Logic: Chapter Two: Section IV

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Logic Chapter Two Section IV

• Jay Odenbaugh
• Philosophy
• Lewis and Clark College

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Definitions

• Critical thinking involves paying attention to
  language as we have seen in the case of ambiguity
  and vagueness.
• Thus, we must pay attention to the definitions of
  words and concepts and we must recognize that
  there are several types of definitions and keep
  them straight since they have different purposes.

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Ostensive Definitions

• An ostensive definition of a term is a definition
  that occurs by displaying an object in the
  extension of the term.
• Think of a small child who learns the meaning of
  the words Dad or ball.
• We do this by pointing and ostending the meaning
  of the term.

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Ostensive Definitions, Cont.

• There are limitations though for ostensive
  definitions
• Misapplication - how do you know which object is
  ostended?
• Generality - how can one know the meaning of
  general terms through ostension?
• Absent objects - how can one refer to an object
  which is not present?
• Abstract objects - how can one ostend an abstract
  object like a number?

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Verbal Extensional Definitions

• The extension of a term is the set of objects
  that the term refers to.
• A verbal extensional definition of a term occurs
  by listing or naming objects in the extension of
  the term
• For example, we can provide such a definition for
  the even natural numbers 2, 4, 6, 8, 10,

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Verbal Extensional Definitions

• There are several limitations of this type of
  definition
• Incompleteness - if the set is sufficiently
  large, then we cannot list all of its members.
• Nameless members - if not every member is named,
  then we cannot list all the members.

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Intentional Definitions

• The intension of a term is the set of all and
  only those properties an object must possess for
  a term to apply to it.
• An intensional definition of a term occurs by
  stating the properties an object must possess for
  the term to apply to it.
• For example, we can provide such a definition for
  the term bachelor - someone is a bachelor just
  in case they are an unmarried man.

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Intentional Definitions, Cont.

• Thus, we can say the following
• (NEC) If someone is a bachelor, then they are an
  unmarried male.
• (SUFF) If someone is an unmarried male, then they
  are a bachelor.
• Having the property of being an unmarried male is
  both necessary (you must have the property) to be
  a bachelor, but it is also sufficient to be a
  male (you need no other properties)

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Intentional Definitions, Cont.

• There are different types of intentional
  definitions depending on ones purposes
• Definitions that show how a word is commonly used
• Definitions that introduce a new word into the
  language.
• Definitions that reduce vagueness
• Definitions for theoretical purposes
• Definitions designed to transfer emotive force

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Lexical Definitions

• Definitions that show how a word is commonly
  used.
• A lexical definition is used when one wants to
  present the accepted standard use of a term what
  is a dictionary or explicative definition.
• Make sure the definition offered is not too
  narrow or wide and it should not be circular.

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Lexical Definitions, Cont.

• Exercise Set 2.3
• We have said that abstract objects such as
  numbers cannot be ostensively defined. But
  numerals, which are conventional representations
  of numbers can be ostensively defined.
• Give an ostensive definition of the Roman numeral
  that represents the number three. Answer III
• Given an ostensive definition of the Arabic
  numeral (Arabic, base 10) for the number seven.
  Answer 7
• Give an ostensive definition of the binary
  numeral (Arabic, base 2) for the number two.
  Answer 11

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New Terms

• Definitions that introduce a new word into the
  language.
• Term should (1) not already have a widely
  accepted standard meaning and (2) should be a
  useful addition to a language (otherwise
  jargon).

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Precising Definitions

• Definitions that reduce vagueness of words or
  concepts.
• Precising definitions reduce the vagueness of a
  term.
• Exercise Set 2.4
• 1. Adult (as applied to humans) is a vague term.
  For what purposes might a precising definition of
  adult be required? Discuss some of the problems
  that arise in formulating such a definition.

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Theoretical Definitions

• Definitions for theoretical purposes.
• A theory is a set of interrelated of statements
  that predict or explain phenomena. A theoretical
  definition of a term involves defining a concept
  through the means of a theory.
• Heat mean kinetic energy species a group of
  interbreeding organisms reproductively isolated
  from other such groups.

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Persuasive Definitions

• Definitions designed to transfer emotive force.
• A persuasive definition of a term is designed to
  express or evoke an approval or disapproval
  toward objects referred to by the term.

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Persuasive Definitions, Cont.

• Exercise Set 2.5
• The following argument, used by John Rock, who
  was a principal designer of the Pill, depends on
  the meaning of natural. What theoretical
  considerations enter into the definition of
  natural?
• In nature, during pregnancy, progestin is
  produced to block the release of additional eggs.
• The Pill is progestin in tablet form.
• Therefore, the Pill is a natural method of birth
  control.

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Syntactic definitions and implicit definitions

• A term that does not refer can be defined by its
  grammatical role in a language.
• For example, the logical connectives
• If-then, and, or, if and only if, etc.

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Operational Definition

• An operational definition characterizes a term by
  specifying a publicly observable and repeatable
  operation.
• For example, one substance is harder than
  another just in case one scratches the surface of
  the the other when the two are rubbed together.
• Temperature is that property that is measured by
  thermometers.