A mistake the book?

Philosophical, mathematical and computational logic, linguistics, formal argument, game theory, fallacies, paradoxes, puzzles and other related issues.

A mistake the book?

Postby BadgerJelly on March 8th, 2018, 1:47 am 

I have just read something from "The Cave and The Light" by Arthur Herman and I am taking the firm stance that it is a horrible mistake.

Sorry, on phone so "quoting" is an issue:

"All human beings are rational.
Some human beings are American.
Therefore, some Americans are rational."

And the funny thing is ... now that I've just typed this out I now see that it is actually correct! Haha!

The problem is what we understand an American to be. I am assuming all Americans are human, but the logical statements are arbitrary, in the sense that we come to the statement with semantic knowledge, so whilst we can say that the statement is "true" in a purely logical sense (ignoring the semantic weight of particular terms of category) it is also contradictory because we know well enough that Americans are all human so all Americans must be rational according the first statement.

I think this example show well the easy misconceptions that pop up in logic. The first two statements must be taken together and bracketed out from any other inference. The problem then is the value of the statement becomes completely mute.

What the statements really say, ignoring the American/human issue, is that some Americans are definitely rational and the rest of the Americans we cannot comment on and that can wrongly be taken to insinuate that the "other" Americans are not rational when in fact no such conclusion is apparent and we merely fall prey to our automatic bias of placing every item of experience into direct polar opposition.

I found this interesting, yet all too obvious.

Note: I did not make up the start for effect. I literally thought it was wrong! Haha!
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Re: A mistake the book?

Postby -1- on November 15th, 2018, 6:39 pm 

Very, very important for those studying syllogisms, to consider that in syllogisms "some" means "at least one". It is easy to misconceptualize that it means "at least two", because it draws the verb in the plural. But it has been established by the Greeks, starting with Aristotle, and has been accepted in a consensus, that "some" means "at least one".

From the syllogism quoted, there is a conclusion "All Americans are rational", but if all Americans are rational, then some Americans are also rational. "Some" means "At least one", and there is no upper limit. If all Americans are rational, then it's necessarily true that at least one American is rational. This presupposes that there is a number of Americans, and that number is not zero.

If you say
"Some Americans are rational
All Americans are humans
Therefore some humans are rational"

Then in the first premise you leave the possibility (without absolute certainty) open that not ALL Americans are rational.

The problem with syllogism is that it is not the same as set theory and though syllogisms can be illustrated as Venn diagrams, syllogism differ somewhat from set theory.

For instance, in set theory you can establish exact numbers other than zero, greater than zero, and all. In syllogisms you are restricted to these only three.

For instance, in set theory you can say "I got ten chickens, five red ones, seven that are each over ten lbs in weight, and some that are not red and under ten lbs each." In the language of syllogism, you can only say "I got some red chickens, some chickens that are over 10 LBS each in weight, and some chickens that are under ten lbs and not red."
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Re: A mistake the book?

Postby Serpent on November 15th, 2018, 8:05 pm 

BadgerJelly » March 8th, 2018, 12:47 am wrote:
"All human beings are rational.
Some human beings are American.
Therefore, some Americans are rational."

And the funny thing is ... now that I've just typed this out I now see that it is actually correct! Haha!

Correct as to the conclusion.
The syllogism is valid, the logic is valid - but these things always depend on the assumptions used as premises. Premise 2 is provably correctly; Premise 1 is not.
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Re: A mistake the book?

Postby wolfhnd on November 16th, 2018, 12:38 am 

The implication in the statement is that some Americans are not human because unless all Americans are rational that would mean some are not human. Pretty clever subliminal manipulation to make a propagandic message appear as a simple mistake without reducing it's emotional impact.
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Re: A mistake the book?

Postby BadgerJelly on November 16th, 2018, 3:28 am 

Yeah, it’s basically avoiding saying that all Americans are human. We tend to imply this to be the case yet in the premises set out this is not the case.

I’ve been arguing elsewhere about the use of logic in common speech but it appears some people refuse to see beyond the logical propositions and take any old opinion to be a means to creating a sound argument.

If we were to simply replace the American, human, and rational with an arbitrary X, Y and Z then no one would concern themselves with the meaning behind the terms X, Y and Z. The “social weight” of “human,” “American” and “rational” hide the obvious logic due to the emotional reaction to the words.
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Re: A mistake the book?

Postby Serpent on November 16th, 2018, 10:57 am 

Buffalo, coyotes and iguanas are American. Chances are, they're also rational, but that's not stated.
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Re: A mistake the book?

Postby wolfhnd on November 16th, 2018, 11:04 am 

Serpent » Fri Nov 16, 2018 2:57 pm wrote:Buffalo, coyotes and iguanas are American. Chances are, they're also rational, but that's not stated.


You finally have come to accept your place in the universe as one among many rational beings? :-)
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Re: A mistake the book?

Postby Serpent on November 16th, 2018, 1:03 pm 

wolfhnd » November 16th, 2018, 10:04 am wrote:
You finally have come to accept your place in the universe as one among many rational beings? :-)

Not at all. If you check above, it was Premise #1 I considered incorrect. Humans are the only irrational animal on this planet, with chimpanzees exhibiting the odd lapse. I have never made a secret of my low opinion of human sanity.

