Chapter 8
Please note that some of the items on this post are clickable to further your knowledge on a particular issue/idea/theory.
Goals of this chapter:
1). Identify the essential attributes of a deductive argument.
2). Distinguish between validity, invalidity, and soundness in a deductive argument.
3). Learn how to recognize and evaluate arguments by elimination, mathematical arguments, and argument from definition.
4). Study the different types of hypothetical syllogisms, including modus ponens, modus tollens, and chain arguments.
5). Learn how to recognize standard-form categorical syllogisms.
6). Reevaluate categorical syllogisms using Venn diagrams.
7). Practice putting arguments that are in ordinary language into standard form.
8). Analyze different arguments regarding the justification of the death penalty.
*A deductive argument claims that its conclusion necessarily follows the premises.
*Certain words and phrases are commonly used in deductive arguments; these include certainly, absolutely, definitely, conclusively, must be, and it necessarily follows that. However, not all deductive arguments contain indicator words.
*Deductive arguments are often presented in the form of syllogisms, with two supporting premises and a conclusion.
*A deductive argument is valid if the form of the argument is such that they conclusion must be true if the premises are true. The form of an argument is determined by its layout or pattern of reasoning. An argument is sound if both (1) it is valid, and (2) the premises are true.
Note: Valid and Invalid arguments are discussed starting on page 239. Make sure to pay close attention to valid and invalid arguments.
Types of Deductive Arguments:
There are three that are used in everyday reasoning.
1). Arguments by elimination rule out different possibilities until only one possibility remains.
2). Arguments based on mathematics depend on mathematical or geometric equations to generate conclusions.
3). In an argument from definition, the conclusion is true because it is based on a key term or essential attribute in a definition.
Hypothetical Syllogisms
*Hypothetical reasoning involves "if.....then...." reasoning.
*A hypothetical syllogism is a form of deductive argument that contains two premises, at least one of which is hypothetical or conditional if.....then statement.
*There are three basic patterns of hypothetical syllogisms:
1). Modus ponens (affirming the antecedent): there is one conditional premise, a second premise that states that the antecedent, or if part, of the first premise is true, and a conclusion that asserts the truth of the consequent, or the then part, of the first premise.
The following structure is used:
If A, then B.
A.
Therefore, B.
So......
Premise 1: If I get this raise at work, then I can pay off my credit-card bill.
Premise 2: I got the raise at work.
Conclusion: Therefore, I can pay off my credit-card bill.
Or......
If A (antecedent), the B (consequent).
A.
Therefore, B.
Does this make sense? If not, go back and read through the examples on page 247.
2). Modus tollens (denying the consequent): The second premise denies the consequent, and the conclusion denies the truth of the antecedent.
The following structure is used:
If A, then B.
Not B.
Therefore, not A.
So......
If Morgan is a physician, then she has graduated from college.
Morgan did not graduate from college.
Therefore, Morgan is not a physician.
Or........
If A (antecedent), the B (consequent).
Not B.
Therefore, not A.
You can read more about this on page 248.
3). Chain argument: are made up of three conditional propositions - two premises and one conclusion - linked together. A chain argument is a type of imperfect hypothetical syllogism since it may contain more than three propositions.
The following structure is used:
If A, then B.
If B, then C.
Therefore, If A, then C.
So......
If it rains tomorrow, then the beach party is canceled.
If the beach party is canceled, we're having a party at Rachel's house.
Therefore, if it rains tomorrow, we're having a party at Rachel's house.
There are more examples in the course text on page 249-250. This section also discusses chain arguments with more than two premises.
Evaluating Hypothetical Syllogisms for Validity
*Not all valid arguments are sound. Rewording arguments in ordinary language in the form of hypothetical syllogisms can help you expose faulty premises. They are also useful as clarification tools, and as decision-making aids.
These are a type of deductive argument that categorizes or sorts things into specific classes, such as mammals, students, or countries. A categorical syllogism is composed of a conclusion, two premises, and three terms, each of which occurs exactly twice in two of the three propositions. In the following categorical syllogism, each of the three classes or terms - in this case "mammals", "cats", and "tigers" - appears in two propositions.
All tigers are cats.
Some mammals are not cats.
Therefore, some mammals are not tigers.
*Categorical syllogisms can be written in any of 256 standard forms or combinations.
A standard form of categorical syllogism is shown here:
*All P are/are not M. (P=predicate, M=middle term)
*Some S are/are not M. (S=minor term, M=middle term)
*Some S are/are not P. (S=minor term, P=major term)
As with hypothetical syllogisms, if the form of a categorical syllogism is valid, then the argument will be valid regardless of term substitutions.
Are you thoroughly confused yet? Read starting on page 252 to clarify these issues a bit more.
Venn Diagrams
These are useful instruments for diagramming and evaluating categorical syllogisms. They directly engage our spatial reasoning ability and help us to visualize group relationships effectively.
You can read more about Venn Diagrams by clicking HERE, and of course in your course text.
Conclusion:
Knowledge of deductive arguments - including arguments from definition, mathematical arguments, arguments by elimination, and hypothetical and categorical syllogisms - is essential for us to effectively function in the world. As good critical thinkers, we must constantly identify and evaluate these types of arguments, both our own and those presented to us by others.
There are many examples in the course text, boxes with information, exercises, and stories. Please do not skip these things in the course text. Rather, make sure to read them and understand them......for they may appear on a test at some point.......
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