You Don't Know Jack

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You Don't Know Jack

Postby NoShips on June 22nd, 2017, 10:20 am 

Anyone seen the film starring Al Pacino? In the court scene, he appeals, while defending himself, to a syllogism. His particular syllogism deserves euthanasia, as far as I can tell, and I tried to tell many times (yes, these things can be tricky).

There are rules about these things but too tired to look 'em up (undistributed middle term and all that crap).

Now I'm wondering did the producers knowingly include an invalid syllogism in their film, which seems unlikely coz the character Jack is portrayed as very smart. Or did they just screw up, which no one cares about except the sexually frustrated (see me)?
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Re: You Don't Know Jack

Postby NoShips on June 22nd, 2017, 11:07 am 

Ok, here's his syllogism (around 1:59 in the film - yes, told you it's sad. Me, not him)

Direct quotes from Jack questioning a witness:

"Is euthanasia always homicide?" (witness agrees)

"And you stated that homicide is not necessarily always murder?" (witness says nothing)

"Therefore, out of pure logic, wouldn't you say, that euthanasia's not always murder?"


*after objection (for reasons of jurisprudence), Jack says*


"No, it calls for simple logic. It calls for nothing but syllogism"

So, reconstructed:

Premise 1: All Es are H
Premise 2: Not all Hs are M (i.e. some Hs are M)
Conclusion: Not all Es are M (i.e. some Es are M)

Just to prove not all of us were making out with a hot chick in the back row, consider a counterexample:

Premise 1: All ostriches are birds
Premise 2: Not all birds fly (i.e. Some birds can fly)
Conclusion: Not all ostriches can fly (i.e. Only some ostriches can fly)

Jack hoping to convince the court that only some euthanasia is murder; me likewise trying to convince you that only some ostriches fly.

Well, I've never seen an ostrich that flies. Might be close though (hic). Any Venn Diagram specialists with no hot chicks out there?

More like all NoShips who drink German beer can't tell a flying ostrich from a valid syllogism.

Anyway, all part of the training...

Moral of the story: Um, don't trust anyone except relic salesmen
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Re: You Don't Know Jack

Postby Sivad on June 22nd, 2017, 11:26 am 

seems unlikely coz the character Jack is portrayed as very smart


I would use that one on a jury. I wouldn't say syllogism though, big words make juries suspicious. If they start thinking you're trying to trick them then they might catch on.
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Re: You Don't Know Jack

Postby NoShips on June 22nd, 2017, 11:28 am 

Big words don't scare logicians LOL. Of whom, I'm not one.

Am I right, Sivad? I had a few beers and not sure of anything.
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Re: You Don't Know Jack

Postby Sivad on June 22nd, 2017, 12:33 pm 

NoShips » June 22nd, 2017, 8:28 am wrote: I had a few beers and not sure of anything


Sobriety doesn't seem help with that either, so have a few more. Slainte.
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Re: You Don't Know Jack

Postby NoShips on June 23rd, 2017, 9:06 am 

Premise 1: All invalid syllogisms have an undistributed middle term
Premise 2: I have an undistributed middle term
Conclusion: I am an invalid syllogism

:-)

For comparison:

Premise 1: All SPCF moderators are tall and tanned and young and lovely
Premise 2: I am tall and tanned and young and lovely
Conclusion: I am an SPCF moderator

Oh, but I could while away the hours
Conversing over undistributed middle terms
If I only had a Braininvat

Miss ya! Tee hee. No, didn't get the postcard.

http://www.youtube.com/watch?v=NldPFVKYmiw
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Re: You Don't Know Jack

Postby Lomax on June 23rd, 2017, 11:17 am 

NoShips » June 22nd, 2017, 4:28 pm wrote:Big words don't scare logicians LOL. Of whom, I'm not one.

Am I right, Sivad? I had a few beers and not sure of anything.

You're right. The ostrich example is an odd one because it seems to imply there are flying ostriches. (Or consider #notallostriches owe me money.)

I think a simpler example would be:

P1: All natural numbers are numbers
P2: Not all numbers are positive
C1: Not all natural numbers are positive

Positive nonsense, eh.

NoShips » June 23rd, 2017, 2:06 pm wrote:Premise 1: All invalid syllogisms have an undistributed middle term
Premise 2: I have an undistributed middle term
Conclusion: I am an invalid syllogism

:-)

Very clever :)
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Re: You Don't Know Jack

Postby NoShips on June 23rd, 2017, 11:21 am 

With the Lomax imprimatur, I'll sleep well. Thanks!

