• Logic is the study of principles of correct reasoning.

• Logic is interested in the kind of arguments one gives as a reason for accepting the truth of some particular claim.

  • Arguments are pervasive in every aspect of human life.

  • The logician is not interested in the subject matter of the argument, rather argument itself, the pattern of reasoning that it embodies.

Statements

• The conclusion of the argument: the particular claim that an argument is for.

  • The whole purpose of an argument is to provide a reason for accepting the truth of its conclusion

• Statement: something that has to be either true or false, and can't be both.

  • The same statement can be expressed by many different sentences.

    • Ej: I have been here before, It's not the first time I've been here, He estado aquí antes.

• Other types of sentences

  • Declarative: statements.

  • Indexical: might be true while others are false depending on who utters the sentence, and when and where.

  • Ambiguous: a single sentence can be associated with multiple statements

  • Non-declarative: can't be considered true or false. Interrogative, imperative and exclamations.

Premises and conclusions

• Premises: set of statements, the reason for accepting the truth of the conclusion.

  • The argument is made up of premises and a conclusion.

• To identify the conclusion: what claim is the argument's presenter trying to convince you is true?

  • To identify the premise:  what support is the argument's presenter providing for the truth of the conclusion?

• An explanation simply provides information, it doesn't attempt to establish the truth of a statement.

  • A definition defines a word or phrase.

  • A description provides a mental image of the object or situation being described.

• Determine what the passage is doing to know if it is an argument or just an explanation.

  • An argument will try to persuade.

• Rethorical questions and imperatives may sometimes pose as an argument.

Identifying conclusions and premises

• If there is one statement that the author of an argument is going to distinguish as being special, it is the conclusion.

• To identify a conclusion:

  • Sometimes the author may explicitly state the conclusion.

  • They are often stated first and/or last.

  • May be indicated via conclusion indicator words

    • therefore

    • thus

    • hence

    • so

    • consequently

    • as a result

    • it follows that

    • this shows/indicates/means/implies that

  • Identify all the premises, and the statement left will be the conclusion.

• To identify a premise:

  • Identify the conclusion, and everything else will be a premise.

  • Indicator phrases like

    • consider that

    • take as evidence that

    • it is evident that

    • it is a fact that

    • recall that

  • Premise as clause indicators

    • since

    • because

    • for the reason that

    • as

    • inasmuch as

    • as indicated by

Arguments in standard form

• Standard form of an argument: write out all the premises first, then separate the conclusion by drawing a line and setting the symbol ∴ (therefore).

• Example:

  

Why premises and conclusions aren't enough

• What makes an argument a good argument

  • The premises should be true

    • Valid: any argument where the truth of the premises makes it impossible for the conclusion to be false

    • Inductively strong: an argument where the truth of the premises does not guarantee the truth of the conclusion, but rather makes it highly probably to be true

  • The premises of the argument should actually support the truth of the conclusion

    • Sound: arguments that are valid and have true premises

    • Cogent: arguments that are strong and have true premises

• Not all valid/strong arguments are sound/cogent (since some or all of their premises could be false), but any sound/cogent argument is necessarily valid/strong.

Symbolic or formal logic

• The structure of an argument crucially involves the logical structures of the premises and conclusion, as well as the pattern of relationships that hold between them.

• The content of statements is of no consequence for (logical) arguments.

• Each step of the argument is a fundamental pattern or rule of inference that can be applied any time we deal with sentences of the appropriate form.

Proofs

• Proof: an argument that demonstrates its conclusion by a series of logical steps.

Argument diagramming

• Argument diagrams allow us to represent more than just premises and conclusions.

• Each premise is independent, together (joint) they support the conclusion.

Summary

• Chapter overview, including an introductory movie and a statement of the learning objectives for the chapter ahead.

• Declarative sentences express statements, which can be either true or false. Statements are the pieces out of which arguments are constructed.

• Arguments consist of premises and a conclusion, each of which is a statement. Non-arguments have neither premises nor conclusion.

• We discuss various techniques, including the use of particular words and phrases, for indicating that a particular sentence is the conclusion of an argument. As with conclusions, various techniques, including specific words and phrases, indicate that a particular sentence serves as a premise of an argument. Also considered are premises and conclusions that appear as clauses within the same sentence.

• Arguments can be presented in a standard form that clearly indicates what the premises and conclusion of the argument are.

• First, the criteria by which an argument may be considered good or bad are discussed. With that done, examples are compared to illustrate why representing an argument as just a set of premises and conclusion isn't enough to allow a reasonable logical analysis of the argument, and what we need to add to address this deficiency is discussed.

• The motivation for adopting a symbolic approach to logic is discussed.

• Two interesting and historically important proofs are presented as an illustration of the intricate structure an argument can have.

• Argument diagrams are introduced as an alternative to standard form for representing arguments. Premises can provide support for a conclusion either jointly or independently; the technique for reflecting these differences in argument diagrams is discussed.

New terms