1.3 Deduction And Induction
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Course lecture I developed over section 1.3 of Patrick Hurley\\\'s "A Concise Introduction to Logic".
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1.1 arguments, premises, and conclusions
Formal Logic : Leacture 01
Chapter 1: Basic Concepts
1.1 Arguments, Premises, and Conclusions
Follow on Facebook:
https://web.facebook.com/learnforgood...
and on Youtube:
https://www.youtube.com/channel/UC8kUyEAA5ix6Bl5H5gKXo3A
Like, Comment and Share.
Also Subscribe For More Videos.
Learn For Good.
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Course lecture I developed over section 1.4 of Patrick Hurley\'s "A Concise Introduction to Logic".
1.2 Recognizing Arguments
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For more articles please visit: http://onlinemgmtnotes.com or http://www.amcthebest.com
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Understanding arguments, reasoning and hypotheses
As researchers working in government, influencing service design, we need to know that our research is methodologically sound, our research findings are grounded in empirical data and our recommendations are logically derived.
'Understanding arguments, reasoning and hypotheses' is the first in a series of 5 short courses, covering introduction courses to various aspects of methodology in research, from the use of grounded theory in discovery research, to hypothesis testing and sampling in more experimental research.
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The following text material and terms defined at the end comprise .docx
The following text material and terms defined at the end comprise part of what will be asked on the Mid-Term Exam for PHIL 1381.
Logic [excerpt from Stan Baronett, Logic, 2E]
Logic is the study of reasoning. Logic investigates the level of correctness of the reasoning found in arguments. An argument is a group of statements of which one (the conclusion) is claimed to follow from the others (the premises). A statement is a sentence that is either true or false. Every statement is either true or false; these two possibilities are called “truth values.” Premises are statements that contain information intended to provide support or reasons to believe a conclusion. The conclusion is the statement that is claimed to follow from the premises. In order to help recognize arguments, we rely on premise indicator words and phrases, and conclusion indicator words and phrases.
Inference is the term used by logicians to refer to the reasoning process that is expressed by an argument. If a passage expresses a reasoning process—that the conclusion follows from the premises—then we say that it makes an inferential claim. If a passage does not express a reasoning process (explicit or implicit), then it does not make an inferential claim (it is a noninferential passage). One type of noninferential passage is the explanation. An explanation provides reasons for why or how an event occurred. By themselves, explanations are not arguments; however, they can form part of an argument.
There are two types of argument: deductive and inductive. A deductive argument is one in which it is claimed that the conclusion follows necessarily from the premises. In other words, it is claimed that under the assumption that the premises are true it is impossible for the conclusion to be false. An inductive argument is one in which it is claimed that the premises make the conclusion probable. In other words, it is claimed that, under the assumption that the premises are true, it is improbable for the conclusion to be false.
Revealing the logical form of a deductive argument helps with logical analysis and evaluation. When we evaluate deductive arguments, we use the following concepts: valid, invalid, sound, and unsound. A valid argument is one where, assuming the premises are true, it is impossible for the conclusion to be false. In other words, the conclusion follows necessarily from the premises. An invalid argument is one where, assuming the premises are true, it is possible for the conclusion to be false. In other words, a deductive argument in which the conclusion does not follow necessarily from the premises is an invalid argument. When logical analysis shows that a deductive argument is valid, and when truth value analysis of the premises shows that they are all true, then the argument is sound. If a deductive argument is invalid, or if at least one of the premises is false (truth value analysis), then the argument is unsound.
A counterexample to astatement is evidenc.
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How Logical Are You?
· After a momentary absence, you return to your table in the library only to find your smartphone is missing. It was there just minutes earlier. You suspect the student sitting next to you took it. After all, she has a guilty look. Also, there is a bulge in her backpack about the size of your phone, and one of the pouches has a loose strap. Then you hear a “ring” come from the backpack—and it’s the same ringtone that you use on your phone. Which of these pieces of evidence best supports your suspicion?