Told ya they're all all to get me. Even euthanasiasts.

I'll never trust Al Pacino again.

Had to google "imprimatur". Tee hee. Damn loosers.
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Re: You Don't Know Jack

Postby NoShips on June 23rd, 2017, 11:23 am 

I only trust my results when they're replicable. LOL.
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Re: You Don't Know Jack

Postby NoShips on June 23rd, 2017, 11:30 am 

Lomax » June 24th, 2017, 12:17 am wrote:
Positive nonsense, eh.



Very clever! Tee hee. Off to bed. See ya. By the way, did you see the disparaging remarks I made about Nuneaton? See the thread on gravity being an illusion. LOL

Means, I love yar
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Re: You Don't Know Jack

Postby NoShips on June 23rd, 2017, 11:38 am 

Final thought: What are natural numbers again?

Those with clothes off?

Been a while since I was inflicted with maths.
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Re: You Don't Know Jack

Postby Positor on June 23rd, 2017, 9:28 pm 

NoShips » June 22nd, 2017, 4:07 pm wrote:Premise 2: Not all Hs are M (i.e. some Hs are M)

Why "some Hs", rather than "some or no Hs"? Doesn't "not all" include "none"?
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Re: You Don't Know Jack

Postby NoShips on June 23rd, 2017, 9:42 pm 

Positor » June 24th, 2017, 10:28 am wrote:]
Why "some Hs", rather than "some or no Hs"? Doesn't "not all" include "none"?


Good question, Positor! (it crossed my own confused mind too)

In ordinary language, "not all" seems clearly to imply "some".

In formal syllogistic logic, I dunno how this works. Do you?

If not, any logicians out there who can help?
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Re: You Don't Know Jack

Postby Forest_Dump on June 23rd, 2017, 9:45 pm 

Indeed and, of course, there are all kinds of homicides that are not murder including those called justifiable or justified homicides.
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Re: You Don't Know Jack

Postby NoShips on June 23rd, 2017, 9:50 pm 

Forest_Dump » June 24th, 2017, 10:45 am wrote:Indeed and, of course, there are all kinds of homicides that are not murder including those called justifiable or justified homicides.


As I see it, whether Jack's conclusion happens to be (as a matter of fact) true, is besides the point. The worry is that the conclusion is not guaranteed by the premises.
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Re: You Don't Know Jack

Postby Forest_Dump on June 23rd, 2017, 10:21 pm 

The conclusion is certainly valid. "Not all ostriches can fly" is a correct conclusion its just not as precise as it could be.
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Re: You Don't Know Jack

Postby NoShips on June 23rd, 2017, 11:41 pm 

Forest_Dump » June 24th, 2017, 11:21 am wrote:The conclusion is certainly valid. "Not all ostriches can fly" is a correct conclusion its just not as precise as it could be.


But that's not what I mean. Our concern here is whether the syllogism is structurally valid or not. Whether the conclusion is true or false is besides the point.

(A conclusion can be true or false, but not "valid". It's the syllogism as a whole that is valid or invalid.)

The premises of a valid syllogism must guarantee the conclusion. I'm doubtful that Jack's syllogism is valid, even supposing the conclusion is true (by happenstance).

If Jack's syllogism is invalid then his appeal to logic is in vain, even if he ends up with a true conclusion by luck. His result might be true, but his logic is fubar (if my suspicions are right).
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Re: You Don't Know Jack

Postby Lomax on June 24th, 2017, 12:07 am 

NoShips » June 24th, 2017, 2:42 am wrote:
Positor » June 24th, 2017, 10:28 am wrote:]
Why "some Hs", rather than "some or no Hs"? Doesn't "not all" include "none"?


Good question, Positor! (it crossed my own confused mind too)

In ordinary language, "not all" seems clearly to imply "some".

In formal syllogistic logic, I dunno how this works. Do you?

If not, any logicians out there who can help?

