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Philosophy

<OpenstaxParagraph>
	When we reason inductively, we gather evidence using our experience of the world and draw general conclusions based on that experience. <OpenstaxTerm>Inductive</OpenstaxTerm> reasoning (induction) is also the process by which we <OpenstaxEm>use</OpenstaxEm> general beliefs we have about the world to create beliefs about our particular experiences or about what to expect in the future. Someone can use their past experiences of eating beets and absolutely hating them to conclude that they do not like beets of any kind, cooked in any manner. They can then use this conclusion to avoid ordering a beet salad at a restaurant because they have good reason to believe they will not like it. Because of the nature of experience and inductive inference, this method can never guarantee the truth of our beliefs. At best, inductive inference generates only probable true conclusions because it goes beyond the information contained in the premises. In the example, past experience with beets is concrete information, but the person goes beyond that information when making the general claim that they will dislike all beets (even those varieties they’ve never tasted and even methods of preparing beets they’ve never tried).
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	Consider a belief as certain as “the sun will rise tomorrow.” The Scottish philosopher David Hume famously argued against the certainty of this belief nearly three centuries ago ([1748, 1777] 2011, IV, i). Yes, the sun has risen every morning of recorded history (in truth, we have witnessed what appears to be the sun rising, which is a result of the earth spinning on its axis and creating the phenomenon of night and day). We have the science to explain why the sun will continue to rise (because the earth’s rotation is a stable phenomenon). Based on the current science, we can reasonably conclude that the sun will rise tomorrow morning. But <OpenstaxEm>is this proposition certain</OpenstaxEm>? To answer this question, you have to think like a philosopher, which involves thinking critically about alternative possibilities. Say the earth gets hit by a massive asteroid that destroys it, or the sun explodes into a supernova that encompasses the inner planets and incinerates them. These events are extremely unlikely to occur, although no contradiction arises in imagining that they could take place. We believe the sun will rise tomorrow, and we have good reason for this belief, but the sun’s rising is still only probable (even if it is nearly certain).
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<OpenstaxParagraph>
	While inductive inferences are not always a sure thing, they can still be quite reliable. In fact, a good deal of what we think we know is known through induction. Moreover, while deductive reasoning can guarantee the truth of conclusions if the premises are true, many times the premises themselves of deductive arguments are inductively known. In studying philosophy, we need to get used to the possibility that our inductively derived beliefs could be wrong.
</OpenstaxParagraph>
<OpenstaxParagraph>
	There are several types of inductive inferences, but for the sake of brevity, this section will cover the three most common types: reasoning from specific instances to generalities, reasoning from generalities to specific instances, and reasoning from the past to the future.
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<OpenstaxH3>Reasoning from Specific Instances to Generalities</OpenstaxH3>
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	Perhaps I experience several instances of some phenomenon, and I notice that all instances share a similar feature. For example, I have noticed that every year, around the second week of March, the red-winged blackbirds return from wherever they’ve wintering. So I can conclude that generally the red-winged blackbirds return to the area where I live (and observe them) in the second week of March. All my evidence is gathered from particular instances, but my conclusion is a general one. Here is the pattern:
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<OpenstaxParagraph>
	Instance1, Instance2, Instance3 . . . Instancen --&gt; Generalization
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	And because each instance serves as a reason in support of the generalization, the instances are premises in the argument form of this type of inductive inference:
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	<OpenstaxU>Specific to General Inductive Argument Form:</OpenstaxU>
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<OpenstaxOl>
	<OpenstaxLi>
		Instance1
	</OpenstaxLi>
	<OpenstaxLi>
		Instance2
	</OpenstaxLi>
	<OpenstaxLi>
		Instance3
	</OpenstaxLi>
	<OpenstaxLi>
		General Conclusion
	</OpenstaxLi>
</OpenstaxOl>
<OpenstaxH3>Reasoning from Generalities to Specific Instances</OpenstaxH3>
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	Induction can work in the opposite direction as well: reasoning from accepted generalizations to specific instances. This feature of induction relies on the fact that we are learners and that we learn from past experiences and from one another. Much of what we learn is captured in generalizations. You have probably accepted many generalizations from your parents, teachers, and peers. You probably believe that a red “STOP” sign on the road means that when you are driving and see this sign, you must bring your car to a full stop. You also probably believe that water freezes at 32° Fahrenheit and that smoking cigarettes is bad for you. When you use accepted generalizations to predict or explain things about the world, you are using induction. For example, when you see that the nighttime low is predicted to be 30°F, you may surmise that the water in your birdbath will be frozen when you get up in the morning.
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<OpenstaxParagraph>
	Some thought processes use more than one type of inductive inference. Take the following example:
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	<OpenstaxParagraph>