Answer
The best evidence is undoubtedly the “ring” you hear coming from her backpack, which is the same ringtone as the one on your phone. The weakest evidence is probably the “guilty look.” After all, what, exactly, is a guilty look? The bulge in the backpack and the loose strap are of medium value. The loose strap supports the hypothesis that something was quickly inserted into the backpack. In this section of the chapter you will learn that evidentiary statements form the premises of arguments.
Logic may be defined as the organized body of knowledge, or science, that evaluates arguments. All of us encounter arguments in our day-to-day experience. We read them in books and newspapers, hear them on television, and formulate them when communicating with friends and associates. The aim of logic is to develop a system of methods and principles that we may use as criteria for evaluating the arguments of others and as guides in constructing arguments of our own. Among the benefits to be expected from the study of logic is an increase in confidence that we are making sense when we criticize the arguments of others and when we advance arguments of our own.
An argument, in its simplest form, is a group of statements, one or more of which (the premises) are claimed to provide support for, or reasons to believe, one of the others (the conclusion). Every argument may be placed in either of two basic groups: those in which the premises really do support the conclusion and those in which they do not, even though they are claimed to. The former are said to be good arguments (at least to that extent), the latter bad arguments. The purpose of logic, as the science that evaluates arguments, is thus to develop methods and techniques that allow us to distinguish good arguments from bad.
As is apparent from the given definition, the term argument has a very specific meaning in logic. It does not mean, for example, a mere verbal fight, as one might have with one’s parent, spouse, or friend. Let us examine the features of this definition in greater detail. First of all, an argument is a group of statements. A statement is a sentence that is either true or false—in other words, typically a declarative sentence or a sentence component that could stand as a declarative sentence. The following sentences are statements:
Chocolate truffles are loaded with calories.
Melatonin helps relieve jet lag.
Political can.
1.1Arguments, Premises, and ConclusionsHow Logical Are You·.docx
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How Logical Are You?
· After a momentary absence, you return to your table in the library only to find your smartphone is missing. It was there just minutes earlier. You suspect the student sitting next to you took it. After all, she has a guilty look. Also, there is a bulge in her backpack about the size of your phone, and one of the pouches has a loose strap. Then you hear a “ring” come from the backpack—and it’s the same ringtone that you use on your phone. Which of these pieces of evidence best supports your suspicion?
Answer
The best evidence is undoubtedly the “ring” you hear coming from her backpack, which is the same ringtone as the one on your phone. The weakest evidence is probably the “guilty look.” After all, what, exactly, is a guilty look? The bulge in the backpack and the loose strap are of medium value. The loose strap supports the hypothesis that something was quickly inserted into the backpack. In this section of the chapter you will learn that evidentiary statements form the premises of arguments.
Logic may be defined as the organized body of knowledge, or science, that evaluates arguments. All of us encounter arguments in our day-to-day experience. We read them in books and newspapers, hear them on television, and formulate them when communicating with friends and associates. The aim of logic is to develop a system of methods and principles that we may use as criteria for evaluating the arguments of others and as guides in constructing arguments of our own. Among the benefits to be expected from the study of logic is an increase in confidence that we are making sense when we criticize the arguments of others and when we advance arguments of our own.
An argument, in its simplest form, is a group of statements, one or more of which (the premises) are claimed to provide support for, or reasons to believe, one of the others (the conclusion). Every argument may be placed in either of two basic groups: those in which the premises really do support the conclusion and those in which they do not, even though they are claimed to. The former are said to be good arguments (at least to that extent), the latter bad arguments. The purpose of logic, as the science that evaluates arguments, is thus to develop methods and techniques that allow us to distinguish good arguments from bad.
As is apparent from the given definition, the term argument has a very specific meaning in logic. It does not mean, for example, a mere verbal fight, as one might have with one’s parent, spouse, or friend. Let us examine the features of this definition in greater detail. First of all, an argument is a group of statements. A statement is a sentence that is either true or false—in other words, typically a declarative sentence or a sentence component that could stand as a declarative sentence. The following sentences are statements:
Chocolate truffles are loaded with calories.
Melatonin helps relieve jet lag.
Political can ...
