Wednesday, September 24, 2014

Logic: Self-Contradictory Sentences

For my MCCC Logic students. The following sentences are not propositions or statements. They are meaningless because self-contradictory.

My brother is an only child.
John is a bachelor and his wife’s name is Linda.
There is no such thing as truth.
            1. There is no such thing as truth.
            2. Therefore, premise 1 is not true.
All the statements I make are false.
            1. All S are F.
            2. Premise 1 is S.
            3. Therefore, Premise 1 is F.
All human behavior is determined.
            1. All human behavior is determined.
            2. Making statements is an example of human behavior.
            3. Premise 1 pretends to be a statement.
            4. Premise 1 is determined.
5. Therefore whoever believes Premise 1 is determined to believe Premise 1.
Which is... nonsense.
I only believe things that you can see, touch, hear, taste, or smell.
1.    I only believe things that you can see, touch, hear, taste, or smell.
2.    I believe sentence 1 above.
3.    Therefore I believe something that cannot be seen, touched, tasted, heard, 
or smelled.
There is no such thing as free will.
            1. There is no such thing as free will.
2. Sentence 1 was not freely chosen. Any person who believes Sentence 1 does not willfully believe Sentence 1, but was causally determined to believe Sentence 1.
            3. Therefore there is no good reason to believe that Sentence 1 is  a statement, and true.
The "verification principle." (VP)
            1. A statement is true IFF (if and only if) it : a) can be empirically
            verified; or b) is mathematical (tautological). (This is called the VP.)
            2. The VP claims to be a statement.
            3. The VP itself can be neither a) empirically verified; nor is it b)
            mathematical (tautological; redundant; definitional.
            4. There the VP is false (by its own criteria).
Philosopher Ludwig Wittgenstein wrote: "Most propositions and
questions which have been written about philosophical matters are not false, but
senseless. We cannot, therefore, answer questions of this kind at all, but only
state their senselessness. Most questions and propositions of the philosophers
result from the fact that we do not understand the logic of our language."
All truth is relative.
            1. All truth is relative to individual knowing subjects.
            2. Sentence 1 is true, universally (note the word "all").
            3. Sentence 1 is relative (and thus, by definition, is not
            universally applicable).
4.    Therefore Statement 1 is false.

Hence subjective relativism is nonsense (the idea that some things are, e.g., 
"true for you" but "false for me"). 
See the logic text I am using - Vaughn, The Power of Critical Thinking, Ch. 2, on the 
"subjectivist fallacy."