Examples of Arguments Lacking Horizontal Integration

[Vik]

I am looking for examples of deductive arguments where:

• the premises are true
• the conclusion can be "deduced" from the premises if you forget the rest of human knowledge
• the conclusion is false

Units fitting these criteria would help me distinguish good applications of logic from bad "logic" (e.g. context dropping)

[ruveyn1]

I am looking for examples of deductive arguments where:

• the premises are true
• the conclusion can be "deduced" from the premises if you forget the rest of human knowledge
• the conclusion is false

Units fitting these criteria would help me distinguish good applications of logic from bad "logic" (e.g. context dropping)

There are only two origins of unsound arguments:  1. false premises  and 2.  invalid inference.

 

ruveyn1

[Vik]

I want to emphasize that I am not talking about unsound arguments (where a premise is ambiguous or false).

 

I am talking about arguments where the premises are true, the conclusion is a consequence of the premises, but the conclusion is false.

 

For those unfamiliar with the distinction between horizontal integration and vertical integration:

 

Vertical integration is a process where facts are integrated along the hierarchy of knowledge.  example:  when you subsume a new fact under an established genus to produce a minor premise, e.g. Socrates is mortal.

 

Horizontal integration is the integration of a fact with the rest of one's knowledge. Examples:

• identification of a corollary of some principle, i.e. as an implication rather than a theorem
• spiral learning — integration of new knowledge with familiar context (i.e. new knowledge about previously known something)
• explanation of an effect in terms of what is known
• grasping an existent as part of a system

[FrolicsomeQuipster]

In haiku form:

 

I like presents.

Everyone should give me presents

Bow before me.

[ruveyn1]

In haiku form:

 

I like presents.

Everyone should give me presents

Bow before me.

The syllable count is off.  Haiku has three lines with a syllable count of 5, 7, 5

 

Fix up your syllable count and you will have Hiaku.

 

ruveyn1

[Nicky]

I am looking for examples of deductive arguments where:

• the premises are true
• the conclusion can be "deduced" from the premises if you forget the rest of human knowledge
• the conclusion is false

Units fitting these criteria would help me distinguish good applications of logic from bad "logic" (e.g. context dropping)

An example of context dropping would be starting with the true premise that the average shark can life for 20 years in the ocean, and concluding that the average shark can live for 20 years in the Atacama desert.

 

However, that is not an example of correctly deducing a false conclusion from a true premise. There's no such thing.

[Eiuol]

Swiss cheese has holes.

The moon has holes.

Therefore, the moon is made of swiss cheese.

[Grames]

All men are mortal.

Socrates is a man.

Therefore Socrates is mortal.

 

The kicker indicating further horizontal integration (that there is something more to learn) is needed would be if Socrates never died and is now thousands of years old.

[ruveyn1]

All men are mortal.

Socrates is a man.

Therefore Socrates is mortal.

 

The kicker indicating further horizontal integration (that there is something more to learn) is needed would be if Socrates never died and is now thousands of years old.

If one or more of the premises of a syllogism is false  all bets are off.  In order for the conclusion to be proven true  (1) the premises must be true and (2) the form of the argument must be valid.  Anything less leads to no conclusions.

 

ruveyn1

[Grames]

If one or more of the premises of a syllogism is false  all bets are off.  In order for the conclusion to be proven true  (1) the premises must be true and (2) the form of the argument must be valid.  Anything less leads to no conclusions.

 

ruveyn1

I would NOT leap to the conclusion that one of those premises (either 'All men are mortal' or 'Socrates is a man') premises is outright false.

 

Another example would be the blood types from OPAR chapter 5, where the topic was 'context'.   Horizontal and vertical integration are just two ways to further analyse the idea of context.

[Nicky]

Swiss cheese has holes.

The moon has holes.

Therefore, the moon is made of swiss cheese.

That's just an example of faulty logic. 

I would NOT leap to the conclusion that one of those premises (either 'All men are mortal' or 'Socrates is a man') premises is outright false.

You should. Something is either true or false. It isn't true and false, semi-true, semi-false, not outright false, etc. 

