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This article was originally posted to vulcan-l.
From nobody Tue May 18 15:47:16 2004
From: Randall Raemon 
Newsgroups: alt.fan.surak
Subject: (AFS) FAQ - Logic Primer with addition, updated 10 June 2001
Date: Sat, 08 May 2004 23:18:02 -0500
Organization: vulcan-l mailing list
Message-ID: 
Lines: 477


This is a monthly FAQ posting from our own Rob Zook, with some
commentary updates by Dr. Saurabh Sikka, and with an addition 
by Susanne Liebscher on conditional reasoning. Editing and merging
the various postings is my work, and any resulting errors and 
misinterpretations are mine.

======================================================================
Hi all,

I wrote an introductory logic course for the Internet Starfleet
Academy, so I have shortened that and think it we should include
it in the FAQ.

Rob Z.

----------------------------------------------------------------------
Informal Logic Primer for Vulcan-l

x.0 Logic Terminology:

Informal logic concerns itself with the deductive argumentation one
finds in non-technical writing, like newspapers, popular media,
books or even in verbal situations like television news. So, while in
other branches of logic one can break arguments down into equations,
informal logic sticks to just evaluating an argument in words.

The fundamental unit of any logic is the proposition or statement, 
usually in the form of a declarative sentence. A proposition concerns 
itself with a meaning rather than specific sentence(s). Thus, "Today is 
my birthday" and "My birthday is today", although different sentences 
both describe the same proposition.

Logic concerns itself with the relationships between propositions, how
the truth of one relates to the truth of another. These relationships
take a form called an argument. An argument consists of a set of
propositions forming one or more premises, and a proposition which 
infers something from those premises - a conclusion.

The premise(s) support the inference claimed by the conclusion, and
the conclusion infers something related to the premise.

Learning to think logically first involves recognizing if an argument
has a valid form. If the argument has a valid form, then the argument
will reliable hold true if the premises also hold true. 

First one must identify that a potential argument has premise(s) and
a conclusion, and that the conclusion infers something related to the
premise(s). Next one can try and identify the argument as either a 
valid form, or as a fallicious form.

An argument has validity, if when the premises hold true, the
conclusion must hold true. If the premises can hold true, and the
conclusion can be false then the argument is fallicious.

In informal logic as we see most often on vulcan-l, it's usually
easier to identify an argument as fallicious rather than if it has
a valid form. So the majority of this primer lists the most common
forms of fallacy.

x.1 Fallacies:

We can divide fallacies into two catagories, fallacies of relavence
and fallacies of ambiguity. Fallacies of relevance occur in arguments
where the premises have little or no connection to the conclusion
because they have nothing or little in common with it. All the
premises can be completely true, and yet the conclusion can be
false, or, vice versa.  Fallacies of ambiguity involve the use of
words with two or more meanings in inconsistent ways.

x.1.1 Fallacies of Relevance:

x.1.1.1 Appeal to the People(argumentum ad populum):

In this kind of argument the speaker makes a highly emotional
statement and then tries to use peoples emotional agreement with
that statement as proof of their conclusion. For example:

Klingon's are cold-blooded murderers and pirates. 
We must never make peace with them.

That argument among the higher echelon of the Security Council and
Starfleet Command, kept the Federation from forming closer
relationships with the Klingon Empire, even though the premise
seems totally untrue and unrelated to the conclusion.

x.1.1.2 Appeal to Authority (argumentum ad verecundiam):

This type of fallacy includes the involvement of an expert in some
field, which has no relevance to the conclusion. Like a sports star
promoting the use of a financial plan, or a used car dealership.
This kind of fallacy finds prevalent use in the advertisement
industry, and in news reports.

Use Numbo drops for your cold 
because Jo-Jo the singing Targ uses them.

Joe Bloe Man-on-the-street says that the death penalty is wrong,
therefore the death penalty is wrong.

The use of authority in an argument will seem fallacious unless the 
authority has expertise in a subject relevant to the conclusion of the 
argument. For example, if I cite a conclusion in Astronomy based on the 
research done by a trained or knowledgeable Astronomer, then that would 
represent a valid use of authority in an argument.

