Symbolic Logic question
1. Your friend in graduate school, John Doofus, has in vented a set of rules of inference for the language of first order logic (called ‘FOL' in the book). His system is called ‘Doofus'.
One day you discover that there's an argument, Argument1, that Doofus can prove, but which you can show that Fitch cannot prove.
a) Is Argument1 valid or invalid?
b) What property does Fitch possess that justifies your answer to a)? Include a brief (one or two sentence) justification in your answer.
c) What must be true about Structures in virtue of your answer to a)?
d) What property does Doofus possess in virtue of its ability to prove Argument1?
After further investigation, you discover a new argument, Argument2. You demonstrate that Doofus cannot prove Argument2, but Fitch can prove Argument2.
e) Is Argument2 valid or invalid?
f) What property does Fitch possess that justifies your answer to e)? Include a brief (one or two sentence) justification in your answer.
g) What property does Doofus possess in virtue of its inability to prove Argument2?