## Wordsmith Talk |
About Us | What's New | Search | Site Map | Contact Us | |||

Register Log In Wordsmith.org Forums Words and languages in schools Logic problem Forums Calendar Active Threads Search Forum Help

Previous Thread

Next Thread

Print Thread

Page 3 of 5 1 2 3 4 5

Re: Logic problem #113326

10/10/03 01:26 PM 10/10/03 01:26 PMJoined: Jan 2002

Posts: 1,523

Virginia, USA TheFallibleFiend OP

veteranOP

veteran

Joined: Jan 2002

Posts: 1,523

Virginia, USA

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

k

Re: Logic problem #113327

10/10/03 01:36 PM 10/10/03 01:36 PMJoined: Dec 2000

Posts: 13,803 Faldage

Carpal Tunnel

Carpal Tunnel

Joined: Dec 2000

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.

Re: Logic problem #113328

10/10/03 06:19 PM 10/10/03 06:19 PMJoined: Jan 2002

Posts: 1,523

Virginia, USA TheFallibleFiend OP

veteranOP

veteran

Joined: Jan 2002

Posts: 1,523

Virginia, USA

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

Re: Logic problem #113329

10/10/03 06:43 PM 10/10/03 06:43 PMJoined: Dec 2000

Posts: 13,803 Faldage

Carpal Tunnel

Carpal Tunnel

Joined: Dec 2000

Posts: 13,803

F->T is T

F->F is also T

You lost me.

Re: Logic problem #113330

10/10/03 08:09 PM 10/10/03 08:09 PMJoined: Jan 2002

Posts: 1,523

Virginia, USA TheFallibleFiend OP

veteranOP

veteran

Joined: Jan 2002

Posts: 1,523

Virginia, USA

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

Re: Logic problem #113331

10/10/03 10:24 PM 10/10/03 10:24 PMJoined: Dec 2000

Posts: 13,803 Faldage

Carpal Tunnel

Carpal Tunnel

Joined: Dec 2000

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?"

Re: Logic problem #113332

10/10/03 10:56 PM 10/10/03 10:56 PMJoined: Jan 2002

Posts: 1,523

Virginia, USA TheFallibleFiend OP

veteranOP

veteran

Joined: Jan 2002

Posts: 1,523

Virginia, USA

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

Re: Logic problem #113333

10/10/03 11:31 PM 10/10/03 11:31 PMJoined: Jun 2002

Posts: 7,210

Vermont Buffalo Shrdlu

Carpal Tunnel

Carpal Tunnel

Joined: Jun 2002

Posts: 7,210

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

formerly known as etaoin...

Re: Logic problem #113334

10/11/03 12:35 AM 10/11/03 12:35 AMJoined: Dec 2000

Posts: 13,803 Faldage

Carpal Tunnel

Carpal Tunnel

Joined: Dec 2000

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.

Re: Logic problem #113335

10/11/03 09:07 AM 10/11/03 09:07 AMJoined: Mar 2000

Posts: 6,511

lower upstate New York AnnaStrophic

Carpal Tunnel

Carpal Tunnel

Joined: Mar 2000

Posts: 6,511

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?

Page 3 of 5 1 2 3 4 5

Moderated by Jackie

Forum Statistics Forums16Topics13,887Posts225,263Members9,069 Most Online3,341

Dec 9th, 2011

Newest Members Mcclea10, Dilaon, BloodyAaAssassin, MOAM, Mrcheetah

9069 Registered Users

Who's Online Now 0 registered members (), 127 guests, and 3 spiders. Key:Admin, Global Mod, Mod

Top Posters(30 Days)

Top Posters(All Time) wwh 13,858Faldage 13,803Jackie 11,613tsuwm 10,538LukeJavan8 9,256wofahulicodoc 8,178Buffalo Shrdlu 7,210AnnaStrophic 6,511Wordwind 6,296of troy 5,400

Forum Rules · Mark All Read Contact Us · Wordsmith.org