And some commentary:

> The argument here is based on the premise that Jo-Jo's
> singing performance can be severly affected by his cold, and
> relieved by his use of the cold drops. Hence it is logical to
> conclude that anyone else who is incapacitated by cold may also
> benefit from the use of Numbo drops.
> 
> In such a case it would be illogical to depend on the doctor's
> opinion, because (assuming the drug has no serious side effects),
> it is basically patient relief that is the benchmark of the efficacy
> of a drug.  And of course, if the doctor himself uses Numbo drops
> for his cold, it would be a cast-iron argument in favor of the cold
> medicine.

x.1.1.3 Attacking the Speaker (ad hominem):

The opposite of the appeal of authority, an ad hominem fallacy 
seeks to support a proposition by making disparaging claims 
about an opponent which have nothing to do with the subject of 
the conclusion:

Fred says we should vote for amendment five, but he smells bad.

Now, if amendment five was bringing a waste processing facility 
into a residential area, and Fred cannot smell odors, then the 
author may have a valid point.

This kind of fallacy appears quite frequently in political 
propaganda.

x.1.1.4 Appeal to Ignorance(argumentum ad ignoratiam):

The authors of these kinds of fallacy wish us to agree with 
their conclusions because of the absence of any evidence one 
way or the other. Like this example:

No one has conclusively proven that stars are not 
living creatures. Therefore, stars are living creatures.

x.1.1.5 Accident:

This fallacy involves trying to apply a general rule to a 
specific case where it does not hold:

Vulcan's practice emotional mastery. 
Sybok is a Vulcan. 
Therefore, Sybok practices emotional mastery.

Certainly many, even most Vulcan's practice emotional mastery, but
that alone does not provide sufficient support to conclude that
any one Vulcan will practice emotional mastery.

x.1.1.6 Converse Accident:

The converse accident fallacy involves using a specific 
situation as evidence for a general rule:

Enterprise has the best chief engineer in all of Starfleet. 
Its chief engineer is Scottish. 
Therefore, Scots make the best chief engineers.

Here we have just the opposite, of fallacies of accident. Just the
fact that Scotty was both the best engineer in Starfleet (at the
time), and was born in Scotland, does not establish anything other
than that fact. So trying to use that fact alone to prove a general
rule is fallicious.

x.1.1.7 False Cause (Post hoc ergo Propter hoc/non causa pro causa):

Two kinds of False Cause fallacy exist. In the first, the 
conclusion seeks to establish cause based _solely_ on temporal 
relationship. In other words, it is argued that simply because 
one event occurred before another, the first event caused the 
second event.

I woke up and stubbed my toe on the doorway to the head, and 
then the ship shook. So, stubbing my toe on the doorway to the 
head caused the ship to shake.

The second kind of False Cause fallacy involves mistaking a false 
cause for the real cause:

When I go out for chocolate ice cream, my auto fails to start,
When I go out for vanilla ice cream, my auto starts fine,
Therefore, chocolate ice cream causes my auto to fail.

This argument represents a famous internet story, of someone who
calls up some large auto company, and complains that buying chocolate
ice cream prevents his car from starting. The auto company sends
an engineer out who discovers that car is getting vapor lock. Vapor
lock will normally correct itself given time. In the store where the 
customer bought his ice cream they kept the chocolate ice cream in a 
place closer to the door than the vanilla ice cream, so it took longer 
to buy the vanilla ice cream and the vapor lock was gone by the time
the customer finished buying the vanilla, but not when buying the
the chocolate.

Three things must exist for the _possibility_ of one thing truely
causing another. They must occur together (correlation), one must
precede the other in time (at least at non-quantum levels), and
one must eliminate any other possible cause. If any one of these
parts is missing, then one most likely does not have causation.

x.1.1.8 Begging the Question (petitio principii):

This fallacy involves using the conclusion of an argument as one 
of the premises. 

Polite Vulcans do not talk rudely to strangers, 
because that's not something polite Vulcans do.

