Logical Fallacies

Date: 01/29/2001 at 03:17:37
From: Scavenger
Subject: Logical Fallacies

I am having an argument with someone about logic. I have been arguing 
that fallacious arguments (as in the argumentum ad ignorantiam) are 
representative of ILLOGIC.

For instance, the statement: "God does not exist" is a positivist 
assertion (aka argument) that is a fallacy by dint of being made from 
ignorance.

My respondent says no, the statement itself is "logical" but that any 
"argument" stemming from it will be the fallacy and illogical because 
it is then that it is considered "from ignorance."

My contention is that the statements themselves are the argument/
assertion, and that in order to examine whether or not any given 
statement is logical or illogical, we must understand the terms and 
meanings and simultaneously look for fallacies - thus the statement 
is, on the face of it, illogical.

The best I can offer my opponent is that the statement, if not to be 
considered for the inherent definitions of the terms involved, is 
nonsensical (because once forbidden to consider the term meanings, how 
can any status of logic be derived?) or, at the very best, "alogical," 
meaning that it has no logic or illogic because it is a statement 
bereft of enough information to determine whether it is even a 
fallacy.

In a nutshell: Are logical fallacies considered examples of illogic, 
and how does one determine whether a statement is logical or not when 
one is charging an opponent with the argumentum ad ignorantiam 
fallacy, if the opponent refuses to admit anything beyond the basic 
positivist assertion/statement? (i.e. won't submit to examination for 
the ignorance of the statement, thus imbuing the statement with 
illogic by hindsight, I guess)?

Help.

Date: 01/29/2001 at 15:00:30
From: Doctor Ian
Subject: Re: Logical Fallacies

Hi Scavenger, 

The first thing you need to understand is that logic can't tell you 
whether something is true or not. It can only tell you whether 
particular conclusions can be reached from particular premises by 
following particular rules of derivation. 

This means that a valid argument can yield a false conclusion, if its
premises are false.  For example, this is a valid argument:

  1. Some turtles play golf. 
  2. Any animal that plays golf is a mammal.
  3. Therefore, some turtles are mammals.

Of course, no turtles are mammals, but given the premises as stated, 
the argument is perfectly valid.  

In general, 'illogical arguments' are arguments in which one or more 
of the rules of logical derivation (e.g., modus ponens) have been 
broken; 'alogical arguments' are arguments in which the rules of 
logical derivation are not held to be applicable (e.g., 'arguments' 
based on intuition, or faith, or authority), while 'false arguments' 
are arguments that have been used to reach false conclusions.  

Illogical and alogical arguments can reach true conclusions (since 
they can, in fact, reach any conclusions at all, starting from any 
premises); and logical arguments can reach false conclusions (since 
they can, in fact, be based on false premises).  

In the case of something like 'God does not exist', that by itself is 
not an argument at all, but merely an assertion, which means that the 
concepts 'illogical', and 'alogical' don't really apply to it.

The assertion might be a premise in an argument, and if the rules of
derivation are followed scrupulously, the argument will be valid... 
but the truth of the conclusion will depend on the truth of the 
premise, which remains unestablished.  

Or the assertion might be the conclusion of some argument that you 
haven't shown me, in which case it might be the true conclusion of a 
valid argument; the true conclusion of an invalid argument; the false 
conclusion of a valid argument; or the false conclusion of an invalid 
argument. There is no way to determine that by looking at the 
assertion itself. 

Let me emphasize again that logic does not have the power to support
statements like 'X is true'.  It only has the power to support 
statements like 'IF premises A, B, and C are true, then conclusion X 
is also true'.  

So long as you keep that limitation firmly in mind - and the easiest 
way to do that is to make sure that you always summarize your 
arguments by saying 'From premises blah, blah, and blah, I conclude 
yadda, yadda', which keeps everything out in the open, where it 
belongs - you should be able to avoid disagreements like the one that 
you're currently mired in.  

In a nutshell: If you agree on the premises, but disagree on the
conclusion, then to refute the argument as 'illogical' you need to 
point to the rules that were broken during the derivation. But if you 
disagree on the premises, then there's no point in even discussing the 
conclusion. If you don't accept some assertion as a premise, then you 
have the right to ask your opponent to derive the assertion as a 
conclusion, starting from some premises upon which you both agree, and 
following rules of derivation upon which you both agree.   

Eventually, one of three things will happen. 

   (1) You will be able to find a mutually acceptable set of premises 
and rules, and you will be unable to find a step in the derivation 
that breaks any of the rules. In this case, you must accept your 
opponent's argument as both valid and true.

   (2) You will be able to find a mutually acceptable set of premises 
and rules, but you will be able to find a step in the derivation the 
breaks a rule. In this case, you can denounce your opponent's argument 
as invalid, and therefore as possibly false.

   (3) You will be unable to find a mutually acceptable set of 
premises and rules. In this case, you can only agree to disagree, on 
the grounds that you have incompatible world views (although a duel 
might be in order). 

I hope this helps.  Write back if you'd like to talk about this some 
more (for example, if you think I haven't really understood your 
question), or if you have any other questions. 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/