 

Yes, "true" means "true given a context", but that doesn't change the fact that what's true is true, and what's false is false. In this case, the statement "all men are mortal (where by mortal you mean that someone only lives 80 or so years)", would be false within the context provided (implied, actually, as being the context of human existence up to this point in time). Outright false. 

Edited February 17, 2013 by Nicky

[bert]

For those unfamiliar with the distinction between horizontal integration and vertical integration:

 Not trying to sidetrack the thread but I'm not completely clear on the distinction. Would an example of horizontal integration be relating "all men are mortal" to the mortality of other organisms? I think I remember hearing this somewhere.

 

 

spiral learning — integration of new knowledge with familiar context (i.e. new knowledge about previously known something)

When one deduces Socrates is mortal, isn't that an example of this? Isn't it integrating new knowledge (Socrates is a man) with a familiar context (All men are mortal)? 

[Eiuol]

That's just an example of faulty logic.

It still fits what Vik is looking for. The premises are true, you can deduce the conclusion, but it is false. The only way to reach the conclusion is by dropping context or ignoring knowledge. I say it is a failure of horizontal integration for any of number of reasons. You certainly couldn't say it is obviously true or obviously false. It's faulty logic also because just because two things share a property doesn't make them the same, but can't disprove that the moon is made out of cheese with the deduction. You would have to integrate other knowledge, such as cheese is man-made from cows, so you would not find such a thing in space, formed naturally.

 

(It actually might not be what Vik is looking for after I talked to him in chat.)

Edited February 17, 2013 by Eiuol

[Grames]

...(where by mortal you mean that someone only lives 80 or so years)...

True, but that is not the literal meaning of mortal, which only implies 'subject to death' or 'can die'.

[thenelli01]

P1: If someone yells at you unjustly, then you should not sanction it with friendliness.

P2: This customer at the job I work at yelled at me unjustly. 

Conclusion: I should not sanction it with friendliness.

 

Context dropped: The terms of which you accepted employment. The fact that you are required, by accepting work there, to respond with friendliness to customers, even rude ones.

Edited February 23, 2014 by thenelli01

[Nicky]

All men are mortal.

Socrates is a man.

Therefore Socrates is mortal.

 

The kicker indicating further horizontal integration (that there is something more to learn) is needed would be if Socrates never died and is now thousands of years old.

 

 

P1: If someone yells at you unjustly, then you should not sanction it with friendliness.

P2: This customer at the job I work at yelled at me unjustly. 

Conclusion: I should not sanction it with friendliness.

 

Context dropped: The terms of which you accepted employment. The fact that you are required, by accepting work there, to respond with friendliness to customers, even rude ones.

 

 

For both of these, the context change doesn't just falsify the conclusion, it also falsifies the premise, making the deduction faulty. They're not examples of reaching a false conclusion from a true premise, they're examples of two separate attempts at deduction, in two separate contexts: first deduction correct, second faulty. 

 

In the first context, Socrates is dead, therefor the deduction is correct. In the second one, he's alive, therefor the premise is false. Same with thenelli's example: in the first context, we're talking about a world where there are no work obligations, so the premise and conclusion are both true. In the second context, the premise is false because sometimes you should respond with friendliness to someone who yells at you.

 

Deductions can only be made in a specific context. What is true in one context may not be true in another, so of course anything deduced from it might be false as well. Of course if you change the context, you can reach false conclusions. But you do so by making the premise false, not deduction itself.

[theestevearnold]

In haiku form:

I like presents.

Everyone should give me presents

Bow before me.

I believe haiku require four lines. I aint no naive poet. R U a poet?

I, in the greatest sense of I, (not in the common courtesy of Japan--though, bein born n raised in Hawaii, I share much of their culture, like takin my shoes of before enterin your home and preferrin white rice with meat instead of potatoes) require more than a haiku-ish dictate) shall consider a metaphorical bow if you show me your greatness as a philosopher the way AR did. Or if you have written a great song. Or painted a great picture. Or written a great novel

Why should I bow to you?