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6Deduction and Induction:
Putting It All Together
Wavebreakmedia Ltd./Thinkstock and GoldenShrimp/iStock/Thinkstock
Learning Objectives
After reading this chapter, you should be able to:
1. Compare and contrast the advantages of deduction and induction.
2. Explain why one might choose an inductive argument over a deductive argument.
3. Analyze an argument for its deductive and inductive components.
4. Explain the use of induction within the hypothetico–deductive method.
5. Compare and contrast falsification and confirmation within scientific inquiry.
6. Describe the combined use of induction and deduction within scientific reasoning.
7. Explain the role of inference to the best explanation in science and in daily life.
har85668_06_c06_207-238.indd 207 4/9/15 11:38 AM
© 2015 Bridgepoint Education, Inc. All rights reserved. Not for resale or redistribution.
Section 6.1 Contrasting Deduction and Induction
Now that you have learned something about deduction and induction, you may be wondering
why we need both. This chapter is devoted to answering that question. We will start by learn-
ing a bit more about the differences between deductive and inductive reasoning and how the
two types of reasoning can work together. After that, we will move on to explore how scien-
tific reasoning applies to both types of reasoning to achieve spectacular results. Arguments
with both inductive and deductive elements are very common. Recognizing the advantages
and disadvantages of each type can help you build better arguments. We will also investigate
another very useful type of inference, known as inference to the best explanation, and explore
its advantages.
6.1 Contrasting Deduction and Induction
Remember that in logic, the difference between induction and deduction lies in the connec-
tion between the premises and conclusion. Deductive arguments aim for an absolute connec-
tion, one in which it is impossible that the premises could all be true and the conclusion false.
Arguments that achieve this aim are called valid. Inductive arguments aim for a probable
connection, one in which, if all the premises are true, the conclusion is more likely to be true
than it would be otherwise. Arguments that achieve this aim are called strong. (For a discus-
sion on common misconceptions about the meanings of induction and deduction, see A Closer
Look: Doesn’t Induction Mean Going From Specific to General?). Recall from Chapter 5 that
inductive strength is the counterpart of deductive validity, and cogency is the inductive coun-
terpart of deductive soundness. One of the purposes of this chapter is to properly understand
the differences and connections between these two major types of reasoning.
There is another important difference
between deductive and inductive rea-
soning. As discussed in Chapter 5, if
you add another premise to an induc-
tive argument, the argument may
become either stronger or weaker. For
example, suppose you ar.
2076Deduction and Induction Putting It All Together.docx
207
6Deduction and Induction:
Putting It All Together
Wavebreakmedia Ltd./Thinkstock and GoldenShrimp/iStock/Thinkstock
Learning Objectives
After reading this chapter, you should be able to:
1. Compare and contrast the advantages of deduction and induction.
2. Explain why one might choose an inductive argument over a deductive argument.
3. Analyze an argument for its deductive and inductive components.
4. Explain the use of induction within the hypothetico–deductive method.
5. Compare and contrast falsification and confirmation within scientific inquiry.
6. Describe the combined use of induction and deduction within scientific reasoning.
7. Explain the role of inference to the best explanation in science and in daily life.
har85668_06_c06_207-238.indd 207 4/9/15 11:38 AM
© 2015 Bridgepoint Education, Inc. All rights reserved. Not for resale or redistribution.
Section 6.1 Contrasting Deduction and Induction
Now that you have learned something about deduction and induction, you may be wondering
why we need both. This chapter is devoted to answering that question. We will start by learn-
ing a bit more about the differences between deductive and inductive reasoning and how the
two types of reasoning can work together. After that, we will move on to explore how scien-
tific reasoning applies to both types of reasoning to achieve spectacular results. Arguments
with both inductive and deductive elements are very common. Recognizing the advantages
and disadvantages of each type can help you build better arguments. We will also investigate
another very useful type of inference, known as inference to the best explanation, and explore
its advantages.
6.1 Contrasting Deduction and Induction
Remember that in logic, the difference between induction and deduction lies in the connec-
tion between the premises and conclusion. Deductive arguments aim for an absolute connec-
tion, one in which it is impossible that the premises could all be true and the conclusion false.
