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@VideCorSpoon,

Thank you so much again Spoon!

Why do you do your reference columns in this order:

P Q R
T T T
F T T
T F T
F F T
T T F
F T F
T F F
F F T

Versus...
P Q R
T T T
T T F
T F T
T F F
F T T
F T F
F F T
F F F

I see most texts do it the second way. Does it matter what order you do it in as long as the Q column follows the T T F F T T F F (etc) pattern?

@ValidandNotinUse,

You can do the truth probability matrix in any order you want. The combinations will be the same because all the probability matrix does is simplifying all the possibilities three (in this case) variables can create. We just go from different directions.

My first propositional logic teacher did it the same way you did, which is TTTTFFFF for the first variable. I do it just because it is easier to start off like that for me. But actually if you think about it, doing it your way is actually a lot better, especially if you are just starting out because you know that for three variables, you have to have four T's and four F's (thus 8 lines) and then it's easier to visualize what you have to do next. But yeah, you can write it out either way because you will get the same results.

I've seen one person so acquainted with truth tables (while taking predicate logic) that they could actually visualize the primary connective values all together and find the truth value of the overall truth table without writing anything down. That blows my mind.

@VideCorSpoon,

Okay, so I tried your steps on the following problem but according to my textbook I am still incorrect.

P--> (Q--> R)
~(P --> Q)
-------------
R

http://www.philosophyforum.com/forum/attachment.php?attachmentid=60&d=1240254631

Here is the process I followed:

1. I did the reference columns. Then I put all the P values in the P columns and etc.

2. I calculated the values for the conditionals (except for the one that is after the P in the 4th column P --> (P --> Q), not sure how to do that yet).

3. I negated the ~. I got those values from the conditional from the (P --> Q) in column 5.

Sorry, I must be slowest person on the planet to learn these things!

@ValidandNotinUse,

No problem at all. You've got 99.9% of the problem right. Take a look at how I did the problem.

You did virtually everything I did except for one thing, the central connective in P --> (Q --> R). Remember, you want to attack what is in the parentheses first, and then you use the truth value you come up with in Q -->R, which we will call X. Then, you can do P --> X. The result of that is the truth value of the entire section of this problem. Like this:

1. attack the parentheses first.
2. take the result of the parentheses and put it together with the connective and anything attached to it.
3. solve for the primary truth value!

@VideCorSpoon,

thank you so much!!!! I am finally able to go through the exercises in the chapter without making any mistakes!!!!

Your second diagram where you show the formula as 'P --> X' was especially helpful. I finally now understand where those sorts of values come from. Whew!

wish me luck on my test tomorrow!

@VideCorSpoon,

Umm I'm confused: You argued that the argument:
1. If Alan is running then Bob is running.
2. Bob is not running
3. Therefore, Alan is not running.
is valid (i.e. conclusion follows from the premises if such premises are assumed to be true)...
but surely there is no reason why Alan may be running even if Bob is not? All we know is that IF Alan is running then so is Bob; but the premises do not state that 'If Bob is not running then neither is Alan' it may be that Bob is not running but Alan IS running.
In fact even if Alan were not running then Bob might be running anyway.
The ONLY necessary truth we can deduce is that it is impossible for Alan to be running but Bob not running.

@VideCorSpoon,

There is a misspell in this picture: http://i32.tinypic.com/15g5p8j.jpg
It should be "possibility" not "probability". Smile

@Greg phil,

Greg;67309 wrote:

Umm I'm confused: You argued that the argument:
1. If Alan is running then Bob is running.
2. Bob is not running
3. Therefore, Alan is not running.
is valid (i.e. conclusion follows from the premises if such premises are assumed to be true)...
but surely there is no reason why Alan may be running even if Bob is not? All we know is that IF Alan is running then so is Bob; but the premises do not state that 'If Bob is not running then neither is Alan' it may be that Bob is not running but Alan IS running.
In fact even if Alan were not running then Bob might be running anyway.
The ONLY necessary truth we can deduce is that it is impossible for Alan to be running but Bob not running.

Hi Greg,

The first premise is logically equivalent to "if Bob is not running then neither is Alan". You can see this by what is called transposition. From transposition, we can take the claim that

If Alan is running then Bob is running.

and replace it with:

If Bob is not running then Alan is not running.

This link should help you:

http://en.wikipedia.org/wiki/Transposition_(logic)

It might be useful to think that the first premise, if true, uses bob's running as a truth condition for the truth of Alan's running.

@Greg phil,

Greg;67309 wrote:

Umm I'm confused: You argued that the argument:
1. If Alan is running then Bob is running.
2. Bob is not running
3. Therefore, Alan is not running.
is valid (i.e. conclusion follows from the premises if such premises are assumed to be true)...
but surely there is no reason why Alan may be running even if Bob is not? All we know is that IF Alan is running then so is Bob; but the premises do not state that 'If Bob is not running then neither is Alan' it may be that Bob is not running but Alan IS running.
In fact even if Alan were not running then Bob might be running anyway.
The ONLY necessary truth we can deduce is that it is impossible for Alan to be running but Bob not running.

It's a valid, standard form Modus tollens deduction.

P -> Q
~Q
~P

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