OLI - 1. Statements and arguments

• 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