CHAPTER
1:
STATEMENTS
Subject of this chapter are statements
respectively propositions. These are atomic components which can
be more or less complex grammatical constructions expressing facts.
They form the foundation of propositional logic.
This lesson is devided into two sections. The first one shows you what statements are,
the second one explains some exceptions. In both sections you can test your notion by means
of an exercise.
Definition
An essential property of logical statements is that they have a definite truth value.
Generally each statement is either TRUE or FALSE. However, as in many fields of science
are there excepions caused by incomplete or ambiguous enunciations. These facts nevertheless can
count as statements, but they do not have a definite truth value.
Examples for statements
The following sentences all are statements regardless of its truth value!
- The moon is made of blue cheese.
- Paris is the capital of France.
- Mice chase cats.
- He is older than she is.
Counter examples
To understand what a statement or proposition is, it is may be a good way to show which kinds
of sentences do not count as a statement.
1. A question is definitely not
a statement
How old are you?
Do you love me?
In some cases perhaps it is possible to answer the question with YES or
No, but it makes no sense to speak of any truth value. Both examples are
not statements which can be TRUE or FALSE.
2. Commands do not count as a statement!
Shut the window!
Please turn right!
3. Wishes cannot be a statement
If only I hadn't said her that I'm rich.
Merry Christmas and a Happy New Year!
Lets go to an exercise
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Exercise 1:
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Please read the following sentences
and try to find out whether they belong to statements or not. Do not try
to answer any questions, just take the logical point of view into consideration.
If you think you are sure about your answer make a tick in the corresponding
checkbox and click on the button  .
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Is that a statement?
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Is that a statement?
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Is that a statement?
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To get help, just have a look at the output field below!
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Exercise 2:
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Try to find out which of the following grammatical constractions are statements ...
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Exceptions
Imagine you get a grammatical construction like the following one:
It seems to be a statement, but what is its truth value?
As soon as I say it is true and it is really true, the statement
changes its truth value to false, because I didn't tell a lie. If
I say it is false that means if I lie, the truth value keeps true
but my answer is wrong.
Conclusion: We can say this is a statement, but we get a problem to assign a truth value to it.
Another ambiguous example is the following one:
This appears only as a statement if somewhere in the context is explained
who exactly Andy and Kathrin are. If we choose pronouns instead of the
names, we get the same problem:
Such a statement has no truth value until we discribe who he or she
are. If we explain the coherences and put this together with the statement
without a definite truth value then we get a real statement.
This is a real statement and the people who know the circumstances are able to
determine the truth value of this statement.
Lets go to an exercise again
To get help, just have a look at the output field below!
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Exercise 3:
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Try to find out which of the following statements have a definite truth value...
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©1996 HTW Dresden (FH) Andreas
Wintergerst
©2001 HTW Dresden (FH)
Gerald Zschornak (last update 25-04-2001)