As for the universe, there must be many thousands of intelligent species out there, but we'll never know how many are rational.
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Re: A mistake the book?

Postby -1- on November 20th, 2018, 9:48 am 

Very, very important for those studying syllogisms, to consider that in syllogisms "some" means "at least one". It means nothing more, and it means nothing less.

The syllogism's two premises allows the conclusion "Therefore all Americans are Rational." But it also allows "Therefore some Americans are rational."

Why? because "some" means "at least one." You MUST see, that if all Americans are rational, then at least one is also rational. (Since all of them are rational, there is no way that less than one can be rational.)

Forget your previous witticisms and explanations.

It is horribly misguided what you say. Please check and verify if you like (in fact, I urge you to do this) that what I said is right. I am not a researcher, so I am not going to scour the literature for this. But it is right. I studied syllogisms extensively. So please please please believe me or else check reliable and dependable outside sources.

This what you guys wrote above, is painful. My opinion is not meant as a put-down, but if you know syllogisms, then you realize that immediately.
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Re: A mistake the book?

Postby BadgerJelly on November 20th, 2018, 10:49 am 

-1-

What I said was correct. I was merely pointing out that if it said All “woodles” then no one would have anything to say. The problem people have is with the semantic weight of “American.”
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Re: A mistake the book?

Postby Serpent on November 20th, 2018, 12:47 pm 

-1- » November 20th, 2018, 8:48 am wrote:
The syllogism's two premises allows the conclusion "Therefore all Americans are Rational." But it also allows "Therefore some Americans are rational."


All includes some, but some does not include all. Your use of the word 'some' is correct in the context of an indefinite/unknown quantity of items, but incorrect in a context where it refers to parts of a whole.
The statements "I ate a few of the candies," "I ate some of the candies," "I ate most of the candies," and "I ate all the candies" do not convey the same message, even if 'few', 'some' and 'most' are included in all, because these are indefinite comparative terms relating to a definite whole.
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Re: A mistake the book?

Postby -1- on November 20th, 2018, 3:37 pm 

Serpent » November 20th, 2018, 12:47 pm wrote:
-1- » November 20th, 2018, 8:48 am wrote:
The syllogism's two premises allows the conclusion "Therefore all Americans are Rational." But it also allows "Therefore some Americans are rational."


All includes some, but some does not include all. Your use of the word 'some' is correct in the context of an indefinite/unknown quantity of items, but incorrect in a context where it refers to parts of a whole.
The statements "I ate a few of the candies," "I ate some of the candies," "I ate most of the candies," and "I ate all the candies" do not convey the same message, even if 'few', 'some' and 'most' are included in all, because these are indefinite comparative terms relating to a definite whole.

Serpent: you make the fatal mistake of using common English. For the third time (and please check for verification of this, I am not going to say it again): :(

"SOME" IN SYLLYGISMS MEANS EXACTLY AND PRECISELY, NOTHING MORE AND NOTHING LESS, THAN "AT LEAST ONE".

Now try your exercise with this in mind.

Instead of arguing with me, please someone verify my claim. I am not saying it out of the top of my head. This is how syllogisms use "some". You can argue 'till you are blue in the face, but that's not going to change the meaning of "some" as used in syllogisms.

I'm exiting this thread. If you guys can't be diligent enough to hear my plea for the third time, and my trying to tell you how to read syllogisms falls on deaf ears, then I'm obviously totally wasting my time here.

"When the student is not ready, (for instance, because of his/her obstinate stubbornness) then the teacher stays ineffective."
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Re: A mistake the book?

Postby Serpent on November 20th, 2018, 4:24 pm 

Big red font doth not proper usage make. Nor, indeed, does a blue redundant flounce.

When applied to a known composite entity, such as Americans, the word "some" remains relative, meaning, in this case, "more than one, but not all, of 327,653,066".
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Re: A mistake the book?

Postby TheVat on November 20th, 2018, 5:35 pm 

Some days I want to channel my inner Addison DeWitt. The problem lies in the syllogism being vacuous.

If we take the original form...

All human beings are rational.
Some human beings are American.
Therefore, some Americans are rational.

...and explicate each term, we get....

All human beings are rational.
Some human beings live in America and are called Americans.
Therefore, some human beings who live in America are rational.

So the syllogism reduces to...

All human beings are rational, therefore
some human beings are rational.

Well, true, yes, but vacuous.
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Re: A mistake the book?

Postby Serpent on November 20th, 2018, 7:43 pm 

What's the point of a "therefore" clause in stating that all includes some?
Premise one, being all-inclusive, is the only relevant statement.

I thought a syllogism was intended to be the logical deduction of a conclusion from two or more premises that are given as true or assumed. There is no logical deduction in reducing premise #1. to a portion of premise #1, with premise #2 giving no additional information.

All humans are rational.
Americans are human.
Therefore, some rational beings live in America.

is true and valid.
Last edited by Serpent on November 20th, 2018, 8:02 pm, edited 1 time in total.
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Re: A mistake the book?

Postby Serpent on November 20th, 2018, 7:58 pm 

Sorry - accidental replication collateral to editing.
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