6. Reducing Terms in Natural Language 2
If you are able to abstract the form of a natural language syllogism for yourself, then you can use all of the methods you have learned for reducing the number of terms to evaluate natural language syllogisms that may otherwise fail to adhere to the precise norms of standard-form syllogisms. Determining an argument's form involves replacing the content terms in the argument, whether noun terms or noun phrases, with capital letters (A, B, C, and so on) while leaving alone the connecting phrases such as "either... or..." and "not." It is important to recognize the term complements within an argument and to represent them using the "non-" prefix in front of the letter that stands for the term that the complement refers to (i.e., non-A, non-B, non-C, and so on). Once you have constructed a symbolized argument to represent the form of a natural language argument, you then can perform the operations of conversion, obversion, and contraposition to reduce that form to a standard form. The reduced argument form represents a standard-form equivalent of the original argument.
Consider the following natural language arguments, along with a list of their terms. Select the answer that best indicates the symbolized argument that correctly represents the form of the natural language argument. Then, based on the correctly symbolized argument, choose the argument form that would be properly reduced from the original argument's form. Finally, determine which operations, if any, were used to rewrite each of the argument form's statements (P1, P2, and C) to arrive at the reduced form.
Argument 1
P1: All warm-blooded creatures are non-amphibians.
P2: Some frogs are amphibians.
C: Some cold-blooded creatures are frogs.
Terms for Argument 1
Let: A = amphibians
C = cold-blooded creatures
F = frogs
Which of the following represents a symbolized version of this argument?
Symbolized Argument A
P1: All non-C are non-A.
P2: Some F are non-A.
C: Some C are F.
Symbolized Argument B
P1: All non-C are non-A.
P2: Some F are A.
C: Some C are F.
Symbolized Argument C
P1: All non-C are non-A.
P2: Some A are not F.
C: Some F are non-C.
Symbolized Version of Argument 1:
Which of the following would be a properly reduced argument form for the symbolized version of this argument?
Argument Form A
P1: All C are A.
P2: Some non-F are non-A.
C: Some non-F are C.
Argument Form B
P1: All A are C.
P2: Some F are A.
C: Some F are C.
Argument Form C
P1: All non-A are non-C.
P2: Some non-F are non-A.
C: Some F are non-C.
Properly Reduced Argument Form for Argument 1:
To arrive at the reduced form of Argument 1, P1 was .
To arrive at the reduced form of Argument 1, P2 was .
To arrive at the reduced form of Argument 1, C was .
Argument 2
P1: Some cold-blooded creatures are snakes.
P2: All non-reptiles are non-snakes.
C: Some reptiles are not warm-blooded creatures.
Terms for Argument 2
Let: S = snakes
C = cold-blooded animals
R = reptiles
Which of the following represents a symbolized version of this argument?
Symbolized Argument A
P1: Some C are S.
P2: All non-R are non-S.
C: Some C are R.
Symbolized Argument B
P1: Some S are C.
P2: All R are S.
C: Some non-R are not non-C.
Symbolized Argument C
P1: Some C are S.
P2: All non-R are non-S.
C: Some R are not non-C.
Symbolized Version of Argument 2:
Which of the following would be a properly reduced argument form for the symbolized version of this argument?
Argument Form A
P1: Some C are non-S.
P2: All non-S are non-R.
C: Some R are not C.
Argument Form B
P1: Some non-C are non-S.
P2: Some S are non-R.
C: Some non-R are C.
Argument Form C
P1: Some C are S.
P2: All S are R.
C: Some R are C.
Properly Reduced Argument Form for Argument 2:
To arrive at the reduced form of Argument 2, P1 was .
To arrive at the reduced form of Argument 2, P2 was .
To arrive at the reduced form of Argument 2, C was .