Another term used for this type of argument: "circular reasoning".

x.1.1.9 Complex Question:

This occurs when the argument presupposes the truth of the 
conclusion implicitly. The 20th century earth comedian Groucho 
Marx demonstrated this fallacy in his wonderful line:

When did you stop beating your wife?
(1. If you stopped, you agree that you used to beat your wife)
(2. If you haven't stopped, you still agree that you beat your 
    wife)
(3. Therefore, you are a wife-beater)

x.1.1.10 Irrelevant Conclusion:

The fallacy here occurs when the conclusion tries to establish 
one truth, when it's premises support another:

Romulan Ale is wonderful stuff,
because it gives you a terrific hangover.

And some commentary: 

> Again, a bad example, because of semantics. Maybe it is the hangover
> of Romulan Ale that is the wonderful thing about it. Does the word
> 'hangover' necessarily mean 'headache'? Technically, no....just an
> extended period of effect of the ale. As such, having a long
> half-life of metabolism, the Romulan Ale might well provide a
> sustained 'high' and therefore be quite 'wonderful stuff'. The
> common 'hangover'  headache humans experience with alcoholic
> beverages only occurs due to the extended period of dehydration
> caused by the alcohol effect on the brain. Also, the residual effect
> of alcohol intoxication is not appreciated because the party mood
> has left the person, and he finds it irritating in the morning.
> What if one chooses not to, and enjoy that as well?

x.1.2 Fallacies of Ambiguity:

x.1.2.1 Equivocation:

In an equivocation fallacy one uses one meaning of an ambiguous 
word in a proposition, but uses a different meaning of the same 
word in a different proposition.

Really exciting novels are rare. But rare books are expensive. 
Therefore, really exciting novels are expensive.

Here the word rare refers to the "scarcity" of finding exciting 
novels in the first premise, while in the second it means 
"Excellent or extraordinary".

x.1.2.2 Amphiboly:

Amphiboly occurs when the grammar of a premise creates ambiguity 
even when the individual words do not. Thus when Groucho Marx 
says, "I shot an elephant in my pajamas,", his punch line, 
"How he got in my pajamas, I'll never know," seems understandably 
surprising, since one would not expect that kind of inferred 
conclusion. One would expect Groucho was in his pajamas.

x.1.2.3 Accent:

Fallacies of accent arise when a shift in emphasis or tone 
changes the meaning of a statement. Many times news reporters 
misquote others using this kind of fallacy.

Jesus said, "Love thy neighbor as thyself." 
Thus we we should all have sex with our neighbors.

When the speaker shifts the emphasis to the word neighbor, he can 
imply a different meaning to the word love than Jesus probably
intended. 

x.1.2.4 Composition:

Composition fallacies involve the inference that because every 
member of a class possess some attribute that the class itself 
possess the attribute.

I formed my logic faultily, therefore logic failed me.

x.1.2.5 Division:

Conversely, a division fallacy occurs when one tries to conclude 
that every member of some class possesses an attribute of the 
class

Snow Leopards are dying out. 
Simba is a snow leopard. 
Therefore, Simba is dying out.

And some commentary:

> Semantics! First of all, we are all dying. The individual creature,
> be it encased in human, Vulcan or snow-leopard appearance, experiences
> the 6-fold change in body, viz.  birth, growth, sustainance, disease,
> degeneration and death.  So not only snow leopards, but all humans
> are also dying. We are not dying out of existence, but if our race
> is, so will we. Who will Simba mate with? He must mate with another
> of the same species before he dies, or the snow leopards will become
> extinct. Therefore the survival of the individual is dependent on
> that of his race, and vice versa.  Better not to use such extreme
> examples.  A better example would be:
> 
> Human are reproducing very fast.
> Fred is a human.
> Fred is reproducing very fast.
> 
> Fred might well be a celibate monk! or a 2 year-old
> child.

x.2 Semantics:

One final thing to beware of when arguing logically: does the
dispute really concern the truth of an argument, or could some
hidden ambiguity cause a misunderstanding. 

A genuine disagreement occurs when both parties disagree on the
truth value of an argument and they both agree on the meanings of
all the words involved in the argument.

