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All You Need to Know Logic (Part 2 - Rules of Replacement)
By philobean | June 27, 2007
Some statements may be written differently but logically mean the same thing. For example, the statement ‘if I pass the board exam, then I will inherit a thousand pesos’ is logically equivalent to ‘I will inherit a thousand pesos if I pass the board exam’. Now, this is obvious. Some logical equivalences are more subtle. Take ‘I will die or I will pass the board exam’. Would you have guessed this is logically equivalent to ‘I will die unless I will pass the board exam’? Notice how changes in phrasing and sentence construction may not affect the logical relations being put forward in a statement.
Now, imagine being asked to analyze a complex argument. Wouldn’t it be easier to analyze some arguments when you convert them into a more familiar form? The examples above show how two different methods of grammatical construction may result in a single logical statement. Other logical statements (while different) may be equivalent to each other. Thus, it is possible to use them interchangeably.
For example, ‘if it rains, then the ground is wet’ (symbolized: ‘r : w’) is logically equivalent to ‘it doesn’t rain or the ground is wet’ (symbolized: ~r v w).
While there are many possible logical equivalencies (thus, many possibilities for replacement), all these can be reduced to a finite number of fundamental rules. These are called the rules of replacement.
These rules are summaried here.
Topics: Academic |