Krissa Randolph's Library tagged logic →  View Popular

Contexts for Consideration











1. Cultural/Social
   
2. Scientific
3. Educational
4. Economic
5. Technological
6. Ethical
7. Political
8. Personal Experience






Personal observation, informal character

Invalid:

Every criminal opposes the government.

Everyone in the opposition party opposes the government.

Therefore everyone in the opposition party is a criminal.

This is invalid because the premises fail to establish commonality between membership in the opposition party and being a criminal. This is the famous fallacy of the undistributed middle.

Forms
a = b Ca (where C is an intensional context). Therefore, Cb.



Ca (where C is an intensional context).

Not-Cb.

Therefore, it is not the case that a = b.ExamplesThe masked man is Mr. Hyde.

The witness believes that the masked man committed the crime.

Therefore, the witness believes that Mr. Hyde committed the crime.

The witness believes that the masked man committed the crime.

The witness doesn't believe that Mr. Hyde committed the crime.

Therefore, Mr. Hyde is not the masked man.Counter-ExamplesThe masked man is Mr. Hyde.

The witness claims that the masked man committed the crime.

Therefore, the witness claims that Mr. Hyde committed the crime.

The witness claims that the masked man committed the crime.

The witness denies that Mr. Hyde committed the crime.

Therefore, Mr. Hyde is not the masked man.




Exposition:





Substitution of Identicals, also known as "Leibniz' Law", is a validating form of argument so long as the context in which it occurs is extensional, or referentially transparent. For instance, given that Mark Twain wrote Huck Finn and that Sam Clemens was the same person as Mark Twain, then Sam Clemens wrote Huck Finn. The context "x wrote Huck Finn" is extensional, which means that we can validly substitute identicals within it. In contrast, if Joe said "Mark Twain wrote Huck Finn", it does not follow that he said "Sam Clemens wrote Huck Finn", for he may have said no such thing.



A quoted context is an intensional—or, referentially opaque—context, as are such other contexts as:




• Propositional attitudes: belief, desire, fear, etc.
  
  
• Modal contexts: necessity, possibility, etc.





The Fallacy of Illicit Substitution of Identicals—or, more colorfully, "The Masked Man Fallacy"—is an application of Leibniz' Law within an intensional context. The most familiar uses of Substitution of Identicals are mathematical, where the contexts are always extensional. This may mislead one into thinking that substitution is valid in all contexts, but we have seen that this is not the case.







Source:

Example:

"Tavis Smiley (interviewer): How are you going to respond to folks on the campaign trail when they ask what qualifies you to be the commander-in-chief given that you have not served in the country's military?

"Al Sharpton (interviewee): I think that just because one served in the military does not make one a competent commander-in-chief."

Analysis

Example:

"…I want to list seventeen summary statements which, if true, provide abundant reason why the reader should reject evolution and accept special creation as his basic world-view. …

"14. Belief in evolution is a necessary component of atheism, pantheism, and all other systems that reject the sovereign authority of an omnipotent personal God."


Source: Henry M. Morris, The Remarkable Birth of Planet Earth, (Creation-Life Publishers, 1972), pp. vi-vii.

Analysis

Counter-Example:

If it's raining, then the streets are wet.

It isn't raining.

Therefore, the streets aren't wet.