		Every cat I have ever petted doesn’t tolerate its tail being pulled.
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		So this cat probably will not tolerate having its tail pulled.
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</OpenstaxBlockquote>
<OpenstaxParagraph>
	Notice that this reasoner has gone through a series of instances to make an inference about one additional instance. In doing so, the reasoner implicitly assumed a generalization along the way. The reasoner’s implicit generalization is that no cat likes its tail being pulled. They then use that generalization to determine that they shouldn’t pull the tail of the cat in front of them now. A reasoner can use several instances in their experience as premises to draw a general conclusion and then use that generalization as a premise to draw a conclusion about a specific new instance.
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<OpenstaxParagraph>
	Inductive reasoning finds its way into everyday expressions, such as “Where there is smoke, there is fire.” When people see smoke, they intuitively come to believe that there is fire. This is the result of inductive reasoning. Consider your own thought process as you examine <a href="#fig-00001">Figure 5.5</a>.
</OpenstaxParagraph>
<OpenstaxFigure id="fig-00001" src="https://openstax.org/apps/archive/20240226.174525/resources/30f599485ffec87be857c0df48e51ed2a08e296f" alt="Small wisps and large clouds of smoke rising above the trees and into the sky above a mountain horizon." mediaType="image/jpeg" width="800" height="600" />
<OpenstaxFigureText width="800">
	Figure 5.5 “Where there is smoke, there is fire” is an example of inductive reasoning. (credit: “20140803-FS-UNK-0017” by US Department of Agriculture/Flickr, CC BY 2.0)
</OpenstaxFigureText>
<OpenstaxH3>Reasoning from Past to Future</OpenstaxH3>
<OpenstaxParagraph>
	We often use inductive reasoning to predict what will happen in the future. Based on our ample experience of the past, we have a basis for prediction. Reasoning from the past to the future is similar to reasoning from specific instances to generalities. We have experience of events across time, we notice patterns concerning the occurrence of those events at particular times, and then we reason that the event will happen again in the future. For example:
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	<OpenstaxParagraph>
		I see my neighbor walking her dog every morning. So my neighbor will probably walk her dog this morning.
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	Could the person reasoning this way be wrong? Yes—the neighbor could be sick, or the dog could be at the vet. But depending upon the regularity of the morning dog walks and on the number of instances (say the neighbor has walked the dog every morning for the past year), the inference could be strong in spite of the fact that it is possible for it to be wrong.
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<OpenstaxH3>Strong Inductive Inferences</OpenstaxH3>
<OpenstaxParagraph>
	The strength of inductive inferences depends upon the reliability of premises given as evidence and their relation to the conclusions drawn. A <OpenstaxEm>strong</OpenstaxEm> inductive inference is one where, if the evidence offered is true, then the conclusion is probably true. A <OpenstaxEm>weak</OpenstaxEm> inductive inference is one where, if the evidence offered is true, the conclusion is not probably true. But just how strong an inference needs to be to be considered good is context dependent. The word “probably” is vague. If something is more probable than not, then it needs at least a 51 percent chance of happening. However, in most instances, we would expect to have a much higher probability bar to consider an inference to be strong. As an example of this context dependence, compare the probability accepted as strong in gambling to the much higher probability of accuracy we expect in determining guilt in a court of law.
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<OpenstaxParagraph>
	<a href="#fig-00002">Figure 5.6</a> illustrates three forms of reasoning are used in the scientific method. Induction is used to glean patterns and generalizations, from which hypotheses are made. Hypotheses are tested, and if they remain unfalsified, induction is used again to assume support for the hypothesis.
</OpenstaxParagraph>
<OpenstaxFigure id="fig-00002" src="https://openstax.org/apps/archive/20240226.174525/resources/2df282cd1868f29ada58b0b6b95f803d7970ea4d" alt="Three box represent the relationship between induction, deduction, and abduction. The first box, labeled inductive, shows the words observations and generalization. An arrow, labeled abductive, points from the word generalization in the first inductive box points to the word hypothesis in the second box. This second box, labeled deductive, lists the steps, hypothesis, experiment, analysis, and conclusion. So the abductive arrow indicates that generalizations obtained from induction lead to hypotheses that are then tested through induction. An arrow from the word conclusion in the second deductive box points back to the word observations in the first inductive box. This arrow is labeled falsified and indicates that if the conclusion of an experiment falsifies the hypothesis, scientists return to the observations and begin the inductive process again. An arrow labeled unfalsified points to the word support in the third box. The third box, labeled inductive, features the words support and theory. This indicates that theories are formed from supporting evidence through induction. An arrow labeled abductive points from the word theory in the third inductive box back to the word hypothesis in the second deductive box." mediaType="image/png" width="1451" height="600" />
<OpenstaxFigureText width="1451">
	Figure 5.6 Induction in the Scientific Method (attribution: Copyright Rice University, OpenStax, under CC BY 4.0 license)
</OpenstaxFigureText>

5.4.2 Inductive Inferences

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

5.2.1 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

5.4.3 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