When we claim that a false statement is true or that a true statement is false, this is a moral wrong, called lying. But if we refuse to draw the proper conclusion of a valid argument, I do not know of a similar verb in English, a word that will make clear the ethical nature of such bad reasoning. But that it can be an ethical issue seems undeniable. This appears to be the failing of the Jewish leaders in John 5:39-40, who refused to accept that Jesus was the Christ, and of those who suppress the truth in unrighteousness in Romans 1, who are said to be “without understanding.”
Daily Archives: February 19, 2015
Symbolizing “nor” and “both”
Hello!
The problem today was the difference between using a “vel” for “nor” vs. using a “dot” for nor, the other was where the parenthesis were when the word both was used. We (the kids too) saw a difference in a couple of them – but one looked exactly like the other – with two different symbolic statements.
Any assistance would be greatly appreciated.
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There are two ways to write “neither p nor q”:
1) ~(p ∨ q)
2) ~p • ~q
As for the use of “both”, the phrase “not both p and q” should be ~(p • q), whereas “both not p and not q” should be (~p • ~q). So the proposition “Betty and Jon are not both eighth graders” could be symbolized ~(B • J), while the proposition “Betty and Jon are both not eighth graders” would be (~B • ~J).
Blessings!
Symbolizing Exercise 3, problems 13-15
Hi Josiah,
How do you translate the following words into symbolic propositions?
- “A false proposition is not true.”
- “It is false that a true proposition is not false.”
- “It is true that it is false that a true proposition is not false.”
I am discombobulated. Continue reading Symbolizing Exercise 3, problems 13-15