Material Implication: Logic
Snidely
Join Date: 2003-02-04 Member: 13098Members
Join Date: 2003-02-04 Member: 13098Members
<div class="IPBDescription">Argh!</div> <!--QuoteBegin--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> </td></tr><tr><td id='QUOTE'><!--QuoteEBegin-->“Material Implication”:
A (materially) implies B, denoted as A -> B, is false if and only if A is true but B is false.
The truth table for -> is:
A | B | A->B
T | T | T
T | F | F
F | T | T
F | F | T
In other words, A -> B is true if and only if it is not the case that A is true but B is false.<!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
An example is when A equals "it rains" and B equals "we shall get wet". For the first row, that would mean "if it rains, we shall get wet", and is true.
What I don't get is this:
The second line is false, but the third line is true. The reason for the third line is apparently that you could get wet because you were hosed, hit by a water balloon, or whatever. Why does rain imply wetness, then? Why is the second line false, since it could rain, but you could be indoors, or have an umbrella?
Edit: Uh oh, meant to post this in discussion forums.
Edit number two: I guess I owe Talesin a drink.
A (materially) implies B, denoted as A -> B, is false if and only if A is true but B is false.
The truth table for -> is:
A | B | A->B
T | T | T
T | F | F
F | T | T
F | F | T
In other words, A -> B is true if and only if it is not the case that A is true but B is false.<!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
An example is when A equals "it rains" and B equals "we shall get wet". For the first row, that would mean "if it rains, we shall get wet", and is true.
What I don't get is this:
The second line is false, but the third line is true. The reason for the third line is apparently that you could get wet because you were hosed, hit by a water balloon, or whatever. Why does rain imply wetness, then? Why is the second line false, since it could rain, but you could be indoors, or have an umbrella?
Edit: Uh oh, meant to post this in discussion forums.
Edit number two: I guess I owe Talesin a drink.
Comments
This is what I don't get about the explanation I've been given. None of the other expressions (such as AND, OR, exclusive OR or material equivalence) need to look outside their universe of discourse to explain themselves.
EDIT: The "~" stands for "not", so "(not A) or B".
A | B | A->B
1)T | T | T
2)T | F | F
3)F | T | T
4)F | F | T
All cheerleaders are pretty
Jenny is a cheerleader, so jenny is pretty. (T)
Jenny is a cheerleader, but jenny is not pretty. (F)
Jenny isn't a cheerleader, but jenny is pretty. (T)
Jenny isn't a cheerleader, jenny isn't pretty. (T)
"Implies" means that the conditional, as above, must work out to be true. If A -> B it sorta means that a condtional is set up, and only when it is a false condition, like in the above examples, does the entire statement prove to be false.
The condition is that "If it rains, you'll get wet", right?
Snidely is in the rain, and he's wet - T
Snidely is in the rain, but he's not wet - F
Snidely is not in the rain, but he's wet - T
Snidely is not in the rain, nor is he wet - T
"Snidely is in the rain, but he's not wet" makes the condition false, but "Snidely is not in the rain, but he's wet" doesn't actually disprove the condition, since the condition relies on the rain. Am I right?
Basically by definition <!--emo&::nerdy::--><img src='http://www.unknownworlds.com/forums/html/emoticons/nerd-fix.gif' border='0' style='vertical-align:middle' alt='nerd-fix.gif' /><!--endemo-->
A is a true statement (the statment which we will call C)
B is a true statement (the stament which we will call C)
In fact the true statement © for both A and B is exactly the same. Its the same sentence even.
So keeping that in mind.
If A = C
and
B = C then by this logic A is = to B.
Simple basic logic.
But
What if I were to say,
All Christians believe in one God =True
All Muslims believe in one God = True
Both are true statements with the same variable, A and B both believe in one God.
By this logic A and B, Christians and Muslims are the same.
But in reality we know this to be false.
Dont you love logical fallacies? <!--emo&:p--><img src='http://www.unknownworlds.com/forums/html/emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /><!--endemo-->
A banana is yellow.
A school bus is a banana?
<!--emo&???--><img src='http://www.unknownworlds.com/forums/html/emoticons/confused-fix.gif' border='0' style='vertical-align:middle' alt='confused-fix.gif' /><!--endemo-->
Who says that that's logic? That's not logic, it's coincidence that it comes out true occasionally. <!--emo&::marine::--><img src='http://www.unknownworlds.com/forums/html/emoticons/marine.gif' border='0' style='vertical-align:middle' alt='marine.gif' /><!--endemo-->
A is a true statement (the statment which we will call C)
B is a true statement (the stament which we will call C)
In fact the true statement © for both A and B is exactly the same. Its the same sentence even.
So keeping that in mind.
If A = C
and
B = C then by this logic A is = to B.
Simple basic logic.
But
What if I were to say,
All Christians believe in one God =True
All Muslims believe in one God = True
Both are true statements with the same variable, A and B both believe in one God.
By this logic A and B, Christians and Muslims are the same.
But in reality we know this to be false.
Dont you love logical fallacies? <!--emo&:p--><img src='http://www.unknownworlds.com/forums/html/emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /><!--endemo--> <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd-->
No. No, no, no.
"A is a true statement (the statment which we will call C)"
This is not proper at all. Your statement A does not equal some "truth statement C". A has the property of being true. To say "A = C where C is 'this statement is true'" is not correct.
The only logical fallacy is in your reasoning.