Arguments that achieve this aim are called valid. Inductive arguments aim for a probable
connection, one in which, if all the premises are true, the conclusion is more likely to be true
than it would be otherwise. Arguments that achieve this aim are called strong. (For a discus-
sion on common misconceptions about the meanings of induction and deduction, see A Closer
Look: Doesn’t Induction Mean Going From Specific to General?). Recall from Chapter 5 that
inductive strength is the counterpart of deductive validity, and cogency is the inductive coun-
terpart of deductive soundness. One of the purposes of this chapter is to properly understand
the differences and connections between these two major types of reasoning.
There is another important difference
between deductive and inductive rea-
soning. As discussed in Chapter 5, if
you add another premise to an induc-
tive argument, the argument may
become either stronger or weaker. For
example, suppose you ar ...
Fallacy of logic
There are some common Fallacies
1) Fallacy of Equivocation
2) Fallacy of Amphiboly
3) Fallacy of Composition
4) Fallacy of Division
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Deductive ReasoningmoodboardThinkstockLearning Objectives.docx
Deductive Reasoning
moodboard/Thinkstock
Learning Objectives
After reading this chapter, you should be able to:
1. Define basic key terms and concepts within deductive reasoning.
2. Use variables to represent an argument’s logical form.
3. Use the counterexample method to evaluate an argument’s validity.
4. Categorize different types of deductive arguments.
5. Analyze the various statements—and the relationships between them—in categorical arguments.
6. Evaluate categorical syllogisms using the rules of the syllogism and Venn diagrams.
7. Differentiate between sorites and enthymemes.
By now you should be familiar with how the field of logic views arguments: An argument is just a collection of sentences, one of which is the conclusion and the rest of which, the premises, provide support for the conclusion. You have also learned that not every collection of sentences is an argument. Stories, explanations, questions, and debates are not arguments, for example. The essential feature of an argument is that the premises support, prove, or give evidence for the conclusion. This relationship of support is what makes a collection of sentences an argument and is the special concern of logic. For the next four chapters, we will be taking a closer look at the ways in which premises might support a conclusion. This chapter discusses deductive reasoning, with a specific focus on categorical logic.3.1 Basic Concepts in Deductive Reasoning
As noted in Chapter 2, at the broadest level there are two types of arguments: deductive and inductive. The difference between these types is largely a matter of the strength of the connection between premises and conclusion. Inductive arguments are defined and discussed in Chapter 5; this chapter focuses on deductive arguments. In this section we will learn about three central concepts: validity, soundness, and deduction.
Validity
Deductive arguments aim to achieve validity, which is an extremely strong connection between the premises and the conclusion. In logic, the word valid is only applied to arguments; therefore, when the concept of validity is discussed in this text, it is solely in reference to arguments, and not to claims, points, or positions. Those expressions may have other uses in other fields, but in logic, validity is a strict notion that has to do with the strength of the connection between an argument’s premises and conclusion.
To reiterate, an argument is a collection of sentences, one of which (the conclusion) is supposed to follow from the others (the premises). A valid argument is one in which the truth of the premises absolutely guarantees the truth of the conclusion; in other words, it is an argument in which it is impossible for the premises to be true while the conclusion is false. Notice that the definition of valid does not say anything about whether the premises are actually true, just whether the conclusion could be false if the premises were true. As an example, here is a silly but valid ar.
