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The Three Forms of Proof  

Classical rhetoricians believed that the credibility of the speaker mattered greatly. The more authority a speaker was believed to have,  the more likely he was to win his case. This form of proof was ethos or ethical proof. 

A modern example of ethos:   In aspirin commercials, we often see and hear  a man claim, "I am not a doctor, but I play one on TV."  The man is trying to establish credibility as an authority on pain medications. Does this actor really know that Bufferin  is better than Tylenol? 

        Credibility counted for much among classical rhetoricians, but if the case was not strong, then the orator would just as easily lose the debate. It was up to the speaker to prove that his case was factual and correct. This form of proof  is called logos or logical proof. 

A modern example of logos:  We probably have heard the toothpaste commercial that claims, "4 out of 5 dentists prefer this toothpaste." Are those statistics accurate?  Who did they survey to get their findings? How can we, the audience, be assured that those facts are correct? 

        Pathos or pathetic proof was evidence that was intended to sway the audience emotionally. 
Pathos usually involves puppies, babies, kittens, flowers, couples, or anything that tugs at our feelings. Pathos can also be considered the heart-strings appeal - whatever tugs at the heart-strings makes for great rhetorical proof.  
A modern example of pathos:  We see the image of a happy  baby sitting in the middle of a radial tire. 
  

Induction and Deduction 

These two logic  structures are the basic foundation for most logical structures. 

Induction is the logical movement from specific details to a general principle. 
Detail:   This is an orange. 
Detail:   This is a sphere. 
General Conclusion: All oranges are spheres. 

Deduction is the movement from a general theory to the tiniest detail. 
General Theory: All oranges are spheres. 
Detail: This is a sphere. 
Conclusion detail: This is an orange.  

 More on Induction and Deduction.