse is not true. Oftentimes X is not the only way for something to be Y. Returning to our example, being a bachelor is not the only way to be unmarried. Being a dog is a sufficient condition for being a mammal, but it is <OpenstaxEm>not necessary</OpenstaxEm> to be a dog to be a mammal since there are many other types of mammals.
</OpenstaxParagraph>
<OpenstaxFigure id="fig-00001" src="https://openstax.org/apps/archive/20240226.174525/resources/d762f827f36af2e10ef3b626fff1aa2e2996bd76" alt="Dog in a field with a person and two sheep." mediaType="image/jpeg" width="800" height="594" />
<OpenstaxFigureText width="800">
	<strong>Figure 5.4</strong> All dogs are mammals, but not all mammals are dogs. Being a dog is a sufficient condition for being a mammal but it is not necessary to be a dog to be a mammal. (credit: “Sheepdog Trials in California” by SheltieBoy/Flickr, CC BY 2.0)
</OpenstaxFigureText>
<OpenstaxParagraph>
	The ability to understand and use conditionals increases the clarity of philosophical thinking and the ability to craft effective arguments. For example, some concepts, such as “innocent” or “good,” must be rigorously defined when discussing ethics or political philosophy. The standard practice in philosophy is to state the meaning of words and concepts before using them in arguments. And oftentimes, the best way to create clarity is by articulating the necessary or sufficient conditions for a term. For example, philosophers may use a conditional to clarify for their audience what they mean by “innocent”: “If a person has not committed the crime for which they have been accused, then that person is innocent.”
</OpenstaxParagraph>
<OpenstaxH3>Counterexamples</OpenstaxH3>
<OpenstaxParagraph>
	Sometimes people disagree with conditionals. Imagine a mother saying, “If you spend all day in the sun, you’ll get sunburnt.” Mom is claiming that getting sunburnt is a <OpenstaxEm>necessary</OpenstaxEm> condition for spending all day in the sun. To argue against Mom, a teenager who wants to go to the beach might offer a <OpenstaxTerm>counterexample</OpenstaxTerm>, or an opposing statement that proves the first statement wrong. The teenager must point out a case in which the claimed necessary condition <OpenstaxEm>does not occur</OpenstaxEm> alongside the sufficient one. Regular application of an effective sunblock with an SPF 30 or above will allow the teenager to avoid sunburn. Thus, getting sunburned is not a necessary condition for being in the sun all day.
</OpenstaxParagraph>
<OpenstaxParagraph>
	Counterexamples are important for testing the truth of propositions. Often people want to test the truth of statements to effectively argue against someone else, but it is also important to get into the critical thinking habit of attempting to come up with counterexamples for our own statements and propositions. Philosophy teaches us to constantly question the world around us and invites us to test and revise our beliefs. And generating creative counterexamples is a good method for testing our beliefs.
</OpenstaxParagraph>

5.2.1 Conditionals

1 Introduction to Philosophy

1.1 What Is Philosophy?

1.1.1 Historical Origins of Philosophy

1.1.2 How It All Hangs Together

1.2 How Do Philosophers Arrive at Truth?

1.2.1 Sources of Evidence

1.2.2 Logic

1.2.3 Conceptual Analysis

1.2.4 Trade-offs

1.3 Socrates as a Paradigmatic Historical Philosopher

1.3.1 “The Life Which Is Unexamined Is Not Worth Living”