Critical Task 3 Rubric Critical Elements Exemplary (1.docx
Critical Task 3 Rubric
Critical Elements Exemplary (100%) Proficient (85%) Needs Improvement (55%) Not Evident (0%) Value
Main Elements Includes all of the main
elements and requirements
and cites ample appropriate
support to illustrate each
element
Includes most of the main
elements and requirements
and cites appropriate support
to illustrate each element
Includes some of the main
elements and requirements
Does not include any of the
main elements and
requirements
25
Inquiry and Analysis Explores multiple reasons and
offers accurate and in-depth
analysis of the argument in its
structural form
Explores some reasons and
offers somewhat accurate and
somewhat in-depth analysis of
the argument in its structural
form
Explores minimal reasons and
offers minimally accurate
analysis of the argument in its
structural form
Does not explore reasons and
analysis of evidence and does
not offer accurate analysis of
the argument in its structural
form
25
Integration and
Application
All of the course concepts are
correctly applied
Most of the course concepts
are correctly applied
Some of the course concepts
are correctly applied
Does not correctly apply any of
the course concepts
10
Critical Thinking Demonstrates comprehensive
exploration of issues and ideas
before accepting or forming an
opinion or conclusion about
the argument
Demonstrates moderate
exploration of issues and ideas
before accepting or forming an
opinion or conclusion about
the argument
Demonstrates minimal
exploration of issues and ideas
before accepting or forming an
opinion or conclusion about
the argument
Does not demonstrate
exploration of issues and ideas
before accepting or forming an
opinion or conclusion about
the argument
20
Reflection and
Research
Incorporates a highly pertinent
life goal or issue of significant
importance
Incorporates a life goal or issue
of somewhat significant
importance
Incorporates a life goal or issue
of minimally significant
importance
Does not incorporate a life goal
or issue of significant
importance
10
Writing
(Mechanics/Citations)
No errors related to
organization, grammar and
style, and citations
Minor errors related to
organization, grammar and
style, and citations
Some errors related to
organization, grammar and
style, and citations
Major errors related to
organization, grammar and
style, and citations
10
Earned Total 100%
HYPOTHETICAL SYLLOGISMS
Hypothetical thinking involves “If . . . then . . .” reasoning. According to some psychologists, the mental model for hypothetical thinking is built into our brain and enables us to understand rules and predict the consequences of our actions. We’ll be looking at the use of hypothetical reasoning in ethics in greater depth in Chapter 9. Hypothetical arguments are also a basic building block of computer programs.
A hypothetical syllogism is a form of deductive.
Reflect back on what you have learned in this course about how to .docx
Reflect back on what you have learned in this course about how to construct high-quality arguments for positions. “refer to the attached reading chapter for help”
· Give an example of how the ability to think logically and to construct good arguments could help you in your career and in your daily life?
· In what ways the skill of being able to evaluate the quality of reasoning on all sides will better enable you to discover what is true and to make better choices?
· Finally, consider the argument you have been developing for your writing assignments. How has fairly considering multiple points of view helped you clarify your own perspective?
· What advice would you give to people to help them understand issues more clearly and objectively while being fair to all sides? Feel free to comment on any other values you have gained from this course so far.
Your journal entry must be at least 250 words. You do not need to follow APA style for this journal entry, but you should proofread your work to eliminate errors of grammar and spelling.
3
Deductive Reasoning
White cups stacked with one red cup in the middle.
moodboard/Thinkstock
Learning Objectives
After reading this chapter, you should be able to:
Define basic key terms and concepts within deductive reasoning.
Use variables to represent an argument’s logical form.
Use the counterexample method to evaluate an argument’s validity.
Categorize different types of deductive arguments.
Analyze the various statements—and the relationships between them—in categorical arguments.
Evaluate categorical syllogisms using the rules of the syllogism and Venn diagrams.
Differentiate between sorites and enthymemes.
By now you should be familiar with how the field of logic views arguments: An argument is just a collection of sentences, one of which is the conclusion and the rest of which, the premises, provide support for the conclusion. You have also learned that not every collection of sentences is an argument. Stories, explanations, questions, and debates are not arguments, for example. The essential feature of an argument is that the premises support, prove, or give evidence for the conclusion. This relationship of support is what makes a collection of sentences an argument and is the special concern of logic. For the next four chapters, we will be taking a closer look at the ways in which premises might support a conclusion. This chapter discusses deductive reasoning, with a specific focus on categorical logic.
3.1 Basic Concepts in Deductive Reasoning
As noted in Chapter 2, at the broadest level there are two types of arguments: deductive and inductive. The difference between these types is largely a matter of the strength of the connection between premises and conclusion. Inductive arguments are defined and discussed in Chapter 5; this chapter focuses on deductive arguments. In this section we will learn about three central concepts: validity, soundness, and deduction.
.
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