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#113326 - 10/10/03 01:26 PM Re: Logic problem Joined: Jan 2002

Posts: 1,523 TheFallibleFiend

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Virginia, USA

Excellent! If the premises are false, then any conclusion is always TRUE!

k

#113327 - 10/10/03 01:36 PM Re: Logic problem Joined: Dec 2000

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Posts: 13,803 If the premises are false, then any conclusion is always TRUE!

Attually®, premises can be true or false, conclusions can be valid or invalid and a true conclusion can result validly from false premises.

All lizards have feathers

All robins are lizards

Therefore: All robins have feathers.

The conclusion is both valid and true but the premises are both false.

#113328 - 10/10/03 06:19 PM Re: Logic problem Joined: Jan 2002

Posts: 1,523 TheFallibleFiend

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Sorry, got in a rush. If the premises are false, then regardless of whether the conclusions are true or false, the proposition itself evaluates to true.

(Of course you know this, but everyone may not.)

F->T is T

F->F is also T

BTW, I just got an email from the county thanking my daughter for catching the error - which appears to have happened at the printers.

k

#113329 - 10/10/03 06:43 PM Re: Logic problem Joined: Dec 2000

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Posts: 13,803 F->T is T

F->F is also T

You lost me.

#113330 - 10/10/03 08:09 PM Re: Logic problem Joined: Jan 2002

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There's an explanation at http://pluto.fss.buffalo.edu/classes/psy/segal/416f2001/logic/98logic2.html.

Go to the bottom of the page and check out columns 1,3, and 5. In logic, that "contains" symbol (the sideways U) means "implies" or "if ... then ..."

"If P, then Q" is a proposition that has a value that depends on the values of P and Q. Extracting from that truth table:

P Q P->Q

T T T

T F F

F T T

F F T

The only time P->Q is false is when the premise (antecedent) is true and the conclusion (consequent) is false.

I was kidding a little in my response to Mav - but only a little. I'm not sure that a contradiction can be treated as a false statement. Intuitively it seems that it could, though.

k

#113331 - 10/10/03 10:24 PM Re: Logic problem Joined: Dec 2000

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Posts: 13,803 I see part of the problem. You're calling "if P then Q" a proposition. I would call it the major premise. And it looks to me like you've got it backwards.

The syllogism would go:

Major Premise: If P then Q

Minor Premise: P

Conclusion: Q

From this it is valid to say:

If not Q then not P

but not:

If not P then not Q

Now. Are you talking about the last Table on the page?

a. I would call the normal AND

b. is the standard inclusive OR

c. looks like P AND NOT Q

d. is the standard exclusive OR (XOR)

The standard colloquial defintion of "or" is d. The conflict between b. and d. is the basis for the joke question, "Did you take the bus or bring your lunch?"

#113332 - 10/10/03 10:56 PM Re: Logic problem Joined: Jan 2002

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And it looks to me like you've got it backwards.

I'm not sure what I have backwards. A proposition is a sentence that is either true or false. In a conditional sentence, the premise (the if part) can be true or false and the conclusion (the then part) can be true or false. That is, each component (P and Q) is a proposition and the statement P->Q (which can be read as "P implies Q" or "if P then Q") is also a proposition. If you call P the minor premise and P->Q the major premise, it's okay with me. I don't specifically recall seeing that nomenclature, but the terminology doesn't change the underlying logic, so I accept it.

Now. Are you talking about the last Table on the page?

a. I would call the normal AND

b. is the standard inclusive OR

c. looks like P AND NOT Q

d. is the standard exclusive OR (XOR)

The standard colloquial defintion of "or" is d. The conflict between b. and d. is the basis for the joke question, "Did you take the bus or bring your lunch?"

a. yes. this is AND.

b. yes. this is OR.

c. no. this is "P implies Q" that sideways U symbol reads (P implies Q, which can also be written P->Q which can also be written as "not P or Q").

d. yes. equivalence is identical to XOR.

Back to c.

Let's look at the table again, only I'm going to add new fields for "NOT Q" and "P and not Q" (C means conditional, Q' means not Q, and Z means "p and not q"P Q C Q' Z

T T T F F

T F F T T

F T T F F

F F T T F

We note Column C (P implies Q) is not the same as column Z ("P and not Q"). This time I add columns P' and W (not P or Q).P Q C P' Z

T T T F T

T F F F F

F T T T T

F F T T T

We note that column C is the same as column Z.

You can check out http://www.merriam.uiuc.edu/ps481/lectures/topic6/advancedrules.html

and search for "Material implication" and an little more detailed explanation at http://secure.yournotes.com:81/notes/fall98/cse260/cse260_082898.shtml

(the same thing I've done above, but considerably neater).

k

#113333 - 10/10/03 11:31 PM Re: Logic problem Joined: Jun 2002

Posts: 7,210 Buffalo Shrdlu

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Vermont nice job with the [ pre's ] and queues...

formerly known as etaoin...

#113334 - 10/11/03 12:35 AM Re: Logic problem Joined: Dec 2000

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Posts: 13,803 I don't think we're talking about the same thing. Maybe you're not looking at it backwards, but we're looking at it from different directions. I think we actually agree. I screwed up on that c. I misread it or something. I don't see the lazy U, my browser is showing a rectangle*, but that's no excuse.

Meanwhile, I'm trying to figure how this relates to our original problem. I think we agree that it was messed up and if they want to say it was a screw up at the printer, I guess we'll just have to accept that as long as they got it fixed.

*Pretty much its feeble attempt at reproducing something it doesn't have in its font.

#113335 - 10/11/03 09:07 AM Re: Logic problem Joined: Mar 2000

Posts: 6,511 AnnaStrophic

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lower upstate New York BTW, I just got an email from the county thanking my daughter for catching the error - which appears to have happened at the printers.

FF, what precisely was the error?

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