1.3.2 Human Wisdom Is Worth Little or Nothing

1.3.3 The Importance of Doing No Harm

1.4 An Overview of Contemporary Philosophy

1.4.1 What Can You Do with a Philosophy Major?

1.4.2 An Overview of Your Philosophy Textbook

2 Critical Thinking, Research, Reading, and Writing

2.1 The Brain Is an Inference Machine

2.1.1 The Brain’s Adaptive Ability to Plan Ahead

2.1.2 The Evolutionary Advantage of Shortcuts

2.2 Overcoming Cognitive Biases and Engaging in Critical Reflection

2.2.1 Critical Reflection and Metacognition

2.2.2 Cognitive Biases

2.3 Developing Good Habits of Mind

2.3.1 Strive for Objectivity

2.3.2 Adopt Epistemic Humility

2.4 Gathering Information, Evaluating Sources, and Understanding Evidence

2.4.1 Start with a Strong Foundation

2.4.2 The SIFT Method (Four Moves for Student Fact Checkers)

2.5 Reading Philosophy

2.5.1 Prepare to Read

2.5.2 Engaging with Philosophical Texts

2.5.3 Pre-reading

2.5.4 First Read

2.5.5 Close Read

2.6 Writing Philosophy Papers

2.6.1 Identify Claims

2.6.2 Collect Evidence and Build Your Case

2.6.3 Organize Your Paper

3 The Early History of Philosophy around the World

3.1 Indigenous Philosophy

3.1.1 Challenges in Researching Indigenous Philosophy

3.1.2 Indigenous African Philosophy

3.1.3 Indigenous North American Philosophical Thought

3.1.4 Mesoamerican Philosophy

3.2 Classical Indian Philosophy

3.2.1 The Vedic Tradition

3.2.2 Classical Indian Darshanas

3.3 Classical Chinese Philosophy

3.3.1 Early Chinese Philosophical Thought prior to Confucius

3.3.2 Confucianism

3.3.3 Daoism

3.3.4 Mohism

4 The Emergence of Classical Philosophy

4.1 Historiography and the History of Philosophy

4.1.1 Presentist Approach

4.1.2 Contextualist Approach

4.1.3 Hermeneutic Approach

4.2 Classical Philosophy

4.2.1 Egyptian Origins of Classical Philosophy

4.2.2 Ancient Greek Philosophy

4.2.3 The Presocratics

4.2.4 Socrates and Plato

4.2.5 Aristotle

4.2.6 Epicureans

4.2.7 Roman Philosophy

4.3 Jewish, Christian, and Islamic Philosophy

4.3.1 Defining Jewish, Christian, and Islamic Philosophy

4.3.2 Early Jewish Philosophy

4.3.3 Early Christian Philosophy

4.3.4 Islamic Philosophy

4.3.5 Late Medieval Philosophy in Christian Europe

4.3.6 Jewish Philosophers in the Christian and Islamic Worlds

4.3.7 The Rise of Reason in the Early Modern Era

5 Logic and Reasoning

5.1 Philosophical Methods for Discovering Truth

5.1.1 Dialectics and Philosophical Argumentation

5.1.2 The Use of Reason to Discover Truth

5.1.3 Testing Hypotheses

5.1.4 Laws of Logic

5.1.5 Normativity in Logic

5.2 Logical Statements

5.2.2 Universal Statements

5.3 Arguments

5.3.1 Getting to the Premises

5.3.2 The Difference between Truth and Logic

5.4 Types of Inferences

5.4.1 Deductive Reasoning

5.4.2 Inductive Inferences

5.4.3 Abductive Reasoning

5.5 Informal Fallacies

5.5.1 Fallacies of Relevance

5.5.2 Fallacies of Weak Induction

5.5.3 Fallacies of Unwarranted Assumption

5.5.4 Fallacies of Diversion

6 Metaphysics

6.1 Substance

6.1.1 Fundamentality: The One and the Many

6.1.2 Ontological Perspectives on Substance

Question	Answer
a logical statement that expresses a necessary and a sufficient condition. Conditionals are usually formulated as if–then statements.	Conditional
an example that proves that either a statement is false or an argument is invalid.	Counterexample
X is a necessary condition for Y if and only if X must be true given the truth of Y. If X is necessary for Y, then X is guaranteed by Y—without the truth of X, Y cannot be true.	Necessary condition
X is a sufficient condition for Y if and only if the truth of X guarantees the truth of Y. If X is sufficient for Y, then the truth of X is enough to prove the truth of Y.	Sufficient condition