Thursday, March 8, 2012

[PL 211] Categorical Syllogisms and Inductive Arguments

In Introduction to Logic and Critical Thinking (Fifth Edition, 2007), Merrilee H. Salmon compares the categorical syllogism to what she describes as "an incorrect form of inductive argument" (p. 127). The categorical syllogism has the following form (Salmon 2007, p. 128):
All Fs are Gs.
All Gs are Hs.
All Fs are Hs.
For example (Salmon 2007, p. 128):
All humans are mammals.
All mammals are animals.
All humans are animals.
According to Salmon (2007, p. 128), "This particular form of the categorical syllogism is valid, which means the consistent substitution of any class for each occurrence of the letters F, G, and H will result in a [valid] deductive argument."

Salmon then compares the categorical syllogism with the following form of an inductive argument by replacing all with most (Salmon 2007, p. 128): 
Most Fs are Gs. 
Most Gs are Hs.  
Most Fs are Hs.
Salmon says that this argument is inductively incorrect. To illustrate this, Salmon gives the following argument (Salmon 2007, p. 128):  
Most physicists are men. 
Most men are nonphysicists. 
Most physicists are nonphysicists.
And then Salmon (2007, p. 128) gives the following explanation:
Despite its true premises, the conclusion of this argument is a self-contradiction. This incorrect form exemplifies the danger of supposing that all correct inductive argument forms are just slightly weakened versions of deductive forms.
This passage suggests that Salmon thinks that this inductive form is incorrect because the conclusion of this inductive argument is a self-contradiction. However, the fact that the conclusion of this argument is a self-contradiction cannot be what makes it an instance of an incorrect inductive form. To see why, consider the categorical syllogism again and the following substitution instance:
All physicists are men. 
All men are nonphysicists. 
All physicists are nonphysicists.

The conclusion of this argument is also a self-contradiction. So, if we say that the aforementioned inductive argument exemplifies an incorrect form of inductive argument because its conclusion is a self-contradiction, wouldn't we also have to say, by parity of reasoning, that this deductive argument exemplifies an invalid form of deductive argument because its conclusion is a self-contradiction? And, if this is correct, does this mean that the categorical syllogism is an invalid form of deductive argument?

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