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Philosophy

<OpenstaxParagraph>
	Logic, like the sciences, has laws. But while the laws of science are meant to accurately describe observed regularities in the natural world, laws of logic can be thought of as rules of thought. Logical laws are rules that underlie thinking itself. Some might even argue that it is only by virtue of these laws that we can have reliable thoughts. To that extent, laws of logic are construed to be laws of reality itself. To see what is meant by this, let’s consider the <OpenstaxTerm>law of noncontradiction</OpenstaxTerm>.
</OpenstaxParagraph>
<OpenstaxH3>Noncontradiction</OpenstaxH3>
<OpenstaxParagraph>
	To understand the law of noncontradiction, we must first define a few terms. First, a <OpenstaxTerm>statement</OpenstaxTerm> is a sentence with truth value, meaning that the statement must be true or false. Statements are declarative sentences like “Hawaii is the 50th state to have entered the United States” and “You are reading an online philosophy book.” Sometimes philosophers use the term “proposition” instead of “statement,” and the latter term has a slightly different meaning. But for our purposes, we will use these terms as synonyms. Second, a <OpenstaxEm>negation</OpenstaxEm> of a statement is the denial of that statement. The easiest way to turn a statement into its negation is to add the qualifier “not.” For example, the negation of “My dog is on her bed” is “My dog is not on her bed.” Third, a <OpenstaxTerm>contradiction</OpenstaxTerm> is the conjunction of any statement and its negation. We may also say that any statement and its opposite are <OpenstaxEm>contradictory</OpenstaxEm>. For example, “My dog is on her bed” and “My dog is not on her bed” are contradictory because the second is the negation of the first. And when you combine a statement and its opposite, you get a contradiction: “My dog is on her bed and my dog is not on her bed.”
</OpenstaxParagraph>
<OpenstaxParagraph>
	The law of noncontradiction is a law about truth, stating that contradictory propositions cannot be true <OpenstaxEm>in the same sense, at the same time</OpenstaxEm>. While my dog may have been on her bed earlier and now she’s off barking at squirrels, it cannot be true <OpenstaxEm>right now</OpenstaxEm> that my dog is both on her bed and not on her bed. However, some of you may be thinking about dogs who lie half on their beds and half on the floor (Josie, the dog belonging to the author of this chapter, is one of them). Can it not be true that such a dog is both on and not on their bed? In this instance, we must return to the phrase <OpenstaxEm>in the same sense</OpenstaxEm>. If we decide that “lying on the bed” means “at least 50% of your body is on the bed,” then we must maintain that definition when looking at propositions to determine whether they are contradictory. Thus, if Josie is half out of the bed with her head on the floor, we can still say “Josie is on the bed.” But notice that “Josie is not on the bed” remains false since we have qualified the meaning of “on the bed.”
</OpenstaxParagraph>
<OpenstaxParagraph>
	For Aristotle, the law of noncontradiction is so fundamental that he claims that without it, knowledge would not be possible—the law is foundational for the sciences, reasoning, and language (Gottlieb 2019). Aristotle thought that the law of noncontradiction was “the most certain of all principles” because it is impossible for someone to believe that the same thing both is and is not (1989, 1005b).
</OpenstaxParagraph>
<OpenstaxH3>The Excluded Middle</OpenstaxH3>
<OpenstaxParagraph>
	The law of the excluded middle is related to the law of noncontradiction. The <OpenstaxTerm>law of the excluded middle</OpenstaxTerm> states that for any statement, either that statement is true, or its negation is true. If you accept that all statements must be either true or false <OpenstaxEm>and</OpenstaxEm> you also accept the law of noncontradiction, then you must accept the law of the excluded middle. If the only available options for truth-bearing statements are that they are true or false, and if a statement and its negation cannot both be true at the same time, then one of the statements must be true while the other must be false. Either my dog is on her bed or off her bed <OpenstaxEm>right now</OpenstaxEm>.
</OpenstaxParagraph>

5.1.4 Laws of Logic

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

5.1.5 Normativity in Logic

5.2 Logical Statements

5.2.1 Conditionals

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 statement that is always false. A contradiction is the conjunction of any statement and its negation.	Contradiction
a logical law that states that contradictory statements/propositions can never be true in the same sense at the same time.	Law of noncontradiction
a logical law that states that for any statement, either that statement or its negation is true.	Law of the excluded middle
a sentence with a truth value—a sentence that must be either true or false.	Statement