Friday, December 27, 2013

Deductions about Deductive Arguments

Logic is a bit outside of the basic topic of this blog, but I haven’t been blogging much over the last couple of months and I am teaching logic this next semester.  Bear with me.  It does have some relevance to things I have been writing about here. 
I have always included a little basic logic in my Introduction to Philosophy course.  One thing that always troubled me was a difficulty in defining deductive arguments.  The standard definition goes like this:
A deductive argument is one in which it is claimed that the conclusion follows necessarily from the premises.
Unpacking that, “follows necessarily” means that it is logically impossible for the premises to be true and the conclusion false.  The meaning of “claimed” is more difficult.  It seems to be included in the definition to make it easier to define an invalid argument. 
An invalid argument is a deductive argument in which, even if the premises are true, it is still possible for the conclusion to be false. 
Now suppose you wanted to define a deductive argument without the “claim” part:
A deductive argument is one in which the conclusion follows necessarily from the premises.
That would result in a contradiction in the definition of an invalid argument.  Yet we clearly want “invalid arguments” to be deductive arguments that fail and not arguments that fail to be deductive.  The standard definition of deductive argument attempts to avoid this by including the reference to a claim. 
The problem I have with that is that it runs a serious risk of transforming any argument into a deductive argument if only someone claims that it is one.  Thus “the pavement is wet so it must have rained” becomes deductive if I claim (falsely) that the conclusion follows necessarily from the premise.  If we are to allow for the existence of failed deductive arguments, we must presumably include the intention of the argument in the definition; however, if we “deductive” to be an objective characteristic of an argument, then it cannot ride solely on intention.  Above all, we don’t want to christen any argument as deductive merely because it is called so. 
I suggest the following resolution by means of an analogy.  Consider the following scenario:
I believe that I will someday rob a bank.
Can you conclude from this alone that I am guilty of a crime?  I submit that you cannot.  What about this scenario?
I intend to someday rob a bank.
Knowing that I have formed such an intention, but knowing nothing else, can you conclude that I am guilty of any crime?  Again, I say not.  You may come to some unfavorable conclusions about my character, but nothing more. 
I plan to rob a bank; I have purchased a gun and a ski mask; I have discussed my plans with several partners. 
Now we have the makings of a good case for a conspiracy to commit robbery.  Even if I haven’t gone through with it yet, I am very probably guilty of a crime.  On the other hand:
I have purchased a gun and a ski mask and I have discussed the act of robbing a bank with several others; however, we have no plans to actually rob a bank. 
Without the actual intention, I might be nothing more than a would-be mystery writer who wants to stimulate his imagination.  I am guilty of nothing.  A genuine crime would seem to require that a genuine intention be expressed in some kind of action, even if the action involves only preliminary steps and planning. 
Using this analogy, I think we can understand what it means to commit a deductive argument, valid or invalid.  Arguments are mental actions.  Some arguments result in physical actions, as when I conclude that eating nuts is good for my health and then actually eat nuts.  Some do not, as when I conclude that there is no life on Mars.  I wasn’t going there anyway. 
A genuine deductive argument must be read as an expression of a certain intention: to logically guarantee some statement by inference from some statement or statements.  Only if my intention is expressed in the form of the argument can the argument be identified as genuinely deductive.  This may sometimes involve judgment calls, but there are at least some cases where objective verification is possible.  For example:
All mammals are animals.  My pet is a mammal.  Therefore it is an animal. 
While it is not impossible that such a series of statements is random, it is safe to assume that it expresses my intention to draw a necessary conclusion from two premises because this makes a genuinely valid argument.  If the premises are in fact true, the conclusion does necessarily follow.  Valid arguments are the easiest case.  What about this one:
All mammals are animals.  My pet is an animal.  Therefore it is a mammal. 
This argument is rather obviously invalid.  My pet might be an alligator: an animal but not a mammal.  Yet its structure suggests that I was aiming at certainty rather than probability.  This is a frequently committed fallacy: confirming the consequent.  That it has such a title means that we can recognize it as a failed attempt to construct a valid deductive argument. 
Returning to our first definition:
A deductive argument is one in which it is claimed that the conclusion follows necessarily from the premises.
We can now understand the meaning of claim to involve not only the motive or conception that the person making the argument may have, but the expression of intention in the form of the argument.  I take such forms to be platonic realities. 

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