I am but a humble bartender, but I've done my fair share of wasting my youth. In predicate logic we can interpret

Not all bartenders do logic


As either

~(Ax(Bx > Lx))


("it is not the case that anyone who is a bartender does logic") or as

Ex(Bx & ~Lx)


("there exist people who are bartenders who do not do logic"), but natural language gives us the ability to talk about differences among various non-existent bartenders, which most formal logics don't do. "Free logics" are an exception. Anyway, if there are no bartenders then as far as most mathematical logicians are concerned, that makes "bartenders" = the empty set, 0. Which means that under some logics "all bartenders do logic" and "all bartenders do not do logic" are both true, and under other logics they are both meaningless.

So this sort of thing depends on which formal logic we are going with. The short answer is that "not all" does get treated by many logicians as meaning "some", which leads to some unusual outcomes, because we are introducing existential quantifiers where they might not belong. It allows us, for instance, to prove that it is logically necessary that something exists:

| ~Ex(x=x)
| Ax(x≠x)
Ex(x=x)

(Hypothesise that it is not the case that something exists which is equal to itself. Therefore everything is not equal to itself. Hypothesis proven false by contradiction. Therefore something exists which is equal to itself. QED.)
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Re: You Don't Know Jack

Postby Positor on June 24th, 2017, 12:16 am 

Re NoShips's latest post:

I am sure that Jack's syllogism is invalid.

Euthanasia is a subset of homicide; homicide is not always murder; but any subset of homicide may always be murder.
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Re: You Don't Know Jack

Postby NoShips on June 24th, 2017, 12:18 am 

Ok, it's easy enough if you draw Venn diagrams. Jack's syllogism is invalid, i.e., it may or may not yield a true conclusion depending on the values we assign to A, B, and C. Hence invalid. (It doesn't matter whether we interpret "not all" as "some" or "some or none").

This is the structure of Jack's syllogism (Edit: ignoring complications with "none"):

Premise 1: All As are B
Premise 2: Some Bs are C
Conclusion: Some As are C


Here's a case where true premises yield a true conclusion:

Premise 1: All men are human
Premise 2: Some humans are blind
Conclusion: Some men are blind

And here's one where true premises yield a false conclusion:

Premise 1: All men are human
Premise 2: Some humans have vaginas
Conclusion: Some men have vaginas

(We assume here no men have vaginas *cough*)
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Re: You Don't Know Jack

Postby Positor on June 24th, 2017, 12:36 am 

Lomax » June 24th, 2017, 5:07 am wrote:Anyway, if there are no bartenders then as far as most mathematical logicians are concerned, that makes "bartenders" = the empty set, 0. Which means that under some logics "all bartenders do logic" and "all bartenders do not do logic" are both true, and under other logics they are both meaningless.

But does "Not all bartenders do logic" include the possibility that there are bartenders but none of them do logic? It seems to me that it does; so it is not equivalent to "some bartenders do logic".
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Re: You Don't Know Jack

Postby Lomax on June 24th, 2017, 12:45 am 

Positor » June 24th, 2017, 5:36 am wrote:
Lomax » June 24th, 2017, 5:07 am wrote:Anyway, if there are no bartenders then as far as most mathematical logicians are concerned, that makes "bartenders" = the empty set, 0. Which means that under some logics "all bartenders do logic" and "all bartenders do not do logic" are both true, and under other logics they are both meaningless.

But does "Not all bartenders do logic" include the possibility that there are bartenders but none of them do logic?

My shorter paragraphs were intended to demonstrate that it only matters how we interpret the sentence. "Not all bartenders do logic" can be read as "It is not the case that all bartenders do logic" or as "of the bartenders, not all do logic". The former interpretation does not commit us to the existence of bartenders; the latter does. In your quotidian mathematical logics, ~AxLx tends to be treated as entailing Ex(~Lx), which does allow for the possibility you mention. But just be aware of its weakness, which is that it commits us to the existence of anything with variable predicates. In other words "Not all unicorns do logic" just as legitimately entails that "there are unicorns" and includes the possibility that none of them do logic. So we may not want to be too literal when translating natural-language claims into formal-language propositions.
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Re: You Don't Know Jack

Postby NoShips on June 24th, 2017, 12:49 am 

Given the ambiguity in "not all" -- a liberal interpretation (inclusive of "none") and a strict interpretation (exclusive of "none", i.e. = "some") -- there are four possibilities:

1. All As are B; No Bs are C
This entails "no As are C" thus the conclusion "Not all As are C" is true on the liberal interpretation of "not all" -- there are no As that are C

2. All As are B; Some Bs are C (but no As are C)
Conclusion: True -- "not all As are C" (none are)

3. All As are B; Some Bs are C (and some As are C)
Conclusion: True -- "not all As are C" (only some are)

4. All As are B; Some Bs are C (and all As are C)
Conclusion: False! It is not the case that "not all As are C" (they all are)


Jack, move to the bottom of the class!
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Re: You Don't Know Jack

Postby Positor on June 24th, 2017, 1:05 am 

NoShips » June 24th, 2017, 5:18 am wrote:(It doesn't matter whether we interpret "not all" as "some" or "some or none").

