Why must the sentence form of a valid argument be tautological?

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I was thinking along the lines of the obvious, such as when found tautological the form must have been valid but I'm sure there is a more in-depth explanation that I can't reach.

Maria

Posted 2016-02-01T06:08:44.773

Reputation: 9

Question was closed 2016-02-05T19:27:09.350

2Could you please add some background information: What is the sentence form of an argument, what is a tautological sentence form? Can you give an example, thanks. – Jo Wehler – 2016-02-01T06:22:47.830

Answers

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There's nothing deeper going on here. An argument, "P proves Q" is valid iff it is true for all assignments P,Q iff P-> Q is a logical truth, also known as a tautology

This does invoke soundness/completeness.

Stella Biderman

Posted 2016-02-01T06:08:44.773

Reputation: 512

I just spoke to my AI and he said that what my professor really wanted was for me to prove that is was impossible to have a valid argument NOT be tautological. So basically show, in an example, that if you assume an argument to be valid and then assume that it is not tautological you will reach the conclusion that it is both invalid and valid when doing the a table, leading to the statement that "the sentence form of a valid argument must be tautological" because otherwise, the argument, which we said was valid, is actually invalid. She just wanted the reasoning behind it ig, thank you! – Maria – 2016-02-01T21:15:26.257

@noni have you figured that out? If not, can you provide your definitions of tautology and valid so I can explain? – Stella Biderman – 2016-02-01T21:19:00.023

yes, my AI explained it to me, thank you though! – Maria – 2016-02-01T21:29:46.443