Edited February 23, 2014 by theestevearnold

[theestevearnold]

I believe haiku require four lines.

Three lines was correct for haiku, but the syllabic meter requires a 5/7/5.

Try karaoke. It's fun.

Regarding the OP: if you don't drop context, you're problem is non-occuring in reality.

Edited February 23, 2014 by theestevearnold

[Harrison Danneskjold]

p-  Whatever is profitable is also moral

p-  Organs can be sold for astronomical profit

C-  It is moral to sell all of your internal organs

 

The horizontal misintegration is in the implicit definition of "profit" as restricted exclusively to finance.  The first premise can actually be completely in line with rational selfishness, depending on the specific referents of "profit".

If you replace "your internal organs" with "other peoples' organs" then you've got the reasoning behind all organized crime, summarized in a single syllogism; the mistake is identical.

[Harrison Danneskjold]

p-  It's wrong to end peoples' lives

p-  Animals have lives too

C-  It's wrong to end animals' lives

 

The misintegration is a mistake of relevance.

[Vik]

p-  Whatever is profitable is also moral

p-  Organs can be sold for astronomical profit

C-  It is moral to sell all of your internal organs

 

The horizontal misintegration is in the implicit definition of "profit" as restricted exclusively to finance.  The first premise can actually be completely in line with rational selfishness, depending on the specific referents of "profit".

If you replace "your internal organs" with "other peoples' organs" then you've got the reasoning behind all organized crime, summarized in a single syllogism; the mistake is identical.

 

This is a good one.

[Vik]

p-  It's wrong to end peoples' lives

p-  Animals have lives too

 

No conclusion is possible from these premises.

[Harrison Danneskjold]

Sorry; got slightly carried away.

[ReasonFirst]

@Grames

Quote

I would NOT leap to the conclusion that one of those premises (either 'All men are mortal' or 'Socrates is a man') premises is outright false.

 

Another example would be the blood types from OPAR chapter 5, where the topic was 'context'.   Horizontal and vertical integration are just two ways to further analyse the idea of context.

You mentioned you would not regard the "All Men are Mortal" generalization as "false" if Socrates never died just that it would mean there would be "more to learn."  I remember Dr. Peikoff mentioned something similar like that if I "happen to observe Socrates go on forever and ever and ever" I would "have to integrate the fact that Socrates has never died" to the syllogism you mentioned.  There is a lot about this imaginary scenario that is left unsaid though.  Firstly, a long time (thousands of years) is not actually forever and ever and ever.  Also, Dr. Peikoff did not mention if, in this scenario, I observed Socrates to be aging or not (I am not clear if you implied it when you brought it up, you did mention that Socrates was "thousands of years old" so I am not sure if you are stating that he has been observed to be aging).  Thirdly, I would argue the "All Men are Mortal" generalization never actually specifies how long it should take for a man to perish.  At the stage when you integrate it to machines wearing out, all you would conclude is something like "the human body is heading toward collapse."  So it just means that he will perish someday in the future.  So if you observe him to live for thousands of years, you should still be able to rely on deducing from the knowledge that the process of life causes aging and Socrates will one day perish.  Would this not also be a horizontal integration?

Edited September 7, 2024 by ReasonFirst

[Doug Morris]

On 2/17/2013 at 2:04 AM, Vik said:

I want to emphasize that I am not talking about unsound arguments (where a premise is ambiguous or false).

  On 2/28/2014 at 7:15 PM, Harrison Danneskjold said:

p-  Whatever is profitable is also moral

p-  Organs can be sold for astronomical profit

C-  It is moral to sell all of your internal organs

 

The horizontal misintegration is in the implicit definition of "profit" as restricted exclusively to finance.  The first premise can actually be completely in line with rational selfishness, depending on the specific referents of "profit".

If you replace "your internal organs" with "other peoples' organs" then you've got the reasoning behind all organized crime, summarized in a single syllogism; the mistake is identical.

On 2/28/2014 at 9:15 PM, Vik said:

This is a good one.

Actually, this is an example where a premise is either ambiguous or false, due to switching or sloppiness in the definition of "profit".