Translating into Standard Form

1
Translating into Standard Form

• A great deal of what we say and write can be
  translated into one of the standard form
  categorical statements.
• A proper translation is one that captures the
  meaning of the original statement.

2
The Meaning of Meaning

• Translations into standard form often produce
  statements that sound somewhat awkward.
• The goal in translating is to produce a statement
  that is logically equivalent to the original.
• -The point of the translation is to make
  explicit the underlying logical form of ordinary
  language claims

3
Why Bother?

• By making the logical form of ordinary language
  claims explicit, we can more readily test the
  validity of arguments containing those claims (by
  using Venn diagrams and the square of opposition)
• Proper translation requires paying close
  attention to how words are used in a sentence.
• While there are no formal rules that tell you how
  to translate every claim into a standard form
  statement, there are several guidelines that can
  assist you in the process

4
Lets Look at Examples

• Puppies are cute! cries your annoyingly
  cheerful roommate.
• Two things to notice
• No explicit quantifier
• Cute is not a noun, but an adjective
• But we can translate this claim into a standard
  form statement.

5
Continued

• In this case, your roommate is making a claim
  about all puppies, so we should translate her
  assertion as an A statement.
• We can get rid of the adjective cute by
  replacing it with the noun phrase cute things
  (cute expresses an attribute, not a class of
  things, so in order to construct a categorical
  statement, we need to find a suitable class term)
• Result All puppies are cute things

6
Next Example

• The Bears suck
• Notice that this truism is about an individual
  team and lacks the copula are.
• But we can still translate it into a standard
  form categorical statement

7
Continued

• Terms/phrases that refer to individuals can be
  replaced with terms that refer to classes with
  exactly one member
• All teams identical to the Bears picks out a
  class of things with exactly one member (the
  Bears)
• We can introduce the copula by translating the
  claim thusly
• All teams identical to the Bears are teams that
  suck

8
Whenever and Wherever

• Spatial and temporal adverbs can be replaced with
  terms denoting classes of places and times
• Mary always wins at darts translates into
• All times Mary plays darts are times when Mary
  wins
• He is liked wherever he goes translates into
• All places he goes are places where he is liked

9
Anyone, Everything, Whatever

• Anyone who votes for Clinton is a fool becomes
  All people who vote for Clinton are fools
• Everything happens for a reason becomes All
  things that happen are things that happen for a
  reason
• Whatever he says is stupid becomes All things
  he says are stupid things

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Other Common Phrases

• Not all men are pigs denies the A claim All
  men are pigs. Because we know that the denial
  of an A claim is logically equivalent to an O
  claim, we can translate this as Some men are not
  pigs
• Phrases with a few or at least one or there
  are should be translated into an I or O claim.
• Example There are smart socialists becomes
  Some socialists are smart people

11
Conditionals

• Many conditional claims can be translated into
  standard form categorical propositions
• If introduces the antecedent of a conditional,
  which is expressed as the subject term
• Example If it acts like a duck, then it is a
  duck becomes All things that act like a duck
  are ducks
• Notice the original claim is equivalent to It
  is a duck if it acts like a duck. Even though
  it acts like a duck comes at the end, it is
  still the antecedent because it follows if