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