Understanding sentence tableau!!
Just took first year philosophy and I'm lost, assignments due soon.. please help!
|Understanding sentence tableau!!|
Joined: Mar 22, 2012
Total Topics: 1
Total Posts: 1
Posted Mar 22, 2012 - 11:02 AM:
Subject: Understanding sentence tableau!!
I read over the notes and I do understand this in a very simple manner but not thorough enough to answer this question. Please help!
The argument is as follows:
[[Q^R] -> S]
I need to construct a sentence tableau to confirm that this is a tautologically valid argument.
Im really lost. Step by step help to the answer is much appreciated.. I have another question like this which also needs answering... hopefully through the first example I will better understand the second one? Please help.
The second question:
Show by sentence tab. method that the sentence '[Sv-S] is a logical consequence of any sentence 'R'
Joined: Jan 04, 2008
Total Topics: 41
Total Posts: 872
Posted Mar 23, 2012 - 3:00 PM:
At the risk of oversimplifying, a tableau fundamentally tests for consistency. However, tableaux can also be finessed to test for validity. We simply need to note that premises entail a conclusion iff the conjunction of the premises and the negation of the conclusion is inconsistent. I am not used to writing tableaux online, so apologies if the below is hard to read.
First, we write the premises.
4. [[Q^R] -> S]
Next, we write the negation of the conclusion (to test for inconsistency).
Then we apply the tableau rules for each connective, continuing until we reach an inconsistency. [P>Q] is true just in case ~P or Q, so we split the tableau into two branches, one for each connective.
6. ~P Q
Note that the path from P on line 1 to ~P on line 6 produces an inconsistency, so we do not need to develop this branch further. The next formula is "[[Q^R] -> S]," so we add ~[Q^R] and S under Q on line 6.
7. ~[Q^R] S
Note that the path ending in S is inconsistent. Under ~[Q^R]:
8. ~Q ~R
Both of these paths are inconsistent. All paths are inconsistent, so the conjunction of the premises and the negation of the conclusion is inconsistent. The argument is valid.
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