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Chapter 1: What logic Studies

Logic is the study of reasoning. Its aim is to differentiate correct native incorrect thinking by developing the rules or fads of successful arguments. Typically, we begin a examine of logic with a conversation of specific features of language crucial to arguments.

You are watching: One way to make an inductive argument weaker is to __________.

A. Statements and Arguments

A statement is a sentence the is either true or false, the is, a statement has a truth value. Statements space the primary building blocks of one argument. One argument is a repertoire of 2 or more statements, among which is sustained by the other or others. The conclusion is the supported sentence, if the premises are the sentence that support the conclusion.

The score of every discussion is to develop the conclusion ~ above the basis of the evidence provided by the premise or premises. For this reason what distinguishes an argument from other collections of explanation is that is inferential nature. An argument’s elements reflect a conceptual flow from basic to conclusion. So, “inference” method the reasoning process expressed by an argument.

“Statement” is distinguished from “sentence” and “proposition” together follows:

1. A sentence is a set of words complete in itself, together in a statement, question, or exclamation.

2. A declare is a sentence that has actually two feasible truth values: true and also false.

3. A proposition is the information content or definition of a statement.

B. Recognizing Arguments

An dispute is identified from other collections of declaration by that is inferential nature. Unlike other passages, an discussion involves drawing an inference from one or an ext statements to one more statement. Us say that a passage provides an inferential claim once it expresses a thinking process, i.e., the the conclusion adheres to from the premises.

Drawing an inference is a purely intellectual act. Because that example, friend don’t know what a dibbeltot is, nor execute you recognize what fizzlestrums and poggurets are. Nevertheless, you can attract an inference native the following statements:

No dibbeltot is a fizzlestrum. Every fizzlestrum is a pogguret.

The inference you draw is “No dibbeltot is a pogguret.”

One way to recognize the elements of an debate is through indicator words. Conclusion indicators alarm you come the illustration of a conclusion, when premise indicators alert you come the illustration of a premise. In every case, indicator words tell you the a conclusion or premise is about to be asserted or has actually just to be asserted.

 

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C. Arguments and also Explanations

Distinguishing in between arguments and also non-arguments deserve to sometimes be tricky. This is particularly the situation with explanations. Relying on the context, an explanation deserve to be taken because that an argument and also vice versa. In addition, both arguments and also explanations frequently use the very same indicator words. The an important distinguishing function of an debate is that the conclusion is at issue. So, even when one explanation entails indicator words, if over there is nothing at issue, the i does not end up being an argument: “Because you were late conference me at the restaurant for dinner, ns went ahead and placed mine order.” Here, an explanation is readily available for ordering food. Over there is no will to prove something or work out some sort of issue.

D. Truth and also Logic

Because an discussion involves an inferential claim, us say that the truth of the conclusion counts on how an excellent a job the premises do in developing that truth. In this way, logic is involved with fact in a fairly different way than we recognize the fact or falsity of a offered statement. Logical analysis entails bearing in mind this distinction. Take one more look at the instance in B above:

No dibbeltot is a fizzlestrum.

Every fizzlestrum is a pogguret.

Therefore, no dibbeltot is a pogguret.

Consider another type of example:

Whenever i come home, mine dog is therefore happy to see me that he jumps all over me. So, as soon as I get home later today, my dog will be so happy to check out me the he’ll jump all over me.

Whether or no each that the explanation is true is irrelevant to the inquiry of whether or no the premises execute a good job of establishing the conclusion.

E. Deductive and also Inductive Arguments

Arguments autumn into one of two types: those that count on experience and those that do not. Every of the two debates we just saw in D above is an example of, respectively, deductive and also inductive argumentation. We do not need experience—what we smell, taste, see, etc.—in bespeak to factor to the conclusion, “No dibbeltot is a pogguret.” In fact, we have no suffer of these things. Nevertheless, we deserve to reason efficiently to the conclusion by the way the premises’ facets relate to every other. The dog discussion is different in that the conclusion is a forecast which relies on past experience.

A deductive argument is one in which the conclusion is asserted to monitor necessarily indigenous the premises. In other words, the basic are declared to insurance the conclusion, or that is impossible for the conclusion to it is in false if the premises room true.

An inductive argument is one in i m sorry the conclusion is claimed to follow through a level of probability. In various other words, the premises make it likely for the conclusion to it is in true, or it is improbable that the conclusion is false if the premises are true.

F. Deductive Arguments: Validity and Truth

Deductive disagreements are either precious or invalid, and also sound or unsound. A valid deductive debate is one in which that is impossible for the conclusion to be false, if the premises room true. One invalid dispute is one in which the is feasible for the conclusion to be false, if the premises room true.

A sound discussion is valid, and its premises room actually true. All invalid arguments are, by definition, unsound.

Valid + True premises = Sound

Valid + At least One False Premise = Unsound

Invalid = Unsound

A practically test the validity is the counterexample method. If friend can discover a counterexample to an argument’s conclusion (while the premises room true), girlfriend have displayed the conclusion is false. As soon as you expand this technique to an argument, you demonstrate the discussion is invalid. First, however, be sure that your counterexample matches the initial argument’s form.

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G. Inductive Arguments: Strength and also Truth

Inductive arguments are evaluated first according come how solid or weak the relation is between the premises and the conclusion. One inductive dispute is strong when, suspect the premises are true, the is improbable because that the conclusion to be false. One inductive discussion is weak when, presume the premises room true, the is probable because that the conclusion to be false.

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A more evaluation requires the actual fact of the premises. A solid argument is cogent once the premises room true. A solid argument is uncogent once at the very least one that the basic is false. All weak disagreements are uncogent, because strength is a part of the definition of cogency.