Sometimes comparing how each person interprates key terms
in an argument can reveal they use very different meanings. In
which case the dispute maybe purely verbal, and once they agree on
common meanings the dispute is resolved.

====================================================================

> Message-Id: 
> Date: Fri, 06 Apr 2001 13:01:52 +0200
> From: Susanne Liebscher 
> To: vulcan-l\@shikahr.com.inter.net
> Subject: Reasoning (long) [ slightly edited for inclusion in the FAQ ]

Greetings!

I'd like to propose an extension to the logic-faq. 

Conditional reasoning: 
----------------------

Assumption:
If it rains then the street is wet.
If      p   then        q         .

Modus Ponens:
 It is raining therefore the street is wet.
        p      =>          q

Modus Tollens:
 The street isn't wet so it isn't raining.
     not q            =>     not p

Modus Ponens and Modus Tollens are correct forms of conditional
reasoning. Most people get the first one right but the second is
obviously more complicated as psychological research shows. Often people
produce the following:

Denial of the Antecedent: 
 It isn't raining therefore the street isn't wet.
     not p        =>        not q
(Wrong -- The street could be wet because of damage to some water pipes
or because it is cleansed.)

Acceptance of Consequent:
 The street is wet so it is raining.
       q           =>        p
(Wrong -- Same reasons as above.)

Psychologists explain this phenomenon with a general tendency in Human
beings to make conclusions that equal the statement. So e. g. if the
statement is negative the conclusion is negative (not p => not q). But
they also say that isn't this bad because the Modus Tollens is very rare
in real life. So it's probably an evolutionary adaption.

Forms of Reasoning:
-------------------
 
There are three kinds of reasoning: 
   - induction 
   - deduction 
   - abduction 

Assumptions:
1. All balls in the green box are red.(all-statement)
2. This ball is from the green box.   (case, instance)
3. This ball is red                   (evidence or sypmtom)

Deduction:

You need 1. and 2. From the general (All balls...) you draw an
conclusion for a certain instance (This ball...)

  All balls in the green box are red.
  This ball is from the green box.
  -----------------------------------
  This ball is red.

Such conclusions are always true.

Induction:

You need 2. and 3. From one instance (This ball...) you conclude of the
general (All balls...) If you'd like to have a good hypothesis you
should take more than one instance.

  This ball is from the green box.
  This ball is red.
  --------------------------------
  All balls in the green box are red.

An example from reality: Many people think that all swans are white
until they encounter a black swan. But the new hypothesis that swans can
be black or white must not necessarily be true even if all swans that
live today are black or white. We can never know if somewhere in the
future there will be swans which are colored in another tone. (Or maybe
the first swan was pink.)

Such conclusions *could* be true. You never know. You can't prove
they're right. You can only falsify them with an example that disproves
them. 

Abduction:

You need 1. and 3. From the general (All balls...) and something you
know about the instance you conclude a possibility.

  All balls in the green box are red.
  This ball is red.
  -----------------------------------
  This ball is from the green box.

Exactly you should say: This ball could be from the green box.
Abduction is something that is seldom part of scientific research.
But it could be that it is useful for everyday life. Imagine you
go to the doctor. Your doctor only asks you some standard questions
(temperature, how high, how long, pains...) In order to come up
with a theory about your illness according to probability s/he'd
have to ask you all parameters that could be important for all
illnesses in the world since conditional probability calculation
(Bayes formula) needs completeness. An example:  You have high
temperature and you tell this to your doctor. S/He'd probably think:
could be a flu or a simple cold, and start asking questions that
go in this direction, distinguishing between the two.  S/He oviously
has a theory before s/he starts asking! But scientificaly a theory
is only to be formed after all data is available! So first asking
and then theorizing! And now you tell that you had been on a safari
in Africa last week. Probably s/he would assume that it has something
to do with your illness. Another theory! The right form of asking
would be one question after the next maybe for hours and after
that: It's ... It's clear that this is impracticable.
(I don't know if I succeeded to make clear what I mean.)


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