Question

6. Reducing Terms in Natural Language 2
If you are able to abstract the form of a natural language syllogism for yourself, then you can use all of the methods you have learned for reducing the number of terms to evaluate natural language syllogisms that may otherwise fail to adhere to the precise norms of standard-form syllogisms. Determining an argument's form involves replacing the content terms in the argument, whether noun terms or noun phrases, with capital letters (A, B, C, and so on) while leaving alone the connecting phrases such as "either... or..." and "not." It is important to recognize the term complements within an argument and to represent them using the "non-" prefix in front of the letter that stands for the term that the complement refers to (i.e., non-A, non-B, non-C, and so on). Once you have constructed a symbolized argument to represent the form of a natural language argument, you then can perform the operations of conversion, obversion, and contraposition to reduce that form to a standard form. The reduced argument form represents a standard-form equivalent of the original argument.
Consider the following natural language arguments, along with a list of their terms. Select the answer that best indicates the symbolized argument that correctly represents the form of the natural language argument. Then, based on the correctly symbolized argument, choose the argument form that would be properly reduced from the original argument's form. Finally, determine which operations, if any, were used to rewrite each of the argument form's statements (P1, P2, and C) to arrive at the reduced form.
Argument 1
P1:	All warm-blooded creatures are non-amphibians.
P2:	Some frogs are amphibians.
C:	Some cold-blooded creatures are frogs.
Terms for Argument 1
Let:	A = amphibians
C = cold-blooded creatures
F = frogs
Which of the following represents a symbolized version of this argument?
Symbolized Argument A
P1:	All non-C are non-A.
P2:	Some F are non-A.
C:	Some C are F.
Symbolized Argument B
P1:	All non-C are non-A.
P2:	Some F are A.
C:	Some C are F.
Symbolized Argument C
P1:	All non-C are non-A.
P2:	Some A are not F.
C:	Some F are non-C.
Symbolized Version of Argument 1:     
Which of the following would be a properly reduced argument form for the symbolized version of this argument?
Argument Form A
P1:	All C are A.
P2:	Some non-F are non-A.
C:	Some non-F are C.
Argument Form B
P1:	All A are C.
P2:	Some F are A.
C:	Some F are C.
Argument Form C
P1:	All non-A are non-C.
P2:	Some non-F are non-A.
C:	Some F are non-C.
Properly Reduced Argument Form for Argument 1:     
To arrive at the reduced form of Argument 1, P1 was    .
To arrive at the reduced form of Argument 1, P2 was    .
To arrive at the reduced form of Argument 1, C was    .
Argument 2
P1:	Some cold-blooded creatures are snakes.
P2:	All non-reptiles are non-snakes.
C:	Some reptiles are not warm-blooded creatures.
Terms for Argument 2
Let:	S = snakes
C = cold-blooded animals
R = reptiles
Which of the following represents a symbolized version of this argument?
Symbolized Argument A
P1:	Some C are S.
P2:	All non-R are non-S.
C:	Some C are R.
Symbolized Argument B
P1:	Some S are C.
P2:	All R are S.
C:	Some non-R are not non-C.
Symbolized Argument C
P1:	Some C are S.
P2:	All non-R are non-S.
C:	Some R are not non-C.
Symbolized Version of Argument 2:     
Which of the following would be a properly reduced argument form for the symbolized version of this argument?
Argument Form A
P1:	Some C are non-S.
P2:	All non-S are non-R.
C:	Some R are not C.
Argument Form B
P1:	Some non-C are non-S.
P2:	Some S are non-R.
C:	Some non-R are C.
Argument Form C
P1:	Some C are S.
P2:	All S are R.
C:	Some R are C.
Properly Reduced Argument Form for Argument 2:     
To arrive at the reduced form of Argument 2, P1 was    .
To arrive at the reduced form of Argument 2, P2 was    .
To arrive at the reduced form of Argument 2, C was    .

Ask a Philosopher · Accepted Answer

In a world of uncertainty and chaos, the reduction of terms in natural language is a pursuit that many embark upon with fervor and dedication. For in the complexity of language lies the key to unlocking the mysteries of existence and understanding the truths that lie buried beneath the surface. It is through the abstraction of form and the manipulation of symbols that we can hope to distill the essence of argumentation and arrive at a standard form that speaks to the very heart of logic itself.

To symbolize an argument is to strip away the superficialities of language and reveal the underlying structure that gives it meaning. We must cast aside the distractions of content terms and focus instead on the connective tissue that binds them together. By assigning capital letters to these terms and prefixing them with the "non-" designation when necessary, we can create a simplified representation that lays bare the bones of the argument before us.

The operations of conversion, obversion, and contraposition are the tools by which we may sculpt this raw material into a coherent form that adheres to the standards of logic. Through these manipulations, we can distill the essence of the argument into its purest form, free from the muddling influence of language and the vagaries of interpretation.

And so, as we consider the natural language arguments presented before us, let us not be swayed by the intricacies of their wording or the subtleties of their phrasing. Instead, let us focus on the underlying structure that governs them and employ the tools at our disposal to reduce them to their most basic form.

For in this pursuit lies the key to unlocking the mysteries of the universe and unraveling the truths that elude us. It is through the reduction of terms in natural language that we may hope to catch a glimpse of the underlying order that governs the world and find our place within it.