Chapter 01 Summary

Chapter 1: Introducing Logic

Summary

 

  •  Logic is the study of argument. It may also be thought of as the rules of what follows from what, of which consequences derive from which assumptions.
  • An argument is a set of statements, called premises, together with a claim, called the conclusion, which the premises are intended to support or establish.
  • A conclusion is an argument’s main claim. It is what the argument seeks to establish.
  • Premises are statements that intend to provide the support necessary to establish an argument’s conclusion.
  • To establish a claim is to justify or provide evidence for it.
  • A proposition is a statement, often expressed by a declarative sentence, which has a truth value. The propositions belonging to the languages studied in this text will be interpreted as having only two possible truth values; they are either true or false, and not both.
  • Arguments can be evaluated in two distinct ways: (1) we can see whether the conclusion follows from the premises, and (2) we can see whether the premises are all true.
  • If the conclusion of a deductive argument follows from the premises, the argument is valid. This means that the conclusion is a logical consequence of the premises (regardless of whether the premises are true or not).
  •  In a valid argument, if all of the premises are true, then the conclusion must be too. It is this truth-preserving feature of valid arguments that makes them such powerful tools.
  • If all of the premises of an argument are true and the form is valid, then the argument is said to be sound. This means that the argument has succeeded in establishing its conclusion.
  • If any of the premises of an argument are false, the argument is said to be unsound.
  • The first step in analyzing arguments is to identify a conclusion, and separate it from the premises.
  • Premise indicators are words or phrases such as ‘since’, ‘because’, ‘for’, and ‘given that’, which often—though not always—precede an argument’s premise. They can be useful for helping us to separate an argument’s conclusion from its premises.
  • Conclusion indicators are words or phrases such as ‘therefore’, ‘thus’, ‘hence’, and ‘it follows that’, which often—though not always—precede an argument’s conclusion. They can be useful for helping us to separate an argument’s conclusion from its premises.
  • A regimentation is a way of rewriting an argument to better reveal its logical structure. This can be done either by putting the argument into numbered premise-conclusion form or by translating the argument into a formal language.
  • Natural languages are the languages we all grow up speaking, such as English, Spanish, or Swahili.
  • Object languages are formal languages, such as those studied in this book. They are useful for gaining precision and for clarifying ambiguities present in natural languages.
  • Meta-languages are combinations of natural languages with additional symbols and technical terms. They are useful for studying and speaking about formal languages.
  • Syntax specifies the vocabulary of a given language and its rules of grammar. It tells us which expressions are well formed.
  • Semantics specifies how a given language is to be interpreted. It tells us the meaning or truth conditions of any and all well-formed expressions.

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