If we interpret "not all" as "some or none", then your earlier ostrich example yields a true conclusion:

Premise 1: All ostriches are birds [true]
Premise 2: Not all birds fly, i.e. some or no birds fly [true: some birds fly]
Conclusion: Not all ostriches fly, i.e. some or no ostriches fly [true: no ostriches fly].

However, the following yields a false conclusion:

Premise 1: All eagles are birds [true]
Premise 2: Not all birds fly, i.e. some or no birds fly [true: some birds fly]
Conclusion: Not all eagles fly [false: all eagles fly].
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Re: You Don't Know Jack

Postby NoShips on June 24th, 2017, 1:10 am 

Yes, Positor. Your eagle example is exactly analogous to my Case 4 (immediately above your post)
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Re: You Don't Know Jack

Postby NoShips on June 24th, 2017, 1:17 am 

Hey wait. Don Henley can't fly!

P,S. I just added the following to my vagina post for clarity: (Edit: ignoring complications with "none")

What you said about ostriches is correct.
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Re: You Don't Know Jack

Postby Dave_Oblad on June 24th, 2017, 5:25 am 

Hi all,

In the term:
"Not all ostriches can fly"
is weak English.. it implies some ostriches can fly.

The correct logical version would be:
"Not (All ostriches can Fly)"

Thus if the bracketed statement is "(All ostriches can Fly)" then the "Not" term in front implies inversion or opposite of what's bracketed, which redefines the statement meaning that: "No ostriches can Fly".

But how does one indicate inversion of a subject in a spoken sentence?

Perhaps "Air Quotes"?.. lol.

Regards,
Dave :^)
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Re: You Don't Know Jack

Postby NoShips on June 24th, 2017, 7:34 am 

Dave_Oblad » June 24th, 2017, 6:25 pm wrote:Hi all,

In the term:
"Not all ostriches can fly"
is weak English.. it implies some ostriches can fly.

The correct logical version would be:
"Not (All ostriches can Fly)"

Thus if the bracketed statement is "(All ostriches can Fly)" then the "Not" term in front implies inversion or opposite of what's bracketed, which redefines the statement meaning that: "No ostriches can Fly".

But how does one indicate inversion of a subject in a spoken sentence?

Perhaps "Air Quotes"?.. lol.

Regards,
Dave :^)


LOL Dave. Thanks for that. But...

Dave_Oblad » June 24th, 2017, 6:25 pm wrote: But how does one indicate inversion of a subject in a spoken sentence?


That's classified. I could tell you, but then I'd have to kill you.

(see 0:25 - 0:30)

http://www.youtube.com/watch?v=wUZxSf_P2r0

You did say "weak" after all. LOL. Messed with the wrong pilot.
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Re: You Don't Know Jack

Postby NoShips on June 24th, 2017, 7:43 am 

But seriously, Dave, I think what you're getting at is... and Lomax in the Latex covered this already, I think, is a question of "scope".

The scope of what? A predicate? Aristotelian syllogistic logic didn't, or did it, cover scope stuff?

Beats me.

We must remember, Jack appealed to Aristotle (erm, assuming Aristotle has the patent on syllogisms), not Frege (Lomax saw this already)

I have no idea if what I said is relevant, but you always make me think, Dave, Shanks!

Times like these... oh wait, does a knowledge of logic get a man laid a lot?
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Re: You Don't Know Jack

Postby NoShips on June 24th, 2017, 9:25 am 

Ok, since we have nothing to do (oops) now, thanks to you brainy dudes....

"There's nothing you can do that can't be done" - J Lennon

Is this a tautology? I'd try contraposition but it's late.

Is there anything that you can do that can't be done?

Does my ex-wife count?

And if you did it, what happens? And is it dangerous?

Or, in layman's terms, all you need is a bartender trained in formal logic.

Which, after all, is why we came here. Tee hee.
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